Cordus
Conjecture
Quis es tu
et
quo
vadis,
photon?
Third edition
Pons
i
Cordus
Conjecture
The Cordus Conjecture is a conceptual
model that integrates the particle and
wave behaviour of light into a single
model.
Quis es tu et quo vadis, photon?
Quantum behaviour of individual photons is weird, in
the way they defy rationality. Sometimes they behave
like waves, and sometimes like particles, depending
on how they are observed. They are capricious and
apparently have an element of wilfulness in their
behaviour: they seem to know when a path is
blocked, without even going down it. Also, they seem
to adapt their behaviour in response to whether the
Observer is there or not (e.g. Schrodinger’s Cat, Zeno
effect). If this is quantum mechanics, then it is no
wonder that people consider it beyond weird. Even
physicists struggle to explain it.
The usual explanations put forward have their share
of eeriness too: virtual ghost particles that cannot
ever be observed, spooky intelligence in the photon,
philosophical dilemmas about the power of the
Observer to affect the rest of the physical world and
its future merely by looking at it, and parallel
universes beyond the cosmos which are forever
unreachable to us.
There are good theories for pieces of the problem,
but only parts. For example, wave theory is good for
predicting the behaviour of beams of light, and
quantum mechanics for the particle effects. However
there is no integrative theory, so the present situation
in physics is an incongruous amalgam of theories,
with weird implications.
Is there a way to explain quantum effects of the
photon rationally, without resorting to bizarre nonphysical causality? Is there a way to integrate wave
and particle views in a way that makes sense? Is it
possible to conceive of a new physics?
The cordus concept is
surprisingly
simple,
yet
powerful and able to explain
many
phenomena
and
paradoxes in physics:
double-slit experiment;
Heisenberg's
uncertainty principle;
Zeno effect;
fringes;
diffraction;
Mach-Zehnder
interferometer;
transparency;
reflection;
refraction;
absorbance;
tunnelling;
entanglement;
emission;
matter waves;
superposition;
coherence;
Schrodinger's Cat;
entropy, irreversibility;
strong force;
force unification;
antimatter;
annihilation;
asymmetrical genesis;
time
ii
CORDUS CONJECTURE
Edition 3
2012
Pons D.J., Pons A.D. Pons A.M., Pons A.J.
Published in New Zealand
This book is a compilation and adaption of several papers by the Pons research, conceptual
design, and authoring team: Dr Dirk Pons (Principal Researcher and Lead author), Arion
Pons, Ariel Pons, and Aiden Pons. Please address any correspondence to the Lead author at
dirk@pons.ws.
Copyright Dirk Pons 2011-2012. This edition of the work is made available under the Creative
Commons Attribution-Non-Commercial-ShareAlike 3.0 license. Individual papers available at
http://vixra.org/ under the same copyright release, but may be older versions. See also
http://cordus.wordpress.com/ for subsequent developments and commentary.
Revision history
Edition 3.0 of 11 February 2012: Additional papers on antimatter and neutrinos included.
Edition 2.3 of 20 August 2011: Addition of summary papers on Wave-particle duality, and QM scaling problem.
Minor changes to existing material regarding conceptual clarification, correction of typos.
Edition 1.2 of 9 April 2011: Minor format edits. Edits to parts 4: changed position on directionality of gravitation,
added summary for force. More specifically identified potentially testable differentiating effects throughout.
Edition 1.0 of 6 April 2011: First public release to cordus.wordpress.com and vixra.org
Permissions
The image ‘Figure 1: Cordus model of the photon’ of ‘Cordus conjecture: Overview’ has been released into the
Wikimedia commons and may be freely reused.
http://en.wikipedia.org/wiki/File:CordusConjecture2.21_PhotonCordus.png
iii
Contents
Part 0: Overview ..................................................................................................11
Wave-particle duality: A proposed resolution.......................................................12
1
2
3
4
4.1
4.2
4.3
5
6
Integration problems in fundamental physics.................................................................. 14
Approach taken ............................................................................................................... 16
Cordus conjecture............................................................................................................ 17
Cordus mechanics ............................................................................................................ 20
Cordus frequency............................................................................................................. 21
Reflection ........................................................................................................................ 22
Refraction ........................................................................................................................ 24
Discussion ........................................................................................................................ 26
Conclusions...................................................................................................................... 29
Why does quantum mechanics not scale up? .......................................................34
1
Introduction..................................................................................................................... 34
2
Cordus conjecture............................................................................................................ 36
3
Conceptual evaluation of QM .......................................................................................... 37
3.1
The fallacy that particles are points ................................................................................ 37
3.2
The fallacy of Bell’s theorem and locality........................................................................ 38
3.3
The fallacy of superposition being the reality ................................................................. 39
3.4
The fallacy of causal variability ...................................................................................... 40
3.5
The fallacy of easy coherence ......................................................................................... 41
3.6
The fallacy of scale invariance......................................................................................... 43
3.7
The fallacy that fields and particles are independent...................................................... 45
5
Discussion ........................................................................................................................ 46
6
Conclusions...................................................................................................................... 52
References................................................................................................................................... 54
Cordus Conjecture: Overview ...............................................................................56
1
2
3
4
4.1
4.2
4.3
4.4
5
Introduction to cordus ..................................................................................................... 56
Integration problems in conventional physics.................................................................. 57
Approach taken ............................................................................................................... 59
Cordus mechanics ............................................................................................................ 62
Cordus Conjecture ........................................................................................................... 62
Cordus optics ................................................................................................................... 64
Cordus matter.................................................................................................................. 65
Cordus in extremis ........................................................................................................... 68
Conclusions...................................................................................................................... 71
Part 1: Cordus first principles ...............................................................................76
Cordus Conjecture - Quis es tu photon?................................................................78
1
Introduction: Wave-particle duality ................................................................................. 78
2
Method............................................................................................................................ 79
3
Cordus conjecture............................................................................................................ 80
3.1
Cordus model of the photon ............................................................................................ 81
Causa 1
Cordus underlying mechanisms............................................................................. 81
iv
3.2
4
Application to quantum measurement effects................................................................. 85
Conclusions...................................................................................................................... 85
Photon path dilemmas: Quo vadis, photon?.........................................................87
1
Introduction: Photon Path dilemmas ............................................................................... 87
2
Existing approaches ......................................................................................................... 87
3
Particle behaviour in the Double-slit experiment............................................................. 88
4
Mach–Zehnder interferometer ........................................................................................ 92
Lemma L.7
Beam-splitter ........................................................................................................ 94
5
Conclusions...................................................................................................................... 99
Explanation of fringes ........................................................................................101
1
Introduction................................................................................................................... 101
2
Wave theory explanation of interference ...................................................................... 102
3
Cordus solution.............................................................................................................. 103
Lemma L.4
Internal and external variables of the photon ..................................................... 103
Lemma L.5
Span length ......................................................................................................... 104
4
Wave behaviour in single gaps: diffraction .................................................................... 105
Lemma L.6
Cordus hyff for the photon.................................................................................. 106
5
Fringes in the Double-slit device .................................................................................... 111
6
Discussion ...................................................................................................................... 116
7
Conclusions.................................................................................................................... 117
Part 2: Cordus optics ..........................................................................................121
Cordus Frequency ..............................................................................................123
1
Introduction................................................................................................................... 123
2
Cordus Transparency and Opacity.................................................................................. 125
Lemma O.1 Electron interaction determines Transparency and Opacity................................ 126
3
Cordus Frequency .......................................................................................................... 127
Lemma O.2 Cordus Frequency ............................................................................................... 127
Causa 2
Working model for frequency ............................................................................. 129
4
Tunnelling ...................................................................................................................... 131
5
Conclusions.................................................................................................................... 132
Cordus Reflection...............................................................................................135
1
Introduction................................................................................................................... 135
2
Cordus effects at surface interfaces ............................................................................... 137
Lemma O.3 Surface interaction.............................................................................................. 137
3
Cordus model for Reflection .......................................................................................... 138
3.1
Reflection in general ...................................................................................................... 138
3.2
Critical angle for total internal reflection ....................................................................... 142
4
Discussion ...................................................................................................................... 144
Cordus Refraction ..............................................................................................147
1
Introduction................................................................................................................... 147
2
Cordus refraction ........................................................................................................... 148
Lemma O.4 Refraction ........................................................................................................... 148
2.1
Derivation of Snell’s Law................................................................................................ 149
2.2
Brewster's angle ............................................................................................................ 151
2.3
Mixed reflection and refraction ..................................................................................... 154
v
3
Discussion ...................................................................................................................... 156
Part 3: Cordus matter.........................................................................................160
Wider Locality....................................................................................................162
1
Introduction................................................................................................................... 162
2
Entanglement ................................................................................................................ 164
Lemma M.1
Photon-photon interaction ............................................................................ 164
3
Complementary frequency state synchronisation (CoFS) ............................................... 165
4
Locality and Bell's theorem ............................................................................................ 166
5
Principle of Wider Locality ............................................................................................. 168
6
Conclusions.................................................................................................................... 168
Matter particuloids ............................................................................................172
1
Introduction................................................................................................................... 172
2
Cordus model of the Electron......................................................................................... 172
Lemma M.2
Electron ......................................................................................................... 173
2.1
Wave-particle duality of the electron ............................................................................ 173
2.2
Aharonov-Bohm effect................................................................................................... 174
2.3
Electron configuration, Orbitals, Spin ............................................................................ 175
Lemma M.2 continued............................................................................................................... 176
2.4
Atomic bonding ............................................................................................................. 178
3
Application to matter generally ..................................................................................... 180
Lemma M.4
Matter ........................................................................................................... 180
4
Conclusions.................................................................................................................... 183
Energy cycles within matter ...............................................................................186
1
2
3
4
5
Introduction................................................................................................................... 186
Cordus model for photon absorption............................................................................. 187
Recycling the energy: reversibility, elasticity, entropy ................................................... 189
Photon Emission ............................................................................................................ 191
Conclusions.................................................................................................................... 192
Special states of matter .....................................................................................194
1
2
3
4
5
6
Introduction................................................................................................................... 194
Superposition ................................................................................................................ 195
Coherence...................................................................................................................... 196
Superfluidity ................................................................................................................. 199
Superconductivity .......................................................................................................... 201
Conclusions.................................................................................................................... 204
Schrödinger’s Cat reconceptualised....................................................................208
1
2
3
4
5
6
7
Introduction................................................................................................................... 208
Contrasting interpretations: Quantum and Cordus mechanics....................................... 209
Heisenberg uncertainty principle ................................................................................... 210
Schrödinger’s Cat ........................................................................................................... 211
Contrast: String Theory .................................................................................................. 214
Discussion ...................................................................................................................... 214
Conclusions.................................................................................................................... 215
vi
Part 4: Fields, forces, and fabric..........................................................................218
Electromagnetism..............................................................................................220
1
2
2.1
2.2
2.3
2.4
2.5
3
Introduction................................................................................................................... 220
Field forces .................................................................................................................... 222
Quantum mechanics interpretation of fields ................................................................. 222
Cordus electrostatics...................................................................................................... 223
Electric field ................................................................................................................... 224
Cordus magnetism ......................................................................................................... 228
Magnetic interaction ..................................................................................................... 232
Conclusions.................................................................................................................... 236
Fabric of the universe.........................................................................................240
1
Introduction................................................................................................................... 240
2
Temporal capacitance.................................................................................................... 241
3
Cordus Fabric-of-the-universe conjecture ...................................................................... 242
E.3 Fabric hyff Lemma................................................................................................................ 242
4
Conclusions.................................................................................................................... 246
Gravitation, Mass and Time ...............................................................................249
1
2
E.4
2.1
2.2
3
E.4
4
E.5
5
E.6
6
Introduction................................................................................................................... 249
Cordus Gravitation......................................................................................................... 250
Gravitation and mass Lemma......................................................................................... 251
Mechanism for gravitational interaction force............................................................... 251
Features of cordus gravitation ....................................................................................... 254
Mass .............................................................................................................................. 255
Additional lemmas continued ........................................................................................ 255
Cordus Time................................................................................................................... 259
Time Lemma .................................................................................................................. 259
Force and the Principle of Geometrically Constrained re-energisation........................... 263
Force Lemma ................................................................................................................. 263
Conclusions.................................................................................................................... 263
Cordus Quarks ...................................................................................................266
1
2
3
4
5
6
7
Introduction................................................................................................................... 266
Existing interpretations for the strong interaction ........................................................ 267
Cordus quark mechanics ................................................................................................ 267
Quark structures ............................................................................................................ 269
Level of assembly........................................................................................................... 272
Conclusions.................................................................................................................... 276
Closing summary............................................................................................................ 277
Part 5: Matter and antimatter ............................................................................283
Mirror images: Matter and Antimatter...............................................................284
1
2
3
4
4.1
Introduction................................................................................................................... 284
The conventional perspective of antimatter .................................................................. 285
Background: Cordus conjecture ..................................................................................... 286
Cordus model for matter and antimatter....................................................................... 288
Consolidating existing principles.................................................................................... 288
vii
4.2
Cordus hand: ma............................................................................................................ 289
4.3
Cordus matter and antimatter ....................................................................................... 290
4.4
Lemma........................................................................................................................... 293
5
Discussion ...................................................................................................................... 294
5.1
Outcomes: what has been achieved?............................................................................. 294
5.2
What are the implications?............................................................................................ 295
5.3
What are the limitations and implications for further research? ................................... 297
6
Conclusions.................................................................................................................... 298
References................................................................................................................................. 298
Contrasting internal structures: Photon and electron .........................................300
1
2
2.1
2.2
2.3
3
Introduction................................................................................................................... 300
Structural differences between photon and electron..................................................... 301
Photon as a fibrillating hyff-pump ................................................................................. 302
Electron as a pulsating hyff-pump.................................................................................. 303
Explanation of various effects........................................................................................ 303
Discussion ...................................................................................................................... 305
Annihilation mechanisms: Intermediate processes in the conversion of electron
and antielectron into photons............................................................................309
1
Introduction................................................................................................................... 309
2
Cordus Background........................................................................................................ 312
3
Cordus mechanics for annihilation................................................................................. 313
3.1
Complementarity of ma hand is the underlying principle.............................................. 313
3.2
Annihilation of matter and antimatter.......................................................................... 314
3.3
Lemma........................................................................................................................... 322
4
Discussion ...................................................................................................................... 323
4.1
What has been achieved? .............................................................................................. 323
4.2
What are the implications?............................................................................................ 324
4.3
What are the limitations and implications for further research? ................................... 326
5
Conclusions.................................................................................................................... 327
References................................................................................................................................. 327
Cordus process diagrams: Symbolic representation of annihilation mechanics....330
1
Introduction................................................................................................................... 330
2
Approach ....................................................................................................................... 332
2.1
Process diagram............................................................................................................. 332
2.2
HED notation ................................................................................................................. 334
3
Positronium annihilation .............................................................................................. 336
3.1
Parapositronium ............................................................................................................ 337
3.2
Orthopositronium.......................................................................................................... 339
3.3
Comparison: parapositronium vs. orthopositronium ..................................................... 340
3.4
Scattering....................................................................................................................... 341
3.5
Lemma........................................................................................................................... 341
4
Conclusion ..................................................................................................................... 342
References................................................................................................................................. 342
Part 6: Neutrino mediated effects ......................................................................346
Structure of the neutrino and antineutrino ........................................................347
1
2
Introduction................................................................................................................... 347
What we know about neutrinos .................................................................................... 348
viii
3
Method.......................................................................................................................... 350
4
Neutrino structure ......................................................................................................... 352
4.1
Neutron structure .......................................................................................................... 352
4.2
Beta- decay and the antineutrino (v) HED structure....................................................... 353
4.3
Beta+ decay and the neutrino (v) structure.................................................................... 356
4.4
Electron capture ............................................................................................................ 358
4.5
Alpha decay ................................................................................................................... 358
5
Discussion ...................................................................................................................... 359
5.1
What has been achieved? .............................................................................................. 359
5.2
Implications ................................................................................................................... 360
6
HED lemmas.................................................................................................................. 368
7
Conclusions.................................................................................................................... 372
References................................................................................................................................. 372
Weak interaction: Reassembly of particules .......................................................374
1
Introduction................................................................................................................... 374
2
Background.................................................................................................................... 374
3
W and Z bosons reconceptualised.................................................................................. 376
3.1
W- boson ....................................................................................................................... 376
2.2
W+ boson....................................................................................................................... 377
3.3
Z boson .......................................................................................................................... 378
3.4
The cordus interpretation of the W and Z bosons .......................................................... 378
3.5
Neutrino-antineutrino annihilation................................................................................ 379
4
Boson lemmas ............................................................................................................... 380
5
Discussion ...................................................................................................................... 381
6
Conclusions.................................................................................................................... 382
References................................................................................................................................. 382
Stability and decay: Mechanisms for stability and initiators of decay in the neutron
..........................................................................................................................383
1
Introduction................................................................................................................... 383
2
Background.................................................................................................................... 384
2
Neutron beta- decay ...................................................................................................... 385
2.1
Stable in, unstable out ................................................................................................... 386
2.2
Decay initiators.............................................................................................................. 387
2.3
Implications of the two decay routes............................................................................. 388
3
Stability and disassembly lemmas ................................................................................. 392
4
Discussion ...................................................................................................................... 393
5
Conclusions.................................................................................................................... 395
A
Appendix: Other beta decays ........................................................................................ 396
A.1
Beta minus decay n => p + e + v ..................................................................................... 396
A.2
Beta plus decay p => n + e + v ........................................................................................ 397
A.3
Electron capture p + e => n + v ....................................................................................... 397
References................................................................................................................................. 398
The preponderance of matter: Asymmetrical genesis via the antineutrino route 400
1
2
3
3.1
3.2
3.3
3.4
Introduction................................................................................................................... 400
Method.......................................................................................................................... 404
Genesis via discarded neutrinos..................................................................................... 405
Production of an electron-antielectron pair................................................................... 405
Remanufacture of the antielectron................................................................................ 409
Dominance of the matter-production stream ................................................................ 410
Other implications ......................................................................................................... 412
ix
4
Discussion ...................................................................................................................... 412
4.1
What has been achieved? .............................................................................................. 412
4.2
What are the implications?............................................................................................ 413
5
Genesis lemmas ............................................................................................................. 415
6
Conclusions.................................................................................................................... 416
References................................................................................................................................. 416
Part 7: Philosophy and physics ...........................................................................419
Limits of coherence: Where and why is the transition to discoherence?..............420
1
2
3
Introduction................................................................................................................... 420
Reconceptualising coherence......................................................................................... 422
Discussion ...................................................................................................................... 428
Time: Frequency, irreversibility, and connectedness of matter ...........................432
1
Introduction................................................................................................................... 432
2
Background.................................................................................................................... 433
3
Time at the assembly level............................................................................................. 437
3.1
Time at the particule level: frequency (level 1) .............................................................. 437
3.2
Time at the level of molecular assembly (level 2) .......................................................... 437
3.3
Time at the level of organic life: chemistry (level 3) ....................................................... 439
3.4
Time at the cognitive level: phenomenal (level 4).......................................................... 439
3.5
The connectedness of time ............................................................................................ 440
4
Discussion ...................................................................................................................... 441
4.1
Outcomes ...................................................................................................................... 441
4.2
Arrow of time ................................................................................................................ 442
4.3
Implications: Addressing common questions about time............................................... 443
5
Conclusions.................................................................................................................... 446
References................................................................................................................................. 448
Possibly testable predictions of cordus mechanics .................................................................... 451
Index.......................................................................................................................................... 453
x
Cordus
Conjecture
Part 0: Overview
Summary of the main
features
of
the
cordus conjecture
11
Wave-particle duality: A proposed resolution
Pons, D.J. 1 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
There are several integration problems of fundamental physics that still
lack coherent solutions, the case in point being wave-particle duality. While
empiricism and mathematical modelling have served physics well, they
have not yet been able to achieve integrated causal models. Conventional
theories and approaches have only provided partial solutions, and it is
possible that a more radical reconceptualisation of fundamental physics
may be required. This work comes at the issue from a totally different
approach: it applies engineering design thinking to the problem. The result
is the cordus conjecture, which proposes that the photon, and indeed all
matter ‘particles’, has an internal structure comprising a 'cordus': two
reactive ends that each behave like a particle, with a fibril joining them.
The reactive ends are proposed to be a small finite distance apart, and
energised [typically in turn] at a frequency. When energised they emit a
transient force pulse along a line called a hyperfine fibril [hyff], and this
makes up the field. This concept is used to explain the path dilemmas of
the single photon in the double-slit device, and the wave behaviour of light
including the formation of fringes by single photons and beams of light. In
addition it provides a tangible explanation for frequency. It also yields new
quantitative derivations for several basic optical effects: critical angle,
Snell’s law, and elsewhere Brewster’s angle. Thus the proposed cordus
structure resolves wave-particle duality at a conceptual level. The cordus
conjecture does away with the current weirdness of wave-particle duality:
there is no need for virtual particles, superposition, observer dilemmas,
pilot waves, intelligent photons, or parallel universes. A simple
deterministic, unintelligent photon with dual modes of existence is all that
is required. Cordus suggests there is a deeper mechanics that subsumes
both quantum mechanics and wave theory. From this cordus perspective,
wave and particle behaviours are simply the different output behaviours
that the internal system of the photon shows depending on how it is
measured. The duality and the apparent incongruity of quantum
mechanics and wave theory is an artefact of the limited formulations of
those theories, and the conflict does not exist at the deeper level of
mechanics. While the present paper only addresses wave-particle duality,
the wider work provides an integrative conceptual solution for several
other enigmatic effects. Cordus is simpler and more logically consistent
across a wider range of phenomena than quantum mechanics or wave
theory. Even more surprising, and unexpectedly contrary to the prevailing
probabilistic paradigm of quantum mechanics, cordus suggests that the
next deeper level of reality is deterministic.
1
Please address correspondence to Dr Dirk Pons, University of Canterbury, Christchurch, New
Zealand. Email dirk.pons@canterbury.ac.nz Copyright Dirk Pons.
12
Il existe plusieurs problèmes d’intégration de la physique fondamentale
qui requièrent, encore à ce jour, une solution cohérente. Le problème en
question ici est celui de la dualité onde-particule. Alors que l’empirisme et
la modélisation mathématiques ont bien servit la physique, ils n’ont pas, à
ce jour, permis l’élaboration de modèles causaux intégrés. Les théories et
approches conventionnelles n’ont fournit que des solutions partielles, et il
est possible qu’une reconceptualisation plus radicale de la physique
fondamentale soit nécessaire. Ce travail traite ce problème avec une toute
autre approche en appliquant des processus de pensée relatifs au génie de
conception. Le résultat est la « conjecture de cordus « qui propose que le
photon et en fait toute particule matérielle a une structure interne
comprenant un « cordus « : deux extrémités réactives se comportant
comme des particules connectées par une « fibrille «. Il est proposé que
ces deux extrémités réactives, séparées par une petite distance finie, sont
énergisées [typiquement tour à tour] à une certaine fréquence.
Lorsqu’elles sont énergisées, elles émettent une force impulsive transitoire
le long d’une ligne appelée fibrille hyperfine créant ainsi un champ de
force. Ce concept est utilisé pour expliquer les dilemmes de la trajectoire
d’un photon dans l’expérience de la double fente et le comportement
ondulatoire de la lumière incluant la formation de frange par un photon
unique et de rayon lumineux. De plus, cela donne une explication tangible
pour la fréquence. Cela induit également de nouveaux raisonnements
quantitatifs pour plusieurs effets d’optique : l’angle critique, la loi de Snell,
et ailleurs l’angle de Brewster. Donc, la structure en cordus proposée
résout le problème de la dualité particule-onde au niveau conceptuel. La
conjecture cordus élimine l’étrangeté de la dualité particule-onde : il n’y a
pas besoin de particules virtuelles, de superposition, de dilemme
d’observateur, d’ondes pilotes, de photons intelligents, ou d’univers
parallèle. Un simple photon déterministe, non-intelligent avec un mode
d’existence dual est tout ce qui est requis. Cordus suggère qu’il existe un
mécanisme plus profond qui subsume la mécanique quantique et la
théorie des ondes. Vu de cette « perspective cordus », les comportements
ondulatoires et particulaires sont simplement les comportements que le
système interne du photon démontre en fonction de la façon dont il est
mesuré. La dualité et l’apparente incongruité de la mécanique quantique
et de la théorie des ondes ne sont que des artefacts de la limite de la
formulation de ces théories, et ce conflit n’apparait pas au niveau plus
profond de la mécanique. Alors que cet article n’adresse que le problème
de la dualité onde-particule, ces travaux fournissent une solution
conceptuelle intégrative à plusieurs autres effets énigmatiques. Cordus
est plus simple et plus consistant du point de vue de la logique pour un
grand nombre de phénomènes tant quantiques qu’ondulatoire. Encore
plus surprenant et inattendu, en contraste avec le paradigme stochastique
de la mécanique quantique, cordus suggère que le prochain niveau plus
profond de la réalité est déterministe.
Keywords: wave-particle duality, photon, light, double-slit, double slot
Document: Pons_Cordus_0.1_WaveParticleDuality_2011_E2.3.26.doc
Edition 2.3: Included French translation of abstract, Acknowledgements, References added: Leggett, de
Broglie. Replaced Fig1, Fixed 1D point error.
13
1
Integration problems in fundamental physics
The dominant existing frameworks for fundamental theoretical physics are
quantum mechanics [QM] for particles, electromagnetic wave theory [WT]
for light, electrostatics and magnetism, and general relativity [GR] for
gravitation. While those conventional theories are generally accepted as
valid in their particular areas, there is the unfortunate problem that they
do not integrate well, see Figure 1. Furthermore, they sometimes give
weird explanations to simple phenomena, this being particularly the case
with QM. Also, there are many areas that they simply do not explain at all,
or give conflicting interpretations.
A case in point is wave-particle duality. For example in the double-slit
experiment, light apparently sometimes behaves like a wave, and
sometimes like a particle, depending on how it is observed. As Loius de
Broglie stated, 'Now a purely corpuscular theory does not contain any
element permitting the definition of a frequency'. It was precisely for that
reason that he formulated the initial idea of duality: 'This reason alone
renders it necessary in the case of light to introduce simultaneously the
corpuscle concept and the concept of periodicity' [1]. Nonetheless, the
descriptions of WT for the fringe behaviour and QM for the particle
behaviour, do not overlap. Thus there is no single integrated or coherent
explanation for wave-particle duality.
Furthermore, while QM has exquisite mathematical models for the particle
behaviour, the physical interpretation of those models results in really
strange predictions of reality e.g. superposition, and some explanations
that are beyond physics, e.g. virtual particles and parallel universes. That
would not be a problem except that we do not actually see reality
behaving the way QM predicts, especially not at the macroscopic scale.
The null explanation is then to simply accept the paradoxes and consider
the matter intractable. That seems to be the current state of physics. Thus
comparatively little progress has been made at the big-picture level: many
of the issues identified in the figure above have been known for nearly a
century, and are still unresolved. The issue preventing resolution is not
obviously resources, since many people have been engaged in the pursuit
and vast financial resources have been put into large capital works.
Instead, it may be that we have simply painted ourselves into a conceptual
corner, one where there is no solution. The deficiencies in QM are
conceptual rather than mathematical [2-3]. Therefore, there may be value
in coming at the issues from a totally different approach, i.e. use a
different cognitive way of thinking.
Is the duality even worth solving?
It is acknowledged that in many ways wave-particle duality is no longer
relevant to current discourses in physics. Generations of physicists have
been trained to accept the duality as the reality, and it has become an
accepted and seldom-questioned premise. Moreover, it is indeed a
workable premise. This is because the tools of QM and WT, though lacking
integration, are still sufficient for most of what physicists want to do, and
14
the popular many-worlds theory provides a convenient belief-system to
bridge the residual ambiguities. A vast, and very successful, intellectual
edifice in the form of quantum mechanics has been constructed for
physics, despite wave-particle duality. That it has been possible to achieve
so much, without directly solving the duality, seems to be evidence
supporting those who claim that the duality is irrelevant: that it is only a
curiosity and need not be solved at all.
Nonetheless, the underlying cognitive dissonance is still there, even if
papered over with intellectual coping mechanisms. Thus there are two
reasons why we should nonetheless persist with exploring wave-particle
duality. First is the reason of curiosity: because it is still an unanswered
problem, regardless of its perceived relevance. Second is the
epistemological reason: because it is just possible that the weirdness of
wave-particle duality is not so much because reality is weird [a common
interpretation], but rather a symptom that the conceptual foundations of
our existing theories are fundamentally wrong. An example of this latter
position is that of Canals-Frau who, regarding wave-particle duality, felt
that the real issue was that the objects in question were neither waves nor
particles but rather a new type of object, one for which we do not yet have
words or concepts [3]. As he perceived it, there is a need to develop the
necessary new semantic concepts for these objects.
The integration problems in physics therefore suggest that there might be
a deeper physics, a better theoretical foundation that provides a more
coherent explanation across the many phenomena [4]. Thus we take the
perspective of discontent - that cognitive dissonance and lack of
integration between theories are symptoms of a deeper conceptual lack.
We see value in exploring new conceptual solutions to wave-particle
duality, and that is the purpose of this paper and the wider work to which
it refers.
However, if there is a deeper theory, e.g. one that subsumes both wave
and particle perspectives, it is not obvious what that might be. Also, there
is reason to believe, per Bell's theorem, that no theory of internal [or
hidden] variables is possible for the photon and particles generally. Thus
the problem of wave-particle duality may be fundamentally unsolvable.
15
Figure 1: Areas where there are integration problems in conventional
physics. The first shown here is the problem of wave-particle duality, where
light behaves as either a wave or particle depending on how it is observed.
Another is gravitation, particularly the integration of general relativity and
quantum mechanics. Unification of forces is another area of difficulty, the
biggest obstacle being the unification of gravitation with the others. There
is also the more tacit problem of the internal structure of matter: particles
seem to be 1 dimensional points and some theories predict that they have
no further internal structure [e.g. for the photon], yet other particles like
the proton are known to be composed of still smaller particles though the
structure itself is unknown. Finally, there is the problem of the various
anomalous effects: observed phenomena that are difficult to explain. The
wider integration is also missing: an ideal theory would explain ALL of the
above.
2
Approach taken
While empiricism and mathematical modelling have served physics well,
they have not yet been able to achieve integrated causal models. But
epistemic uncertainty is not unique to fundamental physics: other
disciplines have their own conundrums, and have developed their own
methods for complex problem-solving. Perhaps applying a problem-solving
method from outside of physics might give insights? The Cordus
conjecture is the result of an application of engineering design thinking to
the problem.
16
Methodology
This paper applies the cognition of engineering design. The conventional
scientific method involves collecting empirical data, checking hypotheses,
and formulating theories [fitting relationships to data]. Variables are
usually quantitative and the objective is to find precise objective causal
relationships [usually mathematical algorithms] describing how the input
variables determine the observed behaviour. The cognitive skill required is
analysis, and the logic is deductive.
In contrast, design cognition seeks to find a satisfactory rather than a
perfect solution. The cognitive skill required is creativity and intuition.
Design involves multiple sub-optimisations using quantitative and
qualitative variables, being processed by objective algorithms as well as
subjective heuristics, along solution paths that are only partly evident at
the outset. It forms a mechanism for innovation generally and new
product development specifically. It looks like a messy process from the
outside, but has its own logic of synthesis.
Applying design cognition to fundamental physics would not seem a
natural choice of methodology. Nor is it likely to generate the objective
relationships of causality [mathematical expressions] that are so
particularly prized in physics. Nevertheless it is a valid approach
elsewhere, and has potential to provide surprises.
Process
The starting point was that simple yet subtle experiment: wave-particle
duality of the photon in the double-slit device. The process was to apply
design intuition, creativity and simple logic, and come up with a starting
concept. This core concept is called the Cordus Conjecture [5]. As the
name indicates, it is conjectural. This idea is novel in that it does not build
on existing concepts. It is an unorthodox conceptual departure from
existing frameworks and does not need them, and therefore does not
reference them. Thereafter we considered other areas of dis-integration
in physics, and sought to reverse-engineer the known phenomena, adding
conjectures and intuitive material, and noting the necessary assumptions
along the way. Thus the central strand in the Cordus conjecture is a set of
lemmas, and these we do not attempt to prove, nor are they provided in
this summary paper. The resulting Cordus model is primarily conceptual
and descriptive, rather than mathematical, at least at this point in time. It
is a system model created with the logic of synthesis. The results are
likewise descriptive concepts, rather than mathematical expressions. The
Cordus conjecture is given below, followed by an elaboration of its
mechanics, where relevant to the topic of wave-particle duality.
3
Cordus conjecture
The Cordus conjecture is that all 'particles', e.g. photons of light, electrons,
and the protons in the nucleus of the atom, have a specific internal
structure. This structure is a 'cordus': two reactive ends that each behave
17
like a particle, with a fibril joining them. The reactive ends are a small
finite distance apart, and energised [typically in turn] at a frequency.
When energised they emit a transient force pulse along a line called a
hyperfine fibril [hyff], and this makes up the field, see Figure 2 for
application to the photon [6].
Figure 2: Cordus model of the photon. It is proposed that the photon
probably only has a single radial hyff at each reactive end, whereas the
electron has three, but the fundamental structural concept is similar.
Image
is
in
the
common
domain
http://en.wikipedia.org/wiki/File:CordusConjecture2.21_PhotonCordus.png
The core concept in the cordus conjecture is thus a particular bipolar
internal structure for the photon and indeed all ‘particles’. We term this a
cordus, and emphasise that it is the internal structure of what is otherwise
called a ‘particle’, and is not the same as a ‘dipole’ [separation of negative
and positive charges] which is an external structure. Nor is it appropriate
to call this a ‘particle’, because it is not a zero-dimensional [0D] point. The
idea of a cordus allows many puzzling phenomena to be explained at a
conceptual level, starting with wave-particle duality [7-8].
Double slit device
Light seems to behave either as a wave or a particle in the double slit
experiment, and cordus explains this wave-particle duality. Thus the single
photon, made up of a cordus, does pass through both slits: one reactive
end through each slit. The reactive ends therefore take different paths
18
[loci]. The natural variability of the span of the cordus means that the
effect is only approximately dependent on the spacing of the slits.
Particle behaviour
Once through the slits, the whole photon collapses to, and therefore
appears, at the first place where a reactive end is arrested, see Figure 3.
This explains the observed phenomenon that blocking one slit, [or placing
a detector only at one slit] causes the whole photon to appear there.
Figure 3: Photon behaviour in the double-slit experiment
19
The properties are of the particuloid are at a high frequency and therefore
effectively indeterminate until intrusively measured.
Wave behaviour and fringes
This basic idea can also explain how the fringes arise in single gaps and
double-slits. Each of the two reactive ends also interacts, through the hyff
[electric field] with the opaque material bounding the slits. The hyff
become engaged with the surface plane of the material and exert a
quantised force that retards the reactive ends and bends its trajectory by
set angular amounts, causing fringes at set intervals.
The double-slit device best shows the fringe behaviour because the shortspan cordi are barred entry by the medulla. Thus the device imposes an
upper and lower filter on the range of spans admitted. Hence narrower
slits produce more pronounced fringes.
The two locations of the fringe are the modes of the reactive ends, and it
is somewhat random as to which will ground first. Note that this
explanation accommodates the fringe behaviour of both single photons
and beams of coherent light. Thus a solitary photon will be deflected into
discrete angular steps, and will appear at one of the fringe locations. A
whole beam of coherent light will likewise form fringes because all the
photons have the same discrete angular deflection, providing that they are
of the same energy. In the cordus model higher energy particuloids [i.e.
also higher frequency] have shorter spans.
This also explains why both photons and electrons form fringes: in both
cases the fringes arise because of the interaction of the electric field,
which is in discrete pulses, with the frontal surface plane of the matter
bounding the slit.
Wave-particle duality
The significance of this is that one mechanism, the cordus, is able to
explain all three phenomena in the double slit: the blocked-slit behaviour
of an individual photon, the fringes formed by multiple photons taken
singly, and the fringes produced by of a beam of light. The same
mechanisms also explains photon path dilemmas in interferometers.
4
Cordus mechanics
The basic cordus concept is now expanded and grounded in known
phenomena to extract the broader mechanics for optical reflection and
refraction.
20
4.1
Cordus frequency
Conventional particle and wave theories struggle to explain the frequency
of photons and matter in a coherent manner using natural physics. By
comparison, the cordus readily provides a physical interpretation. Thus it is
proposed that there really is a part of the photon cordus that moves with
a frequency [9]. The current working model is for a reciprocal motion: the
energy alternates between the two reactive ends across the span of the
cordus, and the hyff represent the observable electric field, see Figure 4.
Figure 4: Working model for frequency behaviour of reactive ends.
This cordus model for frequency readily explains polarisation too: this is
the orientation of the cordus relative to the line of motion. It also explains
tunnelling. This effect involves a photon occasionally going through a
barrier [e.g. the space between two glass prisms] instead of being
reflected. The effect requires a small gap, and is known to be dependent
on frequency. Tunnelling, from the cordus perspective, is when a reactive
end energises too late for its hyff to respond to the change of media, so
the RE goes right on through into the next medium before it has time to
re-energise.
21
4.2
Reflection
Optical effects such as reflection and refraction are conventionally best
described by electromagnetic wave theory, at least when they involve
beams of light. Wave theory takes the perspective that a beam of light is
not so much a stream of photons, as a continuously existing
electromagnetic wave, comprising an electric field and a magnetic field.
From the perspective of wave theory, reflection is caused by the mirror
surface absorbing and re-emitting its own EM waves. Depending on the
perspective taken, these interfere with each other or with the incident
wave to produce the reflected wave. The mathematics of wave theory
accurately quantifies the phenomenon, though its qualitative explanations
are not intuitive. Nor does that theory does not explain why single
photons should also show such behaviour. Explaining basic optical effects
is not possible with classical particle mechanics, and even with quantum
mechanics it is not straight forward and the descriptive explanations not
particularly intuitive.
Optical effects can be explained from a cordus particuloid perspective [10].
Importantly, this explanation is applicable for single photons and beams of
light. The Cordus explanation is that both reactive-ends of the cordus
separately reflect off the surface as their hyff interact elastically [lossless]
with the substrate. The precise locus taken by a reactive end depends on
its frequency state at the time it approaches the surface, and the nature of
the surface. Thus the reflection is not a sharp instant change in direction
occurring at the surface, but rather a curved transition. Depending on the
situation, that curve might occur above the surface [cisdermis] or beneath
it [transdermis].
Consequently the centreline of the reflected cordus may be laterally offset
from the nominal: the photon is displaced sideways from where it should
be by simple optics. This effect is known for p-polarised light at total
internal reflection, and is termed the Goos–Hänchen effect. The Cordus
explanation is that the actual reflection occurs in the transdermis in this
situation, and Figure 5 provides a graphical explanation of how the offset
arises. Phase changes at reflection are also explainable [10].
22
P
Co ho
o to
sy rdin n’s
st at
em e
t
a2
r
Reflection occurs
before the surface
is reached
Centreline of
cordus is coincident with
nominal reflection
line
a
a1
n1
cisdermis
n2
transdermis
Nominal reflection
centreline
(denser)
(denser)
Nominal reflection
centreline
a2
a1
n1
n2
Centre of cordus
is offset from
nominal reflection
line
(a) Reflection off a
denser material
(n2>n1)
(b) Internal
reflection off a less
dense material
(n2<n1)
cisdermis
transdermis
Reflection occurs
beyond the
surface as the
denser material
pulls the reactiveend back
Figure 5: Reflection occurs as a curved transition some distance off the
surface (a), not an abrupt change at the precise surface. In the case of
internal reflection (b), the transition may occur in the second medium and
result in the centre of the cordus being offset from the nominal.
Cordus derivation of critical angle
Critical angle for internal reflection is also explainable [10]. Internal
reflection is when light passes from a region of high refractive index n1 to
lower n2, e.g. glass to air. The critical angle is where total internal
reflection occurs, i.e. no transmission, and is known to be: Sin(θc) = n2/n1 =
λ1/ λ2 where λ are the wavelengths.
The Cordus explanation is that at the critical angle θc the reactive end a1 is
inserted into in the faster material n2 at t=0, and therefore moves forward
a distance λ2/2, see Figure 6. This motion is parallel to the surface because
this is the angle of refraction. By comparison at the same time reactive end
a2 continues to travel distance λ1 in the slower medium, before it later
also enters the faster medium, at t=1/2 of a frequency cycle. RE a1 is thus
accelerated by the sudden freedom of being in the faster medium. The
angle θc is steep enough to push the RE out of the slower medium, but
only steep enough to place it at the boundary. A moment later the second
RE is likewise positioned at the boundary.
23
Figure 6: Geometry of the cordus at the critical angle θc for total internal
reflection.
The important points are:
Over the period from t=0 to t=1/2 cycles, a1 moves λ2/2 whereas
a2 moves λ1/2, because they are in different media.
The angle θc is such that there is only a half-cycle of frequency
involved.
The angle at which the above two conditions is met is apparent from
inspection of the geometry in the figure, Sin(θc) = λ1/ λ2, and this is the
same as the critical angle derived from optics. For more details see
reference [5].
4.3
Refraction
The bending of light as it enters an inclined boundary is usually explained
in optical wave theory as a change in the speed [phase velocity], such that
the wavelength changes but not the frequency. The angle of refraction θ2
in the second medium 2 is given by Snell's law: sinθ2 = v2/v1 .sinθ1 =
n1/n2.sinθ1 = λ2/λ1.sinθ1 where the angles are measured from the normal
to the surface, and v are the velocities in the two media. Explanations vary
for how the change in speed occurs. The wave interpretation is that the
delay occurs because the electric field interacts with the electrons to
radiate a delayed wave, thereby forming the new but slower wave. Hence
the Huygens–Fresnel principle that each point on the wave propagates
new waves and these interfere.
The Cordus explanation for refraction [11] is that the inclined incoming
cordus strikes the surface and one reactive-end and then the next
penetrates into the second medium n2. Assuming the case where n2 is
more dense, e.g. from air to glass, then the cordus slows down. The case is
shown in Figure 7.
24
Figure 7: Refraction involves a dormant reactive-end penetrating into the
second medium, and being angularly deflected with reduction in speed.
Cordus derivation of Snell’s Law
The separation of the reactive ends along the interface, in Figure 7, is
given by d = λ2/(2.sinθ2) = λ1/(2.sinθ1), which simplifies to Snell’s law. The
frequency and other forms arise by noting that v1=f. λ1 and v2=f. λ2 and n =
c/v where c is velocity of light in vacuum.
Birefringence is also explained by cordus, and Brewster’s relationship
derived. The cordus mechanics for optical phenomena are the same for
single photons and beams of light, which is an advantage compared to
wave theory. The same cordus mechanics are logically consistent with
those for the double-slit device. Therefore cordus can explain particle
behaviour, fringes, and optical effects, using a single coherent mechanics.
The cordus explanation does not need the conventional concept of
‘interference’. In fact cordus refutes interference as a physical mechanism.
Instead cordus asserts that interference is only a mathematical model of
the en-masse behaviour of the hyff from multiple cordi.
25
5
Discussion
Outcomes
What has been shown here is a conceptual resolution of several problems
in fundamental physics:
1. The proposed two-ended cordus structure2 of the photon readily
explains the path dilemmas of the photon in the double-slit
device: one reactive end goes through each slit, and the photon
collapses and becomes detected at the obstacle which first stops
one of the reactive ends. The same principle is also explains the
path dilemmas in the Mach-Zehnder interferometer. Thus the
‘particle’ behaviour of the photon can be explained.
2. The cordus structure can also explain the wave behaviour of light,
particularly the formation of fringes in gaps, apertures, and the
double-slit device. The suggestion is that these fringes form, not
from classical destructive/constructive interference, but by the
interaction of the electric field, which is discrete, with the frontal
surface plane of the matter bounding the slit.
3. Cordus also provides a tangible explanation for frequency of the
photon, electron and matter generally. By comparison the
‘frequency’ of a particle is an abstract indefinite concept in
quantum mechanics.
4. Cordus also provides a novel explanation for the standard optical
effects of reflection and refraction. The cordus conjecture as a
whole is primarily conceptual, being a thought-experiment, but
this is one area where it goes further: it provides a quantitative
derivation of critical angle, Snell’s law, and Brewster’s angle. This is
novel in that the derivations are from a cordus particuloid
perspective, which has a very different set of starting assumptions
to wave theory or quantum mechanics.
Wave-particle duality
Thus the proposed cordus structure resolves wave-particle duality, at least
at a conceptual level.
The Cordus conjecture does away with the current weirdness of waveparticle duality: there is no need for virtual particles, superposition,
observer dilemmas, pilot waves, intelligent photons, or parallel universes.
A simple deterministic, unintelligent photon with dual modes of existence
is all that is required.
2
The cordus conjecture introduces new concepts and these require new words,
some of them invented, e.g. ‘hyff’. This might seem excessive, but as Canals-Frau
noted, ‘it is necessary to start by creating a new concept with the help of a
phenomenological description and by assigning a name to this concept’ 3.
Canals-Frau, D., Comments on some problems of modern physics. Annales
de la Fondation Louis de Broglie, 2003. 28(2): p. 215-223..
26
From this cordus perspective, wave and particle behaviours are simply the
different output behaviours that the internal system of the photon shows
depending on how it is measured. The duality and the apparent
incongruity of quantum mechanics and wave theory are artefacts of the
limited formulations of those theories - the conflict does not exist at the
deeper level of mechanics.
Some may argue from a phenomenological position that no solution of
hidden internal variables, such as cordus proposes, is permissible, as per
Bell’s Theorem. However cordus refutes that theorem and shows it to be
an artefact created by circular reasoning based on the flawed premise
that particles must be 0D point particles [12-13]. Thus Bell’s Theorem is
irrelevant and is not an impediment to hidden-variable solutions.
Leggett inequalities
Bell's theorem constrains against Local hidden variable solutions, and
prohibits them altogether if locality and the 0D point premise are to be
preserved. In contrast, the cordus geometry simultaneously refutes both
locality and the point premise, and thus surpasses Bell's theorem. It is
important to note that cordus does not disagree with the empirical results
regarding entanglement, nor with the predictions of quantum mechanics,
but it does disagree about the conceptual foundation of QM and the
interpretations thereof. While theories using local hidden variables are in
conflict with the experimental results, cordus does not have this difficulty.
Thus cordus is a non-local hidden variable (NLHV) solution. It proposes
that strict 0D point locality does not apply, though a principle of wider
locality does.
One sub-type of NLHV theories are the 'crypto-nonlocal' (CN) theories
[14], which have not been ruled out, though they have been constrained
by the Leggett inequalities. However, Leggett's conceptualisation of
crypto-nonlocal theories was limited to a certain case, namely
independent photons.3 In contrast, cordus includes an entanglement
mechanism to create dependency between photons, plus a mechanisms
for contextual measurement, and is therefore a more complex case than
that used to draw up the CN inequalities. Thus we suggest that cordus
transcends the CN theories and their limitations. As Pepper remarked, 'Any
remaining NLHV theory must be fairly nonintuitive', and indeed cordus is
in a different class of solutions. All these inequalities, Bell's and Leggett's,
and the general disinclination towards hidden variable solutions, are
founded on the 0D point paradigm, which is the fundamental fallacy of
quantum mechanics [13].
3
Leggett's consideration of 'crypto-nonlocal' theories was limited to pairs of photons, where each was
independent to the other. Or as he put it, 'the ensemble of pairs of photons ... each of which ...
behaves (statistically) exactly as if it had been emitted in a single-photon process' (p1470). He found
that 'all CN theories are constrained by inequalities which are violated by the quantum-mechanical
predictions' (p1469).
27
Implications
This paper explains only some of the features of the cordus conjecture.
While it has not solved all the integration issues raised in the introduction,
the wider work progresses this further. The concept has also been applied
conceptually to matter more generally, thus explaining: entanglement,
locality, electron spin & orbitals, Pauli exclusion principle, Zeno effect,
Heisenberg uncertainty principle, Aharonov-Bohm effect, Atomic bonding,
Entropy, Superfluidity including quantum vortices and heat conduction,
Superconductivity including Meissner effect, Josephson effect, Coherence,
Casimir effect, Electrostatic field and granulation [quantisation] thereof,
Magnetism, Gravitation and mass, Spacetime, Lorentz, Relativistic nature
of the vacuum, Finite speed of light in vacuum, Colour and Charge of
quarks, Mass excess/deficit.
Thus one simple cordus idea provides a unified conceptual framework
that gives a logically consistent interpretation across the many physical
phenomena. In almost every case listed above the cordus explanations are
substantially different to those of the conventional theories of quantum
mechanics, wave theory, and general relativity.
Comparison with electromagnetic wave theory
The biggest difference between wave theory and the cordus explanation is
their interpretation of the mechanism for fringes. Wave theory explains
fringes as ‘interference’: two separate waves of light differing by full [or
half] fractions of wavelengths and thus constructively [or destructively]
interfering. From the cordus perspective photons do not actually
physically interfere or add together, and 'interference' is only a convenient
mathematical analogy, not a real physical phenomenon for light.
Nonetheless, the quantitative mathematics of Wave theory is useful as a
computational representation. The Cordus explanation is that fringes are
caused instead by interaction of the hyff with opaque planes.
How do quantum mechanics and wave theory fit in?
From the cordus perspective both conventional theories, quantum
mechanics and wave theory, are mathematical simplifications of a deeper
mechanics. Those theories represent the average and en-masse
[respectively] output behaviour of the particuloid, not the behaviour of the
inner system. The weirdness of conventional wave-particle duality is not
because the photon is fundamentally weird, but because the existing
conceptual frameworks of quantum mechanics and wave theory are
inadequate: their mathematics are sufficient for forward propagation of
effect [prediction], but give unreliable results when used for backward
inference of causality [explanation].
Epistemological implications
Cordus is a thought-experiment. The treatment is primarily conceptual and
descriptive, and the cordus mechanics only lightly sketched out. It is a
conceptual model, not so much a full theory with all the details worked
out. Thus the validity is uncertain, and the concept requires further critical
evaluation. However, if cordus should be correct, then the implications are
28
profound, as it provides a radical and wide-reaching reconceptualisation of
fundamental physics.
The cordus conjecture conceptualises a new candidate solution for the
problem of wave-particle duality. Through the lens of the cordus
conjecture [which we acknowledge may be incomplete or even plain
wrong], a whole new deeper level of fundamental physics becomes visible.
That deeper level seems to subsume the mathematics of quantum
mechanics, wave theory, and general relativity, while simultaneously
invalidating the physical interpretation of superposition and the wavefunction. So cordus may turn out to be a profound epistemic discontinuity,
an earthquake of disruption to the edifices built on conventional theories
of physics, and an entry portal to the next deeper level of mechanics.
As the cordus conjecture shows, the double-slit device and the problem of
wave-particle duality are cognitive springboards: solve them and many of
the other integration problems [see Figure 1] suddenly come within reach,
at least in principle. Thus this is exciting work, and even if the cordus idea
itself ultimately proves not to be the solution, there would seem to be
value in persisting with this design-type of approach, even if it is
unorthodox to mainstream physics.
6
Conclusions
The purpose of this paper was to explore new conceptual solutions to
wave-particle duality, by applying a cognitive style used in engineering
design. The results are radically unorthodox, and surprising. The
implications are that the conceptual foundations of our existing theories
are fundamentally wrong. Change the conceptual foundations and
suddenly the potential exists for solving wave-particle duality, and several
other integration problems.
It is proposed that the photon does have internal structure, and the cordus
conjecture sets out that proposed structure. Thus the photon, and indeed
all so-called matter ‘particles’, has a two-ended cordus structure. This one
idea is conceptually able to explain both particle and wave behaviours. It
explains the path dilemmas in the double-slit device, as well as the fringes
made by single photons or a beam of light. It also derives the quantitative
relationships for several optical reflection and refraction effects. Cordus
makes sense of the concept of frequency, which is otherwise a
problematic concept in physics.
While the present paper only addresses wave-particle duality, the wider
work provides an integrative solution that covers a wide range of
enigmatic effects in physics. Cordus suggests there is a deeper mechanics
that subsumes both quantum mechanics and wave theory. Perhaps
surprisingly, Cordus is also simpler and more coherent across a wider
range of phenomena than quantum mechanics or wave theory on their
own.
29
Even more surprising, and unexpectedly contrary to the prevailing
probabilistic paradigm of quantum mechanics, cordus suggests that the
next deeper level of reality is deterministic.
Acknowledgements
We acknowledge with gratitude the assistance of Dr Mathieu Sellier for
translating the abstract.
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33
Why does quantum mechanics not scale up?
Pons, D.J. 4 Pons, A.D., Pons, A.M., Pons, A.J.
ABSTRACT
The conceptual foundations of conventional fundamental physics are
evaluated for logical consistency. The point of comparison is the cordus
conjecture, that predicts specific internal geometries to ‘particles’, and thus
delivers a coherent set of hidden variables. It is proposed that this deeper
cordus mechanics can explain the quantum mechanics notion of
superposition. Usefully, it also explains coherence. It identifies the
underlying mechanisms whereby coherence arises and predicts the
boundary conditions for this special state. This is then used to explain why
quantum mechanics does not scale up to macroscopic bodies. This also
allows a natural explanation of the Schrödinger’s Cat paradox. The
comparison suggests that QM has seven conceptual fallacies, starting with
the premise that particles are points. Core principles of QM are refuted,
including Bell’s theorem, locality, and superposition, at least as QM
constructs the ideas. Cordus also explains why the mathematical
machinery of QM nonetheless works. Quantum mechanics emerges as only
an approximation of a deeper and more logically consistent cordus
mechanics.
Keywords: quantum scale invariance, myth, fallacy, paradox, realism
Edition 2 > Date: Saturday, 11 February 2012 > Document:
Pons_Cordus_0.2_QuantumScaling_E2.10.42.doc Changes: 2.10 typos fixed
1
Introduction
Quantum mechanics (QM) is the dominant theory for fundamental
physics. Nonetheless it lacks a coherent conceptual foundation, even if its
quantitative algorithms seem functional. Its descriptive explanations
(‘interpretations’) all have elements of incongruity when compared to
reality [4]. Even the deterministic theories, such as the de Broglie-Bohm
pilot wave theory [1, 15-16] that the wave-function guides moving
particles down trajectories with position and momentum being hidden
variables,
is an interpretation of quantum mechanics ('causal
interpretation') rather than a conceptually independent theory.
QM conceptually dominates sub-atomic physics. Yet none of its many
interpretations is able to fully explain the macroscopic world [17], nor do
its explanations always make sense, even to its expert practitioners:
‘I am convinced that quantum mechanics is not a final theory. I
believe this because I have never encountered an interpretation of
the present formulation of quantum mechanics that makes sense
to me’. Smolin [18]
4
Please address correspondence to Dr Dirk Pons, University of Canterbury,
Christchurch, New Zealand. Copyright D Pons 2011.
34
Others have taken the position that the paradoxes about quantum theory
are because it is being applied outside its bounds of validity [3], so that the
paradoxes don't really exist, or that our cognition is inadequate [19].
However that still implies that QM is not a universal theory. But why those
bounds should exist, where they be, and what theory is valid outside
them, are still unanswered questions [20].
In addition to that sense of unease, many of the conceptual premises
underpinning quantum mechanics are questionable. These include
fundamental randomness, virtual particles, and the belief that there is no
reality beyond what is measured [2]. Other theoretical formulations, e.g.
hidden-variable solutions, are actually not prohibited in QM [2]. Feynman
stated that ‘We absolutely must leave room for doubt', and though he did
not necessarily mean that of quantum mechanics in particular, there have
been ongoing concerns about the lack of conceptual coherence and
questions about the veracity of the explanations derived from QM.
Many of the original paradoxes of quantum mechanics that were there at
the outset, such as wave-particle duality and the scaling problem [4, 21],
have never been resolved. Thus while theoretical physics has advanced in
its mathematical modelling, it has not yet revealed a coherent picture for
physics. It has left behind unfinished conceptual business, and it is those
voids that interest us. The purpose of this paper is to examine the
conceptual premises of QM, using a contrast.
Approach
Since the deficiencies in QM are conceptual rather than mathematical [23], there is value in focussing on the former. Working in this area
necessitates a conceptual design methodology, which is necessarily
creative. This type of cognition is not countenanced as much in physics as
in engineering, from whence the design methodology used here is
borrowed. Conceptual design is a risky venture, both in terms of the
subjectivity of the process and the uncertainty of success, but also has the
potential for surprising insights.
The purpose here is to appraise the premises beneath QM and see why it
has the conceptual issues that it does, such as its inability to scale up to
the macroscopic level. To do this requires a point of reference of some
sort, preferably outside of QM. While there are several interpretations of
QM, there are not many viable alternative theories that are external to it,
so we first had to create one. We used concept-design [22] to create a
novel alternative conceptual framework. This is ab initio: from first
principles in a conceptual sense. This involved synthesising a satisfactory
solution with the desired properties to give an adequate fit to observed
quantum reality of the double-slit device, and then purposefully extending
the design to describe other phenomena. This subjective design-cognition
is very different to the mathematical modelling used conventionally in
physics, and we acknowledge it may seem foreign. Nonetheless it created
a concept which is entirely independent of QM conceptually, yet explains
the same basic fundamentals, and is therefore a suitable mechanism for a
35
contrast. The synthesised design is called the cordus conjecture and its
detailed assumptions are described elsewhere [23-24]. Its validity is
unknown, but it does have a high degree of logical consistency, and it
provides opportunity for evaluating QM in ways not previously possible,
because new ideas suggest new comparisons.
2
Cordus conjecture
The cordus conjecture [25] is that all 'particles', e.g. photons and electrons,
have a specific internal structure of a cordus, comprising two reactive
ends, with a fibril joining them. The reactive ends are a small finite span
apart, and energised (typically in turn) at a frequency, at which time they
behave like a particle. When energised they emit a transient force pulse
along a line called a hyperfine fibril (hyff), and this makes up the field. See
Figure 1 for application to the photon.
Figure 1: Cordus model of the photon. It is proposed that the photon
probably only has a single radial hyff at each reactive end, whereas the
electron has three, but the fundamental structural concept is similar.
How does the cordus idea help?
The cordus particuloid oscillates its appearance between its two reactive
ends, so it looks like a single ‘particle’ when it collapses to one of its two
modes. This explains why particles seem to be in two places as once: these
are the two modes of the cordus reactive ends. However it should be
noted that in this variant of the cordus conjecture only one reactive end is
energised at any one time, not both simultaneously. The probabilities of a
particle being in one particular location, rather than the other, arise simply
as the cutting points on the frequency. Stop the experiment with the
photon in a different part of its frequency cycle and it may appear in the
other position. Cordus particuloids look like point particles at a large scale.
A cordus is not the same as a ‘dipole’, which is a separation of negative
and positive charges.
Thus in this conceptual model the cordus is the deeper structure: the
‘particle’ nature appears in turn at the two reactive ends, as does the
36
‘wave’ nature in the hyff. The cordus is neither a wave nor a particle but
behaves as either depending on the measuring method. If the experiment
is arranged to detect a particle, then the cordus simply collapses to one of
its two modes, and a particle will be detected. It never collapses anywhere
but one of its two modes. Likewise wave-detecting apparatus will not
collapse the cordus but instead detect the hyff and a wave will be
detected. The measurement method unavoidably changes how the cordus
behaves, so wave and particle duality are only measuring artefacts, not the
reality in this model.
The cordus idea is a conjecture and unproven, but offers a logically
consistent conceptual explanation across many phenomena: it explains
wave-particle duality in the double-slit device [23], and derives the basic
optical laws for reflection and refraction from scratch, among other
outcomes [24]. The fact that it is possible to present a coherent counterpoint to QM, provides an opportunity to re-evaluate QM in ways not
previously possible.
3
Conceptual evaluation of QM
Quantum mechanics and the cordus conjecture both describe phenomena
at the particle level, but from such radically different conceptual
perspectives that the comparison provides a high degree of contrast. The
comparative analysis identifies the following conceptually erroneous
beliefs [‘fallacies’] in QM.
3.1
The fallacy that particles are points
The QM concept of 'particle' is generally of zero-dimensional points, of no
physical size at all, and no internal structure. QM accepts that the atom is
not really indivisible, and assumes that particles may comprise still smaller
particles, but does not explain how those particles are held in assembly.
From the contrasting perspective the particle, e.g. photon or electron, is
neither a point nor a sphere in the first place, but rather a cordus with two
reactive ends and emitting hyff, the zone of influence of which extend
beyond its geometric modes. The particuloid only appears to behave as a
point particle when viewed from a coarser level. From this perspective the
QM wave-function is an approximate descriptor of the average behaviour
of the particuloid. The probabilistic nature of QM thus arises because
there are deeper degrees of freedom in the structure of the photon
(internal variables) that are not under experimental control nor
represented in the wavefunction.
Thus from the contrasting perspective it is a fallacy to assume that
particles have to be points. The cordus conjecture demonstrates a
coherent solution without using points, so points have to be considered
an optional concept, if not rejected outright. Thus all physical
interpretations, including superposition, that are based on the point
37
paradigm are questionable. This means that cordus also challenges the
entrenched paradigm that conceives of a particle as a sedate, stable, solid,
in-one-place, well-defined sphere (of mass or charge), as if it were a
planet. It is not even remotely meaningful, from the cordus perspective, to
perceive the atom as hard little balls orbiting around a nucleus made of
compacted other balls, as shown in the popular symbol for the atom. 5
3.2
The fallacy of Bell’s theorem and locality
The principle of locality is that the behaviour of an object is only affected
by its immediate surroundings, not by distant objects or events elsewhere.
Thus a 'particle' is only affected by the values of the fields
(electromagnetic, gravitational, etc.) at the infinitesimally small location of
the point. Hence also local realism: that the properties of an object preexist before the object is observed. Entanglement appears to require the
principle of locality to be violated: twin particles may be linked, such that
changing the state of one instantly changes the other, even if they are
separated by macroscopic distances. The mechanisms are incompletely
understood in conventional physics, but the effect seems real. Bell’s
theorem sets these against each other by implying that only one
perspective can be correct: either superluminal effects or local realism
does not exist. The many actual experimental results are generally
interpreted as supporting non-locality behaviour in quantum mechanics. A
common interpretation is to accept Bell's theorem and conclude that no
viable hidden-variable solution of any kind can exist.
The cordus perspective is that a principle of Wider locality [26] applies: a
cordus particuloid is affected by the cumulative effect of the fields in its
local surroundings, these being the space to which its hyff have access.
Further, hyff have access to spaces that the reactive ends do not. Thus
cordus also explains the Aharonov-Bohm effect [27]. The cordus
explanation for entanglement is that the fibrils of two cordi become
synchronised through mutual hyff interactions, called complementary
frequency state synchronisation (CoFS) such that changes to the one affect
the other even when the span of the fibril is stretched. The fibrils still
retain their ability to communicate practically instantly [26]. Changing one
5
What is the diameter of a particle?
The conventional premise is that a particle is a stable aggregate of one or more semi-permanently
existing sub-particles, hence that it is meaningful to ask questions like ‘what is the diameter of the
particle, e.g. proton?’ From a cordus perspective this is an invalid question: it is not meaningful to talk
about the diameter of say a proton, as if it had a hard surface. Existing methods of attempting to
measure the ‘diameter’ of the proton involve measuring its interaction with electrons, either in
bonding situations or impact-scattering. From a cordus perspective these experiments are measuring
the average interaction geometry of the electron and proton, not a physical diameter. It is natural to
call this the ‘diameter’ of the proton, but that really is only an interpretation based on the premise,
which cordus refutes, that a particle should be a sphere of charge. Cordus further suggests that the
measurement is dependent on the probing particle, since its span is inversely related to its energy and
mass. This is consistent with the observation that the diameter of the proton is measured to be smaller
when the muon is used as the probing particle. Thus cordus predicts that a proton has no solid
diameter but instead will have many ‘diameters’ depending on the nature of the probe.
38
reactive end at one site therefore changes the other, and that change can
be immediately observed at the other site.6
The cordus model demonstrates that there is no problem with having all of
superluminal effects, hidden variables, and some degree of wider locality.
From this perspective Bell’s theorem is a fallacy that uses circular
reasoning: it makes the implicit prior premise that particles are points,
applies locality to the phenomenon of entanglement, concludes that
particles are points, and hence infers that there are no internal structures
(hidden variables) to particles. Bell’s theorem is a self-sustaining beliefsystem, not a logical necessity. It is only an obstacle to hidden-variable
solutions, if one has the prior belief that the solution must be limited to
only zero-dimensional particle designs [2].
3.3
The fallacy of superposition being the reality
Superposition from the QM perspective is that a particle occupies all
possible quantum states simultaneously, and only collapses to one when
the variable is measured. According to most interpretations of QM it is
only probability that drives this, there is no underlying variable.
From the cordus perspective, superposition and the wavefunction are
simply approximations to the deeper mechanics of the cordus particuloid
physically oscillating between its two mode positions. The cordus
particuloid (e.g. photon cordus) collapses to one of these ends when it is
grounded.
The probabilistic nature only emerges because the observer inserts
indeterminacy by selecting, even inadvertently, the moment to make the
measurement, and therefore the frequency state of the cordus and
ultimately the reactive end at which it will be found. Thus it is possible to
refute the Copenhagen interpretation that the probability is the reality:
from the cordus perspective superposition is not a physical state but
simply a misinterpretation of the mathematics, and the measured
probability is only an artefact of the observation process. It is not God that
6
Cordus Complementary frequency state synchronisation (CoFS) and coherence
This principle from the cordus conjecture explains is important in several
explanations and briefly elaborated below. Since a photon has two reactive ends,
and these are not energised all the time, it is possible for a second photon to
occupy the same space, or to co-exist nearby. This requires that the frequency
states be complementary, i.e. the reactive-end a1 of photon a is in the opposite
state to b1 of photon b, and physically near each other, mutually affecting each
other through the hyff to provide synchronisation. Likewise a2 and b2 at the
opposite end. With entanglement the photon spans are stretched so that the
reactive ends are far apart. It only looks like there is a whole photon at each
location, when actually there are two photons sharing the space such that only
one is visible at the location at any particular time. The bonds between any
cordus particles are hyff and carry forces that synchronise the cordus frequency
and phase of particuloids.
39
plays dice – the observer does, by selecting the method and moment at
which to make the observation. 7
3.4
The fallacy of causal variability
From the contrasting perspective, superposition confounds two different
effects: positional and causal variability.
Positional variability is ambiguity about where the particle (cordus
particuloid) actually ‘is’ at any one moment. For QM this corresponds to
the un-collapsed wavefunction, and the interpretation is that the particle
is simultaneously in two places at once. For the cordus interpretation the
positional variability instead corresponds to the statistical modes of the
two reactive ends. Only one end is actually reactive and in the place at any
one time, it is just that if the measurement frequency is not high enough
then it appears that the particuloid is simultaneously in both positions.
Causal variability is multiple consequences in time, i.e. divergent system
states. Consider a subatomic event that has two possible outcome, e.g. a
photon that could take path A or B. Once either of these states occurs,
then there are say two more outcomes: A1 or A2 for the A path of the
tree, and B1 or B2 for the B branch. Thus after time the system state has
diverged into various temporal outcomes, hence ‘causal variability’.
Quantum mechanics routinely assumes that causal variability necessarily
occurs with positional variability.8
7
Superposition: To put it another way, the root cause of the problem with superposition is deficiency
in its statistical formulation. Quantum mechanics was originally built with a statistical methodology
that approached the problem as a cross-sectional statistical design (single point in time). Therefore the
mathematical representations that QM developed are only applicable to average particle behaviour, at
one point in time, because that is all that a cross-sectional design is valid for. Quantum mechanics is
outside its base of validity for its statistical methodology when it tries to provide physical
interpretations for longitudinal effects (multiple consecutive points in time). An average is
fundamentally an unreliable predictor of longitudinal future outcomes when the population is
bimodal. This criticism stands regardless of the validity of the cordus conjecture.
8
In what ways does quantum theory misuse Causal variability?
The QM thinking goes something like this: ‘the particle is in two places at once,
but the choice of which has not yet been made. There are subsequent events
<notice the insertion of a time and causality premise here> the outcome of which
will depend on which location the particle chooses. Therefore those subsequent
events are also in superposition, i.e. exist simultaneously’. An example of this QM
logic is: ‘The quantum world … is 'both/and': a magnetic atom, say, has no trouble
at all pointing both directions at once. The same is true for other properties such
as energy, location or speed; generally speaking, they can take on a range of
values simultaneously, so that all you can say is that this value has that
probability. When that is the case, physicists say that a quantum object is in a
'superposition' of states.’28.
Ball, P., Physics: Quantum all the way. Nature
News, 2008. 453(30 April 2008): p. 22-25.
QM commonly extrapolates this further to whole bodies: ‘Therefore the object or
person <notice the insertion of a premise of body-coherence here> in question
will simultaneously be in several states, i.e. in different futures.’ From there it is a
very short logical step to the idea of a separate universe, one for every causal
outcome of every superposition states, hence the ‘many worlds’ theory. The
40
QM fails to differentiate these phenomena: it assumes that causal
variability necessarily occurs with positional variability. This fallacy is an
integral part of all interpretations of QM, which are thereby also refuted.
Thus the contrasting perspective deflates the many-worlds/multiverse
theories, and shows that the weirdness in quantum mechanics arises not
from inadequate human comprehension, but from deep conceptual flaws
in QM itself.
Thus from the cordus perspective, a particuloid that oscillates between
two reactive ends (modes) does not have dual futures: it only has one
even if it is unclear at the time, and the driving mechanisms are
fundamentally deterministic even if at too high a frequency to detect. The
confounding of these two types of variability drives the paradox of
Schrödinger’s Cat, as will be shown.
3.5
The fallacy of easy coherence
From the QM perspective coherence is the ability for particles to interfere.
This includes constructive and destructive interference of photons or
waves (hence fringes), and dependencies (‘correlation’) between two
different particles. The dependency may exist to a greater or lesser
extent, i.e. involving more variables between the particles. There is also
the matter of how strongly the dependency is preserved over time. The
concept of coherence also includes the idea that only one wave or particle
is involved: that its properties at one instant of time can be linked those at
a different location or time (‘self-coherence’). Examples of QM coherence
at the large-scale include the laser, electrical superconductivity, and
superfluidity. Nonetheless, even within QM there are differences of
opinion about the interpretation of coherent states [29].
The QM expectation is that all objects, subatomic as well as macroscopic,
should follow quantum theory and exhibit superposition, but the reality is
that only particles and some microscopic objects show the behaviour. The
latter are inanimate objects that have been cooled to close to absolute
zero temperature (referred to as their ‘ground state’) [30-31]. There is
much hope that superposition and quantum behaviour will be attainable
in larger and warmer objects [32], as QM suggests should happen. It is not
clear where the boundary is between the quantum world of particles and
the macroscopic world that we perceive, and quantum mechanics itself
cannot identify why there should be a boundary, nor where it would be.
The contrasting cordus interpretation is different. Coherence is when all
the cordus particuloids, which may be photons, electrons, protons, atoms,
etc., have synchronised frequencies and phases thereof (see CoFS above).
combinatorial branching on that tree of universes must be enormous if every
superposition of every quark for all time, is to be accommodated. It is currently
one of the favourite contenders for a qualitative description of how QM works,
but from a logical perspective it creates more problems, and is hardly
parsimonious or even physically measureable.
41
This particular state, where all the particuloids in the body of matter are
synchronised, is termed ‘body coherence’. For photons in light beams,
where the bonds are weak if they exist at all, the coherence may be mainly
temporal and coincidental. In superfluidity and superconductivity the
coherence is substantial [33]. However these are special states of purity
and temperature, and macroscopic objects at our level of existence
generally do not show this degree of coherence.
The cordus conjecture can also predict what extent of coherence should
be visible, and why. The critical factors for body-coherence are predicted
to be temperature, homogeneity of composition, internal thermodynamic
processes, internal mechanics, and gross size. It comes down to a
sufficiently stiff structure: one where the bonds between atoms are
consistent, firm enough to sustain the synchronicity, and there are
minimal phonons. Coherence becomes difficult to sustain when one part
of the body goes in a different direction, e.g. internal motion, or living
physiology.
Single cordus particuloids, such as electrons, are self-coherent under any
conditions. Entangled particuloids, such as electrons sharing orbits, are
also coherent. Entanglement is thus a simple form of coherence between
two particuloids, see the CoFS principle above. Cordus predicts that
sufficiently small bodies, typically atoms and molecules, should be able to
diffract, form fringes through gaps, and pass through the double-slit
experiment with the usual outcomes, providing they are in bodycoherence – though that will be increasingly difficult to achieve as the
bodies become larger and warmer. Indeed, largish molecules have shown
some of these behaviours [34].
Microscopic sized bodies, including viruses but excluding cells functioning
at the time, should be capable of body coherence at low temperature, and
thus exhibit bimodal positional variability (i.e. what QM would interpret as
superposition). Indeed, resonance has been observed for small engineered
objects [30-31]. It has also been proposed for viruses [35], and cordus also
suggests that is feasible.
Large macroscopic bodies of homogeneous composition, e.g. liquid helium,
cooled to near zero should be able to be placed into coherence as a type of
supersolid, and should be able to diffract and form fringes through
sufficiently large gaps or at edges, though the effects will be miniscule.
Large macroscopic bodies are predicted to be unable to form fringes
through the double-slit device, because the whole object needs to be able
to go through a slit at each of its positional extremes, and this will
effectively delete the medulla and convert the experiment to a gap.
However, getting a large macroscopic body of inhomogeneous composition
and ambient temperature into body-coherence is likely to be next to
practically impossible, especially for something like a motor car with
moving parts. Or a cat. Cordus predicts that practically every object at
ambient temperature and visible with the naked eye is not going to form
42
matter waves or fringes, nor display superposition (neither positional nor
causal) [33].
If cordus is correct, then coherence is a special state, and QM is in error by
assuming that it readily applies. Coherence is therefore not practical for
realistic every-day bodies, living creatures, or the universe at large: there is
too much temperature (phonons), diversity of atomic composition, and
internal mechanics/thermodynamics to create the CoFS state. QM
assumes that decoherence arises because the body interacts with the
external environment in some unspecified way. Cordus identifies the
factors and qualitatively describes their interaction. Thus it explains why
small objects are more easily coherent, even at high temperatures,
whereas large objects are not. The dominant disruptive mechanism is thus
the response of the body to phonons. Identifying this fallacy, and
understanding why it arises, is important in the following explanation of
why quantum mechanics does not scale up.9
3.6
The fallacy of scale invariance
We now come to the central puzzle of QM: why the effects it predicts are
only visible at sub-microscopic scale. Why does QM not scale up properly?
If it is valid at subatomic scale, what is preventing it from working at
macroscopic scales? This is not something that QM has itself been able to
explain.
For example, particles seem to be able to appear in more than one place,
and the act of observing them does seem to influence their location. Yet
macroscopic bodies show no such tendency. This is a particularly serious
issue for theories of cosmology, which have to take a position on this. 10
The general premise in physics is that quantum mechanics is the reality,
and the classical world that we perceive emerges from that [28], but how
this happens is unknown. It is generally believed that the macroscopic
body loses coherence (hence decoherence) in some way because of some
9
Why has QM persisted in the false belief of easy coherence for macroscopic
bodies, despite all the empirical evidence to the contrary? Is it because it needs to
be true for the integrity of the QM paradigm? QM consists of a set of interlocked
premises (wavefunction, superposition, coherence, interference) that make up its
conceptual model. If QM is to be a theory of everything, then it needs to scale up
to macroscopic bodies, and all the above premises are needed for that. Of those
four, coherence is the weakest and most in need of being true if the belief system
as a whole is to be sustained. Quantum mechanics is an adequate descriptor of
much of subatomic reality, but clearly is not the complete reality because it does
not explain all things in physics. To believe that QM is the reality necessarily
requires personal belief to bridge the residual ambiguities and sustain the
cognitive congruence of the mental-model.
10
The various forms of conventional cosmology accept the QM perspective, but are then faced with
the implication that the universe as a whole is constantly in a state of superposition ('multiverse'), and
thus leads to philosophical dilemmas about how and who the observer might be that collapses the
wavefunction to give the world that we see. If these collapses do occur, they are not physically
apparent to us, not for objects that we can hold with our hands, nor for the universe at large.
43
interaction with the rest of the environment, or the process of
observation, e.g. [17], but the detailed mechanisms are still uncertain. Not
only are the mechanisms unknown, but so too is where the transition lies.
The contrasting cordus interpretation has already explained why
coherence does not readily occur, and in turn this explains why quantum
mechanics does not scale up. It is because macroscopic bodies are
impractical to place into body coherence. Internal entropy prevents
formation of the CoFS state.
Thus the next deeper question is why entropy arises at all, given that
atomic interactions are reversible. This is not easily answerable with QM,
but again cordus offers an explanation. An atom that has surplus energy,
say from an incoming photon, can dispense it in five main forms: electron
orbital change (including bonding), electron ejection, photon ejection,
electron flow (displacement of free electrons or plasmons), and phonon
propagation (vibrational strain between the electrons making up the interatomic bonds, hence conduction). These mechanisms, especially phonons,
distribute the energy to further atoms in the bulk, diluting it in the
process. Through any of these mechanisms a remote atom might receive
energy and then in turn emit a photon. Even if that photon was sent
straight back to the original atom, there would still be less energy in the
feedback loop because of the phonon dilution in the intervening bulk, the
time required for the photon flight, and the expansion of space in the
intervening period. The geometric and micro-structural complexity of the
matter accessible to the photons and phonons introduces so many dilution
paths that it is extremely unlikely that the energy fragments will
spontaneously recombine using the thermionic effect to recreate the
original photon. Thus the individual mechanisms are all reversible (elastic),
but the system as a whole is not, hence entropy and thermodynamic
irreversibility.
The scaling problem of QM is thus explained as entropy causing an inability
to sustain body-coherence. So the particuloids in the body are unable to
move in synchrony but instead have different frequencies and phases, and
thus have to find locations for their reactive ends by negotiating with their
neighbouring particuloids, through the hyff. The fallacy in QM is the
assumption that its principles and mathematical formulations are
universally true and therefore invariant with scale. It fails to adequately
conceptualise entropy and the different mechanics that operates. Thus
quantum mechanics becomes irrelevant at macroscopic scales. It is only
useful for the narrow range of scales where (1) things look like particles
(i.e. not too small), and (2) where body-coherence is attainable (i.e. small,
cold, inanimate, not too large).
Thus the cordus conjecture is able to offer an explanation as to why
quantum mechanics does not scale up to the macroscopic objects at
ambient conditions, nor the universe in general. Cordus explains how the
decoherence arises. It also answers the question as to where the boundary
lies between the quantum and classical worlds, and predicts what should,
and should not, be achievable in quantum behaviour.
44
3.7
The fallacy that fields and particles are independent
Quantum mechanics includes concepts of both fields and particles, but has
no coherent unified model of causality for these. There is ongoing debate
as to which is the more fundamental [2]. The case has been made that
even quantum field theory, which nominally is about fields, is actually a
theory of particles [2], and therefore that particles are the more
fundamental entity. Indeed, as that author points out, it is only particles
that are observed in the collisions of high-energy physics. Yet quantum
mechanics has the internal inconsistency of elsewhere taking the wave
interpretation: that particles 'always behave as waves' [2].
In contrast the cordus model shows it is possible to conceive of a tight
dependence between fields and particles. The energy shuttles between
the internal structures (fibril, reactive ends, hyff) and what happens to one
affects the other [36]. Thus the process of measurement, whether of field
or particle, fundamentally changes the internal energy mechanisms of the
cordus and thereby influences the outcome that will be observed.
There is a measurement interlock: whatever happens to the field affects
the particle, and the inverse. Hence the measured reality is contextual: it
depends on the intrusiveness of the observation itself. Different
observation processes applied to the same underlying reality will therefore
yield different measurements. Specifically, if we apply an intrusive
observation like putting a screen in the path of a photon, then we force
the cordus to collapse to one of its reactive ends, and therefore the
measurement shows a ‘particle’. Alternatively, if we put an antenna near a
passing photon, then we interact dynamically with its hyff, perhaps
delaying or speeding up the hyff emission process, and therefore our
measurement shows a ‘wave’ has passed by. Thus from the cordus
perspective QM makes the additional error of carelessly confounding
different types of measurement. Cordus identifies the mechanisms
whereby taking a measurement of a particuloid can collapse it altogether,
or pump energy into/out of the cordus, or steer the reactive ends to
appear in certain locations (this is also the cordus mechanism for force), or
do nothing at all to the cordus. The current word ‘measure’ is unreliable
(‘deceptive’ [3]) because different types of measurement impose different
behaviour on the particuloid.11
Therefore the debate as to which is more fundamental, fields or particles,
is sterile, as both are equally important. They can communicate with each
11
The measurement interlock also has something to say about the philosophical debate of the role of
the Observer, and of free-will. Although the underlying cordus mechanics is deterministic, this does
not mean that free-will is abolished. At our level of existence the determinism is inaccessible.
Furthermore, cordus states there are different ways in which we can Observe, as discussed above, and
the way the philosophical debate uses the term 'Observer' confounds these. There is a need to tighten
up the terminology. Cordus would generally agree with 't Hooft's idea that 'an observer has the free
will to modify the setting of a measuring device, but has no control over the phase of its wave function'
(2007), except would replace 'wave function' with 'frequency'.
45
other through the internal structures. This fundamental concept, which
QM does not grasp, is essential in understanding why the cordus
particuloid is able to shape-shift in response to the type of external
measurement, and thereby show wave or particle behaviour. Thus also the
concept of ‘noninvasive measureability’ [17] is also refuted by cordus: it is
not possible to measure a quantum system without affecting the inner
variables.
In the cordus perspective wave and particle behaviours are simply
artefacts of the observation process, and partial representations of the
deeper cordus mechanics. That ‘wave-particle duality’ is even a paradox
is therefore a consequence of the QM fallacy that fields and particles are
independent. Embrace the deeper interaction and the duality dissolves
[23].
Cordus also refutes the QM premise that there is no reality beyond that
which is measured. Instead cordus suggests that the measured outcome is
an artefact of the chosen observation process, and the way that
dynamically interacts with the internal structures of the cordus.
5
Discussion
Using a radical contrasting conceptual model we have shown that it is
possible in principle to refute the core premises of QM. Thus: (1) it is
unnecessarily limiting for physics to conceive of particles as points; (2)
Bell's theorem is refuted; (3) QM fundamentally mis-conceptualises
superposition; (4) QM confounds positional and causal (temporal)
variability; (5) QM is in error in thinking that coherence is easy to achieve;
(6) QM is wrong in expecting its principles to be scale invariant; and (7) it is
a mistake to consider fields and particles as causally independent
phenomena. These statements will be controversial, since they call so
much of QM into question and challenge the orthodoxy. However they are
only true to the extent to which the cordus conjecture is valid, and since
that is unproven, the whole exercise should be considered only a thoughtexperiment at this stage.
Even so, we can apply it to answer some of the other interesting cases
where quantum mechanics is at a loss: wave-particle duality [23],
unification of electro-magneto-gravitional force [EMG] [37], and the strong
force [38]. Next we show how it solves two other enigmas of QM:
Schrödinger’s Cat, and objective reality.
Unlocking Schrödinger’s Cat
Schrödinger’s Cat is a thought-experiment in superposition: the basic idea
is that a cat is placed in a box with a radioactive sample rigged up so that
decay emits a particle which breaks a vial of poison that kills the cat [21]. If
the box is closed and no-one can see inside, in what state is the poison and
the cat? This is an extension of the idea in quantum theory that a physical
system can be in multiple configurations (dead vs. alive), and therefore
from the quantum perspective is simultaneously in all those configurations
46
until the act of observation forces it to one particular configuration, i.e.
collapses the waveform. Alternatively that each of the other non-selected
configurations does continue, but in another parallel universe. Yet there is
nothing in our usual experience that suggest that reality behaves this way.
Unlooked-at cats do not really seem to be in an indeterminate state of life
and death. Why not? Is quantum mechanics wrong? Or are our cognitive
constructs of reality wrong?
With cordus the paradox becomes easy to unlock, by noting that it invokes
superposition, causal variability, easy coherence, and scale invariance: all
of which have been refuted. Thus from the cordus perspective there need
be no dilemma about the state of the cat before opening the box, in the
sense that it is not simultaneously alive and dead but instead simply still
alive or already dead. A simple act of passive observation does not change
the system’s state.12 Thus cordus asserts that the presence of the passive
Observer does nothing, and this voids the existential Observer dilemmas,
and the many-worlds theory. Something as large and internally dynamic
(nerve impulses, flowing blood, etc.) as a cat cannot have that CoFS bodycoherence in the first place: initially imposing the coherence would
deprive it of life. Only small, cold, inanimate things of relatively
homogeneous composition can be put into body coherence.
But if Schrödinger’s Cat dilemma collapses because of lack of coherence of
the cat, then what about replacing the cat with an electron: something
that can generally be thought of as in ‘quantum superposition’? Will the
dilemma still be sustained then? Is the electron simultaneously blasted
and not-blasted by the radioactive decay? QM states that the electron
occupies all possible quantum states simultaneously, so the electron
should be in normal and high energy states simultaneously, and only
collapse to one when measured. The answer, according to the cordus
conjecture, is no: those are the fallacies of superposition and causal
variability at work. Not-observing the electron makes no difference either.
The fact that no-one has yet implemented the experiment is interpreted as
circumstantial evidence that superposition is merely a mathematical
approximation for handling positional uncertainty, not a real physical
effect, nor a temporal one, and macroscopic physical bodies cannot be
assumed to be in body coherence.
Schrödinger‘s Cat is not physically realisable, nor does it prove quantum
mechanics is correct. That it is even considered a paradox shows how
difficult it is for the limitations of quantum theory to be comprehended
from within the QM paradigm.
12
Passive observation is inconsequential, whereas passing observation
(interrogation of the hyff) can have consequences, the Zeno effect being an
example. The most intrusive form of measurement is ‘intrusive’ as the term
suggests, and this forces the cordus to collapse at one of its reactive ends.
47
Is there an objective reality?
Quantum mechanics has difficulties with both realism and with locality,
not made any easier by QM confounding (‘blending’ [17]) the terms.13
Realism is that the properties of an object pre-exist before, and
whether or not, the object is observed. It has been a major
philosophical ambiguity for QM [2, 17, 21, 39]. It is difficult to
assign physical meaning to its mathematics. Cordus has already
indentified that one of the causes is that QM confounds several
types of Observation.
The principle of locality is that the behaviour of an object is only
affected by its immediate surroundings, not by distant objects or
events elsewhere. Physics generally feels that that the principle of
locality should apply, but the empirical evidence for entanglement
suggests it is unrealistic. But what the mechanisms might be for
non-locality, other than superposition, is uncertain. In contrast,
cordus suggests that locality is not preserved, though a principle of
wider locality applies.
The difficulty for quantum mechanics, which tends to deny realism and
locality, is to explain why both of those do seem to apply at the
macroscopic level of classical mechanics [17]. The even deeper
unanswered question is: What is the fundamental reality of matter, light,
forces, and time?
By contrast the cordus conjecture does provide an objective reality. It
describes internal sub-structures (fibril, reactive ends, hyff) for the photon
and matter particuloid, and it provides a basic set of causal relationships
for their interaction: a type of descriptive mechanics. The cordus
conjecture also shows how these internal structures manifest as external
variables, including the flexibility to appear as wave or particle depending
on how the Observer makes the intervention, i.e. contextual observation.
Cordus also suggests that the concept of realism needs careful treatment:
that the various current definitions may be confounding subtlety different
effects. For example, here we adopted the perspective: ‘Realism is that
the properties of an object pre-exist before, and whether or not, the object
is observed’. However this is not same as ‘Each photon … possesses a
complete set of properties in its own right’ [17]. The issue is with
‘complete’ and the implication of a fixed prior set of hidden variables. This
is a common tacit premise of hidden-variable solutions. Cordus refutes this
as too simplistic, and an example of the fallacious independence of fields
and particles. Instead the internal properties are dynamic and their
expression depends on the method of observation (due to the deeper
interaction mechanisms between hyff and reactive-end). Therefore it is
13
As Leggett (2008) observed, ‘Perhaps the lesson is that while the concept of ‘local realism’ is clearcut, to try to analyze it in terms of its two prima facie components may not in the end be a particularly
meaningful exercise. Certainly, in QM itself the two concepts, or rather their absence, in some sense
appear blended, in that once one has the (nonrealistic) concept of a quantum superposition then the
idea of applying it to the coupled state of two spatially remote objects is an entirely natural
development.’
48
important to be careful in the meaning assigned to ‘realism’, and physics is
generally careless in this regard.14
Concerning the bigger picture, whether microscopic objects and
macroscopic
bodies have properties that exist independently of
observation, the cordus answer is yes, but with qualifications. Yes, the
properties exist, for both small and large objects. No, the expression of the
properties is not independent of observation, at least for microscopic
coherent particuloids. No, macroscopic discoherent bodies do not have
usefully measureable quantum properties, and instead classical properties
are more useful. Yes, at a deeper level the system of properties exists
independently, for all matter in whatever state. Thus realism also depends
on what meaning one infers in ‘properties’. Nonetheless from the simple
pragmatic every-day perspective (non-physicists and non-philosophers),
the answer is yes, realism as we know it does apply. Thus quantum
mechanics is profoundly and very fundamentally wrong about reality, if
cordus is correct.
In summary, the constructs of quantum mechanics are fundamentally
inadequate to explain reality, realism, and locality. Cordus offers a
radically different conceptualisation which not only explains those, but
also goes beyond QM to provide a foundation for interpretations, albeit
speculative, for the things that are really interesting: What is matter made
of? What is light? How does force operate on matter? What is time? [37]
Limitations
The cordus conjecture was used for the de-biasing conceptual perspective.
We are not saying that cordus is necessarily valid, only that it can
conceptually explain many effects from a single logically-consistent
foundation, and is a useful contrast. Even then it is not necessarily the only
solution.
The unknown validity is not a limitation for the present study. Falsification
of the cordus conjecture might invalidate the specific criticism of
superposition (#3 above), but the point about particles (#1) probably still
stands, as does the criticism of Bell’s theorem (#2) and the confounded
variability (#4). Even if the precise explanation of the difficulty of obtaining
coherence in macroscopic objects (#5) should fail, there is every reason to
believe that QM still has a problem in this regard. Likewise, until QM itself
can give a coherent physical (as opposed to metaphysical) explanation of
why it does not appear to scale up (#6), then that criticism also stands.
Even if cordus is incorrect about the tight dependence between field and
particle (#7), QM will still need to solve this problem sometime. It is
inescapable that there are serious failings in the fundamental constructs
of quantum mechanics.
14
To address Leggett’s three postulates, cordus (1) refutes locality, (2) partly
accepts temporal causality (induction), though not the idea that properties are
only determined at the source (cordus adds a contextual measurement
mechanism), and (3) supports realism (at least some definitions thereof).
49
Cordus interpretation of where quantum mechanics goes wrong
From the cordus perspective, the classical world does not emerge from the
quantum world, nor is quantum mechanics the reality. Rather there is a
deeper mechanics from which both emerge. Quantum mechanics only
approximates some of the deeper behaviour, and even then only for a
limited range of geometric scales. Classical physics emerges directly from
the deeper mechanics when many pieces of matter are aggregated and
the inter-particuloid behaviour (e.g. phonons, entropy) dominates over
the intra-particuloid behaviour (e.g. coherence and CoFS).15
In this sense QM may be a conceptual dead-end. Its conceptual
foundations are adequate on which to build a pretty-good set of
quantitative algorithms, but the mathematics does not describe the
reality, only the approximation of the reality. Thus all the attempts to
derive a physical interpretation from the mathematics of QM are fraught,
hence their weirdness.
What quantum mechanics has done is take some flawed conceptual
foundations, derive some beautiful and dazzling mathematics, ignore the
foundations, and then in a recursive way attempt to infer physical
interpretations for the foundations from the mathematics. Those
interpretations of QM have generally been incongruous with reality, but
physics has tended to insist that QM has universal validity [17], and reality
must really be weird, or our human perception inadequate [19].16 The
obvious alternative conclusion has been ignored: there has been a failure
to logically trace the chain of reasoning back to the conceptual
foundations to check whether they are sound.
Current quantum theory has become an interlocked belief system, with a
reliance on mathematical modelling, and sustained by confirmation bias. It
no-longer needs, and therefore is disconnected from, its conceptual
foundation. Hence there is little orthodox interest in retooling the basic
concepts. Furthermore, theoretical physics is disinterested in conceptual
methodologies in general. Its methodology is mathematical [40], which
dominates all other ways of thinking. The mathematical method of physics
has been successful for incremental advancement of the field, but it has
not produced a coherent explanation consistent with macroscopic reality despite a hundred years of trying by thousands of physicists. Schrodinger's
Cat is just as much an enigma today as it was then. Nor has it produced
innovative concepts, only reinforcement of existing thinking. Quantum
mechanics and mathematical physics have an epistemic co-dependency,
15
To put this another way, the presence of the hyff from other matter messes up
the overall hyff environment, and makes the complementary frequency
synchronised (CoFS) states more complex and eventually unattainable, thereby
causing decoherence.
16
QM offers a solution, of sorts, for wave-particle duality: first by positing that particles are wavepackets, second by assuming that particles can be in multiple places at once (through superposition or
virtual twins), third by assuming that the state of a particle can only be known as a probability, and
fourth that the actual position of the particle is only determined when it is observed, hence collapsing
the wave-function. Thus from the QM perspective the strangeness of wave-particle duality is only an
artefact of our inadequate human cognition: ‘the <paradox> is only a conflict between reality and your
feeling of what reality <ought to be>‘ (Feynman).
50
that limits what constructs are admitted to the discourse. Given this
dependency, and the unreliable premises of its conceptual foundation, it is
not too severe a criticism to say that QM is an interlocked belief system.
Like any other belief system, QM has major gaps and cognitive
dissonances, the bridging of which requires faith.
Quantum mechanics is generally considered valid. But the fact that many
of its predictions are consistent with experiment is only evidence of
correlation, and it is unreliable to interpret that as universal validity [17]
until we can be quite sure that there is no other alternative solution.
Hence the interest in QM for placing bounds on what those other solutions
might be, viz. Bell’s theorem. We suggest that not only is quantum
mechanics built on deeply flawed conceptual foundations, but the search
for alternative constructs has been too limited to the vicinity of QM.
Quantum mechanics cannot provide a coherent description of current
physics, has deep conceptual flaws that it is unable to address, and there is
no guarantee that its current interpretations or its mathematical
methodology are capable of finding the next deeper level of physics.
This is a serious criticism, and we look forward to a spirited explanation
from orthodox physics as to why the above fallacies should not apply to
QM. If the criticism holds and the fallacies cannot be refuted, then it
means that quantum mechanics may be conceptually deficient at its most
fundamental level and an unsuitable foundation for an all-inclusive theory
of physics.
Implications
The contrast used here has refuted much of the conceptual foundation of
quantum mechanics. If so, why does QM work at all? The answer is that
the mathematical machinery of QM is a sufficiently good approximation
for small particles within a certain scale-range where components of
matter approximate point particles, and coherence can be obtained. Thus
we suggest that the QM machine works adequately for many things that
practical physicists need to compute, while being profoundly and very
fundamentally wrong in the conceptual sense. This is why it does not show
good agreement with reality regarding very small objects (e.g. waveparticle duality) or macroscopic bodies (scaling problems), and its
qualitative descriptions are incongruent (inconsistent with reality).
Future work
One may or may not agree that cordus is correct in identifying all these
fallacies in QM, but cordus has arguably got further than QM in explaining
the paradoxes of particle behaviour even if QM is more advanced in its
mathematical modelling. However mathematical algorithms can readily be
added to cordus: much of the quantum machinery can probably be
repurposed as a starting point, since cordus has no issues with the
mathematics of QM being an adequate representation of the average
behaviour of a cordus. However we do not attempt that detailed design
here, as our interest is in first developing the concept. The cordus
conjecture is a class of solutions, and even if the particular design variant
51
(‘working model’) used here is invalidated, cordus has other variants to
offer.
The cordus conjecture, incomplete though it be, has the potential to be
what Kuhn termed 'revolutionary science' [41], since it rivals the existing
QM framework. Cordus is not simply an extension of QM, but a different
concept altogether ['incommensurable'], with a different method of
thinking and new words for new concepts [3]. It redefines what might be
possible to achieve in theoretical sub-atomic physics. It resolves deep
outstanding problems in physics, in ways that cannot be comprehended
from within the QM framework, but it does so in such a way that leaves
much of the existing QM machinery intact [Kuhn's 'concrete problem
solving activity'], which is consistent with how Kuhn predicted such
developments might occur.
6
Conclusions
The purpose of this paper was to critically appraise the conceptual
foundations of quantum mechanics, using a contrasting perspective. If one
wishes to objectively and creatively critique so established a theory as QM,
one must seek a conceptual position well outside it. Unfortunately there is
a dearth of viable alternative theories, but the new cordus conjecture
provides such a vantage. Therefore, while we acknowledge the subjectivity
of the analysis, we do not apologise for it, because there really seems to
be no other way to appraise quantum mechanics without being dominated
by its way of thinking.
If the cordus conjecture is correct then the comparison suggests that
quantum mechanics is conceptually fallacious in several areas. (1) Particles
need not be zero-dimensional points after all, and this immediately
erodes several other premises of QM. (2) Bell’s theorem is refuted as being
not universally applicable, and the principle of locality also fails. (3) The
wavefunction is a mathematical approximation of a deeper reality, and
superposition is not a physical state but simply a misinterpretation of the
mathematics and an artefact of the observation process. Only one end of
the cordus is actually reactive and in the place at any one time, it is just
that if the measurement frequency is not high enough then it appears that
the particuloid is simultaneously in both positions. (4) QM’s superposition
is identified as a confounded concept that mixes positional and causal
(temporal) variability, and this is found to be the cause of much of the
weirdness of the QM interpretations of reality. (5) QM is mistaken in
assuming that coherence of a physical object is automatic and easy to
obtain, and cordus identifies the factors that cause decoherence and
qualitatively describes their interaction. (6) Cordus explains why quantum
mechanics does not scale up to macroscopic objects, and why it does not
represent finer structures either. (7) It is fallacious to consider fields and
particles as independent phenomena. Instead they are closely and
dynamically coupled in the cordus, and this explains the measurement
context.
52
These assertions refute many of the core principles of QM, and so the
implications are that the foundations of quantum mechanics lack
conceptual integrity. This is likely to apply to all interpretations and
derivatives of quantum mechanics, because they all use the same
premises.
The mathematical machinery of quantum mechanics is a reasonable
approximation to reality, even if the concepts are not, and the comparison
with cordus shows why. Thus the mathematics works, at least within a
certain scale-range where: (1) things look like particles and the proposed
cordus structure is not evident (i.e. not too small) and (2) where bodycoherence is attainable (i.e. not too large). Outside of that range quantum
mechanics seems neither conceptually nor mathematically relevant. The
same analysis predicts QM is unlikely to scale down to the next deeper
level of physics. The implications are that QM itself is profoundly deficient
in its conceptual foundations, and is only an approximation of a deeper
and more logically consistent mechanics.
Extended Abstract
Quantum mechanics (QM) has the problem of lacking a coherent
conceptual foundation, even if its quantitative algorithms are functionally
adequate. The conceptual logic beneath quantum mechanics is evaluated
using as the point of reference a novel alternative conceptual framework
called the cordus conjecture. The comparison suggests that quantum
mechanics is conceptually fallacious in several areas: (1) Particles need not
be zero-dimensional points after all. (2) Bell’s theorem is refuted as being
not universally applicable, and the principle of locality also fails. (3) The
wavefunction is a mathematical approximation of a deeper reality, and
superposition is not a physical state. (4) Superposition confounds
positional and causal (temporal) variability, and this causes the weirdness
of the QM interpretations. (5) Cordus identifies the factors that cause
decoherence and (6) explains why quantum mechanics does not scale up to
macroscopic objects. (7) It is fallacious to consider fields and particles as
independent phenomena. Instead they are closely coupled in the cordus,
and this explains the measurement context. Several core principles of QM
are thereby refuted. The paradox of Schrödinger’s Cat is explained as an
artefact of these flawed premises. The paper also explains why the
mathematical machinery of quantum mechanics is a reasonable
approximation to reality, even if the concepts are not. The mathematics
works, at least within a certain scale-range where: (a) things look like
particles and the proposed cordus structure is not evident (i.e. not too
small) and (b) where body-coherence is attainable (i.e. not too large).
Outside of that range quantum mechanics seems neither conceptually nor
mathematically relevant. The same analysis predicts QM is unlikely to scale
down to the next deeper level of physics. The implications are that QM is
profoundly deficient in its conceptual foundations, and is only an
approximation of a deeper and more logically consistent mechanics.
53
Brief: Quantum mechanics compared to cordus conjecture > core premises
of QM found fallacious > locality and realism reconceptualised >
Schrödinger’s Cat explained and put aside > explains why QM does not
scale up to macroscopic objects >
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55
Cordus Conjecture: Overview
Dirk J. Pons, 17 Arion D. Pons, Ariel M. Pons, Aiden J. Pons.
Abstract
The Cordus conjecture suggests there is a deeper, simpler, deterministic,
and more elegant reality beneath quantum mechanics and wave theory.
Revision 2.1 E2.1.05 Fixed 0D point image 2
Document: Pons_Cordus_0Summary_E2.1.05.doc
1
Introduction to cordus
What is the Cordus conjecture?
The Cordus conjecture is that all 'particles', e.g. photons of light, electrons,
and the protons in the nucleus of the atom, have a specific internal
structure. This structure is a 'cordus': two reactive ends that each behave
like a particle, with a fibril joining them. The reactive ends are energised at
a frequency, and emit a force line called a hyff that makes up the field, see
Figure 1 for application to the photon.
Hyper-fine fibrils
(hyff) emitted
from reactive end
Reactive end (RE)
energised at
frequency of
particuloid
Motion of
photon
Fibril, does not react
to matter, maintains
frequency reenergisation.
Spacing is the span
Other reactive end,
in a complementary
frequency state
Figure 1: Cordus model of the photon
The idea of a cordus allows many puzzling phenomena to be explained at a
conceptual level. For example, light seems to behave either as a wave or a
particle in the double slit experiment, and cordus explains this waveparticle duality. Curiously, the same cordus concept flows across as an
explanation for many other baffling effects in fundamental physics. It
therefore provides an explanation that is logically consistent across a wide
range of effects.
Why is it called a 'conjecture'? Is it valid?
17
For
commentary,
discussion
and
feedback,
please
see
http://cordus.wordpress.com. Please address correspondence to Dr Dirk Pons,
University of Canterbury, Christchurch, New Zealand. Copyright D Pons 2011.
56
As the term ‘conjecture’ shows, it is a guess based on intuition. It is a
conceptual and descriptive model. There is no guarantee that the cordus
conjecture is correct. It is a thought-experiment rather than a fully
worked-out or validated theory. Some or all of it may be entirely wrong.
Is cordus accepted by the broader scientific community?
Cordus is an unusual idea, and it produces a radical re-conceptualisation of
fundamental physics. It is unorthodox, and cuts across conventional
physics and challenges the premises on which those theories have been
built. However it is simply a process of taking a creative idea and running it
through to its logical conclusions.
It is in those conclusions that, if cordus is correct, there are causalities for
existing principles of conventional physics. For example, cordus invalidates
the ‘particle’ premise of quantum mechanics, refutes superposition,
redefines the principle of locality, denies the existence of ‘virtual
particles’, refutes the concept of interference of light, asserts that Bell’s
theorem is wrong, re-introduces a modified concept of the aether, and
reconceptualises the fundamental forces. Cordus explains why Quantum
mechanics, which seems to apply at the level of individual particles, does
not scale up to macroscopic bodies: something that QM itself has been
unable to explain. Furthermore, cordus proposes a set of new principles
for the next deeper level of physics.
How is it beautiful?
Cordus is a wild idea, in that it is totally different to conventional physics,
and is based on conjecture and intuition with all the attached subjectivity.
It is not an incremental extension of existing theories, but a disruptive new
idea and a drastically different way of thinking. That does not necessarily
make it valid, but it is beautiful albeit in a different way to the usual
standard of beauty in physics or mathematics. Cordus has a beauty in its
coherence: it provides logically consistent explanations across a broad
range of physical effects. It does so without the weirdness that is so typical
of the conventional explanations. It is also beautiful in the way it
unexpectedly shows that the next deeper layer of reality is deterministic,
not probabilistic as usually thought. There are many surprises in the
cordus conjecture.
What are the implications if the theory was to be true?
There is, as we have taken care to point out, no certainty that this
thought-experiment is really valid. Nonetheless, if it were to be true, then
the implications are that there is a deeper mechanics beneath the
conventional theories of quantum mechanics (QM) and electromagnetic
wave theory (WT). Both QM and WT emerge as outward, and in the case
of QM only approximate, mathematical representations of a deeper
behaviour within particuloids. The extreme predictions of cordus also
encompass general relativity (GR).
2
Integration problems in conventional physics
The dominant existing frameworks for fundamental theoretical physics are
Quantum mechanics (QM) for particles, Electromagnetic wave theory (WT)
for light, electrostatics and magnetism, and General relativity (GR) for
57
gravitation. While those conventional theories are generally accepted as
valid in their particular areas, there is the unfortunate problem that they
do not integrate well, see Figure 2. Furthermore, they sometimes give
weird explanations to simple phenomena, this being particularly the case
with QM. Also, there are many areas that they simply do not explain at all,
or give conflicting interpretations.
A case in point is wave-particle duality. For example in the double-slit
experiment, light apparently sometimes behaves like a wave, and
sometimes like a particle, depending on how it is observed. WT and QM
adequately describe the fringe and particle behaviours respectively, but
their explanations do not overlap. Thus there is no single integrated
explanation for wave-particle duality. Furthermore, while QM has
exquisite mathematical models for the particle behaviour, the physical
interpretation of those models results in really strange predictions of
reality e.g. superposition, and some explanations that are beyond physics,
e.g. virtual particles and parallel universes. That in itself would not be a
problem except that we do not actually see reality behaving the way QM
predicts, especially not at the macroscopic scale.
All these issues suggest that there might be a deeper physics, a better
theoretical foundation that provides a coherent explanation across the
many phenomena. However, if there is a deeper theory, one that
subsumes both wave and particle perspectives, it is not obvious what that
might be. Also, there is reason to believe, per Bell's theorem, that no
theory of internal (or hidden) variables is possible for the photon and
particles generally. Thus the problem of wave-particle duality may be
fundamentally unsolvable. The null explanation is then to simply accept
the paradoxes and consider the matter intractable.
58
Figure 2: Areas where there are integration problems in conventional
physics. Cordus addresses all of these with a radically new conceptual
framework that provides a logically consistent description across all the
effects.
3
Approach taken
The Cordus conjecture started as an attempt to create a more rational
explanation for wave-particle duality of the photon in the double-slit
device. The method did not follow the conventional method of physics,
which relies on derivation of beautiful mathematics and subsequent
extrapolation to explanation, but rather used the logic of creating a system
model by reverse-engineering known phenomena, adding conjectures and
intuitive material, and noting the necessary assumptions along the way.
Thus the central strand in the Cordus conjecture is a set of lemmas, and
these we do not attempt to prove. The resulting Cordus model is primarily
conceptual and descriptive, rather than mathematical, at least at this point
in time. It is likely that much of the mathematics of conventional physics
can be adapted and re-contextualised for a Cordus Mechanics, because
the issues are not with the mathematics but the explanations of
conventional physics.
59
Quis es tu, cordus?
Cordus asserts there is no such thing as a ‘particle’. Instead the basic
structure for a photon, electron, proton etc., is a cordus with two reactive
ends, with a physical gap between them, held together with a fibril. The
reactive ends may be energised to various degrees, and in turn consist of
hyff force lines. The energy shuttles between the ends, and this also
means that the particuloid does not exist continuously at one location, but
at two, and oscillates between them at a frequency. Consequently, cordus
suggests that all the principles of physics that are built on a ‘particle’
premise are of dubious validity, especially at the finer scales.
Outcomes
The idea of a ‘cordus’ was first created to explain photon path dilemmas in
the double-slit, and then extended to explain fringes too. This provided a
conceptual resolution of wave-particle duality. The principle was then
extended to optical effects of reflection and refraction. The next step was
application to matter effects, particularly the electron and special states of
matter. It is here that the contrast between Cordus and Quantum
mechanics is most evident. Thereafter the cordus principle was pushed to
the extremities, out of curiosity. This last set of papers is therefore the
most radical – and the least likely to be correct but the most disruptive to
conventional theories of physics if true. It provides a new perspective on
fields, unifies gravitation with electromagnetism, and infers the structure
of quarks.
A major benefit of the Cordus conjecture is that it provides a conceptual
framework that is coherent across many physical phenomena. The effects
explained include:
Internal structure of the photon
Path dilemmas of the photon in the double-slit device and Mach-Zehnder
interferometer
Wave-particle duality of the photon, electron, and matter waves
Fringes in gaps, apertures, and double slit, diffraction of single photons
and beams
Near field
Beam divergence
Frequency of photon, electron and matter generally
Zeno effect
Heisenberg uncertainty principle
Entanglement
Aharonov-Bohm effect
Electron orbital shape
Spin angular momentum
Pauli exclusion principle
Atomic bonding
Entropy
Superfluidity including quantum vortices and heat conduction
Superconductivity including Meissner effect
Josephson effect
Coherence
Quantum mechanic’s scaling problem: why does QM not apply at
macroscopic levels?
Casimir effect
60
Tunnelling
Reflection including derivation of critical angle from a particuloid
perspective
Refraction and Snell’s law derived
Brewster’s angle derived
Polarisation
Electrostatic field and granulation [quantisation] thereof
Magnetism
Gravitation and mass
th
Spacetime, but not time as 4 dimension
Lorentz
Relativistic nature of the vacuum
Finite speed of light in vacuum
Colour of quarks
Charge of quarks in 1/3 units
Mass excess in the atom
Parity violation
The implications of cordus are that several existing principles of
conventional physics may need to be revised or abandoned:
Particle: invalidated, does not exist as QM assumes, replaced with
‘cordus particuloid’
Virtual particle: invalidated, unnecessary and confounded concept,
replaced with ‘hyff’
Many-worlds interpretation: irrelevant
Interference of light: refuted, does not occur as Wave Theory describes.
Useful mathematical concept, worth keeping if limitations respected.
Locality: invalidated, replaced with new ‘Principle of Wider locality’
Power of Observer choice to change outcomes: invalidated, instead the
way the Observer sets up the experiment determines the behaviour the
photon will evidence
Heisenberg uncertainty principle: minor adjustment
Bell’s Theorem: refuted
Beam splitter: reconceptualised
Superposition: refuted as a physical effect, but useful as a rough
statistical approximation
Coherence: reconceptualised, limitations applied
Schrodinger’s Cat: irrelevant as based on flawed premises
Quantum mechanics: only applicable on average over many ‘particles’,
and only at a level where things look like points
Copenhagen interpretation: a mathematical simplification of deeper
effects, is not the reality
Wave theory: validity limited primarily to light en-masse
Fundamental forces limited to electrostatic, magnetism, and gravitation.
Common unified underlying mechanism provided. Abandon strong and
weak interactions – nothing specially fundamental about them.
Invariance of the speed of light in the vacuum: not supported, instead is
variable depending on fabric.
Aether re-introduced in modified form, but not a matter or particle based
one.
The cordus conjecture also introduces some new concepts that do not
exist in conventional physics:
Cordus structure and mechanics
61
Complementary frequency state synchronisation (COFS) as the
underlying mechanism for electron orbitals, Pauli exclusion principle,
entanglement, internal structure of proton, atomic structure, atomic
bonding, strong force
Principle of wider locality
Internal structure of the photon
structure of quarks
Internal structure of the proton and neutron
Electric field and granulation thereof
Electric field cannot be shielded
Magnetism: new concept
Gravitation: new concept, integrated with electromagnetism, granulation
Fabric of the Universe
Mass: new concept of underlying mechanism, granulation and transient
nature
Time: new concept, and how atomic time aggregates to personal sense of
time
Vacuum: new concept of what it contains, fabric hyff, differentiation
from ‘void’
Strong force (interaction): not a fundamental force but a COFS effect
Weak interaction: not a fundamental force or interaction but same class
of interactions as photon emission
Level of assembly: new concept for understanding why smaller
particuloids are heavier (explains mass excess)
Conservation of mass: reformulated
Synchronous hyff emission direction (SHED) as mechanism for strong
interaction holding quarks together
As the method explains, the treatment of these matters is by logical
inference, and the results are primarily conceptual. The validity of the
results is uncertain and it is to be expected that some or all of the model
may be wrong or require revision. Nonetheless, the ideas build a novel
conceptual framework for fundamental physics. This framework is
coherent in its ability to explain a wide range of phenomena in a physically
descriptive way.
4
Cordus mechanics
The following is a summary of the cordus conjecture and its mechanics.
Each of the parts is a paper on its own.
4.1
Cordus Conjecture
Cordus Conjecture: Part 1.1 Quis es tu photon?
This paper introduces the core idea: a new conceptual model is proposed
for the internal structure of the photon, and the mechanics thereof. This
internal structure is called a cordus. The cordus consists of two reactive
ends (RE) connected together with a fibril. The fibril connecting the two
reactive ends does not interact with other matter. Each of the two reactive
ends behaves like a whole photon in its ability to interact with other
matter, including reflection, transmission, and the ability to take two
paths, though it collapses to only one location. The reactive ends emit
62
hyperfine fibrils (hyff) which are force lines. The cordus structure is neither
a particle nor a wave, though can appear as either in certain
circumstances. [42]
Cordus Conjecture: Part 1.2 Quo vadis, photon?
Photon path dilemmas are a difficult area for conventional physics. Typical
situations are the double-slit device and interferometers. The problem
manifests as an apparent ability of the photon to simultaneously take all
paths through the device, but eventually only appear at one. Neither
Electromagnetic wave theory nor Quantum mechanics provides a fully
coherent explanation for the behaviour of light in the double-slit device,
and the integration of ‘wave-particle duality’ is poor. It is shown that a
cordus structure is conceptually able to resolve the path dilemmas in
wave-particle duality. Explanations are given for the double-slit device and
interferometers. The Cordus conjecture implies there is a deeper, simpler,
deterministic, and more elegant reality beneath quantum mechanics and
wave theory. [43]
Cordus Conjecture: Part 1.3 Explanation of fringes
The cordus concept is shown to be able to explain wave behaviour in
gaps, and fringes in the double slit device. This is useful because one of the
enigmas of the double-slit device is that single photons form fringe
patterns. Cordus explains fringes in terms of force lines called hyperfine
fibrils (hyff) and their interaction with the edges of the light path. This also
explains beam divergence and near-field effects. The significance of this is
that it shows it is conceptually possible to create a solution for fringes
based on a particuloid interpretation of light, without using the concept of
interference. This means that the Cordus solution has coherence over a
wider range than simply the path-ambiguity problems. [44]
The biggest difference between Wave theory and the cordus explanation is
their interpretation of the mechanism for fringes. Wave theory explains
fringes as ‘interference’: two separate waves of light differing by full (half)
fractions of wavelengths and thus constructively (destructively)
interfering. From the Cordus perspective photons do not actually interfere
or add together, and 'interference' is only a convenient analogy. The
Cordus explanation is that fringes are caused instead by interaction of the
photon hyff with opaque edges.
Comments on the bracket of ‘Cordus Conjecture’ papers as a whole
Wave theory and quantum mechanics are functionally adequate theories
on their own, and powerful in their ability to predict how beams of light
and individual photons, respectively, will behave in a given situation.
However, despite their mathematical sophistication, they are incongruous
explanations of reality when wave and particle behaviours occur in the
same situation, e.g. the double-slit device. In these situations their
explanations are weird, which suggests that the models of causality are
incomplete. The problem has been that wave theory and quantum
mechanics are just so good, that it has been difficult to see what the
63
deeper mechanics could be, especially as Bell's theorem seems to prohibit
solutions with hidden variables.
How do Quantum mechanics and Wave theory fit in?
From the cordus perspective both conventional theories, quantum
mechanics and wave theory, are mathematical simplifications of a deeper
mechanics. Those theories represent the output behaviour of the inner
system. The weirdness of conventional wave-particle duality is not
because the photon is fundamentally weird, but because the existing
conceptual frameworks are inadequate: their mathematics are sufficient
for forward propagation of effect (prediction), but give unreliable results
when used for backward inference of causality (explanation).
Resolution of wave-particle duality
The Cordus conjecture does away with much of the weirdness of waveparticle duality: there is no need for virtual particles, superposition,
observer dilemmas, pilot waves, intelligent photons, or parallel universes.
A simple deterministic, unintelligent photon with a dual existence is all
that is required.
From this perspective wave and particle behaviours are simply the
different output behaviours that the internal system shows depending on
how it is measured. The duality and the apparent incongruity of Quantum
mechanics and Wave theory is resolved: the conflict no longer exists at the
deeper level.
Thus Cordus offers a deeper mechanics that subsumes both quantum
mechanics and wave theory. This bracket shows how it resolves waveparticle duality, and other papers extend it to other enigmatic effects, as
well as the mundane. Perhaps surprisingly, Cordus is also simpler and
more coherent across a wider range of phenomena than quantum
mechanics or wave theory on their own. Even more surprising, and
unexpectedly contrary to the prevailing probabilistic paradigm of Quantum
mechanics, Cordus suggests that the next deeper level of reality is
deterministic.
4.2
Cordus optics
Cordus optics: Part 2.1 Frequency
Conventional particle and wave theories struggle to explain the frequency
of photons and matter in a coherent manner using natural physics. This
paper applies the cordus conjecture to develop a model for frequency of
the photon. The interpretation is that there really is a part of the photon
cordus that moves with a frequency. The working model is for a
reciprocal motion: the energy alternates between the two reactive ends
across the span of the cordus, and the hyff represent the observable
electric field. This cordus model for frequency readily explains polarisation
and tunnelling, and the concept is fundamental to other developments of
the cordus mechanics including the reflection and refraction of
particuloids. The implications are that frequency is not just an intrinsic
64
variable, but a physical effect within the photon. The cordus frequency is a
fundamental conceptual building-block in creating an integrated solution
that unifies wave and particle behaviour. It is a powerful concept that is
coherent across many other phenomena too, including matter particuloids
and it contributes subsequently to the cordus model for granular fields.
[45]
Cordus optics: Part 2.2 Reflection
Optical effects such as reflection and refraction are conventionally best
described by Electromagnetic Wave theory, at least when they involve
beams of light. However that theory does not explain why single photons
should also show such behaviour. This paper shows that optical effects
can also be explained from a cordus particuloid perspective. Several
principles are proposed for the interaction of a cordus photon with an
optical surface, and these are used to explain reflection and subsequently
refraction. The formula for critical angle is derived from a particuloid basis.
The cordus and wave theory perspectives are compared and contrasted.
The significance of this work is that the cordus mechanics explains the
reflection and refraction behaviour of both single photons as well as
beams of light, so it is a more universal explanation. [46]
Cordus optics: Part 2.3 Refraction
Explaining basic optical effects is not possible with classical particle
mechanics, and even with quantum mechanics it is not straight forward
and not particularly intuitive. The problem is much simpler when solved in
the cordus domain. This paper provides cordus explanations for Snell’s
Law and Brewster’s Angle, and quantitative derivations too. This is
significant because the cordus mechanics were derived for single photons,
and immediately generalise also to beams of light. Therefore cordus can
explain particle behaviour, fringes, and optical effects, using a single
coherent mechanics. The cordus explanation does not need the
conventional concept of ‘interference’. [47]
4.3
Cordus matter
Matter is conventionally thought to consist of particles, and quantum
mechanics (QM) is the dominant, and apparently mostly sufficient, theory
for this area. The application of cordus concepts to the particle world of
quantum mechanics consequently has some surprises.
Cordus matter: Part 3.1 Wider Locality
Quantum mechanics does a good job of providing mathematical
descriptions of particle effects, and the fact that it can do so is usually
taken as circumstantial evidence that QM must be correct. Unlike other
areas, such as wave-particle duality, there is no major competing
interpretation to QM in the area of sub-atomic particles. All the same, QM
is not particularly effective at providing a qualitative description of the
effects, and this makes it complex and difficult to understand at an
intuitive level, and consequently people generally, though perhaps not
physicists specifically, perceive QM as strange. Maybe the effects really are
65
intrinsically complex, and the mathematical formulations are the reality:
the simplest possible way to express the underlying mechanisms of
causality. [48]
Einstein called entanglement ‘spooky action at a distance’ and it continues
to sit uneasily within physics since a qualitative explanation is lacking even
though the reality is accepted. It is contrary to relativity, and to the
principle of locality. Nor can entanglement satisfactorily be explained with
existing hidden-variable theories. However it is consistent with quantum
mechanics. The principle of locality is that an object is only affected by its
immediate surrounding. Entanglement appears to require the principle to
be violated: twin particles may be linked, such that changing the state of
one instantly changes the other, even if they are separated by
macroscopic distances. The mechanisms are incompletely understood in
conventional physics. [48]
This particular paper shows how entanglement is readily explained as a
natural consequence of the cordus. This obviates the need for the usual
spooky and metaphysical interpretations. The paper also introduces the
principle of complementary frequency state synchronisation (CoFS). This is
an important concept in that later papers show how it underpins the Pauli
exclusion principle, coherence, and the strong interaction.
More radically, Cordus suggests that Bell’s Theorem is only applicable to
point particles, and is thus generally irrelevant. It is an artefact of the
flawed particle premise of conventional physics, and is not an obstacle to
models of hidden variables. Another radical suggestion from Cordus is that
the principle of locality is not viable in its present form and needs to be
widened.
These are unorthodox predictions. The implications are that the ‘particle’
conceptual foundation of Quantum mechanics is invalid. QM only applies
at the level at which small pieces of matter look like point particles, and is
invalid at smaller scales.
Cordus matter: Part 3.2 Matter particuloids
While matter forms the tangible substance of our world, our
understanding of it at the atomic level is far from complete. Some of the
most enigmatic effects in the physics of electrons are its wave-particle
duality and the Aharonov-Bohm and Casimir effects. Even relatively core
concepts of atomic physics, like spin and the Pauli exclusion principle, lack
satisfactory descriptive explanations. This paper shows that application of
the cordus principle can explain these effects in a coherent manner. [49]
Cordus matter: Part 3.3 Energy cycles within matter
The interaction of light with electrons is one of the fundamental
perceptual realities of what we see. Yet that interaction is only partly
understood. Cordus concepts are applied to develop a descriptive model
of the mechanisms whereby photons are absorbed into electrons and
emitted. From the Cordus perspective, the temperature of a body is
primarily a measure of its phonons (lattice-vibrations). Cordus shows why
66
entropy occurs, despite the individual mechanisms being reversible. An
understanding of the mechanisms for entropy is relevant to the
understanding of coherence, superfluidity and superconductivity. Cordus
suggests that a failure to adequately conceptualise entropy leads to
misapplication of coherence and ultimately to unreliability in the premise
of superposition. [50]
The cordus re-conceptualisation of entropy might seem basic and almost
self-evident in hindsight, but it is a core concept in understanding why QM
does not scale up to the macroscopic world. Entropy is the Achilles heel of
Quantum mechanics.
Cordus matter: Part 3.4 Special states of matter
The Cordus principle of complementary frequency states (CoFS) is used to
develop a novel descriptive model for the mechanisms underlying
superfluidity and superconductivity. In both cases Cordus explains the
effects as synchronisation of forces between electrons and atoms. Several
associated effects are likewise explained, including quantum vortices, heat
conduction in superfluids, and the Meissner effect in superconductors.
Cordus also asserts that superposition does not exist, at least not the way
QM conceptualises it. In particular, that the mathematics of superposition
and the wavefunction are not the reality, only mathematical
approximations of deeper effects, and are unreliable qualitative
descriptors of those underlying mechanisms. [51]
Cordus makes the unorthodox assertion that superposition does not exist,
at least not the way QM conceives of a whole particle or body being fully
in two places at once. Cordus provides for positional variability: the two
reactive ends of a cordus are in different places, and extends that to larger
assemblies of matter only if such objects can be placed in full bodycoherence (which is rare). However Cordus rejects the QM superposition
concept of causal variability: the idea that the whole particle or body is
simultaneously in both and neither positions and therefore has two
futures before it, which can diverge.
Cordus asserts that QM is only approximately accurate at the sub-atomic
scale because of the problem with superposition, and not at all at the large
scale. Briefly, the reason is that large bodies have too much internal
entropy (disorder) to have the necessary coherence to appear in more
than one location. Even if they did have body-coherence the results would
be minuscule (small span) and not as dramatic as popularly imagined. The
mathematics of QM are premised on coherence, and thus the explanations
of QM are unreliable where body-coherence fails. In most roomtemperature applications this is the atomic level. Quantum mechanics
therefore does not practically apply to large bodies, living creatures, or the
universe as a whole.
Cordus re-conceptualises, or at least conceptually clarifies the concept of
‘coherence’, and describes why that state cannot be readily achieved. Thus
Cordus predicts what size bodies should and realistically cannot be made
into matter-waves. Thus the concept of large macroscopic objects, such as
67
motor-cars, being able to go through a double slit, is proposed to be a
fallacy. This also allows Cordus to explain why Quantum mechanics, which
seems to apply at the level of individual particles, does not scale up to
macroscopic bodies: something that QM itself has been unable to explain.
Cordus matter: Part 3.5 Schrodinger’s Cat reconceptualised
Quantum mechanics is the dominant conceptual foundation for
fundamental physics. Nonetheless there are effects that it does not
explain, or explains only by reference to metaphysical effects. While many
have wondered whether there could be a more-complete explanation, the
solution has been elusive. Cordus suggests that the necessary deeper
mechanics is only accessible by abandoning the premise of ‘particle’, and
shows how to achieve this. The resulting Cordus mechanics provides a new
way of thinking and a radically different conceptual foundation. This paper
primarily contrasts Quantum and Cordus mechanics. In the process,
Cordus re-conceptualises Heisenberg’s uncertainty principle. It also
provides an explanation for the paradox of Schrödinger’s Cat, and shows it
to be based on unrealistic and unattainable premises. [52]
Cordus does not support the idea of virtual particles, nor the interference
thereof, nor the collapse of the wavefunction. For Cordus the particuloid is
neither a wave nor a particle but behaves as either depending on the
measuring method. The measurement method unavoidably changes how
the particle behaves, and this is particularly pronounced with the photon.
The Experimenter's choice of method therefore limits the type of results
that will be observed. Wave and particle duality are only measuring
artefacts, not the reality.
4.4
Cordus in extremis
The Cordus concept as a whole is conjectural, and the previous papers
have taken care to ground the concepts by comparing them against wellknown physical phenomena. The present bracket of papers is less
cautious. The purpose here is to audaciously push the cordus concept to
see if it has novel suggestions about deeper mechanisms, particularly the
propagation of light and fields in general. As always, we are not saying that
the results are necessarily valid, only that they are logical and curious. In
extremis therefore refers both to the subject of fields and the cosmos, and
the conceptual extrapolation of doubtful validity.
Cordus in extremis: Part 4.1 Electromagnetism
The Cordus conjecture is extended to create a conceptual model for
electromagnetic fields. The resulting model shows how a cordus
particuloid generates small transient units of force at the sub-atomic level,
thereby creating the apparently smooth and continuous electric field that
we more commonly perceive. The starting premise is that all fields are
hyff, of one sort or another. Hyff are directional force lines that extend
out into space from their basal particuloid, and where the force appears in
pulses that travel outwards along the line (hyffons). Thus fields consist of a
rapid sequence of discrete impulses of transient force, radiating out from a
68
cordus at the centre. However we do not see this granularity at our level
of perception. Instead we perceive fields to be smooth, continuous, and
uniform in all directions. This is because of the en-masse effect of many
particuloids being involved.
Cordus also reconceptualises how magnetism is generated at the subatomic level, and likewise explains how the granularity arises. From the
Cordus perspective, a static charge only generates an electrostatic force,
without magnetism, because the hyff are straight outwards. However a
moving charge causes bending of the e-hyff, and this is what we perceive
as magnetism. Any moving mass generates curvature of the hyff, and
these generate the magnetic field, except that neutral-charge mass has no
observable magnetic field because it emits positive and negative hyff. Thus
electrostatic forces are a position effect, while magnetism is a velocity
effect. However the same basic structure, the hyff, is responsible for both.
Cordus electromagnetism is applied to explain the electric field
surrounding a wire carrying current, the locus of moving test charges in a
magnetic field, and the mechanism for how force arises in permanent
magnets. The contribution made by this paper is a description of
electromagnetism that goes to the next deeper level: it explains the
underlying mechanisms for how the forces arise. Also, it provides a
mechanism for fields to be granular and directional at the small scale, but
smooth and continuous at larger scale. [53]
The cordus explanation for electromagnetism is unorthodox in several
areas. First, it dispenses with the need for additional particles, and
conventional references to ‘virtual particles’ of any kind are thus reinterpreted as a hyff effect. Second, conventional theories tend to portray
electric fields and magnetic fields with equal standing: they are
interchangeable concepts. By contrast, Cordus suggests that the electric
field is the fundamental effect, and the magnetic field is a derivative. Thus
electrostatics is a reactive end position effect, magnetism a RE-movement
phenomenon, and (yet to be shown) gravitation a RE-acceleration effect.
Third, Cordus is unconventional in asserting that the electric field cannot
be shielded, and that what looks like shielding is only localised
neutralisation.
The results show that the Cordus conjecture can be extended to
electromagnetic fields. Doing so permits novel re-conceptualisation of
some fundamental paradigms of conventional physics, and lays the
foundation for the next ideas.
Cordus in extremis: Part 4.2 Fabric of the universe
The concept of the vacuum is problematic for conventional physics.
Electromagnetic wave theory models it as consisting of nothing at all, but
yet paradoxically having finite electric and magnetic constants. Quantum
mechanics models it as consisting of temporary particles, but no average
substance. General Relativity theory includes a spacetime medium,
without describing the composition. In all cases the underlying physical
mechanisms are obscure. Furthermore, these existing perspectives conflict
69
in their expectations, so the integration is poor. The treatment is not
always logical either: conventional theories find the idea of the matterbased aether thoroughly unacceptable, yet ironically all include something
that looks conceptually much like a medium. The Cordus conjecture
provides a conceptual solution for the composition of the vacuum: it
provides a fabric that is granular (similar to quantised) at the smallest
scale, scales up to a continuum, provides a medium for propagation of
disturbances and waves, provides a medium for electromagnetism and
gravitation, is relativistic, is not a matter aether, and includes a time
signal. In the cordus solution the vacuum is made of tangled hyff (force
lines) from all the surrounding matter particuloids. This cordus fabric
concept also provides a descriptive explanation as to why the speed of
light is a finite value. The fine structure constant is given a physical
interpretation, as a measure of the transmission efficacy of the fabric.
Cordus also distinguishes between the fabric that makes up the vacuum of
space, as opposed to the void which has neither fabric nor time as we
perceive it. This model is radically unorthodox in suggesting that the speed
of light is relativistic but not invariant; that it depends fundamentally on
the fabric density and hence the accessible mass density of the universe at
that locality. [54]
Cordus in extremis: Part 4.3 Gravitation, Mass and Time
Gravitation is conceptually problematic to General Relativity and Quantum
mechanics in that the fundamental mechanisms are unknown to both, and
the theories have different requirements that are difficult to reconcile into
a single model. Cordus gravitation offers a solution to the problem. It
provides a mechanism whereby gravitation is not continuous but in
discrete force (or displacement) increments similar to quanta (but not
uniform increments). Also, the closing force between two masses is
transient. In this idea, gravitation, and therefore also mass, is a
discontinuous property: i.e. a particuloid emits gravity (has mass) at some
moments but not others. Thus gravitation is an effect that a mass does to
the whole universe, not to targeted other bodies, and in this regard
Cordus is consistent with General relativity. Both QM and Cordus agree
that gravitation is quantised. Cordus conceptually integrates the different
effects of mass: Gravitation is a particuloid contributing hyff to the fabric;
Newtonian mass is resistance of the reactive ends to unexpected
displacement; Relativistic mass is decreasing efficacy of hyff engagement
with the fabric as velocity of the reactive end increases; Momentum is a
frequency mechanism that ensures the reactive end re-energises on-time
and in-place; particuloids like nucleons have mass to the extent that they
have frequency. Furthermore, Cordus offers an explanation of how time
arises at a sub-atomic level by the cordus frequency, and how this
aggregates to the sense of time that we perceive biologically. Thus Cordus
offers a radically new way of thinking about the problem of gravitation,
mass and time that is quite unlike conventional physics, yet includes
concepts that might be recognisable to those other physics. [55]
Cordus in extremis: Part 4.4 Quarks
A conceptual model is created for the composition of quarks and the
internal structure of the proton and neutron. In this model the charge of a
70
quark indicates the number of hyff (force lines) it emits. Cordus also
explains the colour and provides a mechanism for the strong interaction
(both the attraction and repulsive components). The model also explains
why parity violation occurs. A new concept of the ‘level of assembly’ is
introduced and used to explain mass excess and why smaller particuloids
have greater mass. Cordus also predicts non-conservation of mass. [56]
Fundamental forces
In this extrapolation of the Cordus conjecture, gravitation is caused by
acceleration of the basal cordus particuloid, magnetism by velocity of the
reactive ends, and electrostatic force by position thereof. These are the
only three fundamental forces: the strong and the weak ‘forces’ are aptly
named ‘interactions’ and in the same categories as orbitals and photon
emission respectively, i.e. not fundamental forces.
The important concept here is that one mechanism, the emission of hyff,
provides the underlying mechanism for electrostatics, magnetism, and
gravitation. These forces are intrinsically unified. In contrast, QM
perceives these forces, together with the strong and weak nuclear
interactions, as mediated by virtual particles and tries to unify them on
that basis. Cordus suggests the so called virtual particles are simply
different measurement artefacts of the hyff, not the real interactions.
5
Conclusions
The cordus concept was originally created to explain wave-particle duality
of the photon. It turns out to be much more adaptable and powerful, in a
descriptive way, than simply a solution for the photon. Cordus is a
conceptual solution that shows it is possible to conceive of fundamental
physics in a radically different way.
Cordus challenges the conventional idea of zero dimensional points, and
the whole conceptual edifice of quantum mechanics built thereon. The
concept that emerges here is that ‘particles’ are not actually points,
neither are they waves. Instead ‘waves’ and ‘particles’ are simply the
external manifestations of hidden internal structures. Thus Cordus offers
a deeper mechanics that subsumes both quantum mechanics and wave
theory, and thereby resolves wave-particle duality and several other
enigmas. Perhaps surprisingly, Cordus is also simpler and more coherent
across a wider range of phenomena than quantum mechanics or wave
theory on their own. Radically and contrary to the prevailing probabilistic
paradigm of quantum mechanics, Cordus suggests that the next deeper
level of reality is deterministic.
Cordus is a thought-experiment. The treatment is primarily conceptual and
descriptive, and the cordus mechanics only lightly sketched out. It is a
conceptual model, not so much a full theory with all the details worked
out. While it has been thought-tested against many physical phenomena,
it has not been checked against all. Furthermore, it is based on intuition
and conjecture, and makes many assumptions (lemmas) that have yet to
71
be tested. Thus the validity is uncertain. Nevertheless, Cordus is a
purposely audacious idea: it explores new ways of thinking, and therefore
deliberately puts forward tentative explanations. We don’t believe the
particular design variant developed in this set of papers is necessarily the
only or the final solution, and we are open to the possibility that it could
be totally wrong. Thus the cordus concept and the specific working models
presented here are simply concepts to be critically evaluated.
The conceptual contribution of this work is the demonstration that it is
indeed possible to create hidden-variable models, and that Bell's theorem
is not a limitation. It shows that the application of logic and semantic
inference to existing experimental observations can give interesting new
insights. The beauty of the Cordus Conjecture is that it provides an
explanation that is coherent across wave and particle effects, photons and
matter, ‘particles’ and macroscopic bodies.
Thus the primary contribution of the Cordus work as a whole is that it
provides a new conceptual framework for thinking about fundamental
physics. Cordus may or may not be a robust solution, but it does show that
there are other ways of thinking about the issues. Therefore we do not
need to be discouraged by the staleness of the debates about waveparticle duality, nor stuck in the fixed paradigms of existing theories, nor
perplexed by their weirdness. Even if Cordus is not the deeper mechanics,
there can now be no doubt that a deeper mechanics does exist. Perhaps
the biggest contribution is simply the intellectual stimulus to think
creatively and more deeply intuitively about topics that we thought we
already understood.
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Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., Cordus
optics: Part 2.2 Reflection. 2011.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., Cordus
optics: Part 2.3 Refraction. 2011.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., Cordus
matter: Part 3.1 Wider Locality. 2011.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., Cordus
matter: Part 3.2 Matter particuloids. 2011.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., Cordus
matter: Part 3.3 Energy cycles within matter. 2011.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., Cordus
matter: Part 3.4 Special states of matter. 2011.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., Cordus
matter: Part 3.5 Schrodinger’s Cat reconceptualised. 2011.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., Cordus in
extremis: Part 4.1 Electromagnetism. 2011.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., Cordus in
extremis: Part 4.2 Fabric of the universe. 2011.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., Cordus in
extremis: Part 4.3 Gravitation, Mass and Time. 2011.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., Cordus in
extremis: Part 4.4 Quarks. 2011.
74
75
Cordus
Conjecture
Part 1: Cordus first principles
Reconceptualising
fundamental physics,
starting with the
internal structure of
the
photon
particule
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Cordus Conjecture - Quis es tu photon?
Cordus Conjecture Part 1.1
Pons, D.J.,18 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
A new conceptual model is proposed for the internal structure of the
photon, and the mechanics thereof. This internal structure is called a
cordus. The cordus consists of two reactive ends (RE) connected together
with a fibril. The fibril connecting the two reactive ends does not interact
with other matter. Each of the two reactive ends behaves like a whole
photon in its ability to interact with other matter, including reflection,
transmission, and the ability to take two paths, though it collapses to only
one location. The reactive ends emit hyperfine fibrils (hyff) which are force
lines. The cordus structure is neither a particle nor a wave, though can
appear as either in certain circumstances.
Keywords: wave-particle duality; wave theory; quantum mechanics;
double slit;
Edition 2.11 Fixed typos, Clarified measurement interlock > Date: Saturday, 11 February 2012 >
Document: Pons_Cordus_1.1Conjecture_E2.11.80.doc
1
Introduction: Wave-particle duality
Wave-particle duality is a mostly-sufficient explanation of the behaviour of
light, but fundamentally incomplete because of its lack of an integrated
theoretical foundation or a coherent explanation that is consistent with
reality. It gives rise to sometimes weird explanations, for example in the
double-slit experiment, light apparently sometimes behaves like a wave,
and sometimes like a particle, depending on how it is observed.
The Wave theory (WT) part of the duality perceives light as
electromagnetic (EM) waves, and uses this to explain various optical
effects. From this perspective light is a temporally continuous beam. Thus
the light going into an object, e.g. a mirror or a double-slit device, exists at
the same time as it exits and can therefore interfere with itself.
Interference is therefore a core concept throughout the WT perspective.
WT is an effective predictor of large scale optical effects and fringes.
However WT is incapable of dealing with individual photons, and therefore
with certain classes of effects, such as single photons into the double-slit
device with a blocked slit.
The other part of the duality is Quantum mechanics (QM). It takes the
particle perspective and treats light as a series of photons. It can thus
explain effects involving single photons, e.g. the photo-electric effect, that
WT cannot. QM states that the photon’s particle properties are described
18
Please address correspondence to Dr Dirk Pons, University of Canterbury,
Christchurch, New Zealand. Copyright D Pons 2011.
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Quis es tu?
by a probabilistic wave-function, and that superposition applies, so that its
location is indeterminate while it is flight: the wave-function supposedly
collapses only when it is observed. QM is an excellent predictor of how
particles will behave, though WT is better for beams of light. However QM
is a mathematical and statistical solution that suffers from poor physically
meaningfulness: ‘mechanics’ is not particularly apt. It is good at providing
a quantitative prediction of what can happen, but weak at giving a
qualitative description of how the causal mechanisms operate.
Wave theory and Quantum mathematics accurately predict physical
outcomes, but neither is completely sufficient as an explanation of reality,
and they do not integrate well. However, if there is a deeper theory, one
that subsumes both wave and particle perspectives, it is not obvious what
that might be. Also, there is reason to believe, per Bell's theorem, that no
theory of internal (or hidden) variables is possible for the photon. Thus the
problem of wave-particle duality may be fundamentally unsolvable. The
null explanation is then to simply accept the paradoxes and consider the
matter intractable.
Is there a way to integrate wave and particle views? Is there a deeper
mechanics, one wherein the paradoxes dissolve? Yes, we think so. This
paper introduces a novel concept, the Cordus conjecture, and shows how
it can resolve elements of wave-particle duality. This primary paper
conceptually sketches out the underlying mechanics, and anticipates the
internal structure of the photon. Companion papers extend the concept to
explain the optics of light beams, matter, and fields. Taken together, the
papers sketch out a conceptual foundation for a proposed cordus
mechanics: a candidate for a deeper mechanics beneath both quantum
mechanics and wave theory.
This paper is part 1 in a bracket of three. The first part describes the
fundamental cordus concepts. i.e. the proposed internal structure of the
photon. The second part solves the apparent path-dilemmas in the
double-slit device, and also interferometers. The third develops a novel
mechanism for the formation of fringes. Other brackets of papers apply
the Cordus concept to optical effects (ref. ‘Cordus Optics’), matter (ref.
‘Cordus matter’), and fields (ref. ‘Cordus in extremis’), and each of those
have several parts.
2
Method
The objective was to identify, at a conceptual level, whether there could
be internal structures and properties to the photon that could explain its
observed behaviour.
The approach taken was a logical rather than mathematical one: by
knowing the behaviour of the photon in various experimental situations,
infer the possible internal variables that could give rise to this behaviour.
This is a typical system-thinking approach to reverse-engineering a product
or process. It is a process of working out what the black box might contain
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Quis es tu?
by observing its outputs in different situations. The process is necessarily
conjectural, and is more a thought-experiment with demonstrations than a
conclusive proof.
Existing photon effects are accepted as veritas, including the wave and
particle outcomes in the double-slit experiment: an interference pattern is
created even from single photons (eventually, given enough photons). A
new structure for the photon was then conjectured. This is a conceptual
model of what the mechanisms might be within the photon that could give
rise to those observable effects. The concept was then tested against
various other optical and quantum phenomena. It was deliberately tested
in areas of theoretical incongruence and discontinuous output behaviours,
because these are potentially where the system variables are most
exposed. Also, such cases are opportunities to think of radically new
concepts, less cognitively encumbered by existing theories.
Then additional lemmas (premises, assumptions) were added to the basic
cordus concept to explain these other situations. This process further
defined, constrained, and developed the concept in a process of synthesis
to match the veritas. New variables were added parsimoniously where
necessary for requisite variability.
Cordus is intended to be a thought-experiment rather than a proof, and
therefore seeks to create coherent conceptual links between topics.
Consequently it offers explanations rather than mathematical proofs.
Tentative explanations are put forward, and even speculative
extrapolations. The latter are labelled 'in extremis' to show they are
secondary explanations and not core requirements.
The cordus concept is a class of solutions that permits several design
variants. Where necessary we selected a particular variant, referred to as
the working model. The result is a type of 'hidden-variable' solution, that
identifies internal variables within the photon and shows how they cause
the external behaviour.
3
Cordus conjecture
The cordus conjecture proposes a radically different structure for the
photon. It is a structure that is neither a particle nor a wave, though can
appear as either in certain circumstances. Instead it is proposed that the
photon consists of a cordus: two reactive ends (RE) connected together
with a fibril. The fibril connecting the two reactive ends does not interact
with other matter. Each of the two reactive ends behaves like a whole
photon in its ability to interact with other matter, including reflection,
transmission, and the ability to take two paths, though it collapses to only
one location. Applying some assumptions about the basic sub-structure of
this cord, permits the concept to be expanded and used to explain a
variety of effects.
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3.1
Cordus model of the photon
The starting cordus concept is that the
photon does pass through both slots in the
double slit experiment, and therefore has two
ends that are in communication. This is called
a ‘cordus’: two reactive ends (RE) connected
together with a fibril, see Figure 1.
Figure 1: The cordus consists of two reactive
ends, functionally connected by a fibril. The
effective mean centre of the photon is at the
midpoint, but the statistical modes are at the
REs, i.e. the photon is only every found at the
ends.
Reactive
End
Fibril
Motion of
photon
This is a functional concept. Exactly what
geometry or physical sub-structure creates
this cordus functionality is not prescribed at
this point. It is necessary to add further assumptions (lemmas) to construct
a workable model, Hence the following additional. The first focuses on the
path-ambiguity behaviour, and others follow to address fringes.
Lemma L.1
Behaviour of the cordus
L.1.1 Each of the two REs behaves like a whole photon in its ability to
interact with other matter, including reflection, transmission, and
absorption.
L.1.2 The fibril connecting the two reactive ends does not interact with
other matter.
L.1.3 The REs may take different paths to each other: spatially distinct;
angularly distinct; reflect off different surfaces.
See Causa 1 for a working model of the possible underlying explanations.
Causa 1
Cordus underlying mechanisms
Several possible underlying mechanisms may be anticipated. Note that
these are simply a selection of design variants to consider. The cordus (see
Figure 2) may consist of:
C.1.1 Two particle-like reactive ends with a fibril connecting them (‘bolafibril’)
C.1.2 Fibril with reactive ends (‘open-fibril’)
C.1.3 Fibril that vibrates, where the vibrations create the functionality of
reflect/transmit/collapse, only appears when the energy is in the
condensed state at the reactive ends.
C.1.5 Fibril where the energy reciprocates and there is a field effect at
reactive ends, i.e. it is the vibration that interacts (‘reactive’) with
other structures (‘thick-fibril’)
C.1.4 Fibril where the energy reciprocates from one side to the other.
The reactive end appears momentarily as a ‘particle’ when the
energy is in its arrested or condensed state before deconstructing
and changing direction again (‘teleport fibril’). Several sub-versions
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Quis es tu?
C.1.6
might include a single ‘particle’ that traverses the entire span, i.e.
the cordus has two ends but only one is active at a time (‘full-span
shuttle’); two ‘particles’ each reciprocating between the centre
and an end (‘twin half-span shuttle’); two particles of which one is
a different type and reciprocating over the full or half span (‘antiparticle shuttle’). In all cases the energy is non-reactive to other
matter while in transit, and the particle nature, e.g. the ability to
the ends (hyff model, see later). The energy appears at one end
while the other is dormant, and then withdraws and changes to
the other end. At any one moment only one end is active.
In this variant the energy retracts at one end (C+) and extends at
the other (C-), before reversing. There is only an instant when a
reactive end is neither C+ nor C-, unlike the C.1.5 model where one
end is dormant for a full half cycle.
Figure 2: Several different design variants for the cordus structure, by way
of illustration of the concept. No specific variant is preferred or necessary
at this stage. The dashed lines represent the frequency component.
The preferred design variant is C.1.6, though this only emerges
subsequently as the bigger picture is built up.
The concept now is that the photon does actually pass through both slits in
double-slit experiment, i.e. that the observed behaviour is the reality.
However additional lemmas are required to explain the selective
appearance of the photon.
Lemma L.2
Collapse of the cordus
L.2 Collapse of the cordus
L.2.1 When one reactive end touches a material that absorbs photons
(i.e. an opaque material) then that RE is ‘grounded’.
L.2.2 Once one RE grounds, the cordus collapses.
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Quis es tu?
One design variant is that the fibril withdraws the other reactive
end and collapses the cordus to the location of the grounded RE.
However the preferred explanation using C.1.6 is as follows:
L.2.2.1
Only an energised reactive end can ground.
L.2.2.2
At the time of grounding, the other (free) reactive end
ceases to exist at the next frequency cycle.
L.2.3 Once grounded, the photon appears as a stationary point, and an
injection of energy into the lattice of the material.
L.2.4 The first RE to be grounded collapses the cordus. This corresponds
to the shorter of the two temporal optical paths.
L.2.5 The (statistical) mode of the collapse location is not the mean
photon location. Mode is determined by the location of the two
reactive ends, and this is where grounding occurs, whereas Mean
is optical centre line and the geometric centre of the fibril.
The mode of the collapse-location for a cordus is not precisely on the
optical centreline of the photon, but will instead be at one of the reactive
ends. The non-grounded reactive end simply ceases to exist at the next
frequency reversal. Therefore the reactive end does not need to be
dragged through the material, so the optical properties of the intervening
material is of no consequence at collapse.
With Lemma 2 it is now possible to explain the quantum behaviour of the
double-slit experiment, as will be shown. However to resolve the observer
paradoxes requires another related lemma on detection.
Lemma L.3
Detection and Observers
L.3 Detection and Observers
L.3.1 Detecting the position of a photon requires arresting the cordus
entirely. Detecting the photon’s position is intrusive observation as
it collapses the cordus. Intrusive observation may be used to
detect the position of a single photon or beam of photons.
L.3.2 The cordus is not collapsed, nor the position of the photon
detected, by transparent media or reflective surfaces.
L.3.3 Passive observation is simply looking at the experiment and not
interfering with the cordus. Passive observation is inconsequential
for the photon.
L.3.4 Passing observation is detecting that a photon has passed a point,
e.g. by detecting its effect on other material or fields, without
collapsing the cordus.
L.3.5 The internal variables of the photon are bi-directionally linked
(coupled) to the external electromagnetic (EM) fields that it
generates, see also C.6 hyff lemmas.
L.3.5.1
Passing observation can add or subtract energy from the
photon, via the coupling.
L.3.5.2
Passing detection alters the state of the photon.
L.3.5.3
Passing observation cannot determine location of the
photon.
Thus Cordus differentiates between types of Observers: passive, passing,
and intrusive. Lemma 3 states that detecting a photon’s position
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corresponds to intrusively collapsing the cordus entirely, whereas
reflection and transmission through a transparent material do not.
Whether the reactive end strikes an opaque material, absorbing detector,
or the eye of an Observer is all the same: the cordus collapses. It is
analogous to measuring the speed of a small moving motor-car by placing
a loaded shipping container in front of it: the car is arrested and smashed
in the process and its previous functional capability is destroyed.
Observation of a photon’s position collapses the cordus and destroys its
functionally expanded state.
However passing observation is unreliable for measuring properties of a
single photon, since the process of measurement changes other properties
of the photon. However it can be more reliably applied to beams of
multiple photons, where the sacrifice of a few is immaterial. Depending on
the measurement, it may unduly preserve the configuration of the photon,
or attract/push it into a different state, transferring energy.
Quantum mechanics views fields and particles as different and
independent structures, and has no coherent unified model of causality for
these. The cordus perspective is very different, in that it suggests that
fields and particles are tightly dependent, even interlocked. A simple
concept, with profound implications. The cordus model is that a
particuloid like a photon or electron has internal sub-structures [fibril,
reactive ends, hyff]. Thus it has internal variables, corresponding to
parameters of those sub-structures, that exist even when they are not
measured. As the work on frequency shows [1], the hyff [‘field’
component] and the reactive ends [which represent what QM terms the
‘particle’] are closely coupled: the energy shuttles between them.
Therefore what happens to one affects the other. We call this the
measurement interlock between fibril, reactive ends, and hyff. Or, to put it
in the language of quantum mechanics, what happens to the field affects
the particle, and the inverse. Thus the process of measurement, whether
of field or particle, fundamentally changes the internal energy distribution
of the cordus. Therefore the process of measurement, and the nature of
that measurement, influence the outcome that will be observed. Thus the
measured reality is contextual: it depends on the type of observation
itself. 19
There are different types of observation, with different degrees of
intrusiveness: passive, passing, and intrusive. The different types of
observation have implications for the detection of position and velocity,
as the next section shows.
19
By implication the quantum mechanics premise is invalid that claims that there
is no reality beyond that which is measured. Instead cordus suggests that the
measurement is an artefact of the chosen measurement process applied to
reality; that different measurement processes applied to the same underlying
reality will therefore yield different measurements.
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3.2
Application to quantum measurement effects
Heisenberg’s Uncertainty Principle
The Heisenberg Uncertainty Principle states that it is impossible to
simultaneously know the position and momentum of a photon. Further,
that the effect arises because it is fundamentally unknowable, not from
limited precision of measurement. The Cordus Conjecture is consistent
with this Principle, and suggests that the explanation is that the
momentum and position are measurements of different states of the
photon: in flight vs. arrested. Measure it in flight and only the presence of
the photon can be inferred, using passing observation (L.3.4). The dynamic
and twin-headed nature of the photon in flight means that it
fundamentally has no physically measurable centroid, even if it has modes.
Measuring its location can be done but requires intrusive detection, which
collapses the cordus and destroys the kinetic state. Thus the choice of
measurement constrains the behaviour of the photon and thus the
measured outcome. The flight and static states of the photon are
physically mutually exclusive: so too are the measurements thereof.
Zeno effect
The Zeno effect is that observation of a quantum state can preserve the
configuration or hasten its change, depending on how the measurement is
made. The cordus explanation is that these measurements are of the
passing type, and therefore add or subtract energy from the photon
(Lemma 3.4), thus constraining the photon’s configuration.
4
Conclusions
Wave-particle duality, which has been enigmatic to conventional physics,
is shown to be conceptually solvable by a new way of thinking about the
photon. A particular internal structure, called a cordus, is proposed for the
photon, and the underlying mechanics sketched out. In subsequent papers
it is shown that a cordus structure is conceptually able to resolve waveparticle duality, i.e. explain both wave and particle effects.
1.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.,
Cordus optics: Part 2.1 Frequency. 2011.
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86
Photon path dilemmas: Quo vadis, photon?
Cordus Conjecture Part 1.2
Pons, D.J. , 20 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
Photon path dilemmas are a difficult area for conventional physics. Typical
situations are the double-slit device and interferometers. The problem
manifests as an apparent ability of the photon to simultaneously take all
paths through the device, but eventually only appear at one. It is shown
that a cordus structure is conceptually able to resolve the path dilemmas in
wave-particle duality. Explanations are given for the double-slit device and
interferometers. The Cordus conjecture implies there is a deeper, simpler,
deterministic, and more elegant reality beneath quantum mechanics and
wave theory.
Keywords: wave-particle duality; double slit; interferometer
Edition 2.10 Fixed typos, Clarified measurement interlock > Date: Saturday, 11 February 2012 >
Document: Pons_Cordus_1.2PathDilemmas_E2.10.79.doc
1
Introduction: Photon Path dilemmas
There are various path problems and paradoxes in wave-particle duality,
and are a difficult area for conventional physics. Typical situations are the
double-slit device and interferometers. The problem manifests as an
apparent ability of the photon to simultaneously take all paths through the
device, but eventually only appear at one. Existing theories of physics only
partially explain the phenomena. This paper applies the cordus concept to
conceptually resolve path dilemmas.
2
Existing approaches
Wave theory (WT) apparently adequately explains the situation as
interference. However, that only applies to beams of light, whereas the
behaviour also exists for individual photons. Quantum mechanics (QM)
offers a solution for the particle case, using the concepts of superposition
and wavefunction. However the explanations are strange and inconsistent
with experience in the everyday world. The ideas of ‘wavefunction’ and
probabilistic ‘superpositon’ are intrinsically mathematical, and attempts to
translate these into physical mechanisms have not fared well. For
example, the explanation that relies on virtual (or ghost) particles only
adds more problems, because of the supposed undetectability of these
particles.
20
Please address correspondence to Dr Dirk Pons, University of Canterbury,
Christchurch, New Zealand. Copyright D Pons 2011.
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Quo vadis?
There are two easy-to-understand explanations for the path dilemma in
wave-particle duality, intelligent photons and parallel universes, but both
have difficulties. The first is to assume some intelligence in the photon:
that photons know when a path is blocked, without even going down it
(e.g. Mach-Zehnder interferometer), and adapt their behaviour in
response to the presence of an Observer (e.g. Schrodinger’s Cat, Zeno
effect). This also raises philosophical problems with choice and the power
of the Observer to affect the physical world and its future merely by
looking at it. Thus the action of observation supposedly affects the locus
taken by a photon, and thus the outcome. This concept is sometimes
generalised to the universe as a whole. The second, and related solution is
the metaphysical idea of parallel universes or many worlds, i.e. that each
statistical outcome that does not occur in this universe does in another.
This is currently a popular explanation. However it is fundamentally
problematic in that these other universes are beyond contact and
therefore the theory cannot be verified. Nor is it clear who/what keeps
track of the information content of the vast number of universes that such
a system would generate. There is no empirical evidence for the Parallel
universes solution, so it requires faith to trust that as the solution. Both
these explanations are cognitively convenient ways of comprehending the
practicalities of wave-particle duality, but they sidestep the real issues.
The cordus concept provides an elegant solution for the path conundrum.
In particular, an explanation is given here for the quantum particle
behaviour of the photon in the double-slit experiment. Cordus provides a
simple physical explanation for the particle-choice problem. Internal
variables of the photon are inferred, and a physical interpretation is given
of frequency. The concept of hyff is introduced. The path dilemmas in the
Mach-Zehnder interferometer are explained, and in doing so a novel
explanation arises for what a beam-splitter really does.
This paper is part 2 in a bracket of three. The first part describes the
fundamental cordus concepts. i.e. the proposed internal structure of the
photon. The present part solves the apparent path-dilemmas in the
double-slit device, and also interferometers. The third develops a novel
mechanism for the formation of fringes.
3
Particle behaviour in the Double-slit experiment
The Cordus concept offers an explanation of the quantum behaviour of the
double-slit experiment: The photon is a cordus, and one reactive end
passes cleanly through each slit. The fibril passes through the material
between the two slits, but does not interact with it. The cordus
explanation is that the photon does pass through both slots, not as ‘real’
and ‘ghost’ particles, but instead as a twin-ended particuloid. The variable
nature of the cordus span (Lemma 5) permits the photon to go through
gaps of different width, providing the gaps are small and arranged
symmetrically along the path.
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Quo vadis?
Default behaviour in double-slit
If a detector is placed proximal behind each slit in the double-slit device,
then whichever reactive end first hits the plate will be grounded (L.2.1)
and the cordus will collapse to a single energy impulse at that detector,
see Figure 1.
One of the detectors will thus register a photon arrival. However there is
random variability in the position of the reactive ends so the next photon
may ground on the other detector. Over time the two absorbent detectors
will each obtain their share of impacts, providing that they are equally
spaced from the slit.
Quantum behaviour in the blocked double-slit
If one of the slits is blocked by a detector, and the other is open, then the
observed reality is that the photon always appears at the watched slit and
never appears on the backplane.
The Cordus Conjecture explains this quantum behaviour as follows, see
Figure 2. Reactive ends pass through both slots as usual. Whereas the RE
at the open slot is free to continue, that at the blocked slot is obstructed
by the detector. This causes the cordus to be always grounded at the
detector (as per L.2.4). The whole photon collapses at the detector, every
time, even though the cordus did pass through both slots. Since the whole
photon is grounded at the detector, there is no photon left to continue
further, so no fringes appear even if a screen is placed behind the
detector.
The Cordus Conjecture thus explains the observed behaviour. There is no
choice in the photon, no free-will. However, there is still the matter of
how if at all the Observer’s watching of the quantum experiment
predestines the outcome.
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Quo vadis?
Figure 1: Photon behaviour in the double-slit experiment
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Figure 2: Photon behaviour in the double-slit experiment with only one
detector.
Observer’s powers
Whether or not an Observer is looking at the double-slit experiment is
irrelevant: it is whether the observation is passive or intrusive that is
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Quo vadis?
important (Lemma 3). Simply passively watching from outside the lines of
action (optical paths) does not influence the outcome, according to the
present concept. The only thing that is really important is intrusive
observation: when the Observer’s eye (or her proxies in the form of
photon detectors or screens) are in such a position as to intercept the
photon and suitably constructed (opaque) to arrest it.
If the observer uses passing observation at one slot, then it slows that
reactive end and thereby affects fringe patterns, but more of that later.
The Lemmas 1-3 are sufficient to explain path effects, but not fringes, so
the further explanation of the double-slit is delayed until additional
lemmas are constructed.
4
Mach–Zehnder interferometer
Quantum dilemmas also arise in the Mach–Zehnder interferometer. This
device has two output paths, hence two detectors, see Figure 3. The light
source strikes partial mirror PM1, where the beam is ‘split’ into path 7 and
L, the two beams ‘recombine’ at partial mirror PM2, and then proceed to
detectors DA and DB. However there are some anomalous results,
especially for single photons.
MZ Default mode
In the default mode the photon, and indeed the whole beam, will
selectively appear at one of the detectors. This can easily be explained
using conventional optical wave theory. The paths are not identical
regarding the reflection and refraction encountered, and the usual
explanation is based on the delays, i.e. phase shift in wavelength, for the
different reflection and refraction on the two paths.
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Quo vadis?
Figure 3: Mach–Zehnder interferometer in default mode. The photon
appears at DB.
From the wave theory perspective the explanation is that the light beam
experiences a phase shift of half a wavelength where it reflects off a
medium with higher refractive index (otherwise none), and a constant
phase shift k where it refracts through a denser medium.
The beam on path 7 to Detector DB experiences k + ½ + ½ phase-shift (at a,
c, and e), see Figure 3, whereas to reach Detector DA requires an
additional k (at y). Similarly, the beam on path L to Detector DB
experiences ½ + ½ + k (at p, r, and t). As these are the same, the classical
model concludes that the two beams on 7 and L result in constructive
interference at DB, so the whole output appears there, providing that the
optical path lengths around both sides of the interferometer are equal.
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Quo vadis?
The L beam into Detector DA experiences ½ + ½ + k + k phase-shift (at p, r,
t, and v) whereas the 7 beam into DA experiences k + ½ + k phase-shift (at
a, c, v). As these differ by half a wavelength, the usual explanation is that
the two beams interfere destructively and no light is detected at DA. This
is a satisfactory explanation for light beams.
Quantum problems
The quantum weirdness arises because this behaviour still occurs for a
single photon, which is supposed to go down only one path. Thus selfinterference seems to be required, or virtual particles.
Worse, if one of the paths is blocked by a mirror that deflects the beam
away, then the beam still appears at DB, regardless of which path was
blocked. The photon seems to ‘know’ which path was blocked, without
actually taking it, and then take the other. Various explanations have been
put forward for how this might happen, but they tend to be weird rather
than physical.
The obvious Cordus explanation is that each reactive end takes a different
path, and the phase difference (which is accepted by the Cordus
Conjecture) through the glass at y means that the reactive end is delayed
at Detector DA, so does not appear there. The existing Cordus lemmas
could be applied, assuming that each reactive end has a 50% chance of
being reflected at a partial mirror, and the phase delay through the glass
at y means that the reactive end gets to detector DB before DA. However
this is unsatisfactory because a decision tree of the Cordus path options
suggests that ¼ of photons should still appear at DA even if DA is precisely
located relative to DB. Something is missing from the Cordus explanation,
and the solution was to add assumptions about the reflection process,
which are shown in Lemma 7. (For precursor lemmas 4-6 see part 1.3).
Lemma L.7
Beam-splitter
This lemma describes a set of assumptions for how a beam-splitter
operates. It identifies the variables that determine which path the exit
light takes.
Lemma L.7
Beam-splitter
L.7.1 In a usual full-reflection, i.e. off a mirror, both reactive ends of
the cordus, which are separated by the span, separately
reflect off the mirror.
L.7.2 Reflection does not collapse the cordus: it is of the passing rather
than intrusive type.
L.7.3 When encountering a partially reflective surface, e.g. a beamsplitter or partially silvered mirror, the outcome depends on the
state (energised vs. dormant) of the reactive end at the time of
contact.
L.7.3.1 A RE will reflect off a mirror only if it is in one state, here assumed
to be the energised state, when it encounters the reflective layer.
94
Quo vadis?
L.7.3.2 A dormant RE passes some way into a reflective layer without
reacting. Only if it reacts within the layer will it be reflected.
L.7.3.3 If the reflective layer is thin enough, a dormant RE might only reenergise once it is through the layer, in which case it is not
reflected. Hence tunnelling.
L.7.3.4 The thickness of the layer is therefore important, as is the
frequency.
L.7.4 The orientation of the cordus (polarisation) as it strikes the beamsplitter is important in the outcome.
L.7.4.1 If the reactive ends strike at suitable timing such that each in turn
is energised (dormant) as they engage with surface, then the
whole cordus may be reflected (transmitted).
L.7.4.2 It is possible that only one RE is reflected and the other
transmitted straight through.
See Figure 4.
Figure 4: A beam-splitter reflects only the energised reactive end. The
dormant RE passes through. The diagram shows a p-polarised cordus, but
the principles generalise to other forms of polarisation. The key
determinant of path is the state (energised/dormant) of the pair of reactive
ends at contact with the mirror.
The relevant points from that lemma are that a reactive end will only
reflect if it is a suitably energised state at the point of contact. Otherwise it
goes deeper into the material. If by going deeper it passes through the
reflective layer of the beam-splitter, then it continues without being
reflected, see Figure 4. Thus cordus-photons striking the beam splitter will
have two obvious outcomes: both ends reflect, or neither reflect (both
95
Quo vadis?
transmit through). These outcomes depend on the orientation
(polarisation) of the cordus, the precise phase location of the energised
reactive end when it makes contact, and the frequency relative to the
thickness of the mirror. The lemmas also admit the possibility that the
beam-splitter may send one reactive end each way, if the two reactive
ends differ in their state when they impact. If this is the case then it raises
the possibility that the ‘beam-splitter’ is sometimes a ‘photon-splitter’, i.e.
changes the span.
This lemma also explains the variable output of the beam-splitter: with
one input beam, generally two beams will be observed emerging from a
beam-splitter, because of the variable orientations of the input photons
ensure that a mixture of whole and split cordi will go down each path.
However if the polarisation of the input beam is changed then the beam
splitter will favour one output.
Cordus explanation: default MZ mode
With Lemma 7 the Cordus explanation of the MZ device may now be
continued. We consider a single photon, but the principles generalise to a
beam of many. The photon reaches Partial Mirror PM1, see Figure 5; the
energised reactive ends reflect off the mirror, the dormant ends go
through. Depending on the orientation of the cordi, some whole cordi go
down path 7, some down L, and some may be split to go down both. The
polarisation of the photon is therefore important in the outcome.
Reactive
End is
delayed in
the glass
Partial
Mirror
PM1
PATH 7
a
a1
b
a2
a2
p
Light
source
a1
PATH L
Figure 5: First partial mirror of the Mach-Zehnder interferometer.
The whole photons pose no particular problem, but a split cordus needs
explanation: a1 reflects off the surface and continues on path L (pqrst).
The dormant a2 reactive end passes through the mirror surface,
reenergises too late within the transparent backing, does not reflect, and
continues on path 7 (abcd). Note that the order is unimportant: it is not
necessary that the energised RE reaches the surface before the dormant
RE. Nonetheless, regardless of the order, the RE that was energised at the
mirror (a1 in this case), is always reflected (takes path L). This is important
96
Quo vadis?
in the following explanation. Assuming equal optical path length along 7
and L, which is the case, then both reactive ends come together again at
Partial Mirror PM2, having undergone several frequency reversals.
The explanation assumes that the path length is such that the reactive
ends are all in the opposite state to PM1, i.e. the path lengths are not only
equal, but a whole even multiple of half-wavelengths. The cordi that have
travelled whole down path 7 or L now divert to Detector DB. For the split
cordi the explanation follows: when reactive end a1 reaches the mirror
surface of PM2 it is now in the dormant state, and therefore passes
through to Detector DB. By contrast reactive end a2, which was dormant
at PM1 is now energised at PM2, and reflects, taking it also to Detector
DB. See Figure 6.
Figure 6: Second partial mirror of the Mach-Zehnder interferometer.
Therefore the photon always appears at Detector DB, regardless of which
path it took. The partial mirrors achieve this by sorting and if necessary
splitting the photons, and the arrangement between the mirrors ensures
that the second mirror reverses the operation of the first. The effect holds
for single photons as well as beams thereof. From this perspective the MZ
interferometer is an unexpectedly finely-tuned photon-sorting device that
auto-corrects for randomness in the frequency phase.
Cordus explanation: open-path MZ mode
Conventionally the wave-particle dilemma occurs when one of the paths is
blocked, since it suggests the weird solution that photon ‘knew’ which
path was blocked without actually taking it. For example a mirror is
inserted at S, but the photon still appears at Detector DB. Likewise a
mirror at D still causes the photon to appear at Detector DB, see Figure 7,
despite the apparent mutual exclusivity of these two experiments.
97
Quo vadis?
Figure 7: Inclusion of an extra mirror at D still results in photons arriving at
Detector DB.
The Cordus explanation is that the reactive ends are constrained by the
partial mirrors to converge at DB. Regardless of which path, 7 or L, is opencircuited, the remaining whole cordi and the split cordi (providing they are
not grounded first at g) will always appear at DB.
Cordus explanation: sample mode
The MZ device is used to measure the refractivity ks of a transparent
sample placed in one of the legs, say S. The observed reality when using a
beam of photons is that a proportion of the beam now appears at detector
DA. The wave theory adequately explains this based on phase shift and
constructive (destructive) interference. By comparison the Cordus
explanation is that the sample introduces a small time delay to the (say) a1
reactive end of the split cordus, which means that it arrives slightly late at
partial mirror PM2. If sufficiently late then a2 reaches the mirror in an
energised state (it usually would be dormant at this point), and therefore
reflects and passes to detector DA. If a2 is only partially energised when it
reaches the mirror, then its destination is less certain: a single photon will
go to one or the other detector depending on its precise state at the time.
The proportioning occurs when a beam of photons is involved, as the
random variabilities will place them each in slightly different states, and
hence increase the probability of heading to one particular detector.
If the 7 or L path in the MZ device is totally blocked by an opaque barrier
(unlike the mirror mode), then the whole cordi in that leg ground there, as
98
Quo vadis?
do the split cordi. However the whole cordi in the remaining leg continue
to DB as before.
5
Conclusions
Quo vadis, photon? Where is the photon going?
One of the central quantum dilemmas of the double-slit device is the
ambiguity of where the photon is going, and which path it will take.
Existing approaches either reconfigure the photon as a wave, or treat the
problem as simply probabilistic. The solution proposed here is simply that
where the photon appears will depend on which of its two reactive ends
are first obstructed. In turn that depends on how the obstruction is made,
and at which instant the Observer does it.
God does not play dice - the Observer does, by selecting the method of
how intrusively or passively to make the observation, and the timing of
when in the cordus frequency cycle to make the intervention. However the
Observer may have little control over the latter, hence the observed
probabilities of QM emerge as a measuring artefact.
Thus Cordus offers a way to reconceptualise the photon and resolve path
dilemmas in a natural way that does not require invisible particles, parallel
worlds, pilot waves, intelligent photons, or the mere presence of an
Observer. We no longer need the weirdness of conventional explanations.
A companion paper (ref. ‘Cordus matter’) shows why Bell’s Theorem is not
a constraint against hidden-variable solutions.
Cordus also implies that the existing paradigm of quantum mechanics is
not the reality, only a mathematical approximation. In particular, Cordus
suggests that superposition, the ability of a particle to be in two places at
once, is only a high-level simplification of the underlying behaviour of
internal variables. While superposition is a useful rough statistical concept
for average particles, it is unreliable as a physical explanation for individual
cases. The implications of the Cordus conjecture are that there is a deeper,
simpler, deterministic, and more elegant reality beneath quantum
mechanics and wave theory.
99
Quo vadis?
100
Explanation of fringes
Cordus Conjecture Part 1.3
Pons, D.J. , 21 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
The cordus concept is shown to be able to explain wave behaviour in gaps,
and fringes in the double slit device. This is useful because one of the
enigmas of the double-slit device is that single photons form fringe
patterns. Cordus explains fringes in terms of force lines called hyperfine
fibrils (hyff) and their interaction with the edges of the light path. This also
explains beam divergence and near-field effects. The results show that it is
conceptually possible to create a solution for fringes based on a particuloid
interpretation of light, without using the concept of interference. The
biggest difference between Wave theory and the cordus explanation is
their interpretation of the mechanism for fringes. Wave theory explains
fringes as ‘interference’: two separate waves of light differing by full (half)
fractions of wavelengths and thus constructively (destructively) interfering.
From the Cordus perspective photons do not actually interfere or add
together, and 'interference' is only a convenient analogy. The Cordus
explanation is that fringes are caused instead by interaction of the photon
hyff with opaque edges. This bracket of papers therefore offers a resolution
of wave-particle duality by anticipating the internal cordus structure of the
photon and the associated cordus mechanics. From this perspective wave
and particle behaviours are simply the different output behaviours that
the internal system shows depending on how it is measured. Thus Cordus
offers a deeper mechanics that subsumes both quantum mechanics and
wave theory. Surprisingly, Cordus suggests that the next deeper level of
reality is deterministic.
Keywords: wave-particle duality; wave theory; quantum mechanics;
double slit; fringe; interference
Revision 2.10 Added reference to dynamically changing span length, and explanation of single slit.
Minor edits
Document: Pons_Cordus_1_2PathDilemmas_E2.10.79.doc
L.1.2
The fibril connecting the two reactive ends does not interact with
other matter.
1
Introduction
One of the enigmas of the double-slit device is that single photons form
fringe patterns, given enough of them. That light waves should do so is
expected, but the puzzling part is what makes individual photons do so
given that the usual mechanism of interference is unavailable.
21
Please address correspondence to Dr Dirk Pons, University of
Canterbury, Christchurch, New Zealand. Copyright D Pons 2011.
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Fringes
In this paper the cordus concept is expanded to explain wave behaviour in
gaps, and fringes in the double slit device. This paper is part 3 in a bracket
of three. The first part describes the fundamental cordus concepts. i.e. the
proposed internal structure of the photon. The second part solves the
apparent path-dilemmas in the double-slit device, and also
interferometers.
2
Wave theory explanation of interference
The Wave theory explanation is that the fringes, e.g. in a gap, form due to
interference based on phase difference along different optical paths:
each point on the surviving wave-front after the obstacle becomes
a point source and radiates its own secondary wave
these points are separated in space
the distances from central and edge points to the screen is
therefore different
this difference will be a full (half) wavelength at some locations on
the screen and therefore cause constructive (destructive)
interference there
Consequently the secondary waves interfere to produce lighter
and darker regions.
The explanation rests on frequency and phase shifts arising from
geometric path differences.
Limitations in Wave Theory
Optical Wave theory sufficiently explains the behaviour of beams of light.
However it does not explain why multiple separate single photons should
also form fringes. Also, the concept of ‘destructive interference’ is difficult
to reconcile from an energy perspective. How do two photons destroy
each other and leave no residue? With water waves, the peak of one wave
A can be higher where that of B is lower. Peak A is above the mean water
level and therefore has positive potential energy, whereas peak B has
negative. When they meet, the energy excess in A exactly balances the
deficit in B and a flat piece of water results. No energy is lost: the mean
water height is the same.
Destructive interference in light is usually explained similarly, by the
electric fields cancelling. That of course does not explain the observed
interference of individual photons that were never in the same place at
the same time. Furthermore, the wave explanation suggests that the
effect should be seen more often, but the reality is that photons do not
observably interfere with each other, despite their vast quantity in the
world.
Existing attempts at reconciling wave and particle behaviour have tended
to preserve Wave theory and make the particle behave like a wave by
‘interfering’ with itself through a 'virtual' particle. The virtual particle is not
detectable and therefore metaphysical, and this is where weirdness arises.
102
Fringes
What is frequency?
Frequency is a core mechanism in the Wave theory description of fringes.
It is strange that wave theory is so highly dependent on the concept of
frequency, yet cannot explain how frequency arises. In other wave
phenomena such as water waves, the frequency corresponds to a physical
motion of water molecules. What is the comparable phenomenon in light?
The standard wave theory answer is that it is the frequency of oscillation
of the electric and magnetic fields. However this is not entirely satisfactory
as it still does not answer the question, nor explain why the fields reverse
polarity.
Another paradox with wave theory is that many phenomena in optics are
dependent on the wavelength λ, but the dimensions of the experiment are
in the transverse direction. For example, the presence and strength of
fringes depend on the diameter of the aperture or width of the gap. This is
curious, because wavelength is an axial dimension, whereas gap width is
transverse geometry, i.e. the two measurements are perpendicular. If
anything one would expect amplitude to be involved since it is a
transverse measurement. Strangely, amplitude does not feature in the
wave theory descriptors of optical effects, but wavelength does.
Nor can the particle view explain frequency: it hardly even needs the
concept, other than as a measure of energy. Thus neither wave nor
particle perspectives explain the mystery of Frequency. Consequently, a
model that bridges the wave-particle duality and invokes internal variables
will inevitably have to reconceptualise 'frequency'.
3
Cordus solution
The Cordus approach developed up to here can make sense of the photon
path dilemmas, but not of the fringes. The next lemmas show how it can
be extended to solve this, by proposing internal variables for the photon. A
companion paper (ref. ‘Cordus matter’) shows why Bell’s theorem is not a
constraint.
Lemma L.4
Internal and external variables of the photon
This lemma asserts that the cordus has internal physical variables, that
manifest as variables that can be measured (external variables).
L.4
Internal and external variables of the photon
L.4.1 The orientation of the cordus is variable.
L.4.1.1
The cordus may be inclined in pitch, roll, and yaw around
the optical centre line of the photon path.
L.4.1.2
The cordus may rotate around the optical centre line.
L.4.1.3
The above internal variables manifest externally as
polarisation states (V.1.2). For example Circular
polarisation is a transverse cordus with roll angular
velocity, and is therefore handed.
L.4.2 The cordus vibrates, or oscillates.
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Fringes
L.4.2.1
This corresponds to the frequency of the photon and its
energy (V.1.1).
The nature of the vibration is left temporarily unspecified:
oscillation or rotation motion; vibration of the fibril in
radial or axial displacement; reciprocation of parts. Refer
C.1, in part 1.1 where the dashed lines in Figure 2
represent the frequency component. See also lemma 9.
This vibration generates electromagnetic fields (V.1.3),
though the mechanism is left unspecified at this point.
L.4.2.2
L.4.2.3
This provides a physical mechanism for frequency among other external
variables of the photon. Though vague, it is nonetheless sufficient to
proceed, and is further developed later.
The explanation of fringes also needs a mechanism to explain the width of
the cordus, and how it is affected by frequency, hence the next lemma.
Lemma L.5
Span length
The distance between the reactive ends (Span) may vary.
L.5
L.5.1
L.5.2
L.5.3
L.5.4
L.5.4.1
L.5.4.2
L.5.4.3
L.5.4.4
L.5.5
L.5.6
L.5.7
Span length
The Span is plastic. It may be stretched or shrunk. (Nothing yet
suggests it has elastic recoil).
The Span may be changed by the external optical environment,
e.g. by sending the reactive ends along different paths. When thus
forced by the environment, the Span may be large: at least of the
order of metres. In other situations the Span may be small.
For newly created and unconstrained photons the natural
tendency is for the Span to be small and inversely related to the
frequency. The greater the frequency the shorter the Span. Thus
shorter wavelengths have shorter spans.
The Span varies randomly by quantum amounts.
For convenience it is assumed that the Span can take one
of only three changed states: increase, stay the same, or
decrease.
The size of the quantum increment/decrement (delta) is
related to the frequency of the photon. Delta span is
inversely proportional to frequency: high frequency
photons (short wavelength) have smaller spans (L.5.3) and
smaller delta span.
The changes in Span length do not affect the polarisation
or energy of the photon.
The mechanism for span fluctuation is not specified. The
present working model tentatively assumes it is the
resistance to growth of the hyff (see later).
The change in Span occurs at the same time as the frequency
oscillations i.e. synchronised.
Span changes apply symmetrically. (We subsequently identify that
mechanisms instantly communicate changes at one reactive end
to the other).
The span changes dynamically during the frequency cycle.
104
Fringes
From the Cordus perspective span and frequency are the main variables
for optical fringe effects. Wavelength is thus a proxy variable for frequency
and velocity.
Lemma L.5.7 has been added here, because in later developments we
show that there is a coupling between the energy in the fibril and that in
the field (hyff). We call this the 'Principle of mass-field coupling', and
record it as lemma E.7.8 [1]. The energy dynamically shuttles between the
two. We anticipate that the interplay also moves the reactive ends
radially, i.e. the span changes dynamically during the frequency cycle. The
mean span is inversely related to the frequency, mass and energy of the
cordus.
Why some photons will get through even one slit
So, when presented with two slits, some photons will be in a suitable span
to pass through both gaps, regardless of the spacing of the gaps (though
fewer photons will be in very large span states). If one gap is covered over,
then some photons will still get through, because some photons will be in
the small-span states at the time. This providing the photons have low
concentricity with each other, so there are some photons with a
centrepoint sufficiently aligned with the open slit. In most experimental
cases this is not a problem as the beam width of the photons is very much
more than the slit width.
4
Wave behaviour in single gaps: diffraction
Diffraction can mean several things, but here refers to the spreading of a
light wave (i.e. breaking into pieces) through a single optical path, (e.g. a
single slit, aperture, or round the edge of an object), with subsequent
fringes.
A single slit will cause diffraction; which appears as a central region of high
intensity, with fringes to each side. The observed reality is that narrower
gaps produce fewer but more pronounced fringes. The distance from the
gap to the screen (far field) needs to be many wavelengths, which implies
that the angular effect is small and in need of magnification.
In searching for a candidate theory for quantum frequency, we noted that
the fringe pattern is independent of the thickness of the opaque barrier:
thin and thick layers are equally effective. This suggests that the diffraction
effect is governed not by the depth or composition of the material but
simply by the existence of an opaque 2D frontal-plane. If so, this means
that the angular deflection of the photon (diffraction) occurs at the 2D
surface, not in the bulk of the barrier. However there are two problems:
First, the individual photon does not have an obvious mechanism to create
its own angular deflection: common sense has it that it either passes
cleanly through the gap, or slams into the barrier and is no more. If it does
not touch the barrier, how can it be affected by it? Secondly, there is no
obvious mechanism to break the angular deflection into angular quanta
105
Fringes
and hence fringes. This is where the electromagnetic field is recruited as a
ranged-variable, consistent with the passing observation.
Lemma L.6
Cordus hyff for the photon
This lemma accepts the L.1 conjecture that reciprocal motion of some type
occurs, corresponding to frequency, and then couples the frequency to
the electromagnetic field, as follows:
L.6.1 The energy in the cordus oscillates from one reactive end to the
other, at a rate given by the frequency.
L.6.2 The oscillation causes structural transience: the reactive ends
deconstruct and reconstruct. The energy is shuttled between them
by the fibril. That central fibril is a permanent feature of the
cordus in flight, unlike the transient hyff (see below).
L.6.3 The reactive end has a dynamic electromagnetic (EM) field around
it. For simplicity consider primarily the electric field here. The field
is transient and linked to the frequency.
L.6.4 The field is made of hyperfine fibrils (hyff) that extend like hairy
fluff from the reactive end, and these carry the EM field and force.
The hyperfine fibrils collapse and grow as the reactive ends
deconstruct and reconstruct (C.1.5 and C.1.6 hyff photon
model).22 Thus the electric field is emitted and then retracted.
L.6.5 A hyff is attached at one end to a reactive end, and extends
outwards from that base. It can make a temporary bond to other
matter, in which case it exerts a tensile or repulsive force, or
pumps energy into/out of the photon.
L.6.6 A hyff exerts a transient force linked to the frequency. The
oscillation of energy along the cordus results in the extension of
hyff followed by their withdrawal, and the collapse of any force.
This also accommodates the reversal in the observed field.
L.6.7 A hyperfine fibril that engages with matter can exert force on the
photon without necessarily terminating the photon.
L.6.8 The trajectory and dynamic properties of the photon can be
influenced by interaction with matter at a distance, the hyff being
the coupling mechanism. This corresponds to passing observation,
i.e. such observation affects the dynamic properties of the photon
through the coupling.
L.6.9 The photon hyff have a range which is potentially infinite but
practically not, as they have decreasing chance of being in the
outer range, see also L.6.16. The range of the hyff is not the
frequency. Instead frequency is the refresh-rate of the fibril and
hyff.
L.6.10 The hyff have stepped (quantum) force increments. The
mechanism for this is not certain. One candidate is that the hyff
extend stepwise outwards, and another is that the hyff force itself
is quantised. Another is that it is simply the number of hyff
renewal pulses (hyffons, see ‘Cordus in extremis’) that manage to
get an engagement with the edge in passing. This is an open
question. Nonetheless the assumption is that the frequency state
22
The number of hyff per photon does not need to be specified here. A companion paper
(Cordus Optics) suggests that the photon probably has only one hyff at each reactive end, in the radial
direction.
106
Fringes
L.6.11
L.6.12
L.6.13
L.6.14
L.6.15
L.6.16
L.6.17
of the hyff at the RE at the time of engagement with the gap
determines the force.
Higher frequency gives finer force increments.
The force exerted by a hyff is greater at shorter ranges.
The timing of the frequency events for the two reactive ends is not
prescribed here. It could be alternate (the current working model),
simultaneous, or the general case of disjoint (variable phase
difference between ends).
Taking these assumptions together, the force exerted by an
anchored hyff comes in quanta that are stronger at shorter range.
The force corresponds to the angular deflection of the reactive
end, or retardation (phase delay). The force may be attractive or
repulsive.
The communication across the fibril is practically instantaneous.
The growth of the electromagnetic hyff (e-hyff) is at the speed of
light in the medium. (This may also imply that higher frequency
photons have shorter-range hyff).
The reactive ends fade in and out of existence at the ends of the
span. The ‘particle’ nature is in the reactive ends, and in turn these
exist as hyff.
It may be convenient to think of photon hyff as equivalent to fields, e.g.
the evanescent field, or oscillating electric dipoles. The hyff also replace
the concept of virtual particles in QM. At the same time it provides a
simple means to explain frequency, which is otherwise a problematic
concept for both wave and particle perspectives. In a companion paper
the hyff concept is used to explain fields more generally, e.g. how a
charged particle exerts a force at a distance.
Explanation of gap fringes
The Cordus explanation for diffraction in gaps is that the photon cordus is
diffracted (bent) by set angular amounts, by its interaction with the
opaque material surrounding the gap. The hyff become engaged with the
(thin) surface opaque material and thus exert a quantised force that
retards the one reactive end and bends its trajectory, causing fringes at set
intervals. The other reactive end is not affected as much (unless it is close
to its own wall) as the span is plastic.
However that is not the whole story: if only one reactive end of a cordus
goes on a bent trajectory, then the other straight-ahead reactive end will
always ground on the back-plane first, because it is the shorter path, see
point D’ in Figure 1.
107
Fringes
e, Cordus
eccentric to
gap
a1
a2
a1
a2
a1
a2
C
D'
Figure 1: Path of eccentric cordus through a gap. The grazing reactive end
is delayed and angularly deflected more than the medial RE which is
further from its edge.
For fringes in gaps it is important that the cordus is delayed equally at both
reactive ends. This requires that the incident photon be concentric with
the gap, so that its reactive ends are equidistant from the gap edges, and
both are delayed the same. This stretches the span to form symmetrical
fringes, see E and E’ in Figure 2. The figure shows a simultaneous
frequency model (L.6.13), though it is presumed that the effect would also
operate for the more general case of disjoint frequency providing that the
frequency was sufficiently high that both reactive ends had an opportunity
to sense the edge.
Ironically, non-concentric photons ground closer to the centreline of the
gap than concentric photons. So any deviations cause central rather than
peripheral loading. This is consistent with the observation that the central
fringe is wider and brighter than those further out.
Those cordi with span such that a reactive end closely grazes the edge will
have greater hyff force, and therefore be bent more. Cordi that are far
from the edge of the gap will be bent only a little. Thus multiple photons
sent through the gap will bend differently depending on their location
relative to the wall, blurring the fringes.
108
Fringes
Cordus
concentric
with gap
a1
a2
a1
a2
a1
a2
E
E'
Figure 2: A concentric cordus is equally affected at both reactive ends, and
thus the angular deflections are equal. One of the paths will ground first,
and the fringe will start to be built up there.
Are lateral forces realistic?
Thus cordus proposes that fringes are formed by lateral forces between
the particuloid and the material making up the slit geometry. There is no
place in this explanation for the ‘interference’ mechanism of classical and
quantum mechanics. Thus cordus refutes interference as a physical
principle and considers it a flawed concept. Interference is merely an
expedient mathematical representation.
It might seem extravagantly unconventional to suggest, as cordus does,
that fringes are created by lateral forces between the particuloid and the
slit material. We acknowledge it is not an intuitive concept, and that we
have not worked out all the details. Nonetheless, it is the concept that
emerged naturally from cordus and we include it in the current working
model.
Being an unusual concept, even to us, we subsequently searched the
literature to see whether anything similar had been detected. Surprisingly,
this is the case: these lateral forces have been empirically detected
between large molecules and the slits of diffraction gratings [2]. 23 We
interpret this result as confirmation that lateral-force through hyff is a
plausible mechanism for fringes. We acknowledge that cordus goes further
in suggesting these forces are granular, without fully providing details. Yet
later work in the cordus conjecture provides a mechanism for the
23
Similarly: ‘we have clearly detected the effect of the weak van der Waals force
between the molecules and the gratings although the particles typically pass
several
hundred
nanometers
from
any
surface.’
http://www.univie.ac.at/qfp/research/matterwave/talbotlau/index.html
109
Fringes
discretisation of the electromagnetic force, and we suggest that this in
involved in fringe formation.
Gap width
The observed reality is that narrow gaps produce fewer but more
pronounced fringes whereas wide gaps produce many fine fringes. The
Cordus explanation is that narrower gaps admit smaller-span cordi, which
means fewer quantum states for span width (L.5.4) hence fewer quantum
angular deflection outcomes. The eccentricity is predicted not to be the
major effect, instead it simply degrades fringe quality.
In all cases the incident photons need to have the same frequency and
polarisation. Distinct fringes do not appear in decoherent light, e.g.
sunlight, because the different cordi diffract differently and smudge the
fringes.
Apertures and Airy pattern
Circular apertures form circular fringes or Airy patterns. For example
fringes appear at the output of a Sagnac24 or Mach-Zehnder
interferometer when the output beam is focussed by a lens. The lens is
necessary: without it the fringes do not appear. The Cordus explanation is
the same for the gaps considered above: an edge interaction effect for
axially-concentric photons, that causes quantised angular deflection,
which appear as fringes. Thus fringes are an artefact of the lens, and more
specifically an effect caused by the edges of the aperture.
Beam divergence
A laser beam will spread, the divergence from the central axis being
θ=λ/(π.w) where w is the beam waist (approximated by the aperture).
Thus larger aperture beams spread less, as do shorter wavelength. This is
typically explained as a diffraction effect, though the mechanism is
incompletely understood.
Cordus provides several candidate explanations. First a possible
mechanism for spread in a vacuum: the span fluctuates randomly (L.5), but
cannot go negative, and therefore over time some extreme cases tend to
move to larger spans. The span, and span increment, are inversely related
to the frequency (L.5), so high frequency (tight λ) photons grow their span
from a smaller base and therefore more slowly.
24
The Sagnac interferometer is arranged in a ring, with one path clockwise and the other
anti. A circular interference fringe may be visible at the output detector. The optical explanation is
that the light beam splits into the two separate paths, and these subsequently interfere at the output.
The (say) clockwise path encounters 2+2k phase shift, whereas the anticlockwise 1.5 +2k phase shift.
Therefore there is a half wavelength difference between the two exit beams, and this creates the
interference. Rotation of the device causes a further change in timing, and this is evident in the fringes.
The Cordus explanation is that some photons are split down both paths, and delayed
differently. The fringes are formed by the aperture effect. When the device is rotated the delay is
changed, and this changes the timing of REs past the aperture edges, hence changing the fringes.
110
Fringes
In air or a transparent medium, the mechanism for gaps may be involved,
i.e. diffraction, and refraction, with one RE being delayed by an interaction
with matter but not the other, hence bending the overall cordus
trajectory.
For the aperture effect, the starting span cannot be larger than the
aperture w. Whether or not the cordi are symmetrical and span the entire
beam aperture is a second matter. Assuming that they do not, then the
above spread mechanisms can also move a RE towards the centreline, so
the average spread is less. According to this explanation it is not the
aperture per se that is important, but the degree of concentricity of the
photons with the centreline: it is predicted that greater concentricity will
show greater divergence, and the tendency to fringes.
5
Fringes in the Double-slit device
The explanation of conventional optical wave theory is that the incoming
light is a wave that passes through both slits, and the residual waves
interfere with each other constructively (light regions) and destructively
(dark lines). The interference is explained as due to the phase shift in
wave-length, a difference of half a wavelength (λ/2) causing destruction of
the wave. The explanation is adequate for most situations where there is
a beam of many particles. However it does not explain the behaviour of a
single particle, which also ends up in a fringe location even if there is only
one particle in the device at the time.
The quantum mechanics (QM) explanation is that the particle is a wavepacket and thus can pass through both slots, interfere with itself on the
other side, and collapse in one of the fringe locations. Alternatively, that
the particle has a twin ‘virtual’ particle that takes the other slit and then
interferes with the real particle.
The Cordus explanation is a straightforward application of the single gap
model with two additions. Each of the two reactive ends also interacts,
through the hyff [electric field] with the opaque material bounding the
slits. The hyff become engaged with the surface plane of the material and
exert a quantised force that retards the reactive ends and bends its
trajectory by set angular amounts, causing fringes at set intervals. The first
addition is that the short span cordi are barred entry by the medulla. Thus
the device imposes an upper and lower filter on the range of spans
admitted. Hence narrower slits produce more pronounced fringes.
The second is that diffraction occurs at both lateral and medial edges of
the gaps. Lateral diffraction is identical to gaps, and shown in Figure 3.
Symmetrical lateral fringes form. Medial diffraction also occurs, in which
the reactive ends are both angularly deflected inwards, forming fringes as
shown in Figure 4.
The two locations of the fringe are the modes of the reactive ends, and it
is somewhat random as to which will ground first. Note that this
111
Fringes
explanation accommodates the fringe behaviour of both single photons
and beams of coherent light. Thus a solitary photon will be deflected into
discrete angular steps, and will appear at one of two fringe locations
available for each step. A whole beam of light will likewise form fringes
because all the photons have the same discrete angular deflections,
providing that they are of the same energy. In the cordus model higher
energy particuloids [i.e. also higher frequency] have shorter spans.
This also explains why both photons and electrons form fringes: in both
cases the fringes arise because of the interaction of the electric field,
which is in discrete pulses [3], with the frontal surface plane of the matter
bounding the slit.
Figure 3: An Outer grazing cordus is deflected away from the midline by an
angular quantum.
112
Fringes
Figure 4: An Inner grazing cordus is deflected towards the midline by an
angular quantum.
For a concentric photon, the deflection paths are symmetrical. For a beam
of many such photons, each will be deflected differently according to its
span. However the deflections are arranged in angular quanta dependent
on the frequency. A single photon will therefore collapse to one of the
fringe locations. A whole beam of them will do likewise, but to a variety of
fringes, the visible fringes being the sum of the collapse of many individual
cordi. Non-concentric photons will diffract differently on each side, and
not form fringes but instead tend to collapse medially.
Photon path cross-over
The paths for the smallest span cordi will take them medially, and cause
cross-over. The cross-over of the path itself is not perceived as a problem
in the Cordus interpretation, but it will confuse the fringe picture. This is
consistent with the experimental results, and corresponds to the nearfield. A screen too close to the slits, as in Figure 5, will therefore intercept
a number of cross-over cordi, so the fringes will be indistinct.
113
Fringes
Figure 5: Concentric photon cordi of various span will take different paths
a1-a2, b1-b2, etc., and form fringes. Some of the cross-over cordi (shaded
area)will mix with other fringes, at least in the near-field.
The problem dissipates in the far-field, because for small slit pitch w and
large screen distance q, the cordus paths are parallel for similar bunches
(same angular deflection φc1 = φe2), thus pce = slit pitch w. This is shown in
Figure 6 with the c1/e2 bunch. Thus the bunch will consolidate to one
fringe that will be at least w wide. For the fringes to be distinct from each
other it is necessary that w be less than the fringe pitch q.tan(Δφf) where
Δφf is the angular quantum, and this requires a sufficiently large screen
distance q.
114
Fringes
Figure 6: Geometry for far-field. A tolerance frame is included to emphasise
the necessity for the span to be closely symmetrical with the slots.
The Cordus conjecture thus provides a very different explanation to the
optical wave theory and QM. Cordus does not require destructive
interference of photons, nor wave packets or virtual particles.
Why then should wave theory be such a good explanation for the doubleslit, at least for beams of light? From the Cordus perspective this is
because the hyff, being the EM field, are wave-like and the same
mathematics apply.
Curiously, Cordus offers an explanation for another effect that is not
readily explained by either wave theory or QM: the reason why fringes do
not always appear. It is known empirically that the concentricity of the
incident beam on the slits is important, and indeed such an effect is
required by Cordus.
Neither wave theory nor QM explain why the symmetry requirement
should exist for the double-slit device: with both those theories
waves/particles take all available paths, and symmetry issues should not
arise as they do. Experiments on concentricity might test the cordus
principle.
115
Fringes
Thus the Cordus model explains both single photon and beam behaviour.
Together with the earlier work on the path dilemma, this concludes the
conceptual explanation of the double-slit device.
6
Discussion
This paper has expanded the cordus concept to explain wave behaviour in
gaps, and fringes in the double slit device. This is useful because one of the
enigmas of the double-slit device is that single photons form fringe
patterns. Cordus explains fringes in terms of force lines called hyperfine
fibrils (hyff) and their interaction with the edges of the light path. This also
explains beam divergence and near-field effects. The significance of this is
that it shows it is conceptually possible to create a solution for fringes
based on a particuloid interpretation of light, without using the concept of
interference. This means that the Cordus solution has coherence over a
wider range than simply the path-ambiguity problems.
Comparison with Wave theory
The biggest difference between Wave theory and the cordus explanation is
their interpretation of the mechanism for fringes. Wave theory explains
fringes as ‘interference’: two separate waves of light differing by full (half)
fractions of wavelengths and thus constructively (destructively)
interfering. From the Cordus perspective photons do not actually interfere
or add together, and 'interference' is only a convenient analogy. The
Cordus explanation is that fringes are caused instead by interaction of the
photon hyff with opaque edges. This suggests a test.
If Wave theory is correct, coherence is not essential and it should be
possible to construct an interference pattern from two independent light
sources, e.g. one into each slit of the double-slit experiment. The light
sources need not be synchronised nor even exactly the same frequency:
according to WT, interference fringes should nonetheless form, though not
necessarily static. Cordus predicts that the outcome will be two
independent gap-fringes (which is not the same as interference fringes). If
interference fringes cannot be achieved then it suggests that light is not
fundamentally a wave, but only shows wave-like behaviour.
Any truly integrative solution should be capable of explaining conventional
optics too, and companion papers shows how cordus is applicable to
optical effects (ref. ‘Cordus optics’).
Limitations
Cordus is a thought-experiment that challenges fixed ways of thinking. It
asks the awkward questions, 'Is there really no better way of thinking
about photons other than zero-dimensional points, mathematical wavefunctions, or electromagnetic waves? Is there really no deeper
integration?' Cordus is a purposely audacious idea: it explores new ways of
thinking, and therefore deliberately puts forward tentative explanations to
116
Fringes
stimulate new thinking. We don’t believe the particular design variant
developed in this set of papers is necessarily the only or the final solution,
and we are open to the possibility that it could be wrong in places. Thus
the working model presented here is simply a conceptual model to be
critically evaluated.
The treatment of these topics is primarily conceptual and descriptive, and
the cordus mechanics only lightly sketched out. It is a conceptual model,
not so much a full theory with all the details worked out. Effectively we are
proposing internal variables for the photon: a 'hidden-variable' solution.
Therein lies a potential problem: the general interpretation within physics
is that such solutions are expressly prohibited by Bell's theorem. However
that is not an issue as a companion paper refutes Bell's theorem (Ref.
‘Cordus Matter’).
Not all quantum and optical effects have been considered here, nor are
the quantitative cordus mechanics worked out. However, sufficient of the
idea has been sketched out to allow the concept to be evaluated. Open
questions are the mechanics of the fibril (how is the invisible connection
maintained between the REs?) and the mechanism for quantum hyff
forces.
7
Conclusions
Outcomes: what has been achieved?
The Cordus explanation for the double-slit is that the photon cordus really
does pass through both slits. It can subsequently collapse at one of the
detectors and thereby appear to have taken only that path. This concept
explains the dilemma of single-photon behaviour. It also explains fringe
formation from single photons in gaps and slits. Path dilemmas in
interferometers are also solvable from the cordus perspective.
That concludes the original purpose, which was to explore whether there
could be a deeper mechanics that explains wave-particle duality. The
Cordus conjecture does away with much of the weirdness of wave-particle
duality: there is no need for virtual particles, superposition, observer
dilemmas, pilot waves, intelligent photons, or parallel universes. A simple
deterministic, unintelligent photon with a dual existence is all that is
required.
Quis es tu, photon? What is the photon?
The answer to that question, from the Cordus perspective, is that the
photon is a cordus with two reactive ends, with a physical gap between
them, held together with a fibril. The reactive ends may be energised to
various degrees, and in turn consist of hyff force lines. The energy shuttles
between the ends, and this also means that the particuloid does not exist
continuously at one location, but at two, and oscillates between them at a
frequency, see Figure 7.
117
Fringes
Hyper-fine fibrils
(hyff) emitted
from reactive end
Reactive end (RE)
energised at
frequency of
particuloid
Motion of
photon
Fibril, does not react
to matter, maintains
frequency reenergisation.
Spacing is the span
Other reactive end,
in a complementary
frequency state
Figure 7: Cordus model of the photon
How do Quantum mechanics and Wave theory fit in?
From the cordus perspective both conventional theories, quantum
mechanics and wave theory, are mathematical simplifications of a deeper
mechanics. Those theories represent the output behaviour of the inner
system. The weirdness of conventional wave-particle duality is not
because the photon is fundamentally weird, but because the existing
conceptual frameworks are inadequate: their mathematics are sufficient
for forward propagation of effect (prediction), but give unreliable results
when used for backward inference of causality (explanation).
Comments on the bracket of ‘Cordus Conjecture’ papers as a whole
Wave theory and quantum mechanics are functionally adequate theories
on their own, and powerful in their ability to predict how beams of light
and individual photons, respectively, will behave in a given situation.
However, despite their mathematical sophistication, they are incongruous
explanations of reality when wave and particle behaviours occur in the
same situation, e.g. the double-slit device. In these situations their
explanations are weird, which suggests that the models of causality are
incomplete. The problem has been that wave theory and quantum
mechanics are just so good, that it has been difficult to see what the
deeper mechanics could be, especially as Bell's theorem seems to prohibit
solutions with hidden variables.
Resolution of wave-particle duality
This bracket of papers offers a resolution of wave-particle duality by
anticipating the internal cordus structure of the photon and the associated
cordus mechanics. From this perspective wave and particle behaviours are
simply the different output behaviours that the internal system shows
depending on how it is measured. The duality and the apparent
incongruity of Quantum mechanics and Wave theory are resolved: the
conflict no longer exists at the deeper level.
Thus Cordus offers a deeper mechanics that subsumes both quantum
mechanics and wave theory. This bracket shows how it resolves waveparticle duality, and other papers extend it to other enigmatic effects, as
118
Fringes
well as the mundane. Perhaps surprisingly, Cordus is also simpler and
more coherent across a wider range of phenomena than quantum
mechanics or wave theory on their own. Even more surprising, and
unexpectedly contrary to the prevailing probabilistic paradigm of Quantum
mechanics, Cordus suggests that the next deeper level of reality is
deterministic.
References
1.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus in extremis: Part 4.4 Quarks. vixra 1104.0030. (2011)
Available from: http://vixra.org/abs/1104.0030.
2.
Brezger, B., L. Hackermueller, S. Uttenthaler, J. Petschinka, M.
Arndt and A. Zeilinger: Matter-Wave Interferometer for Large
Molecules. Physical Review Letters, 88(10): p. 100404. (2002)
3.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus in extremis: Part 4.1 Electromagnetism. vixra 1104.0027.
(2011) Available from: http://vixra.org/abs/1104.0027.
119
120
Cordus
Conjecture
Part 2: Cordus optics
Application of the
cordus
particule
principle to optics >
physical
interpretation
for
frequency provided >
Snell’s
law
of
reflection derived >
Brewster’s
law
derived > shows that
the particule idea has
good fitness for
optics
121
122
Cordus Frequency
Cordus optics: Part 2.1
Pons, D.J. , 25 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
Conventional particle and wave theories struggle to explain the frequency
of photons and matter in a coherent manner using natural physics. This
paper applies the cordus conjecture to develop a model for frequency of
the photon. The interpretation is that there really is a part of the photon
cordus that moves with a frequency. The working model is for a reciprocal
motion: the energy alternates between the two reactive ends across the
span of the cordus, and the hyff represent the observable electric field. This
cordus model for frequency readily explains polarisation and tunnelling,
and the concept is fundamental to other developments of the cordus
mechanics including the reflection and refraction of particuloids. The
implications are that frequency is not just an intrinsic variable, but a
physical effect within the photon. The cordus frequency is a fundamental
conceptual building-block in creating an integrated solution that unifies
wave and particle behaviour. It is a powerful concept that is coherent
across many other phenomena too, including matter particuloids and it
contributes subsequently to the cordus model for granular fields.
Keywords: particle; wave; frequency; internal variable; electric field;
tunnel; hyff; transmissivity; opacity; electron
Revision 2.10 Minor Edits, added references
Document: Pons_Cordus_2.1Frequency_E2.10.75.doc
1
Introduction
Frequency is an important concept in wave theory, optics, and quantum
mechanics. However those theories struggle to explain frequency in
physical terms.
From the wave theory (WT) perspective, the frequency of light is the
oscillation of the electric and magnetic fields. However this is not entirely
satisfactory as it still does not explain the origins of those fields, nor
explain why the fields reverse polarity. The conventional answer is that
light is nothing more than a self-propagating field disturbance, but that is
arguably only a trite answer. There is a circular reasoning at work that
suppresses the question of ‘what really is frequency?’
Quantum mechanics (QM) does not help either. It perceives the world
ambivalently, either as point particles or spread out in probabilistic wave25
Please address correspondence to Dr Dirk Pons, University of Canterbury,
Christchurch, New Zealand. Copyright D Pons 2011.
123
Frequency
functions. Properties like frequency, spin, and momentum are all
acknowledged, but are simply demoted to being intrinsic variables, i.e.
assumed not to correspond to any real geometry or internal functionality.
Usually Bell’s Theorem is interpreted as meaning there cannot be any
internal variables anyway. So QM does not get us any closer in
understanding what frequency might be, because it uses a denial
reasoning of its own to simply avoid the question.
As Loius de Broglie stated, 'a purely corpuscular theory does not contain
any element permitting the definition of a frequency'. Consequently his
insight was that 'a periodicity had also to be assigned to them
[electrons]'[1]. This approach fixed the problem in that it provided a
mechanism to mathematically link quantum mechanics and wave theory,
and that proved to be very successful for the advancement of the field.
Nonetheless frequency was merely 'assigned' to the particle. There was no
description, and there still is not, as to what that frequency corresponded.
Thus there is an important fundamental question to answer, 'What
constitutes frequency of a particle?' In general physics has given up on this
problem, and instead pushed it aside by dismissing frequency as an
'intrinsic', but non-physical, variable. The machinery of quantum
mechanics has moved on, and no longer needs to know how frequency
arises, because the mathematics works just fine without that
understanding. Nonetheless, the question remains, however obscure it
may have become. Surprisingly, and against all imaginable expectations,
the answering of the frequency question leads to the resolution of waveparticle duality and to a proposed deeper mechanics that underlies both
Wave theory and Quantum mechanics, as this paper shows.
This paper develops a novel model of the underlying mechanism for
frequency of the photon, based on the cordus conjecture [2]. Frequency is
conjectured to be linked to the dynamic internal states of the photon, and
the physical internal structure of the photon, and by implication all
particles, is proposed. Photon tunnelling is also explained along the way.
Companion papers show how the Cordus concept [2] with this frequency
model, also explains conventional optical effects of reflection [3] and
refraction [4]. This is worth doing since particle solutions have otherwise
fared poorly at explaining wave behaviour in a coherent manner using
natural physics. The outcome of this work is a set of basic underlying
principles of the proposed cordus mechanics. Ultimately this results in a
cordus model that resolves wave-particle duality [5]: the present paper
provides the ground-work for this.
Cordus Background
The concept of a cordus is that a photon consists not of a point but of two
reactive ends (RE) connected together with a fibril. The Res emit hyff
(hyperfine fibrils), which are lines of electrostatic force. The companion
paper 'Cordus conjecture' [2], describes the background to this idea,
124
Frequency
applies it to path dilemmas in the double-slit device and Mach-Zehnder
interferometer [6], and uses it to explain fringes [7]. It is shown that the
Cordus conjecture is conceptually able to resolve wave-particle duality.
Method
The approach taken is a continuation of that described in the companion
paper ‘Cordus conjecture’, and not detailed here. Briefly, it involves
reverse-engineering the system: it uses logic, conjecture and intuition to
build on the existing cordus model, thereby postulating a set of
mechanisms that can plausibly explain the known system-behaviour.
Specifically, to postulate internal variables for the photon sufficient to
explain optic effects. It is like trying to work out the contents of a black
box by observing its outputs in different situations, and synthesising a
working-model that is sufficient to explain as many of the situations as
possible.
Results
This is a design way of thinking, being very different to the conventional
mathematical analytic approaches, and the outcome is likewise more
qualitative than quantitative. Thus we term the results a conceptual
solution. Being conceptual means that the broad principles are described,
within which a whole class of solutions are possible. Where possible we
single out the most promising of these specific solutions and term it the
working model. Along the way we note the underlying assumptions as a
series of lemmas. These we do not attempt to prove: they are simply to
make the premises explicit so that they can be evaluated later. The
lemmas make up the central strand through the three papers.
The results follow, starting with some basic preliminary premises on
transparency and opacity, then moving on to develop a model of how
frequency arises within the photon, followed by application to the basic
optical phenomena of reflection and refraction.
2
Cordus Transparency and Opacity
In our daily experience we take for granted that light goes through some
matter, but not others. Why is glass transparent while metals are not?
More importantly, why is diamond transparent while graphite is not? As
the latter question shows, even materials with the same chemical
composition can have different optical properties. Why should light even
be able to pass through solid matter at all?
The explanation up to here is that the photon-cordus is energised at a
frequency (ref. ‘Cordus conjecture’ [2]), and only interacts with material
when energised. However the mechanism for frequency has not been
elaborated until now. Those concepts are now further developed and
extended to provide an explanation for transmissivity. We developed
some new ideas about frequency, and document them as a set of lemmas.
125
Frequency
Lemma O.1
Opacity
Electron interaction determines Transparency and
This lemma puts forward a set of assumptions for how the photon can
transmit through matter.
O.1.1 Electron arrangements, including bonds, determine optical
properties of a material more than nuclear configuration.
O.1.2 Cordus hyff interact with electrons in the substrate material.
O.1.2.1
The difference between transparency and opacity is
whether the interaction is reversible.
O.1.2.2
We differentiate between stiff and compliant electron
structures, corresponding to reversible and irreversible
behaviour respectively, or elastic and inelastic interactions
resp., and ultimately absorbance for the latter.
O.1.3 Stiff and compliant electron structures engage with the hyff force
lines.
O.1.3.1
A reversible interaction occurs when the force is elastically
recoiled (the energy is returned), and this corresponds to a
stiff electron structure. In such cases the electron engages
with the hyff energy but returns it, hence Transparency.
This corresponds to passing observation: the cordus is not
collapsed.
O.1.3.2
If the electrons are able to change energy level or
plastically displace (incl. vibration, phonons, and
plasmons), then this is a compliant electron structure.
Such electrons absorb the energy (absorption is described
later) and collapse the cordus, hence an Opaque material.
This corresponds to intrusive observation.
O.1.4 In transmission through a transparent material, the reactive ends
of the Cordus take time to interact with the material, and this
causes a delay in the respective reactive end. Note that the two
REs may be in different materials and therefore have different
delays. The delay appears as slower speed.
O.1.5 Material variables: Material properties, particularly electron
arrangements, determine reactivity of the material to the photon.
These electron arrangements have their own natural frequencies
and therefore the material properties vary with the frequency of
the photon.26
Transparency
With Lemma 8, transparency exists when the hyff interaction is elastic. The
hyff of the reactive end interact with electrons in the material, but are not
26
Later in the series, (ref. ‘Cordus in extremis’) a mechanism is given
whereby electrons have different frequencies depending on the bonds they are in,
see the Cordus Time and the Level-of-Assembly lemmas.8.
Pons, D.J., Pons,
Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011) Gravitation, Mass and Time.
Cordus in extremis: Part 4.3 viXra 1104.0029, 1-14 DOI: vixra.org/abs/1104.0029.
126
Frequency
absorbed, though they are delayed in the process. Why should such a
delay even exist? Why not instant? We suggest it is because of the
electron’s mass, and any movement of mass requires velocity and
acceleration, and hence time. Thus surface plasmons are electrons that
move in response to input photons. To put it another way, the change in
momentum p=mv of the electron requires a force operating for a period of
time.
Cordus also accommodates the frequency dependence: a material may be
transparent to photons of one frequency, but opaque at another. The
Cordus explanation is that the interaction between cordus and electron
requires a degree of compatibility of frequency. High-energy photons
cannot easily be absorbed by electrons, and so pass through. Conversely,
low-energy photons may be dormant at the time of contact and therefore
tunnel through the material (see below).
The Cordus perspective is that atomic structure, particularly and almost
exclusively electrons and their bonds,
determines opacity and
transmissivity. A specific mechanism for absorption is proposed elsewhere
(ref. ‘Cordus matter’).
3
Cordus Frequency
The observed external behaviour is that light appears to be a electric field
that varies sinusoidally in strength. From the Cordus perspective, the
reactive ends (REs) are the proposed internal structure that creates this
effect, and at this point we need to create a working-model of how the
mechanism might operate. This is necessary in preparation for explaining
reflection and refraction phenomena.
Lemma O.2
Cordus Frequency
The reactive ends of the cordus change with the frequency. Up to here we
have only defined two states: energised and dormant. With this lemma we
set out a set of further assumptions to create a working model about the
frequency behaviour of reactive ends. See also Figure 1.
O.2.1 The electric field of light is the external manifestation of the hyff.
This implies certain features of the cordus frequency mechanism:
O.2.1.1
The electric field does not represent the state of the
photon, nor even the free-body diagram for the reactiveend. Instead it shows the direction and strength of force
on a small test-charge placed near the photon’s locus. The
electric field therefore indicates how the RE is interacting
with charged matter.
O.2.1.2
The direction of the electric field is the same whichever
side of the locus the test-charge is placed.
O.2.1.3
In turn this implies that the forces on the two reactive
ends, a1 and a2, of the photon must be in a consistent
127
Frequency
direction: the direction of hyff force must be preserved
across the span.
O.2.1.4
In turn this implies that the REs must be in opposite
frequency states. See also O.2.3.
O.2.2 The hyff are transient, and manifest externally as the electric field.
O.2.2.1
The hyff are dynamic and grow outwards and then retreat,
at the frequency of the photon.
O.2.2.2
The outward growth of the hyff correspond to say negative
electric field, and retreating to positive field.
O.2.3
We identify four frequency states of the hyff for any one
reactive end:
C- (outward growth of hyff),
C^ (maximum extent),
C+ (hyff retraction),
Co (dormant).
There is a smooth change between these: they are not
discrete states.
O.2.4 The hyff exert forces between the reactive-end and the material in
the medium.
O.2.4.1
The strength of the hyff varies between frequency states.
Whether or not the variation is linear or sinusoidal is not
determined here.
O.2.4.2
Hyff forces are strongest at closer range. Thus range and
strength of hyff are inversely related.
O.2.5 The behaviour of the reactive end depends on its frequency state
at the time it encounters a medium or the surface of a second
medium. The current working model follows.
O.2.6
Assume: C- results in the RE being repulsed by the bulk
(tends to move medially towards the cordus centre-line in
many cases), with the force being determined by the
strength (inverse of range) of the C- hyff and material
properties (e.g. refractive index).
O.2.7
C+ results in the reactive end being attracted into the bulk
(tends to move laterally away from the cordus centre-line
in many cases).
O.2.8
The net force on a RE is the cumulative exposure over the
preceding period. Thus the behaviour in the other states is
influenced by the timing of the C- and C+ states alongside
and this introduces an element of variability to the
outcome.
O.2.9
A dormant reactive-end tunnels (embeds) into the
material, or across the interface, when it is in the Co state.
O.2.9.1
This means that it continues in a straight line, and
its future locus is determined by the next
frequency state.
O.2.9.2
Tunnelling occurs regardless of the material
properties (stiff or compliant) and without the
photon reacting to the material.
128
Frequency
O.2.9.3
O.2.9.4
O.2.10
O.2.10.1.
O.2.10.2
The reactive end can only tunnel through one
dermis (defined below). Thereafter it becomes
reactive with the next frequency cycle, and its fate
is determined by its new frequency state and the
material properties.
If a reflective layer is thin enough, a dormant RE
might only re-energise once it is through the layer,
in which case it is not reflected. The thickness of
the layer is therefore important, as is the
frequency of the photon (wavelength).
Hyff are entirely in the (rt) plane (current working model),
see Figure 1.
It does not make sense to have hyff in the axial
direction (a), given that both the hyff and the
cordus would both be moving at speed c.
Whether the hyff are a flat disk or only a single
filament is unspecified. The current workingmodel is illustrated with only a single hyff in the rplane. This is consistent with the observed
polarisation of the electric field.
If desired for ease of understanding, assign approximate physical
significance to the frequency states: C- is somewhat like an electron, C+ a
positron. They are transient electric fields, but not necessarily a full unit
charge.27 Depending on the frequency model, this gives two or four
change-overs (strokes) per cycle, see Causa 2. The current working-model
is for four strokes.
Causa 2
Working model for frequency
Many variants are possible for how the hyff, electric field, and frequency
operate. The main variables are the number of events (‘strokes’) inside the
photon that are ascribed to one frequency cycle, the relative states of the
reactive-ends (including whether one or both reactive ends are active at
the same time), and the behaviour (including force & extent) of the hyff.
Any model of frequency has to fit the observed electric field of the photon.
Thus we have reverse-engineered a proposed model for frequency, based
on the above lemmas. This working model is shown in Figure1.
The main features of the model are that the C- hyff are outwardpropagating (simply a sign convention), and their interaction with the
surrounding medium is one of repulsion (O.2.6). To the extent to which
the material is able to offer recoil, i.e. higher refractive index, the C- hyff
bends the locus of that reactive end away from the material with higher
refractive index. The C+ hyff have the opposite effect (O.2.7).
27
Later work on quarks and the internal structure of the proton implies
that the photon with its single hyff might have a single +- 1/3 electric charge (ref.
‘Cordus in extremis’). However the exact charge is not relevant at this point.
129
Frequency
Figure 1: Working model for frequency behaviour of reactive ends.
Journey through matter
The two effects constantly counter each other, partially or completely
undoing the course-corrections made by the previous state. When the
cordus is embedded in a homogeneous material then the reactive ends
move in a sinusoidal lateral wriggle, according to this model. The model
predicts the hyff forces on the cordus will put the reactive-ends into
parallel sinusoidal loci. There is a constant interaction between the
momentum of the reactive-end along its current locus, and the hyff forces
deflecting it into a new path. Thus the photon does not travel in a straight
line but weaves from side to side as it interacts with the medium. Hence
the lateral wriggle causes the speed of propagation of light in a material to
be slower than in a vacuum. This also explains why greater density of the
medium causes slower speed of light.28
The locus of the a1 and a2 reactive-ends is shown in Figure 1. The amount
of deviation depends on how forcefully the medium interacts with the
hyff, i.e. the refractive index. This provides a qualitative explanation for
why the speed of light is slower in denser media: it has to travel a longer
path.
28
However this does not explain why the speed of light in a vacuum is
finite. That explanation is given by the Fabric-of-the-Universe concept in ‘Cordus
in extremis’ 9. Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.
(2011) Fabric of the universe. Cordus in extremis: Part 4.2 viXra 1104.0028, 1-8
DOI: vixra.org/abs/1104.0028..
130
Frequency
When the cordus encounters two different materials then the size of the
effect depends on location relative to the two media, and this means that
the corrective forces do not cancel each other, so consequently the
photon takes a bent path. Thus the behaviour of the C- and C+ hyff is
important in the explanation of reflection and refraction effects, as shown
in part 2.2.
The other main feature of the current working model is that the hyff at the
opposite reactive-end act in the same direction, and this makes them the
complementary frequency state: e.g. when a1 is in C- state, a2 will be C+.
Consequently the dormant phase is only momentary, unlike in some of
the other C.2 models. This concept is important later in the introduction of
a fundamental interaction called complementary frequency state
synchronisation (CoFS), which in turn is proposed as the explanation of
photon entanglement, the Pauli exclusion principle, and strong force,
among other effects (ref. ‘Cordus matter’, ‘Cordus in extremis’ [10]).
The current working model is for reactive ends that energise in turn at the
end of a cordus, i.e. a reciprocating frequency model. At this point it is an
open question how the fibril sustains this reciprocation of energy.29
4
Tunnelling
This effect involves a photon occasionally going through a barrier (e.g. the
space between two glass prisms) instead of being reflected. The effect
requires a small gap, and is known to be dependent on frequency. It is
usually explained as a probability from the wave-equation, or the particle’s
evanescent wave leaking through an energy barrier (hence ‘evanescent
wave coupling’).
In the special case where there is a thin later n2, sandwiched between two
other media n1 and n3, then it is known that some photons will pass
through n2 apparently without being affected by it. Specifically, some
photons are not refracted in n2 but continue from n1 to n3 as if n2 did not
exist. This effect is known as tunnelling, and the term is applied to a
variety of situations where a particle appears not to noticing an
intervening barrier, e.g. tunnelling electron microscope.
Tunnelling, from the cordus perspective, is when a reactive end energises
too late for its hyff to respond to the change of media, so the RE goes right
on through into the next medium before it has time to re-energise. Or to
29
Spin is more easily conceptualised as roll rotation that indexes the fibril
o
in 180 increments. If the Cordus conjecture holds up and there arises a need to
explore deeper mechanisms in the fibril, then there may be value in remembering
that reciprocation is the outward functional behaviour of frequency, not
necessarily the internal mechanism.
131
Frequency
put it another way, the RE has a dormant phase during which it does not
react to matter but nonetheless moves forward.
The Cordus explanation is that the gap geometry (width and angle),
frequency, and polarisation are such that (a) the REs both pass through
the reflective layer without reacting (both dormant in turn, from L.7.3.2),
and (b) there is no imbalance in the number of frequency cycles
encountered by the REs in the media, and therefore no pitching moment
and hence no refraction.
High-energy photons, e.g. X-rays, do not reflect easily but tend to pass
through material. The Cordus explanation is that their frequency is too
high for the electrons to engage with, rather than a tunnelling effect. On
the other hand, low energy photons, e.g. radio-waves, can have
appreciable dormant periods in which they don't react to the change in
medium, so they too can tunnel.
5
Conclusions
The concept of ‘frequency’ is a core theoretical construct within wave
theory, optics, and quantum mechanics. Yet strangely none of these
theories are able to explain frequency in physical terms. ‘Frequency’ is
only a disembodied intrinsic property of the wave or photon. In contrast
Cordus offers a physically coherent interpretation for frequency.
This interpretation is that there really is a part of the photon cordus that
moves with a frequency, The working model is for a reciprocal motion: the
energy alternates between the reactive ends across the span. In this way
it is proposed that the photon has internal variables that create the output
that we observe as frequency. This is a type of ‘hidden-variable’ solution,
and while the conventional interpretation of QM is that such solutions are
expressly prohibited by Bell’s Theorem, that theorem is refuted in a
companion paper (ref. ‘Cordus matter’) [11]. The implications are that
frequency is not just an intrinsic variable, but a physical effect within the
photon.
This cordus model readily explains several other optical variables:
polarisation is alignment of the cordus; and tunnelling is travelling through
material when unenergised. The cordus frequency is important in
subsequent explanations of reflection [3] and refraction [4]. As such, it is a
fundamental concept in creating the integrated solution that unifies wave
and particle behaviour [5].
It is a powerful concept as it is coherent across many other phenomena
too. For example the cordus frequency model developed here in an optical
context is also applicable to frequency in the context of particuloids of
matter (ref. ‘Cordus matter’) and permits a re-conceptualisation of de
132
Frequency
Broglie frequency, electron orbitals, atomic structure, proton structure,
and fields.
References
1.
de Broglie, L.: The wave nature of the electron, in Nobel Lecture.
Nobel
Prize
in
Physics.
http://nobelprize.org/nobel_prizes/physics/laureates/1929/brogli
e-lecture.pdf (1929)
2.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus Conjecture: Part 1.1 Quis es tu photon? .
http://vixra.org/abs/1104.0016 (2011)
3.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus optics: Part 2.2 Reflection. http://vixra.org/abs/1104.0020
(2011)
4.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus optics: Part 2.3 Refraction. http://vixra.org/abs/1104.0021
(2011)
5.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: WaveParticle
Duality:
a
Proposed
Resolution.
http://vixra.org/abs/1106.0027 (2011)
6.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus
Conjecture:
Part
1.2
Quo
vadis,
photon?
http://vixra.org/abs/1104.0017 (2011)
7.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus Conjecture: Part 1.3 Explanation of fringes.
http://vixra.org/abs/1104.0018 (2011)
8.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus in extremis: Part 4.3 Gravitation, Mass and Time.
http://vixra.org/abs/1104.0029 (2011)
9.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus in extremis: Part 4.2 Fabric of the universe.
http://vixra.org/abs/1104.0028 (2011)
10.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus
matter:
Part
3.2
Matter
particuloids.
http://vixra.org/abs/1104.0023 (2011)
11.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus
matter:
Part
3.1
Wider
Locality.
http://vixra.org/abs/1104.0022 (2011)
133
13
4
Cordus Reflection
Cordus optics: Part 2.2
Pons, D.J. , 30 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
Optical effects such as reflection and refraction are conventionally best
described by Electromagnetic Wave theory, at least when they involve
beams of light. However that theory does not explain why single photons
should also show such behaviour. This paper shows that optical effects can
also be explained from a cordus particuloid perspective. Several principles
are proposed for the interaction of a cordus photon with an optical surface,
and these are used to explain reflection and subsequently refraction. The
formula for critical angle is derived from a particuloid basis. The cordus and
wave theory perspectives are compared and contrasted. The significance
of this work is that the cordus mechanics explains the reflection and
refraction behaviour of both single photons as well as beams of light, so it
is a more universal explanation.
Keywords: electromagnetic wave theory; reflection; refraction;
Revision 2.10 Minor Edits
Document: Pons_Cordus_2.2Reflection_E2.11.75.doc
1
Introduction
While Electromagnetic Wave theory (WT) adequately describes optical
effects involving beams of light, the explanation of single-photon
behaviour is fundamentally problematic. This paper shows that optical
effects can also be explained as the interaction of a single cordus photon
with the optical surface. Thus Wave theory is not the only way of
conceptualising effects like reflection and refraction.
Background
Wave theory takes the perspective that a beam of light is not so much a
stream of photons, as a continuously existing electromagnetic wave,
comprising an electric field and a magnetic field. This is a powerful
method, and well-suited to the analysis of optical effects, at least of whole
light-beams. Many of the effects in optical devices can be described as
interference between the electromagnetic fields of the incoming and exit
beams. Notice however that the underlying premise of WT is that both
incoming and exit beams exist at the same time, i.e. the fields are
temporally enduring. This becomes a problematic assumption when
considering how an individual photon traverses the device, because a
point particle cannot be in two places at once.
30
Please address correspondence to Dr Dirk Pons, University of
Canterbury, Christchurch, New Zealand. Copyright D Pons 2011.
135
Reflection
The problem may be partly solvable in Quantum mechanics (QM) by
assuming superposition and that the particle is nothing more than a
probability wave-function. Though this solves the mathematical part, it
does little to add explanatory value because of its abstraction and lack of
identifiable natural mechanics.
Wave-particle duality assumes that both WT and QM are needed to model
the behaviour of light: neither is sufficient on its own. However, even
while the combination of theories does cover most of the applications, the
explanatory power is discontinuous. Some explanations rely on QM and
others on WT, and there is no overall integration. It is apparent that
neither WT nor QM fully describe reality, and this raises the question of
whether there might be a deeper or more-integrative mechanics that
does.
What is needed is a mechanics that accommodates both single particles
and beams of light, rather than the separate mechanics at present. The
more problematic area is with the single photons, so the problem may be
reformulated thus: is there a mechanics that shows how a single photon
reflects and refracts, and uses natural mechanics in a coherent manner?
The Cordus conjecture has already shown (ref. ‘Cordus conjecture’) that a
particular internal structure for the photon, namely a cordus, is
conceptually able to explain the photon path-dilemmas in the double slit
device, as well as the fringes that build up from multiple single photons. In
that sense the cordus solution already resolves one important part of
wave-particle duality. However the Cordus conjecture cannot claim to
offer a coherent solution until it is also able to explain conventional
effects, like optical reflection and refraction. This present bracket of
papers shows how the Cordus concept meets that test and is applicable to
explaining conventional optical effects from a particuloid perspective.
Cordus Background
The concept of a cordus is that a photon consists not of a point but of two
reactive ends (RE) connected together with a fibril. The REs emit hyff
(hyperfine fibrils), which are lines of electrostatic force. The companion
paper 'Cordus conjecture', describes the background to this idea, applies it
to path dilemmas in the double-slit device and Mach-Zehnder
interferometer, and uses it to explain fringes.
The first part develops a novel model of the dynamic internal variables
that cause the behaviour we see as ‘frequency’. The second, which is this
paper, uses this to explain the interaction of light with surfaces: reflection.
Mechanisms are provided for reflection, and the critical angle for total
internal reflection is derived. In the third part refraction is explained and
Snell's Law derived.
13
Reflection
The method is described in the previous papers, and the lemmas included
here are a continuation of the previous numbering. The results follow,
starting with some general premises on how the frequency interacts with
the optical surface, and then extending to determine the specific
mechanics of reflection and refraction.
2
Cordus effects at surface interfaces
Reflection and refraction are effects that occur when the photon
encounters the interface between two media. The following assumptions
are made about the behaviour of hyff in these situations. These form a set
of basic principles that are subsequently applied to more specific reflection
and refraction cases.
Lemma O.3
O.3.1
O.3.2
O.3.3
O.3.5
O.3.5.1
O.3.5.2
O.3.5.3
O.3.5.4
O.3.5.5
O.3.5.6
O.3.9
O.3.9.1
O.3.9.2
O.3.10
Surface interaction
The path taken by a reactive-end depends on (1) the frequency
state (see O.2) of the reactive end at the time it contacts the
material, and (2) the material properties.
A reactive-end can therefore take one of many loci as it
approaches a surface, depending on its frequency state (primarily
the strength of C+, C-).
The extreme loci for the reactive-end are termed the C+ and Cextremes. All other loci are within the envelope of those two.
Assume that the analysis of the encounter of a reactive-end with a
surface is sufficiently characterised by the C+ and C- extremes.
The path of the reactive-end at the surface is not a straight line
but rather a bent locus under the influence of the hyff forces.
For reflection the particle does not necessarily touch the
surface.
The hyff may repel before or after nominal contact is
made.
For analysis purposes the effective locus may be
considered a series of straight lines.
Hyff detect the change in medium before the reactive-end
physically reaches that point.
The detection range of hyff is limited. There is effectively a
dermis (skin layer), one on each side of the surface. We
term these the cisdermis (near-side skin) and transdermis
(far-side skin).
Bending of the locus occurs in both derma.
The reactive-end has momentum.
Consequently its current trajectory is determined by its
past locus and the current C+ or C- hyff forces.
If the reactive-end penetrates beyond the transdermis,
then it cannot be recovered back to the first medium.
Net force over the hyff determines the resulting force on
the RE.
13
Reflection
O.3.10.1
The hyff may span different materials. Hyff that
partly straddle a boundary surface will have net
forces dependent on the electron-interaction
properties of the various materials.
O.3.10.2
The REs of a cordus may be in different materials.
O.3.10.3
A RE that re-energises within the bulk of a
material and beyond the dermis has equal hyff
forces around it and hence no net force to bend its
path. However it still has momentum and will
wriggle about the mean.
O.3.11 Forces on a RE, or displacement, cause angular deflections of the
path of that RE only.
O.3.12 Forces collapse when the hyff collapse. The RE is then free to
continue on its path, unless the whole cordus has collapsed.
O.3.13 Geometric variables: The actual hyff frequency state and
strength at the time of meeting the material, and the orientation
of the interface plane of the material, determine the outcome. It
is the behaviour of the electrons in the plane, in response to the
hyff in their (rt) plane, that is important.
O.3.14 Optical activities of materials, namely reflection, transmission,
and absorption, (RTA), depend on the frequency state when the
reactive end strikes the material. Given that multiple cordi strike
the material, each in different frequency states, one material
may do multiple optical activities.
O.3.14.1
RTo: A transparent material (e.g. light on glass)
reflects on one frequency state and not on
another.
O.3.14.2
Roo: An opaque reflective material (e.g. light on
chrome) reflects on all frequency states.
O.3.14.3
ooA: An opaque non-reflective material (e.g. light
on black paint) absorbs all states.
O.3.14.4
It is assumed that the different optical properties
of materials arise from the different mobility of
the electrons (plasmons).
O.3.15 The electron has a span much less than that of an optical wavelength photon, and higher frequency, and therefore greater
mobility other than the hindrance of its mass.
Note the implication of O.3.15 is that electrons are much ‘smaller’ than a
photon, and can move around in response to the relatively large and
slower-frequency photon.
3
Cordus model for Reflection
3.1
Reflection in general
From the perspective of Wave theory, reflection is caused by the mirror
surface absorbing and re-emitting its own EM waves. Depending on the
13
Reflection
perspective taken, these interfere with each other or with the incident
wave to produce the reflected wave. The mathematics of wave theory
accurately quantifies the phenomenon, though its qualitative explanations
are not intuitive.
Cordus model for reflection
The Cordus explanation is that both reactive-ends of the cordus separately
reflect off the surface as their hyff interact elastically (lossless) with the
substrate. The frequency model within Cordus states that the reactive
ends change their state. Thus in some ways the hyff are the reactive ends.
Given the dynamic nature of the hyff, the state of the reactive end at the
time it contacts the surface will determine the path taken by that reactive
end.
Assuming passage into a denser material, as the RE approaches a reflective
surface, its hyff already detect the surface plane some distance before
nominal contact, while in the cisdermis. What happens next depends on
the frequency state:
If the hyff are in the C- frequency state, then they repel the RE
from the electrical plane at the surface. This bends the locus back
into the first medium.
Hyff that are in the C+ state draw the RE towards the second
medium.
The frequency state may change again before the RE has completed the
traverse, in which case the locus may be bent one way and then the other
before the outcome is determined.
Transitional locus at reflection
The Cordus models of reflection suggest that the photon does not reflect
at a single point, but rather at its two reactive-ends. Furthermore, the
precise locus taken by a reactive end depends on its frequency state at the
time it approaches the surface, and the nature of the surface. Thus the
reflection is not a sharp instant change in direction occurring at the
surface, but rather a curved transition. Depending on the situation, that
curve might occur above the surface (cisdermis) or beneath it
(transdermis).
Consequently the centreline of the reflected cordus may be laterally offset
from the nominal: the photon is displaced sideways from where it should
be by simple optics. This effect is known for p-polarised light at total
internal reflection, and is termed the Goos–Hänchen effect. The Cordus
explanation is that the actual reflection occurs in the transdermis in this
situation, and Figure 1 provides a graphical explanation of how the offset
arises.
13
Reflection
P
Co ho
o to
sy rdin n’s
st at
em e
t
a2
r
Reflection occurs
before the surface
is reached
Centreline of
cordus is coincident with
nominal reflection
line
a
a1
n1
cisdermis
n2
Nominal reflection
centreline
(denser)
(denser)
Nominal reflection
centreline
a2
a1
n1
n2
(a) Reflection off a
denser material
(n2>n1)
transdermis
(b) Internal
reflection off a less
dense material
(n2<n1)
Centre of cordus
is offset from
nominal reflection
line
cisdermis
transdermis
Reflection occurs
beyond the
surface as the
denser material
pulls the reactiveend back
Figure 1: Reflection occurs as a curved transition some distance off the
surface (a), not an abrupt change at the precise surface. In the case of
internal reflection (b), the transition may occur in the second medium and
result in the centre of the cordus being offset from the nominal.
This figure only shows the mean loci for the reactive-ends: not shown are
the sinusoidal wriggles that are superimposed. These wriggles add further
braided variability of path (within limits defined by the C+ and Cextremes). This is a simple representation, nonetheless it introduces the
concept that refection is not a simple point bouncing off a surface, but
rather a complex ranged interaction (see also the later Principle of Wider
Locality, in ‘Cordus Matter’).
14
Reflection
Steep incidence
If the cordus strikes the surface nearly perpendicularly (low q1) then the
hyff plane RT is parallel to the frontal plane of the material. The alignment
of the planes maximises the potential for hyff-electron interaction. For RTo
material e.g. chrome, the electrons are able to move about to counter all
the frequency states of the photon, so the reactive ends are reflected. The
dormant phases tunnel through and are absorbed, hence the imperfect
reflection.
Shallow incidence
At shallow grazing incidence (high angle of incidence) the reactive ends of
the cordus have many opportunities to engage with the plane of electrons
that make up the surface, and even materials with low mobility of surface
electrons can support reflection.
Ridged mirrors
If the reflecting surface is very small, then the plane for the hyff to engage
with is small, and normal specular reflection and refraction will be
disrupted. Thus ridged mirrors are used to enhance the reflection of
incident atoms. The tentative cordus explanation is that the valleys
between the ridges provide a second opportunity for reflection for those
REs that tunnelled through the plateau on the ridge.
Phase changes at reflection
The phase of reflected light may be the same or opposite to the incident
light, depending on the ratio of refractive indices. For light reflecting off a
denser material (higher refractive index), e.g. air to glass, then the polarity
is inverted. For reflection off a less dense material, e.g. internal reflection
glass to air, then the polarity stays the same. Why?
The external electric field represents the hyff strength, in cordus. So
reversal of the electric field at reflection corresponds to inversion of hyff but this only occurs for passage to a denser medium (higher n2). Phase is
not simply a planar effect, or a mirroring about the interface, since the
side from which the light comes determines the phase-change.
The cordus explanation follows. We note in passing that phase changes are
an interesting effect because cordus interprets them as showing the
working of deeper mechanisms, which are useful in understanding other
effects.
Reflection involves an interaction between the cordus and the material
through the hyff or EM field, and this delays the renewal of the reactive
end, but only when the denser material is in the transdermis, e.g. air to
glass. This delay corresponds to the λ/2 phase delay in the Wave Theory.
There is no delay in the glass to air case, because the cisdermis is the
denser material and the delay has already occurred (in the form of the
refractive index).
14
Reflection
Postscript: Many concepts and papers later, we find another lemma that
identifies a phase effect, namely annihilation between matter and
antimatter [12]:
Ma.2.2
In this model we define a suitable complementary phase for the
annihilation of electron and antielectron as opposite, i.e. when the
reactive end of the one particuloid is active while that of the other
particuloid is dormant, i.e. 180 degree phase offset. It may take
frequency cycles to accomplish this, hence time.
The implications for the reflection case are that the incoming photon takes
time to interact with the electrons. There is a possibility that the photon
could be absorbed by the mobile electron and then spat out again. If so,
this would be expected to also introduce, on top of the phase inversion, a
brief delay of half a frequency cycle of the electron.
3.2
Critical angle for total internal reflection
Internal reflection is when light passes from a region of high refractive
index n1 to lower n2, e.g. glass to air. Usually some of the light is
transmitted and other reflected back to material 1. The critical angle is
where total internal reflection occurs, i.e. no transmission, and is known
to be: Sin(θc) = n2/n1. Noting that n = c/v and v = f λ where f is conserved
but v and λ change, then: Sin(θc) = λ1/ λ2
The angle is measured off the normal to the surface. At steeper angles (θ1
less than θc) some light reflects and some transmits through. As θ1
increases the refracted ray bends closer to the interface and eventually at
θc the ray is on the boundary. As θ1 increases further refraction ceases
and all light is internally reflected. The usual explanation is that no
refracted ray is possible since it would violate the refraction law. However
that does not explain how the law works.
Also, there is something strange happening from a system perspective.
When total internal reflection occurs, why should properties n2 (or λ2) be
required? Since the light stays on the surface and does not go into the bulk
of medium 2, why should the property n2 affect the phenomenon?
The Cordus explanation is that at the critical angle θc the reactive end a1 is
inserted into in the faster material n2 at t=0, and therefore moves forward
a distance λ2/2, see Figure 2. This motion is parallel to the surface because
this is the angle of refraction. By comparison at the same time reactive end
a2 continues to travel distance λ1 in the slower medium, before it later
also enters the faster medium, at t=1/2 of a frequency cycle. RE a1 is thus
accelerated by the sudden freedom of being in the faster medium. The
angle θc is steep enough to push the RE out of the slower medium, but
only steep enough to place it at the boundary. A moment later the second
RE is likewise positioned at the boundary.
14
Reflection
Figure 2: Geometry of the cordus at the critical angle θc
The important points are:
Over the period from t=0 to t=1/2 cycles, a1 moves λ2/2 whereas
a2 moves λ1/2, because they are in different media.
The angle θc is such that there is only a half-cycle of frequency
involved.
The angle at which the above two conditions is met is apparent from
inspection of the geometry in the figure, Sin(θc) = λ1/ λ2, and this is the
same as the critical angle derived from optics.
The figure illustrates the neat case where a1 is energised precisely at the
boundary. In reality the timing is not always so neat, nonetheless the
process is believed to work with all incoming frequency states and
polarisations because the process itself is gradual, and providing that the
range of the hyff is large enough.
The result is a cordus that exits in n2 along the boundary of the two media.
The fact that this occurs at all, regardless of the incident polarisation,
suggests that the hyff are all in n2, otherwise there would be path
deflection. This in turn suggests that the hyff are not spherical.
14
Reflection
Total internal reflection
Why does total internal reflection occur at all? Why should it be that ALL
the photons are reflected? Why is the effect so absolute? The cordus
interpretation is that for shallow grazing incidence, i.e. θ1 > θc then there is
more than one hyff cycle that engages with the interface (at critical angle
θc there is only one hyff cycle), and therefore certainty that the RE will
detect the interface and reflect off it.
But why does the RE always reflect, regardless of the frequency state?
Why does it not consistently refract? The explanation is that the attraction
to the cis and transdermis sides is not symmetrical, but favours an
interaction with the denser material, see O.4.4 part 2.3. For steeper
incidence, i.e. θ1 < θc, whether the hyff detect the interface depends on
their frequency state (phase) at the time of approach. So some reflect and
others go through (and onwards to refract).
External reflection
Why is total reflection possible off internal surfaces, but not off external?
Why is the effect not symmetrical? This is addressed in O.4.7 (part 2.3).
Why is some reflection possible, off almost any surface, with a sufficiently
shallow incidence (large θ1)? The cordus explanation is that this situation
gives the photon cordus plenty of opportunity to be in an energised state
but with a slow normal closing velocity on the surface (normal
momentum). Therefore the surface is able to repel the occasional cordus
that is at peak energised state at closest proximity, even if the surface is
otherwise not a good reflector.
4
Discussion
While the usual explanation for optical effects such as reflection is wave
theory, this paper shows that it is possible to explain the effects using
cordus particuloids, and simple mechanics. Reflection emerges, in the
cordus perspective, as an effect that occurs at interface surfaces, due to
the interaction of cordus hyff with the electrons, particularly the surface
plasmons. In this model, the surface plasmons are able to dynamically
adjust to the hyff of the approaching photon, and therefore do not provide
resistance in the plane of the interface (horizontal direction in the
diagrams here). However the situation is very different in the normal
direction, since the electrons have limited to no mobility. Consequently
the material does interact with the photon in the vertical direction, and
this results in reflection. Or refraction, depending on the frequency state
at the time.
This model is significant because it shows that the cordus structure of the
photon is conceptually valid over a larger set of effects than simply waveparticle
duality
in
the
double-slit
and
interferometers.
14
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
de Broglie, L., The wave nature of the electron, in Nobel Lecture. 1929,
Nobel Prize in Physics.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011) Quis es
tu photon? Cordus Conjecture: Part 1.1 viXra 1104.0016, 1-8 DOI:
vixra.org/pdf/1104.0016.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011)
Reflection. Cordus optics: Part 2.2 viXra 1104.0020, 1-10 DOI:
vixra.org/abs/1104.0020.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011)
Refraction. Cordus optics: Part 2.3 viXra 1104.0021, 1-11 DOI:
vixra.org/abs/1104.0021.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011) WaveParticle Duality: a Proposed Resolution. viXra 1106.0027, 1-18 DOI:
vixra.org/abs/1106.0027.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011) Quo
vadis, photon? Cordus Conjecture: Part 1.2 viXra 1104.0017, 1-22 DOI:
vixra.org/abs/1104.0017.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011)
Explanation of fringes. Cordus Conjecture: Part 1.3 viXra 1104.0018, 1-18
DOI: vixra.org/abs/1104.0018.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011)
Gravitation, Mass and Time. Cordus in extremis: Part 4.3 viXra 1104.0029,
1-14 DOI: vixra.org/abs/1104.0029.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011) Fabric
of the universe. Cordus in extremis: Part 4.2 viXra 1104.0028, 1-8 DOI:
vixra.org/abs/1104.0028.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011) Matter
particuloids. Cordus matter: Part 3.2 viXra 1104.0023, 1-12 DOI:
vixra.org/abs/1104.0023.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011) Wider
Locality. Cordus matter: Part 3.1 viXra 1104.0022, 1-7 DOI:
vixra.org/abs/1104.0022.
Pons, D.J. (2011) Annihilation mechanisms: Intermediate processes in the
conversion of electron and antielectron into photons viXra 1109.0047, 121 DOI: vixra.org/abs/1109.0047.
145
Reflection
146
Cordus Refraction
Cordus optics: Part 2.3
Pons, D.J. , 31 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
Explaining basic optical effects is not possible with classical particle
mechanics, and even with quantum mechanics it is not straight forward
and not particularly intuitive. The problem is much simpler when solved in
the cordus domain. This paper provides cordus explanations for Snell’s Law
and Brewster’s Angle, and quantitative derivations too. This is significant
because the cordus mechanics were derived for single photons, and
immediately generalise also to beams of light. Therefore cordus can
explain particle behaviour, fringes, and optical effects, using a single
coherent mechanics.
The cordus explanation does not need the
conventional concept of ‘interference’.
Keywords: electromagnetic wave theory; refraction; Snell’s Law; Brewster’s
angle;
Revision 2.10 Minor Edits
Document: Pons_Cordus_2.3Refraction_E2.10.74.doc
1
Introduction
Refraction in general
The bending of light as it enters an inclined boundary is usually explained
in optical wave theory as a change in the speed (phase velocity), such that
the wavelength changes but not the frequency. The angle of refraction θ2
in the second medium 2 is given by Snell's law: sinθ2 = v2/v1 .sinθ1 =
n1/n2.sinθ1 = λ2/λ1.sinθ1 where the angles are measured from the normal
to the surface, and v are the velocities in the two media. Thus the net
angular deflection [θδ = 90o -(θ1+θ2)] is not constant but depends on the
angle of incidence. The refracted ray may be partly polarised. At the same
time, some of the light may be reflected.
The refractive index n measures the speed relative to that of light in a
vacuum. Refractive index is usually linear, but may be non-linear for highintensity light. Refractive index increases approximately linearly with
density for glasses of similar chemical composition. Explanations vary for
how the change in speed occurs. The wave interpretation is that the
delay occurs because the electric field interacts with the electrons to
radiate a delayed wave, thereby forming the new but slower wave. Hence
the Huygens–Fresnel principle that each point on the wave propagates
31
Please address correspondence to Dr Dirk Pons, University of Canterbury,
Christchurch, New Zealand. Copyright D Pons 2011.
147
Refraction
new waves and these interfere. Surface waves of water also refract, and
provide a visual confirmation of the effect.
This paper explains refraction from the cordus perspective. The concept of
a cordus is that a photon consists not of a point but of two reactive ends
(RE) connected together with a fibril. The REs emit hyff (hyperfine fibrils),
which are lines of electrostatic force. The method is described in the
previous papers, and the lemmas included here are a continuation of the
previous numbering.
2
Cordus refraction
The cordus model for refraction uses the frequency lemma from the
earlier paper in the series, and elements of the reflection lemma. It also
requires additional assumptions as follow:
Lemma O.4
Refraction
O.4.1
From the cordus perspective, reflection results from the
interaction of the incoming photon with the electrons in the
surface plane, i.e. surface plasmons. In contrast, refraction is an
interaction with the bulk of the material. Furthermore, that
interaction starts to occur before the photon reaches the bulk
material , and it is that preliminary interaction that bends the
locus.
O.4.2 On approaching the interface (e.g. air to glass) the hyff probe
through both the cis- and trans-dermis. The RE therefore responds
to the upcoming medium before it physically reaches it (Principle
of Wider Locality, see ‘Cordus Matter’). That response varies
depending on the frequency state, and may be attractive or
repulsive.
O.4.2.1
In fact it will be both attractive and repulsive in turn, due
to the frequency effect.
O.4.2.2
See the dermis concept in O.3.5.5, part 2.2
O.4.3 The strength of the response is not constant but becomes stronger
with proximity to the interface.
O.4.4 The material with higher refractive index exerts the stronger
force.
O.4.5 The cumulative effect over several frequency cycles determines
the outcome.
O.4.5.1
Thus the precise frequency state of the RE as it
approaches the surface will the starting point of the
summation and therefore determine the overall outcome
attractive or repulsive result.
O.4.5.2
The immediately previous locus also affects the outcome,
i.e. momentum is involved, see O.3.9, part 2.2
O.4.5.3
The next photon has a different frequency state and
instantaneous direction of momentum may therefore
experience a different reflection or refraction result.
148
Refraction
O.4.6
The geometric positioning of the dynamic hyff with respect to the
two materials, i.e. the angle of incidence, determines the
outcome.
O.4.7 Note that the effect is not symmetrical for layout. Thus for passage
to a material with higher refractive index, e.g. air to glass, the
denser material at n2 causes refraction to dominate. In contrast, at
glass to air, the denser material is at n1 and reflection dominates.
O.4.8 Photons displace electrons (plasmons) in the medium through
which the light travels.
O.4.8.1
Note that the electrons have the higher mobility as per
O.3.15.
O.4.8.2
An ineffective plasmon transport mechanism means that
the material exerts forces on the reactive end.
2.1
Derivation of Snell’s Law
The Cordus explanation for refraction is that the inclined incoming cordus
strikes the surface and one reactive-end and then the next penetrates into
the second medium n2. Assuming the case where n2 is more dense, e.g.
from air to glass, then the cordus slows down. The case is shown in Figure
1.
Figure 1: Refraction involves a dormant reactive-end penetrating into the
second medium, and being angularly deflected with reduction in speed.
149
Refraction
Cordus derivation of Snell’s Law
The refraction geometry is shown in Figure 2, this being the two triangles
comprising the incident cordus and the surface, and the refracted cordus
and the same surface. Since dimension d is common to both triangles, and
the cordus is perpendicular to the loci, it follows by trigonometry that d =
λ2/(2.sinθ2) = λ1/(2.sinθ1). This becomes λ2/sinθ2 = λ1/sinθ1 which is Snell’s
law. The frequency and other forms arise by noting that v1=f. λ1 and v2=f.
λ2 and n = c/v where c is velocity of light in vacuum.
1
2
01
d
2
2
02
Figure R: Refraction geometry
The explanation above has been given for the neat case where the second
reactive end neatly strikes the surface in turn, i.e. t=1/2 gives a precise
λ1/2 displacement for RE a2. It may be shown that the explanation also
works for the messy case where a2 strikes not a half wavelength later but
a fraction k.
The above derivation is for a p-polarised photon. The situation for spolarisation is believed to be similar in that the denser material pulls the
reactive end in, thereby deflecting it. However this is yet to be validated.
Birefringence
Some materials show birefringence. These materials have different
refractive indices in two (or three) directions and therefore light
experiences different refraction depending on its polarisation. Thus the
refractive index varies depending on the orientation (polarisation) of the
incident light. The effect is generally believed to depend on anisotropic
material structure. This may arise from the arrangement of the molecules,
mechanical strain, strain from cooling of plastics from the melt, or
application of an electric or magnetic field.
The Cordus explanation for birefringence is that the atomic spacing affects
the electron compliance. The different geometric spacing in the different
directions creates, through the bonds, corresponding different tension on
the electrons, and this affects their preferred orientation and thus
availability to engage with incoming hyff. For an anisotropic material those
150
Refraction
bonds differ with direction. Any strains deform the bonds and thereby
affects the ability of electrons to interact with the hyff, hence changing
refraction. The orientation, i.e. polarisation, of the incoming cordus
determines which bonds it will interact with. The speed of the cordus in
the material depends on the amount of handshaking it has to do with
electrons, and therefore electrons that are less compliant in one direction
than another will affect the passage of the cordus differently. Incidentally,
this is further evidence in support of the idea that the hyff are not
spherical.
2.2
Brewster's angle
Brewster’s angle θB is an optical refraction and reflection effect that is
dependent on polarisation. For p-polarised light (electric field oscillates in
the plane of the incident ray and the normal to the surface), and for given
refractive indices n1 and n2, there exists an angle of incidence Brewster's
angle θ1 = θB, such that there is no reflection, and all the light is refracted,
this angle being tan(θB) = λ1/λ2 = n2/n1 where λ is the wavelength in the
incident (1) and substrate (2) materials. It is approximately 56o for light
from air to glass. The effect may be derived theoretically using the Fresnel
equations of Wave theory. The challenge is to show how the effect occurs
with a single photon.
The Cordus interpretation is that the reactive-end is doomed to refract,
whatever its frequency state C+ or C-. There is an equifinality about the
outcome, and the RE cannot reflect. This arises because in these special
circumstances of incident angle and refractive indices all loci for reactiveends are positioned right through the transdermis. Therefore they are too
deep to reflect: no subsequent frequency state can recall them back to the
first medium. However, that is not to say all loci are co-linear, as will be
shown.
Any one reactive-end has numerous loci across an interface, depending on
its frequency state at the time. For purposes of illustration we consider the
extreme cases of a single RE in either the C+ or C- state, see Figure 3. We
define the two extreme loci as defgh and qrstuv. Note that these are for a
single reactive-end, nominally termed a1. The a2 reactive-end is not
shown here, but the same explanation applies even if it is a different phase
at contact.
151
Refraction
y
t
Locus horizontal at
transition (for
Brewster’s
conditions)
Locus bent away in
C- phase
r
a
Locus bent towards
n2 in C+ phase
d
Reflected 3
Incident 1
q
1p
e
f
Cycle completes
with locus ready to
refract
g
1
2
1
01
n1
n2
2
h
r
s
j
Locus bent towards
n2 in C+ phase
t
02
Locus vertical at
transition (for
Brewster’s
conditions)
2
For equifinality of
points h and v,
these lines must be
perpendicular
u
2
v
Cycle completes
with locus on
refraction path
Refracted 2
Oscillations
continue around
the refracted
path
Figure 3: Locus diagram for refraction of a p-polarised photon under
Brewster's conditions. The two extreme loci defgh and qrstuv are shown for
a single reactive-end, for one frequency cycle. The frequency states C(blue) and C+ (red) are shown. Also included in this diagram is the
simplified path diagram (dark lines), from which Brewster's formula may
be derived. Points f and t are on the perpendicular to incident ray 1.
Extreme path defgh: For a reactive-end initially in the C- state the hyff
detects the heavier transdermis n2 before the RE actually encounters it,
and moves the RE away, at least initially. By the end of that state the RE is
positioned parallel to the interface (f). Thereafter it changes to the C+
state which pulls it in towards the denser material. This puts it onto the
refracted path θ2 at h.
Extreme path qrstuv: For a reactive-end initially in the C+ state the hyff
detect the approaching transdermis n2 and draw the RE into taking a shortcut into material 2. By the end of that state it is positioned in the material
152
Etc.
x
Refraction
n2 and heading normal to the surface. Thereafter it changes to a C- state
which attempts to undo the changes. However the C- phase cannot bend
the path sufficiently to pull it out of the material and back into a reflection
path, and instead the RE refracts.
The RE refracts regardless of the frequency state or the locus taken. This is
a consequence of the combination of the momentum (direction
determined by the incident angle) and strength of the subsequent forces
(from the refractive indices). These prevent the RE from completing a
reflection manoeuvre. The situation only exists for p-polarisation because
any deviation from this orientation would result in forces that were out-ofplane.
Derivation of Brewster’s relationship
The above is a qualitative description of the refraction and lack-ofreflection effect at Brewster’s angle θB. The cordus explanation also
provides a way to quantify the relationship, as shown in the Figure. The
curved loci are simplified by assuming a small n2 close to n1, which makes
straight lines of the loci and moves points f and t in to the nominal optical
contact point. The result are the lines djh and qjv, shown in dark in Figure
3.
On path qjv the a1 reactive-end travels λ2/2 into material 2, along the
normal to the surface. In the same time interval the djh path moves the RE
a distance of λ1/2 parallel to the surface and still in material 1.
Subsequently each path is bent to conform to θ2. The derivation of
Brewster's relationship is given in terms of the wavelength λ and the
geometry:
Since the djh and qjv paths have equifinality regarding time, line
hv must be perpendicular to the exit trajectory θ2.
This allows the angle JHV to be identified as θ2.
Thus from triangle JHV it emerges that tan(θ2) = λ2/λ1 =
sin(θ2)/cos(θ2) (Eqn 1)
Snell's Law identifies angle JVH as θ1. The derivation is:
Snell's Law: Sin(θ1) = λ1/λ2.sinθ2 (Eqn 2)
Substitute Eqn 1: Sin(θ1) = cos(θ2)/sin(θ2).sinθ2 = cos(θ2)
Thus θ2 = 90o - θ1
Thus tan(θ1) = λ1/λ2 = n2/n1 which is the relationship for Brewster's
angle
Note that different REs may take different loci across the surface (O.3.2).
Consequently this model predicts a braiding of the loci through material 2.
The loci will all be parallel to θ2 but laterally displaced to various extents
within the boundary made by the extreme paths. In addition they have a
superimposed sinusoidal lateral wriggle.32
32
Brewster's angle is interesting for its corollary: At Brewster's angle θ1 =
θB all light except p-polarised is reflected, AND emerges s-polarised regardless of
153
Refraction
Thus Cordus is able to provide qualitative and quantitative explanations of
Brewster's angle, for an individual photon. This demonstrates that optical
phenomena may be explained by particuloid mechanisms too. However it
is not yet a full proof, because it has only been shown for the extreme loci
(as per O.3.4) and by simplifying the paths to segments of straight lines.
We leave a more complete validation as a future task.
2.3
Mixed reflection and refraction
For transparent surfaces some light is reflected and some refracted
(transmitted). The Fresnel equations describe the proportion of light
transmitted (2) or reflected (3). The equations are for either p- or spolarisation. Those for p-polarisation follow. These are more commonly
given in terms of refractive index n, whereas here the wavelength λ form is
also given.
The Fresnel equations give the proportions: these depend on the angles of
incidence and refraction, and the refractive indices, also the polarisation
of the incident light.
The basic principle underpinning the Fresnel equations is that the electric
field components in the plane of the interface are continuous, which
means the planar-components (hence the Cosθ terms) of the incident (1)
plus reflected (3) electric field amplitude equals that of the transmitted
(2). Likewise for the magnetic field, which is at right-angles to the electric
field. For p- and s-polarisation the electric and magnetic fields hit the
interface differently, hence the polarisation effect. However, this
explanation does not explain how the path of an individual photon is
determined.
its initial polarisation. The tentative Cordus interpretation for the s-polarised
reflected light is that the same Brewster's conditions (θ1, n2/n1) that provide the
p-polarised RE with only sufficient momentum to stall against n2, also means that
other polarisations have insufficient momentum to penetrate n2, and only
sufficient momentum to get to the minimal reflected state of flat s-polarisation.
154
Refraction
Being based on Wave theory, the premise underlying the Fresnel
equations is that the incident and exit beams of light exist at the same
time. Thus that particular explanation cannot be applied to a single
photon, which is supposed to exist as a zero-dimensional point. The QM
solution to that problem is to instead model the photon as a wave
function in superposition. That has problems of its own, because it is
uncertain whether that mathematical solution is really representative of
reality. An alternative qualitative description is that the incident light
causes surface plasmons (moving electrons) that later recombine to form
the exit photon.
The cordus explanation is that this depends on the state of the reactive
end at the time of impact: those RE in or close to an energised state are
reflected, while those that are dormant are refracted (O.4.5).
Phase change revisited
It is useful to consider the mechanism for phase change (see part 2.2) and
elaborate. Consider the interaction of the horizontal and vertical
components of the hyff force, as it approaches the optical interface.
Consider also the mobility of the electrons in that medium, and their
response to the photon. There are two cases to consider
Case A: On entry to a denser material, e.g. air to glass, the surface
plasmons (electrons) can easily move aside and back again (see O.3.15) in
response to the dynamic horizontal component of the hyff electric field.
Therefore there is no net horizontal force applied to the RE (though there
are dynamic forces) and hence the horizontal component of momentum of
the photon is unhindered.
However the vertical mobility of electrons in the transdermis bulk is
limited because doing so would build up electrostatic force resisting
further electron transport. Therefore the normal component of the hyff
electric field is either resisted by the n2 transdermis and the RE reflects
back into n1, or is attracted into n2 the case of refraction.
The outcome depends on the frequency state at the time (O.4.5) i.e. a net
dominance of the C- state gives reflection and C+ results in refraction. In
addition, the angle of incidence provides the direction of initial
momentum, so low angle θ1 (steep incidence) tends to predispose towards
the photon continuing straight ahead, which is refraction. With steep
incidence, a large amount of vertical force impulse is required to turn the
reactive end around and reflect it. This does not happen often, not
because the n2 substrate is unable to provide the reaction, but because it
is sensitive to the timing of the frequency: if the reactive end changes back
to C+ before completing the reflection manoeuvre then refraction will take
over.
Case B: For a photon approaching a less dense medium, e.g. glass to air,
internal reflection is the favoured outcome and occurs becomes the
155
Refraction
exclusive outcome when the angle of incidence exceeds the critical angle,
θ1 > θc. Consider a photon in denser n1 and approaching an interface.
While the photon has been deep in n1 the plasmon (electron) transport
mechanisms are fully mobile in both the horizontal and normal directions
(actually the radial and axial). However, as the photon approaches the air
interface, the horizontal transport mechanisms are still fine, but the
normal transport becomes increasingly ineffective. An ineffective plasmon
transport mechanism means that the material exerts forces on the
reactive end (O.4.8.2). Therefore the horizontal momentum of the photon
is not impeded, but the normal is. The denser material is at n1 which thus
provides the greater force on balance, so the RE tends to be pulled back
into n1 and reflection. At shallower incidences than the critical angle, the
momentum is sufficient to ensure reflection regardless of the frequency
state.
We acknowledge that this is only a descriptive explanation, not a
quantitative one, of mixed reflection and refraction. The full derivation of
the Fresnel equations from a cordus basis is an open question. In addition
polarisation in reflection and refraction looks to be an area of further
investigation and potentially deeper insights.
3
Discussion
Explaining basic optical effects is not possible with classical particle
mechanics, and even with quantum mechanics it is not straight forward
and not particularly intuitive. The problem is much simpler when solved in
the cordus domain, as this paper shows for several cases of refraction.
Both Snell’s Law and Brewster’s Angle are explained and quantitative
derivations provided. This is significant because the cordus mechanics
were derived for single photons, and immediately generalise also to beams
of light. Therefore a single mechanism can explain both particle and wave
behaviour, which is otherwise difficult to achieve. This becomes even
more significant when considering that the same cordus concept can also
explain the path dilemmas and fringes of individual photons in the double
slit device. Cordus is therefore one of only a few concepts that can explain
the double slit device as well as conventional optics. We do not dispute
that quantum mechanics can do much of this, but that cordus does it
without resorting to metaphysical effects is unique. Note also that the
cordus explanation does not need the conventional concept of
‘interference’.
All the same, we do emphasise that cordus is a conceptual solution, and
while it has been thought-tested against several physical phenomena, it
has not been checked against all. Furthermore, it is based on intuition and
conjecture, and makes many assumptions (lemmas) that have yet to be
tested. There are many open questions still, the Fresnel equations being
one.
156
Refraction
Contrast: Cordus and EM Wave theory
EM wave theory is the dominant way of thinking for explaining optical
effects, including interference patterns. It has tacit lemmas of its own: e.g.
that light is a disturbance in the electromagnetic field. It relies heavily on
the concept of frequency, particularly that a half wave-length (λ/2) shift
will cause destructive interference. As a theory it is enormously successful.
Even single photons show interference patterns and by implication 'must
be' a wave, hence the wave-function concept in quantum mechanics.
However wave theory has some limitations: the origins of frequency are
mysterious; it does not explain the quantum effects of single photons; and
destructive interference implies destruction of energy.
If the Cordus Conjecture is correct, wave theory is a convenient
mathematical representation of the external behaviour of light en masse,
but not of the internal variables. Light itself is not simply an EM wave: that
is only the physical manifestation of the passage of hyff. The internal
dynamics of the cordus give rise to the externally visible EM fields: the
fields are not the entire existence. Another areas where the perspectives
differ is the interpretation of amplitude (brightness): Wave theory
perceives amplitude to be the strength of the EM field. The Cordus
Conjecture perceives amplitude to be only the cumulative effect of
multiple cordi that are in a similar location at about the same time: an en
masse effect.
The Cordus Conjecture suggests that wave theory is an appropriate
method for modelling photons, with two caveats: it applies to light in
transit; and to light en masse (not single photons).
Conclusion
This paper shows that optical effects can also be explained as the
interaction of cordus photon with the optical surface and the substrate.
Thus Wave theory is not the only way of conceptualising effects like
reflection and refraction.
The conceptual contribution of this bracket of papers is first the creation
of a novel theoretical model for the internal structure of the photon and
the origins of frequency. This model is useful in later work, where it is
generalised to matter particuloids and provides foundational material for a
description of the strong force and the internal structure of the proton.
The second is the evidence, at least at a conceptual level, that the cordus
conceptual framework is able to explain conventional optical effects. This
is significant, because the same framework has separately provided a
resolution of wave-particle duality in the double-slit device (ref. ‘Cordus
conjecture’), and can explain various matter effects that are normally the
preserve of Quantum mechanics (ref. ‘Cordus matter’). Thus cordus offers
a novel mechanics with a high degree of logical consistency across these
various effects.
157
Refraction
158
Refraction
15
Cordus
Conjecture
Part 3: Cordus matter
Cordus
particule
interpretation
of
matter > de Broglie
frequency explained
>
entanglement
between particules >
locality rethought >
energy and entropy
explained > special
super-states
of
matter explained >
why
quantum
mechanics does not
scale
up
>
Schrodinger’s
cat
demystified
160
161
Wider Locality
Cordus matter: Part 3.1
Pons, D.J. , 33 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
The dominant paradigm in conventional physics is that of a ‘particle’,
which this paper suggests is a badly flawed premise. The cordus particuloid
is a more coherent concept in that it offers explanations of phenomena
that are otherwise puzzling, and does so with one conceptual consistent
framework across a wide variety of phenomena. This paper shows how
entanglement is readily explained as a natural consequence of the cordus.
It also introduces the principle of complementary frequency state
synchronisation (CoFS) as the deeper principle beneath the Pauli exclusion
principle, and coherence. It is suggested that Bell’s Theorem is only
applicable to point particles, and is thus generally irrelevant. Specifically,
Bell’s Theorem is not an obstacle to models of hidden variables.
Furthermore, it is suggested that the principle of locality is not viable in its
present form, and a principle of wider locality is proposed.
Keywords: particle; entanglement; Bell’s theorem; locality; fundamental
physics
Revision 2.10 Added EPR paradox, clarified locality, minor edits
Document: Pons_Cordus_3.1Locality_E2.10.86.doc
1
Introduction
Classical mechanics, with its equations for force and motion, are adequate
for the macroscopic bodies in the environment around our human
existence. However, at sub-microscopic scale the behaviour of sub-atomic
particles of matter can be unexpected: entanglement, superfluidity, and
superconductivity, are some examples. Explanations of these effects have
had to rely on adaptations of quantum mechanics (QM) as classical
theories are at a loss.
QM does a good job of providing mathematical descriptions of the effects,
and the fact that it can do so is usually taken as circumstantial evidence
that QM must be correct. Unlike other areas, such as wave-particle duality,
there is no major competing interpretation to QM in the area of subatomic particles. All the same, QM is not particularly effective at providing
a qualitative description of the effects, and this makes it complex and
difficult to understand at an intuitive level, and consequently people
generally, though perhaps not physicists specifically, perceive QM as
strange. Maybe the effects really are intrinsically complex, and the
mathematical formulations are the reality: the simplest possible way to
express the underlying mechanisms of causality.
33
Please address correspondence to Dr Dirk Pons, University of
Canterbury, Christchurch, New Zealand. Copyright D Pons 2011
162
Wider locality
However, there is always the possibility that there might be another way,
different to QM and perhaps even simpler, of understanding the effects.
The purpose of this paper is to explore that possibility, and it does so by
extending the cordus concept [1].
Background: photon cordus
The concept of a cordus is that a photon consists not of a point but of two
reactive ends (RE) connected together with a fibril. The REs emit
directional force lines called hyff, which are detectable externally as a
polarised electrostatic field. The companion paper [1], describes the
background to this idea, applies it to path dilemmas in the double-slit
device and Mach-Zehnder interferometer [2], and uses it to explain fringes
[3]. It is shown that the Cordus conjecture is conceptually able to resolve
wave-particle duality for the photon [4]. Another set of papers show that
the idea describes frequency and the dynamic internal states of the
photon [5] and is applicable to conventional optical effects of reflection
[6] and refraction [7]. We recommend that at least the first bracket of
papers [1-2] be read before this one, as the fundamental concept and
cognitive point of difference are developed there. Also, the frequency
model [5] from the cordus optics set is necessary foundational material.
The present bracket of papers conjecturally builds on those ideas, and
applies them to entanglement, the electron, and matter generally. This
paper is the first in the bracket and addresses entanglement and locality.
Companion papers describe matter more generally including a cordus
model for the electron and its orbitals [8], entropy and coherence [9],
special states of matter – superposition, coherence, superfluidity, and
superconductivity –are re-interpreted in a cordus context, with surprising
results [10]. The closing paper in this bracket contrasts Cordus with QM,
and reconceptualises the issues with Schrodinger’s Cat [11].
Method
The approach taken is a continuation of that described in the companion
paper ‘Cordus conjecture’ [1], and not detailed here. Briefly, it involves
reverse-engineering the system: it uses logic, conjecture and intuition to
build on the existing cordus model, thereby postulating a set of
mechanisms that can plausibly explain the known system-behaviour.
Specifically, the objective is to postulate electron structure and behaviour
sufficient to explain several matter effects. It is like trying to work out the
contents of a black box by observing its outputs in different situations, and
synthesising a working-model that is sufficient to explain as many of the
situations as possible.
Results
This is a design way of thinking, being very different to the conventional
mathematical analytical approaches, and the outcome is likewise more
qualitative than quantitative. Thus we term the results a conceptual
solution. Being conceptual means that the broad principles are described,
within which a whole class of solutions are possible. Where possible we
single out the most promising of these specific solutions and term it the
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Wider locality
working model. Along the way we note the underlying assumptions as a
series of lemmas. These we do not attempt to prove: they are simply to
make the premises explicit so that they can be evaluated later. The
lemmas make up the central strand through the papers. Where relevant
for continuity, references are made to lemmas in the other papers.
The results follow, starting with some basic preliminary premises on the
particle behaviour of photons, then moving on to electrons, followed by
application to matter more generally.
2
Entanglement
Einstein called entanglement ‘spooky action at a distance’ and it continues
to sit uneasily within physics since a qualitative explanation is lacking even
though the reality is accepted. It is contrary to relativity, and to the
principle of locality. Nor can entanglement satisfactorily be explained with
existing hidden-variable theories. However it is consistent with quantum
mechanics.
The principle of locality is that an object is only affected by its immediate
surroundings. Entanglement appears to require the principle to be
violated: twin particles may be linked, such that changing the state of one
instantly changes the other, even if they are separated by macroscopic
distances. The mechanisms are incompletely understood in conventional
physics.
The effect can be addressed by the Cordus Conjecture with the addition of
a further set of assumptions.
Lemma M.1
Photon-photon interaction
This lemma sets out the assumptions for the interaction of the photon
with other photons.
M.1.1 Photons in flight apparently do not interact much with each other.
There is no known evidence of them merging with each other in
flight. However nothing in the Cordus logic requires them to be
incapable of merging. If they don’t merge, the constraint could
simply be that they cannot generally get sufficiently close to each
other, and aligned, and synchronised for long enough to achieve
the union. Nonetheless it is proposed that some interaction is
possible of the passing type.
M.1.2 Photons do not generally interfere with other photons in the sense
of destructively (constructively) creating fringes.
M.1.3 Photons can be initially created identical in certain key regards
(e.g. frequency).
M.1.4 Cordi from different photons may lock onto each other and
become synchronised through the hyff. The hyff provide the
means for coupling into/out of the fibril (hence also passing
observation, see ‘Cordus Conjecture’).
M.1.5 continued below
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Wider locality
There are two candidate Cordus interpretations for entanglement. The
first is that some entanglement devices might not be doing much more
than splitting the photon (Cordus Conjecture L.1.1): that what appear to
be two particles are only two reactive ends of the same cordus.
The second, and the current working model, is that the fibrils of two cordi
become synchronised through mutual hyff interactions, called
complementary frequency state synchronisation (see below), such that
changes to the one affect the other.
3
Complementary frequency state synchronisation (CoFS)
Since a photon has two reactive ends, and these are not energised all the
time, it is possible for a second photon to occupy the same space, or to coexist nearby. This requires that the frequency states be complementary,
i.e. the reactive-end a1 of photon a is in the opposite state to b1 of photon
b, and physically near each other. Similarly for a2 and b2. By
complementary frequency states we mean that the hyff of one photon are
phased to feed into that of the other that is co-located. This concept
originates in the frequency model (ref. ‘Cordus optics’).
Applying this to entanglement, means that it only looks like there is a
whole photon at each location, when actually there are two photons
sharing the space such that only one is visible at either location at any
particular time. The photons are subsequently stretched (Cordus
Conjecture L.1.3) so that the reactive ends are far apart. What looks like
one complete photon at each site is, according to this version of events,
two half photons. The fibrils of each are stretched to much greater
distances than usual, but still retain their ability to communicate
practically instantly (Cordus Conjecture L.6.15). Changing one reactive end
at one site therefore changes the other, and that change can be
immediately observed at the other site.
From the Cordus perspective the entanglement would be somewhat
delicate, since the cordi could be broken by external disturbances to the
hyff. This macroscopic form of entanglement of photons is apparently an
uncommon event
that requires deliberate construction by the
Experimenter.
This CoFS principle is not limited to the photon, but applies to particuloids
generally. As will be described later, all ‘particles’ are cordi, and therefore
the CoFS effect is accessible to other particles too. Thus CoFS is suggested
as the underlying principle for the pairing of electron orbitals, coherence,
and condensed states. From the cordus perspective a CoFS means that
both RE modes of the particuloid (e.g. electron) are fully occupied at any
one time, but not by the same electron. It is an important principle with
wider applicability. It is subsequently used to explain superfluidity and
superconductivity (see part 3.3), where it forms the basis for a new
concept of ‘network of orbitals’. The QM use of the term ‘coherence’
emerges as one application of CoFS, and the Pauli exclusion principle is
165
Wider locality
another. It is also important in understanding why quantum effects do not
scale up to the macroscopic world. A derivative of the concept, called
synchronous hyff emission direction states (SHEDS), explains the strong
nuclear interaction (ref. ‘Cordus in extremis’) and is used to predict the
internal structure of the proton.
Resolving the Einstein-Podolsky-Rosen [EPR] paradox
The principle of complementary frequency states also allows an
explanation of the Einstein-Podolsky-Rosen [EPR] paradox. In this
thought-experiment the variable of one particle, e.g. the spin of an
electron, is measured and then that of a second particle, e.g. the spin of
the other electron in the orbital, is always found to be in the opposite
state. This is considered a paradox because it is unclear how the two
particles interacted to communicate their states to each other to contrive
such a result. Alternatively, it suggests that the uncertainty principle has
been violated. Alternatively, it suggests that the QM wavefunction does
not give the complete description of reality.
That the last interpretation might possibly be the case is beyond credence
for orthodox quantum mechanics, but is exactly what cordus implies. The
CoFS principle readily provides a mechanism whereby two particuloids in
different locations can interact. By sharing space they are forced to
negotiate a mutually satisfactory arrangement of their hyff, and
synchronise them. That necessitates slipping into complementary
geometric configurations. The fact that the electrons are sharing the
orbital means that they have pre-arranged to be in CoFS even before the
Observer started the interrogation, so to the Observer the outcome of the
experiment naturally looks like an act of wilful contrivance by the
‘particles’. The EPR effect is thus explained as a CoFS effect, and the
paradox dissolved.
4
Locality and Bell's theorem
The principle of locality is that the behaviour of an object is only affected
by its immediate surroundings, not by distant objects or events elsewhere.
Hence also local realism: that the properties of an object pre-exist before
the object is observed. Bell’s theorem sets these against each other by
implying that only one perspective can be correct: either superluminal
effects or local realism does not exist. The many actual experimental
results are generally interpreted as supporting non-locality behaviour in
quantum mechanics. The general interpretation is to accept Bell's
Theorem and therefore conclude that no viable hidden-variable solution of
any kind can exist.
Conventional physics has an ambivalent relationship with locality. One
position is that the principle of locality should apply, because it seems
natural. But it is an assumption nonetheless. This confidence is used in the
argument against hidden-variable solutions. The other position questions
whether locality is even valid, given the empirical evidence for
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Wider locality
entanglement. But what the mechanisms might be for non-locality is
uncertain.
Cordus delivers a
hidden-variable solution that accommodates
entanglement and abandons strict zero-dimensional point locality in
favour of a principle of wider locality [below]. In other words, cordus
suggests that there is a shade of grey between the simplistic options
offered by orthodox physics: full locality at a zero-dimensional point, or no
locality at all. It is no wonder that physics finds it hard to chose between
such limited options, nor is it necessary to limit the thinking to such stark
choices, as cordus shows.
The cordus model demonstrates that there is no problem with having all of
superluminal effects, hidden variables, and some degree of locality. The
cordus entanglement mechanism provides superluminal effects through
the instantaneous communication through the fibril (ref. ‘Cordus
conjecture’). But doesn’t Bell’s theorem preclude this? From the Cordus
perspective Bell’s theorem is wrong. It is not applicable to the situation
because it was built on the implicit but limiting premise that a particle is
necessarily a single zero-dimensional point. This is a natural assumption
given the prevailing 'particle' perspective in QM physics, but the theorem
can only be valid to the extent that particles actually are points. As Cordus
shows, there is reason to believe that the issue can be considered very
differently: that the ‘particle’ view is only an approximation of a deeper
‘particuloid’ existence. Therefore Bell’s theorem is only an obstacle to
hidden-variable solutions, if one assumes beforehand that the solution
must be limited to only zero-dimensional particle designs. Cordus is not a
zero-dimensional particle design and therefore Bell's theorem is irrelevant.
What about the assumption of ‘practically instant’ communication
between the two sites? It implies an effect faster than the speed of light
(superluminal): How is that explained? We acknowledge that is an
incompletely resolved matter and offer some responses. The first is that
the communication is not totally instantaneous because time is initially
required to create the photons and separate the reactive ends. Second,
the data can still only be transmitted at one or at most a few bits per
frequency cycle. The latter arises because, according to the Cordus view,
the hyff effect occurs at the speed of light (L.6.16), and is clocked at the
natural frequency of the photon. So even if the data are transmitted
instantly, they can still only can be pumped in and out as fast as the speed
of light, and only as many bits per frequency cycle as cordus variables are
being changed (which will be few).
Third, there is also the matter of passing vs. intrusive detection (L.3) to
consider: if the photon is consumed in the process, or the entanglement
lost, then a new entangled pair will need to be produced, and will require
finite time to move into position. Thus intrusive detection will never be
superluminal overall. Passing detection could allow the entanglement to
be reused for another bit of information, though point two above still
applies. Furthermore, the process of interrogating a photon consumes
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Wider locality
time, even if the photon is not destroyed (ref. ‘Cordus in extremis’, [8]
E.5.2).
An alternative perspective is that the cosmic speed limit does not apply to
the fibril, even if it does to the hyff, and this is the current working model.
After all, if a long wire were inside a sheath, i.e. a Bowden cable, then
pushing one end instantly causes the other to protrude. The cordus is
perhaps similar, and it is debatable whether or not any mass is being
moved (or where in the frequency cycle the mass, if any, is being moved).
That matter of speed aside, we have shown that a hidden-variable theory
is indeed possible, and can explain entanglement, Bell’s theorem
notwithstanding. However whether or not locality is violated is a more
complex case, and discussed next.
5
Principle of Wider Locality
Cordus suggests that the principle of locality is not viable in its current
form. The current principle of locality assumes that a 'particle' is only
affected by the values of the fields (electromagnetic, gravitational, etc.) at
the infinitesimally small location of the zero-dimensional point. Cordus
asserts that particles are not zero-dimensional, but are actually
particuloids (appear to be particles). They have a span, and the reactiveends have hyff zones around them. Therefore Cordus suggests that a
principle of Wider locality applies: a cordus particuloid is affected by the
cumulative effect of the fields in its local surroundings, these being the
space to which its hyff have access. Further, that hyff has access to spaces
that the physical particuloid with its reactive ends does not.
Lemma M.1 continued
To sum up, the additional lemmas are:
M.1.5 Cordi may be in complementary frequency states, sharing modes
for their reactive ends.
M.1.6 Communication across the fibril is instantaneous, whatever the
span of the cordus. However the propagation speed of the hyff is
limited to c, the speed of light in a vacuum
M.1.7 A principle of Wider locality applies: a cordus particuloid is
affected by the cumulative effect of the fields in its local
surroundings, these being the space to which its hyff have access.
Further, that hyff has access to spaces that the physical particuloid
with its reactive ends does not.
6
Conclusions
What has been achieved?
This part has presented a novel conceptual solution to the otherwise
paradoxical problem of entanglement. The dominant paradigm in
conventional physics is that of a ‘particle’. Cordus suggests that conceptual
framework is flawed, and the cause of the weird predictions from QM. The
cordus particuloid is a more coherent concept in that it offers explanations
168
Wider locality
of phenomena that are otherwise puzzling, and does so with one
conceptual consistent framework across a wide variety of phenomena.
This particular paper shows how entanglement is readily explained as a
natural consequence of the cordus. This obviates the need for the usual
spooky and metaphysical interpretations. The paper also introduces the
principle of complementary frequency state synchronisation (CoFS). This is
an important concept in that later papers show how it underpins the Pauli
exclusion principle, coherence, and the strong interaction. It even allows
the internal structure of the proton to be estimated.
Cordus suggests that Bell’s Theorem is only applicable to point particles,
and is thus generally irrelevant. It is an artefact of the flawed particle
premise of conventional physics, and is not an obstacle to models of
hidden variables.
Cordus predicts that the principle of locality is not viable in its present
form and needs to be widened to include hyff interactions. The problems
with the current principle of locality, as evident in entanglement, are also
an artefact of the prevailing zero-dimensional-particle framework of QM.
Cordus proposes a simple principle of wider locality to solve this problem.
These are unorthodox predictions. The implications are that the ‘particle’
conceptual foundation of Quantum mechanics is invalid. The conventional
disinterest in ‘hidden variable’ solutions is a consequence of over-reliance
on a false-negative from Bell’s theorem. QM only applies at the level at
which small pieces of matter look like point particles, and is invalid at
smaller scales. Thus QM is not applicable to the double-slit device.
Nonetheless its statistical mathematics are useful as measures of average
outcomes, though not as specific predictions. Likewise the QM descriptive
explanations are untrustworthy. QM only describes the average outcome.
References
1.
2.
3.
4.
5.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.,
Cordus Conjecture: Part 1.1 Quis es tu photon? .
2011.http://vixra.org/abs/1104.0016
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.,
Cordus
Conjecture:
Part
1.2
Quo
vadis,
photon?
2011.http://vixra.org/abs/1104.0017
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.,
Cordus Conjecture: Part 1.3 Explanation of fringes.
2011.http://vixra.org/abs/1104.0018
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J., WaveParticle
Duality:
a
Proposed
Resolution.
2011.http://vixra.org/abs/1106.0027
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.,
Cordus
optics:
Part
2.1
Frequency.
2011.http://vixra.org/abs/1104.0019
169
Wider locality
6.
7.
8.
9.
10.
11.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.,
Cordus
optics:
Part
2.2
Reflection.
2011.http://vixra.org/abs/1104.0020
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.,
Cordus
optics:
Part
2.3
Refraction.
2011.http://vixra.org/abs/1104.0021
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.,
Cordus
matter:
Part
3.2
Matter
particuloids.
2011.http://vixra.org/abs/1104.0023
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.,
Cordus matter: Part 3.3 Energy cycles within matter.
2011.http://vixra.org/abs/1104.0024
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.,
Cordus matter: Part 3.4 Special states of matter.
2011.http://vixra.org/abs/1104.0025
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.,
Cordus matter: Part 3.5 Schrodinger’s Cat reconceptualised.
2011.http://vixra.org/abs/1104.0026
170
171
Matter particuloids
Cordus matter Part 3.2
Pons, D.J. , 34 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
Some of the most enigmatic effects in the physics of electrons are its waveparticle duality and the Aharonov-Bohm and Casimir effects. Even
relatively core concepts of atomic physics, like spin and the Pauli exclusion
principle, lack satisfactory descriptive explanations. This paper shows that
application of the cordus principle can explain these effects in a coherent
manner.
Keywords: electron; wave-particle duality;
Broglie frequency; matter wave
spin; atomic bonding;
de
Edition 3 > Date: Saturday, 11 February 2012 > Document: Pons_Cordus_3.2Matter_E3.0.88.doc
1
Introduction
While matter forms the tangible substance of our world, our
understanding of it at the atomic level is far from complete. Conventional
physics is based on the assumption that the constituent particles of matter
are just that: zero-dimensional particles.
Thus Quantum mechanics (QM) asserts that the properties of a particle,
e.g. spin, are simply intrinsic, and that the fundamental reality for particles
is probabilistic and described by a wavefunction. This is adequate for
explaining many classes of effects. For example, the electron is known to
pass through the double-slit device and QM has an adequate
mathematical explanation for this. However in the same situation
electrons are also observed behaving as waves, and this wave-particle
duality is poorly explained by QM.
The present paper extends the Cordus concept [1] to the electron and
then to matter generally. It is shown that this yields an explanation for
several electron effects, including wave-particle duality, Aharonov-Bohm
effect, spin, a descriptive explanation of the Pauli exclusion principle,
atomic bonding, and the Casimir effect.
2
Cordus model of the Electron
Previous Cordus papers have explained how the photon could be a cordus
rather than a single zero-dimensional point [1-3]. Electrons also make
fringes, and therefore it is logical to extend the cordus concept to the
34
Please address correspondence to Dr Dirk Pons, University of Canterbury,
Christchurch, New Zealand. Copyright D Pons 2011.
172
electron. This permits the apparent wave-particle duality of the electron to
be explained. It also handily explains several other features of the
electron, including the Pauli exclusion principle for orbitals. The following
lemma extends cordus concepts to the electron.
Lemma M.2
Electron
M.2
Electron: The conjecture is that the electron itself consists of a
type of cordus.
M.2.1 The electron is another type of cordus (e-cordus) and has an efibril and e-hyff (electrical field).
M.2.1.2
The fibril of an electron exerts a restoring force on the
span.
M.2.1.3
The electron's fibril is of similar functionality to that of the
photon.
M.2.1.4
The electron oscillates and appears at the end of its fibril
(energised Electron End) at a frequency (approximately
the de Broglie frequency).
M.2.2 The e-cordus gives the electron two RE statistical mode locations
where it can appear, and when the electron is bound to an atom,
these appear as an orbital or energy shell around the nucleus.
M.2.2.1
In this context a mode is an available location for a
reactive end. While the cordus only has two REs, it may
have more than two modes available to it, due to the
space around it.
M.2.2.2
If a cordus has multiple modes available to it, then the
next one it uses will be determined by the hyff of other
cordi in the environment. Thus cordi influence the location
of each other.
M.2.5 The energy shells are in quantum increments because they need
to include whole frequency-cycles (wavelengths).
M.2.5.1
At a deeper level, not that we need the explanation for
present purposes, this is determined by the need for
multiple standard gauges of assembly in the atom, see
‘Cordus in extremis’, competing with the need to maintain
a CoFS state throughout the atom.
M.2.6 Higher energy electrons have higher frequency.
M.2.7 Higher energy electrons have shorter cordus span.
M.2.8 The RE modes of an electron within an atom are shaped (not
necessarily symmetrically) by the hyff of other electrons in the
atom.
M.2.9 continued below
This lemma may be used to provide a Cordus explanation of several
effects. Later it will be shown that other sub-atomic particles may also be
represented as cordi.
2.1
Wave-particle duality of the electron
The Cordus explanation is as for the photon [1]: the free unbound electron
oscillates its appearance between its two reactive ends. Thus it is able to
pass through two slits that are suitably spaced apart. The fibril passes
173
cleanly through the medulla between the slits, without interacting. Fringes
arise similarly: the reactive ends have electromagnetic hyff, and thus
engage with the edges of the slits in passing, generating forces, thereby
incrementally deflecting the electron, and creating fringes. [3]
2.2
Aharonov-Bohm effect
In the Aharonov-Bohm (AB) effect an enclosed magnet, one from which
magnetic field cannot escape, changes the motion of an electron even
though the particle passes through a magnetic-free region. The
experiment involves a coherent source35 of electrons: one beam passes
through the centre of a toroidal magnet and the other bypasses it; the
electrons thereafter interfere to produce fringes at a biprism (wire with a
positive charge);36 the fringes differ depending on whether or not the
magnetic flux is confined to the magnet (as opposed to leaking into the
hole). The conventional explanation involves use of vector electromagnetic
potentials (in place of electromagnetic fields). Alternative explanations
exist [12].
The significance of this effect is that the electron is affected by a condition
(magnetic field) that is some distance away from it, and to which it does
not have access. Thus the principle of locality seems to be compromised,
as in the case of entanglement. The results are usually interpreted as
evidence that QM's mathematical representations of electromagnetic
potentials are not simply mathematical, but are real effects.
The Cordus explanation of the Aharonov-Bohm effect is: one reactive-end
of the electron cordus goes through the toroidal magnet, and the other
goes past it; the reactive-end itself does not get into the toroid but its hyff
do; the hyff penetrate the (thin) outer layer of the solenoid, and therefore
are able to probe that space despite the electromagnetic barriers
preventing the electron as a whole from entering; the hyff interact with
the magnetic field and this causes a displacement force on the reactiveend; the wire of the biprism provides the edge-effect for the formation of
fringes.37
Thus the AB effect, from the Cordus perspective, is another application of
the Principle of Wider Locality [13].
35
The quantum mechanics concept of a ‘coherent’ source of light or
electrons is not accepted by Cordus, at least not as QM describes it. Instead
Cordus explains this type of light source as reactive ends that have been split to go
down two paths.
36
The fact that fringes in this case are associated with electromagnetic
effects at the edges of objects, is consistent with the explanation for photon
fringes (‘Cordus conjecture’), which are also edge effects.
37
The present working model is focussed on the reactive-end perspective,
and it is possible that an alternative way of looking at it is that the fibril passes
through and is disturbed by the magnetised region.
174
2.3
Electron configuration, Orbitals, Spin
Electrons that are bound to atoms have specific configurations of shell,
sub-shell, orbital, and spin. The standard perspective is that the energy
levels for the electron are in quanta, i.e. discrete steps. These are
explained as arising from the need for the levels to be spaced at whole
numbers of the particle's wavelength, and Cordus is similar in this regard
(M.2.5).
Synchrotron radiation
One of the difficulties with the classical model of the atom is that if an
electron orbits round the nucleus, then it should emit a photon
(synchrotron radiation) and collapse into the nucleus. Quantum mechanics
partly solves this by providing orbitals in which there is only a probability
of the electron appearing. However this is an incomplete solution as it
does not explain how the electron gets from one location to another, and
why it should not emit a photon while doing so.
The Cordus interpretation is that the electron is not continuously in
existence but appears and disappears at each of the ends of its fibril.
When it is not in existence (dormant) then it does not have to emit
synchrotron radiation. Furthermore, the position of those reactive-ends
changes depending on the rest of the local environment of the atom and
neighbouring atoms, because of the influence of the hyff of other
electrons. The positions of the cordus correspond to the orbitals, i.e. the
RE modes. Existing models of the orbitals suggest they are generally
spherical or contain multiples of two modes (most likely locations). The
two-ended nature of the cordus readily lends itself to this type of
outcome. There is no actual ‘orbit’ in the continuous sense, and hence no
radiation of a photon. This does not mean that the electron is stationary:
only that it steps around its orbital, and moves invisibly between steps.
When it has multiple modes accessible to it, then the choice is influenced
by the hyff of surrounding electrons. (See also superconductivity below).
However, when the electron is free of the atom and flowing en masse in a
circular path then there is a small net rotation and translation of the whole
e-cordus at each frequency cycle, and synchrotron radiation occurs there.
Electron orbital shape
Both QM and Cordus suggest that electrons are not orbiting balls. QM
predicts that the shape of electron orbitals is not a circular orbit, but
rather a shaped region of probable location. For example, the s orbital is
spherical and has zero angular momentum, whereas the p orbital has
polar modes. The higher orbitals are not necessarily symmetric. However
all the orbitals have a bipolar shape, even if distorted. This is consistent
with the cordus concept of an electron with two RE modes (M.2.2), where
the modes are shaped (not necessarily symmetrically) by the other
electrons in the atom (M.2.8) and molecule (M.3.5).
175
Note that higher energy electrons in an atom, will according to cordus,
have shorter spans (and higher frequencies). They will therefore need to
either be closer in to the nucleus, or arrayed around the outside. This is
counterintuitive in that conventional models suggest higher energy
electrons are further away from the nucleus.
Spin angular momentum
Particles, including the photon, are known to carry spin angular
momentum. In classical mechanics angular momentum is rotation of a
body around an axis. From the QM perspective, spin refers to a property of
the particle, and it is quantised. QM believes it to be an intrinsic property,
i.e. there is no internal structure nor any actual spinning about an axis.
The spin for fermions (e.g. electrons, quarks) is in ½ units of spin. For
bosons (e.g. photon) it is integer units. It is also known that the spin of a
particle is functionally identical to angular momentum, as shown in the
empirical Einstein–de Haas effect (electric current in a coil causes a
magnet to rotate), and the complementary Barnett effect (an object
becomes magnetised when spun). Trying to reconcile those is not easy, so
spin is conventionally left as a disjoint concept: Classical mechanics can’t
explain quantum spin, and Quantum mechanics can’t explain angular
momentum of a particle. .
Spin
From the Cordus perspective there is significance in the magnitude of spin:
it comes in discrete quanta of ±1/2 multiples of the reduced Planck's
constant ħ = h/(2π), which is termed the spin quantum number. Why ½?
Why not 1/3 or some other fraction?
Cordus suggests that the ½ spin arises from a cordus with two rather than
any other number of reactive ends. Each time the cordus re-energises, the
next reactive end is 180o offset from the previous one, not 120o as would
be for three REs. The implication is that the re-energisation of the cordus is
functionally equivalent to a single reactive end that rotates in 180o
increments.
Cordus suggests that the conventional concept of spin confounds two
similar but different effects: the frequency oscillation whereby the two
reactive ends take turns at being energised, vs. the hyff (force field) that
those REs emit. Thus the following clarifying lemmas.
Lemma M.2 continued
M.2.9 Spin is a compound concept and more usefully partitioned into
different types, based on the underlying mechanics.
M.2.9.1
Cordus-spin: Half-spin fermions (matter particles: electron
& leptons, quarks, & composite particles) are cordus
structures with two reactive ends.
M.2.9.1.1
The re-energisation of the cordus is functionally
equivalent to a single reactive end that rotates in
176
M.2.9.1.2
M.2.9.2
M.2.9.3
M.2.9.3.1
M.2.9.3.2
M.2.9.4
180o
increments. This creates
angular
momentum.
The whole photon cordus can rotate in roll about
its flight a axis. Thus a photon may have either leftor right-handed circular-polarisation: neither more
nor less states than two.
Reactive-end spin: Half-spin fermions can share locations
of their REs providing they are in complementary
frequency states. Specifically, two electrons can be in the
same location, including an orbital, providing they have
opposite spin.
Hyff-spin: Integer-spin (±1) bosons have two variants.
The elementary type are what Cordus calls hyff,
and contribute to the Cordus theory of fields.
These are what QM calls virtual particles. Multiple
hyff force fields can share the same space.
Atoms with full orbitals, e.g. helium-4, have
integer spin overall. This only means that they
have zero net angular momentum.
The photon (but not the virtual photon, which is covered
by M.2.9.3)38 is an exception in that it has elements of
multiple spin behaviours. This is an artefact of the way
compound-spin is defined.
Thus plain ‘spin’ is an overloaded concept that should not be used without
clarification. It primarily refers to the number of reactive ends in the
cordus, and secondly to the ability of cordi and hyff to share space. Thus
spin refers to the frequency model of the particuloid.
Pauli exclusion principle
The Pauli exclusion principle is that electrons (and protons, neutrons, and
fermions in general) must have opposite spin if they are to occupy the
same space. In contrast the photon (and bosons in general) have integer
spin and can co-locate.
From the Cordus perspective, this is covered by M.2.9.2: the exclusion
principle represents the fact that each orbital in the atom can be filled
with only two electrons (no more), and these electrons must have
opposite spin.
The cordus explanation for the Pauli exclusion principle is straightforward:
the electron cordus has two ends, only one of which is fully energised at
any one time, and two such cordi can co-habit, providing they are in
different phases. They achieve this by making complementary frequency
state synchronisations (CoFS), mediated through their hyff.39 Cordus
38
The photon and the ‘virtual photon’ are very different structures
according to Cordus: the photon is a cordus, whereas the virtual photon is just the
hyff component of the cordus. Cordus questions the validity of the term ‘virtual
photon’ since it implies a particle.
39
This is a stable configuration for the electron because it means that
when it is dormant or out of its second mode then another electron is looking
177
further suggests that these pairs of electrons are entangled, i.e. they are
actively influencing each other. The hyff are never completely off, except
momentarily, so the two electrons can affect each other’s location and
frequency states.
2.4
Atomic bonding
The cordus idea extends to explain how bonds operate between atoms.
Each orbital around an atom has two modes (locations) and requires two
full-time-equivalent electrons to fill. However a electron does not have to
be dedicated to the atom: it may be part-time, with only one cordus-end
in the atom under consideration, and the other in a neighbouring atom.
Doing this creates a bond between the atoms. As every electron has two
cordus reactive-ends, it therefore has two possible RE mode locations.
Cordus suggests that the ability of the electron cordus to have one end
associated with one atom and the other end with a different atom is the
underlying mechanism for all bonding between atoms. See M.3.1 below.
Multiple electrons can therefore bind (M.3.2) a series of atoms together
into larger molecules, providing the atoms are sufficiently close that a
geometrically suitable orbital can be offered to the valence electron
(M.3.3).
Cordus does not specify whether or not, within one atom, all the electron
cordus-states are synchronised to just two complementary states, for all
orbitals: i.e. whether the atom as a whole is in a CoFS state. Presumably it
is, at least to some extent, since the relationships between the inner
electrons and the nucleus would seem likely to impose constraints on the
outer electrons (M.2.8). Regardless, the bonds between atoms will
presumably propagate synchronisation across at least the orbitals involved
(M.3.4), and this means into other atoms in the molecule. Thus to some
extent the molecule as a whole will be in an entangled state. Thus cordus
predicts rapid transmission of information within a molecule.
These concepts are summarised in the following lemma.
Lemma M.3 Electron-mediated covalent bonds
M.3
Covalent bonds
M.3.1 Electron covalent bonds are created when one end of the electron
cordus is in a different atom.
M.3.1.1
A covalent bond is effectively a shaped orbital, but
between two atoms rather than only inside one.
M.3.2 The electron cordus is elastic and can exert force that keeps the
ends from separating, i.e. generates a force that bonds the atoms
together. (The photon may not have this capability).
after the mode. The two electrons guard each other’s modes, and this strengthens
their ability to resist disruption by hyff from other electrons within the atom and
externally, hence the stability, and lower chemical reactivity.
178
M.3.3 Suitable geometric arrangement of the atoms is necessary for
bonding to occur: the valence electron needs to have access to an
orbital that is sufficiently within the constraints imposed by its
span, and therefore by its energy. Electron energy, span, available
orbitals, and geometric spacing are therefore bonding factors.
M.3.4 Electrons that are shared between atoms are in CoFS states with
both atoms.
M.3.5 Covalent bonds within the molecule distort the shapes of the
electron orbitals.
Electron bonds have some strength. This is presumed due to the restoring
force of the fibril. When the span is increased, i.e. two reactive-ends of the
electron are separated, then the fibril (or the hyff) exert a force that brings
them closer together (M.2.1.2). However the restoring force does not
close the span completely, but only keeps it within some range of defaultspan. Free electrons have a default span inversely proportional to their
frequency (see M.2.7) [5].40
Ionic bonds are electrostatic attraction effects, caused by the metal having
less affinity for its electron than the non-metal. Van der Waals force may
be caused by the hyff of electrons protruding beyond their orbitals,
especially when existing covalent bonds within the molecule distort the
electron orbitals (M.3.5) and thus cause polarisation effects.
Casimir effect
The Casimir effect is a closing force between two conductive plates that
are close together. The effect also occurs in a vacuum, i.e. when there is
no intervening matter. The conventional explanation is
that
electromagnetic quantum fluctuations occur around the plates, but those
in a narrow gap are weaker than outside, so a force arises pushing the
plates together, i.e. a type of pressure effect.
The Cordus explanation for the Casimir effect is that the plates are so close
that some electrons have a reactive end in each plate, and thus their fibrils
exert a closing force, just as in any other electron bonding situation. The
Casimir effect requires that the plates be conductive, and Cordus
interprets this as necessary for the provision of mobile electrons.
According to Cordus it is the way the electron hyff are free-ranging that
causes the effect, which in turn depends on the material properties (which
can be manipulated). The cordus explanation is similar for the Jospehson
effect, where electrons can cross a thin insulating barrier.
40
However the span in a bonded situation is different: any span-deviance
is accommodated by loaned energy from the other electron, via a small phase
difference in the complementary synchronisation. See also the Level of Assembly
concept in ‘Cordus in extremis’.
179
3
Application to matter generally
de Broglie equations
The de Broglie equations [14-15] describe the wavelength of matter: (a)
Wavelength λ = h/p, i.e. is inversely proportional to momentum p, and (b)
frequency f =E/h with kinetic energy E, and Planck's constant h.
This wavelength is for moving particles. Such a particle appears to behave
as a wave in its ability to diffract into fringes at gaps or double-slits. For
example, electrons form fringes in the double-slit experiment. From a
classical perspective this is unexpected behaviour for a 'particle', and the
usual explanations are that the particle behaved as a wave with the de
Broglie frequency. Quantum superposition of states and probability theory
is another explanation. The de Broglie equations imply that a particle at
rest does not have a wavelength or frequency.
Curiously, the direction of the frequency is ambiguous. The same problem
was encountered with frequency in the case of light waves and photons
(ref. Cordus Conjecture). The quantum perspective is a wave-packet
interpretation: that the particle is a travelling packet of waves. This
conveniently also provides an explanation of a sort for Heisenberg's
uncertainty principle. However the wave packet idea introduces issues of
its own, namely the need for not one but many frequencies to make up
the packet. What does the de Broglie frequency correspond to in a wave
packet? What does ‘frequency’ correspond to in a particle, and to what do
all the wavefuntion frequencies physically correspond? To those
existential questions quantum mechanics has no answer other than the
mantra that there is nothing deeper, not any internal variables, but that
the mathematics is the reality.
Cordus frequency for a particuloid
The Cordus perspective is that all fermion matter ‘particles’ are cordi
(M.2.9.1), and oscillate their appearance at the ends of their span. This
readily accommodates the idea that matter has a frequency.
Cordus goes further than de Broglie to state that matter has a frequency
even at rest. The Cordus and de Broglie concepts of frequency are very
different, and should not be confused. 41 The cordus frequency concept is
further developed in the following lemma.
Lemma M.4
Matter
This lemma extends cordus concepts to matter generally.
M.4
Cordus matter
41
The cordus frequency is not the same as the de Broglie frequency.
Cordus frequency applies to all particuloids, whether or not they are moving,
whereas de Broglie only applies to moving particles. Cordus does not have a
specific frequency for moving particles, but instead includes a motion effect on
frequency in ‘Cordus in extremis’.
180
M.4.1 All particles including the electron, proton, neutron, and quarks,
may be represented as cordi. Thus they have a fibril, reactive ends,
and hyff of some type.
M.4.2 The cordi oscillate with a frequency. This means that matter does
not exist as single-point particles that are continuously in
existence. Instead matter oscillates its appearance at either end of
the cordus span. The cordus frequency is tentatively assumed to
be the de Broglie frequency.
M.4.3 The direction of frequency oscillation represents a polarisation
variable. It is assumed to generally be transverse to the direction
of particle velocity, but not exclusively so.
M.4.3 The cordus frequency exists even when the particle is not moving.
M.4.4 The larger the mass the higher the frequency.
M.4.5 The higher the frequency the shorter the span.
M.4.6 Bonds, e.g. those between protons and neutrons, and also those
between atoms, carry forces that can synchronise the phase of
particles with compatible frequencies, hence coherence.42
M.4.7 Increased kinetic energy of the particle causes increased
frequency.43
M.4.8 Temperature does not apply to a single particle, but to aggregates
of matter, being the vibrational energy stored in the bonds
between atoms (phonons), in turn caused by electrons in
stretched orbital modes.
M.4.9 Assemblies of particles, e.g. molecules and bodies, generally do
not have an observable overall body cordus frequency, unless they
are brought into a state of coherence.
Matter waves
The 'matter wave' phenomenon is explained as a cordus particuloid with
velocity. The oscillation is transverse to the velocity. Heavier cordus
particles have higher frequency and shorter span. Hence a microscope
using electrons has greater resolution than one using photons. The moving
cordus particle has hyff and these engage with the edges of gaps and
cause quantum angular deflection of that reactive end, hence fringes. See
also ‘Wave particle duality of the electron’ above, and 'Large-body matterwaves' below.
From the Cordus perspective the phenomenon is not really a 'matter
wave' but only looks like a 'wave' because the fringes happen to also
follow wave mathematics.
What is the diameter of a particle?
Physics has several interpretations for what a particle consists of.
Mathematically it is treated as a zero-dimensional point source, without
internal structure. At other times it is considered to be a sphere. And at
42
When the internal coherency fails, the atom decays.
43
This lemma is included for consistency with de Broglie's equation. However it is not
immediately needed, and the mechanism is unclear. An in extremis speculation is that the motion of a
particuloid may cause the span to realign normal to the direction of motion, and that the effect is
dependent on mass (hence momentum).
181
yet other times it is considered to be made up of further zero-dimensional
points. For example, the proton has three quarks (UUD) held together by
gluons.
The general premise is that a particle is a stable aggregate of one or more
semi-permanently existing sub-particles, hence that it is meaningful to ask
questions like ‘what is the diameter of the particle, e.g. proton?’ From a
cordus perspective this is an invalid question: it is not meaningful to talk
about the diameter of say a proton, as if it had a hard surface.
From the Cordus perspective the elementary particle, e.g. photon or
electron, is not a sphere in the first place, but rather a three dimensional
rod-like structure (or multiple rods), with fuzzy ends too. Nor does it
permanently exist in one location, but instead oscillates its existence at its
reactive ends.
Cordus suggests that the zone of influence of the particle extends well
beyond its geometric modes. The proton is likely to have hyff that create a
zone of influence: this may be somewhat diffuse, perhaps shaped, and the
outer zone may be considerably larger (though weaker) than commonly
perceived.
Existing methods of attempting to measure the ‘diameter’ of the proton
involving measuring its interaction with electrons, either in bonding
situations or impact-scattering. From a Cordus perspective these
experiments are measuring the average interaction geometry of the
electron and proton, not a physical diameter. It is natural to call this the
‘diameter’ of the proton, but that really is only an interpretation based on
the a priori assumption that a particle should be a sphere of charge.
Cordus further suggests that the measurement is dependent on the
probing particle. This is consistent with the observation that the diameter
of the proton is measured to be smaller when the muon is used as the
probing particle.44 Any cordus particuloid, the proton in this case, adjusts
its span depending on the other particuloid it needs to interact (bond)
with. Thus the effective interaction geometry depends on the participants
in the interaction, and presumably their energies too. There is no solid
physical diameter for a particuloid.
Cordus predicts that a proton will have many ‘diameters’ depending on
what interaction is being measured, and the nature of the probe.
So it does not make sense to think of a particle as a sedate, stable, solid,
in-one-place, well-defined sphere (of mass or charge), as if it were a
planet. It is more like a moving cracking whip. Cordus suggests that
composite ‘particles’, e.g. the nucleus as a whole and the individual
proton, have complex interactions within, as the multiple internal cordi all
seek their place to exist. Furthermore, as the photon cordus relates in
some way to that of the electron, so it seems possible that other sub-
44
The proton would be expected to be slightly heavier in this case, see
‘Cordus in extremis’.
182
atomic cordi-particuloids could also be comprised of yet smaller cordi
interacting in various ways.
It is not meaningful, from the Cordus perspective, to perceive the atom as
hard little balls orbiting around a nucleus made of compacted other balls,
as shown in the popular symbol for the atom.
4
Conclusions
Some of the most enigmatic effects in physics have been wave-particle
duality generally, and in the case of the electron specifically, the
Aharonov-Bohm effect, and the Casimir effect. Even relatively core
concepts of atomic physics, like spin and the Pauli exclusion principle,
have not previous had satisfactory descriptive explanations. The
conceptual contribution of Cordus is that it provides explanations for these
effects. Moreover, these explanations are consistent with its explanations
in other areas, as the companion papers show, so the emergent model has
a high degree of coherence.
This paper has provided a re-conceptualisation of the electron. It is implied
that the same principles apply to matter generally. The better
understanding of the electron that emerges from this paper is useful in
developing a model of other electron functions, particularly its interaction
with the photon, the energy cycles and entropy within matter,
explanations of superfluidity and superconductivity, and ultimately an
understanding of why quantum mechanics does not scale up to
macroscopic objects.
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Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011)
Schrodinger’s Cat reconceptualised. Cordus matter: Part 3.5 viXra
1104.0026, 1-10 DOI: vixra.org/abs/1104.0026.
Yamada, M., Unriddling the Aharonov-Bohm effect. Il Nuovo Cimento A
(1971-1996), 1987. 98(2): p. 205-210.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011) Wider
Locality. Cordus matter: Part 3.1 viXra 1104.0022, 1-7 DOI:
vixra.org/abs/1104.0022.
de Broglie, L., Recherches sur la théorie des quanta (Researches on the
quantum theory). Annales de Physique., 1925. 3(10).
de Broglie, L., The wave nature of the electron, in Nobel Lecture. 1929,
Nobel Prize in Physics.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011)
Quarks. Cordus in extremis: Part 4.4 viXra 1104.0030, 1-15 DOI:
vixra.org/abs/1104.0030.
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Matter particuloids
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Energy cycles within matter
Cordus matter: Part 3.3
Pons, D.J. , 45 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
The interaction of light with electrons is one of the fundamental perceptual
realities of what we see. Yet that interaction is only partly understood.
Cordus concepts are applied to develop a descriptive model of the
mechanisms whereby photons are absorbed into electrons and emitted.
From the Cordus perspective, the temperature of a body is primarily a
measure of its phonons (lattice-vibrations). Cordus shows why entropy
occurs, despite the individual mechanisms being reversible. An
understanding of the mechanisms for entropy is relevant to the
understanding of coherence, superfluidity and superconductivity. Cordus
suggests that a failure to adequately conceptualise entropy leads to
misapplication of coherence and ultimately to unreliability in the premise
of superposition.
Keywords: absorbance; emission; photon; electron; entropy
Changed matter waves to include level of assembly predictions.
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1
Introduction
The starting focus of this set of papers was the behaviour of the photon,
and the loci it takes. However the photon is only the specialist flight-mode
of a larger energy cycle, which we term the life-cycle of the photon. The
electron is the primary device for capturing and emitting these photons.
Photons generally start as energy within matter, are ejected, fly free for a
while, and are then reabsorbed into other matter. Photons are therefore a
way for matter to transfer energy to other matter. Thus light is a
distribution and energy-rebalancing mechanism for matter. Photons do
not exist as identifiable entities within matter: their energy is spread into
it. There is therefore a life-cycle for the photon. Understanding this could
help better understand the photon. This paper, which is part 3 in a series
on matter, explores emission and absorbance of light from the perspective
of the Cordus conjecture.
Also, there is the problem of entropy to deal with. Where does the
inelasticity occur in the life-cycle of the photon? What is the relationship
between photon and heat? Such questions on the interaction of light and
matter are addressed by quantum electrodynamics (QED). Even so,
quantum mechanics struggles to explain how entropy arises: it interprets
45
Please address correspondence to Dr Dirk Pons, University of
Canterbury, Christchurch, New Zealand. Copyright D Pons 2011.
186
Energy cycles
quantum phenomena as superposition and therefore that the matter is in
coherence, and expects that all macroscopic bodies should also show
coherence and superposition. Which they do not, much to the chagrin of
quantum mechanics. Thus, from the QM perspective ‘there is no
conclusive evidence about how the classical world appears’.46 Extension of
the Cordus conjecture suggests other novel ways of looking at the
problem.
2
Cordus model for photon absorption
The mechanism for absorption of a photon into matter is uncertain. The
general interpretation of physics is that photons are absorbed into
electrons. Absorption is not an instant event - it requires some depth to
the material and mass density is one of the factors though known to be
non-linear (Beer-Lambert law). It is known that the process may be
saturated, i.e. dependent on the light intensity - explained as atoms being
excited into upper energy states quicker than they can decay. Also, the
fine-structure constant is (among other things) a constant for the
interaction between electrons and photons.
High energy photons (Compton scattering)
It is possible for the electron to absorb only part of the energy of the
photon, and send the photon on its way with lower energy (hence
frequency), as Compton scattering shows. In this effect a high energy
photon, e.g. X-ray, collides with an electron, and bounces off. The photon
exits with lower energy (lower frequency) on a deflected path, the change
in frequency being related to the angular deflection of the exiting
photon.47 The electron is physically displaced and may be ejected from
the atom. The effect, or at least the equations thereof, are based on the
conservation of energy and momentum, and the assumption that the
photon has momentum. The Compton effect is generally accepted as
evidence for the particle nature of photons, and hence also quantum
theory. In principle the process may be at least partially reversible, since
the inverse also occurs, where low energy photons may be energised to
higher frequencies by interaction with energetic electrons. The Compton
effect only occurs for high-energy photons such as X-rays.
There are two output variables in the Compton effect: the angle of
deflection and the frequency of the leaving photon. Though related by an
equation, neither variable can be directly controlled. So what is the
independent variable and how does the effect work? Cordus suggests that
the photon cordus comes close to that of the electron; the frequencies are
too asynchronous to readily permit their joining (absorption), however
their hyff affect each other; the hyff exert forces between the cordi even if
they are near misses; at comparable frequencies the second reactive end
46
1.
Anastopoulos, C., Frequently asked questions about decoherence.
International Journal of Theoretical Physics, (2002). 41(8): p. 1573-1590.
47
However it may be that the photon is not partly absorbed, but rather
totally absorbed and a new photon emitted.
187
Energy cycles
will experience a similar force to the first. Consequently both ends of the
photon are deflected, rather than one just being delayed. The angular
deflection occurs depending on the positional and angular alignment, and
the phase differences between photon and electron cordi. If the electron
is not quick enough to move, then it gives the energy back to the photon,
which continues on a deflected path with no change in frequency.
Mid energy interactions
Mid energy photons also interact with electrons, in the photoelectric
effect. In this case the photon is absorbed completely, and the electron is
moved to a higher orbital band, or emitted from the atom. The effect is
dependent on the frequency (not the light intensity), and for a given
substrate requires a minimum threshold frequency of the incident
photons. Electrons appear to require a minimum quantum of energy to be
released: any excess is converted to kinetic energy. Light intensity
determines the number of electrons emitted (current), not their energy
(voltage).
The Cordus explanation of absorption is as follows: the incoming photon
comes close to the electron orbital; the hyff of the photon connect to
those of the electron; the two fibrils join; the energy of the photon is
added to that of the electron. If there is sufficient energy in the photon to
make up the requirement for the next energy quantum shell, then the
electron will appear at that higher position at its next frequency cycle.
Now that the electron has more energy it will have faster frequency too,
and shorter span, and can therefore dance around the slower moving
electrons. However, with sufficient energy, the electron-to-nucleus bond is
overloaded and the electron escapes entirely from the atom (photoelectric
effect). If there is not enough to bridge the gap in the first place, or leftover energy, then it goes into heat, i.e. vibration of the lattice, or phonons.
Having absorbed a photon, the electron can also emit a new one, which
does not have to be the same frequency. This gives rise to the effect we
perceive as colour of an object. The absorption effect is dependent on
frequency of the photon. If the incident light is 'white', i.e. made up of
many frequencies, then photons of some frequencies may be absorbed
and others left to transmit through. Thus a body may be opaque to some
frequencies and transparent to others. If it is light, then the exit light has a
particular colour corresponding to the frequencies not absorbed.
We conclude that the energy of a photon can be partly changed, i.e. the
quantum is not strictly fixed.48 The hyff pump energy into and out of the
cordus (photon or electron), as per the concept of passing observation
(ref. ‘Cordus Conjecture’).
48
The term ‘quantum’ is a good one for the energy levels of the electron
orbitals in an atom (see M.2.5) because these are set quantitative increments,
albeit non-uniform. However the ‘quantum’ word has been indiscriminately, even
if enthusiastically, applied to just about everything, and now confounds several
effects. We use ‘quantum’ in the original sense of set intervals, and otherwise use
the word ‘granular’ for fine-scaled discontinuous phenomena.
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Energy cycles
3
Recycling the energy: reversibility, elasticity, entropy
Energy from incoming photons is distributed into the receiving electron
system in several ways: boosts the energy level of the electron (quantum
shell-increment); ejection of the electron with kinetic energy;
displacement of free electrons (plasmons); and vibrational strain between
the electrons making up the inter-atomic bonds (phonons).
The latter energy fragment is distributed to the bulk by vibration, hence
conduction or phonons. That vibration is diluted as it is spread to further
atoms. While it is theoretically possible to reassemble the heat fragments
and recreate the photon, e.g. the thermionic effect, this is impractical as a
spontaneous event as the heat is spread too far away into the bulk of the
matter.
Phonons, heat, and temperature
In thermodynamics, heat is the energy transferred from one body to
another. The nature of that energy is generally left unspecified, so ‘heat’
has many meanings. The cordus perspective suggests that ‘heat’ can be
differentiated into radiation heat, for which the mechanism is photon
transfer, and conductive heat, which uses phonons. Thus what we
perceive as conductive heat is the movement of phonon vibrations
between atoms in a bulk, and Temperature is the measure of the severity
of the phonons. This is why there is an absolute zero temperature: it is
simply when all phonon motions cease. It is also why light does not have a
‘temperature’: light is different to phonons.
The concept of phonons is readily understandable as vibrations in the
lattice of solids. However liquids, and especially gases, do not have
crystalline structures, but they do have conductive heat, so how do
phonons apply there? The cordus perspective is that the e-hyff are able to
communicate force and thus move neighbouring atoms, even if they are
not formally bonded together. This also results in the Brownian motion of
gases. In a gas with many atoms (or molecules), the position of each atom
is determined by the hyff (in different phases) from many other atoms,
and this results in disorderly systems. This is not to say that the systems
are inherently disorderly or probabilistic. Instead the underlying
mechanics is deterministic, but the complexity rises so quickly with the
number of participating atoms, that the system behaviour is practically
disorderly because it is too difficult to predict.
From a Cordus perspective, temperature is phonons, i.e. the relative
motion between atoms, transmitted through the electron bonds. However
the frequency of the electron cordus is intrinsic energy, and is not the
same as temperature. The two are different forms of energy. Hence in the
photovoltaic effect, the energy of the released electron is determined by
189
Energy cycles
the frequency of the incident photon, not the temperature of the
substrate.
Thus higher temperature increases the number and magnitude of
phonons, and thereby adds to the disorderly regime within the material.
Phonons and electron-modes affect each other. Effectively a phonon is a
temporary displacement of one RE mode of the electron from its preferred
position. Energy can be transferred between phonons and electrons, and
again between electrons and photons. Thus electrons are the mediator for
both conductive heat (phonons) and radiation energy (photons), and can
transfer energy between the two forms of energy, albeit with some
dilution losses on the way. In summary temperature is a matter property
determined by phonons. This also implies that the conventional term
‘heat’ is unhelpful as it fails to distinguish between multiple phenomena.
Entropy
Taken together, the implication is that an atom that has surplus energy
can dispense it in five main forms: electron orbital change (including
bonding), electron ejection, photon ejection, electron flow (plasmons),
and phonon propagation. If phonons, then another atom some distance
away receive some of the energy and will likewise use what it can and
dispense with the rest. That remote atom might emit a photon for
example. Even if that photon was sent straight back to the original atom
(which is not generally the case), there would still be less energy in the
feedback loop because of the phonon dilution in the bulk, and the time
required for the photon flight. Thus the individual mechanisms are all
reversible (elastic), but the system as a whole is not, and we suggest this is
what creates entropy.
Both photons and phonons tend to be dispersed out into the surrounding
space or material (respectively), and this dilution of the original energy is
the primary mechanism for thermodynamic irreversibility and entropy.
The geometric and micro-structural complexity of the matter accessible to
the photons and phonons introduces so many dilution paths that it is
extremely unlikely that the energy fragments will spontaneously
recombine.
Geometric separation is another contributory factor: when the matter
separates or radiates photons across space, then the dilution is further
increased and the number of paths reduced by which the energy can come
back together. The enormous radiative loss of photons from stars
contributes to entropy, because that energy cannot realistically all be
recovered after it has travelled billions of years and stopped in our eye,
and even if it were reflected back it would be more billions of years to
travel back.49 In the meantime space expands, which adds to the delay.
The expansion of space in the universe contributes to entropy.
49
As the next bracket of papers, ‘Cordus in extremis’ shows, that
smoothing out of energy means that the fabric of the vacuum is relatively smooth,
and the fabric determines time at the local sub-atomic level. Thus in a way
entropy is linked to the consistency of the universe and the mechanisms whereby
space and time operate.
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Energy cycles
Separation causes the photon to arrive late, the more so if it involves
transmission through denser material. Thus the energy is not delivered at
the time it might have been, but is instead postponed into the future, i.e.
an arrow of time. If that postponement is indefinite, it takes energy out of
the system. This is another barrier to recombining the original energy, and
thus another contribution to entropy.
4
Photon Emission
From the Cordus perspective, photon emission is a reversal of the
absorption process. It starts with the electron being in an energised state
due to other energy input. If there is an unfilled lower energy vacancy then
the e-fibril is drawn to that space by the lack of hyff emanating from that
location. At the next frequency cycle the RE switches its mode to
terminate at that inner vacancy, and the electron now appears there. This
releases a photon containing the surplus energy. The size of the energy
fragment corresponds to the separation of the energy shells, and this is
also associated with the frequency. Hence the frequency (wavelength) of
the emitted light depends on the change in orbitals.
Assuming that multiple atoms in a material generally do not synchronise
their electron frequencies, so each atom will emit a photon when it is
appropriate for it to do so, and the resulting photons will not be in phase
with each other, though they could be the same frequency.
Special case: stimulated emission
In stimulated emission, the incoming photon triggers an electron to drop
energy level and emit another photon. The original photon survives: it
engages with the electron only in passing. The new photon has the same
kinetic properties: frequency, phase, polarisation, and also direction of
travel. If there are other atoms in a similar state of readiness then they too
may be triggered to release photons, and the cumulative effect is the
laser.
The Cordus explanation is that the interactions are of the passing type:
that the hyff attract (repel) the roving electron to align with the photon
cordus, and then precipitate emission of the second photon. The
alignment causes the second photon to have the same phase, polarisation,
and direction of travel as the first. It is a dynamic, on-the-spot form of
CoFS. It is presumed that for the passing interaction to have no
consequence on the flight of the first photon, that the electron must
require negligible energy to change states. In turn this means that the
electron’s surplus energy available to put into the second photon must
closely match that of the incoming photon. Thus the composition of the
medium determine its electron properties and thus frequency of emitted
light. From a Cordus perspective, the second photon is not necessarily
emitted from the same space as the incoming one: it may be offset
laterally or axially.
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Energy cycles
5
Conclusions
The interaction of light with electrons is one of the fundamental
perceptual realities of what we see. Yet that interaction is only partly
understood. Applying the Cordus concept allows a better description of
the mechanisms whereby photons are absorbed into electrons and
emitted. The model also provides an explanation of how the irreversibility
occurs in physical systems, because conventional physics tends to provide
elastic interactions between atoms. From the Cordus perspective, the
temperature of a body is primarily a measure of its phonons (latticevibrations). Cordus shows why entropy occurs, despite the individual
mechanisms being reversible.
An understanding of the mechanisms for entropy is important in the next
paper (part 4) which deals with special states of matter. It is shown that
the conditions for superfluidity and superconductivity are effectively lowentropy states, where the phonon transmission is suppressed. This is also
relevant to the understanding of coherence. Cordus suggests that a failure
to adequately conceptualise entropy leads to misapplication of coherence
and ultimately to unreliability in the fundamental premise of superposition
that underpins quantum mechanics. The cordus re-conceptualisation of
entropy might seem basic and almost self-evident in hindsight, but it is a
core concept in understanding why QM does not scale up to the
macroscopic world. It is the Achilles heel of Quantum mechanics.
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Energy cycles
193
Special states of matter
Cordus matter: Part 3.4
Pons, D.J. , 50 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
The Cordus principle of complementary frequency states (CoFS) is used to
develop a novel descriptive model for the mechanisms underlying
superfluidity and superconductivity. In both cases Cordus explains the
effects as synchronisation of forces between electrons and atoms. Several
associated effects are likewise explained, including quantum vortices, heat
conduction in superfluids, and the Meissner effect in superconductors.
Cordus also asserts that superposition does not exist, at least not the way
QM conceptualises it. In particular, that the mathematics of superposition
and the wavefunction are not the reality, only mathematical
approximations of deeper effects, and are unreliable qualitative descriptors
of those underlying mechanisms. The concept of ‘coherence’ is reconceptualised and the reasons why that state cannot be readily achieved
are discussed. Cordus also explains why Quantum mechanics, which seems
to apply at the level of individual particles, does not scale up to
macroscopic bodies.
Keywords: superfluid; superconductivity; Meissner; superposition;
coherence; hyff; Josephson; quantum vortex; entropy; scale
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Introduction
The cordus concept was originally created as a test solution for photon
path dilemmas, but has been shown to provide insights about a much
wider range of effects. This paper provides a cordus interpretation of
several special states of matter: superposition, coherence, superfluidity,
and superconductivity. The treatment of these topics is conceptual and
descriptive, as opposed to the mathematical approach more
conventionally used.
This particular paper is fourth in a series that apply the Cordus conjecture
to matter. The first part explained entanglement, debunked Bell’s
theorem, and proposed a new principle of locality. The second showed
how the electron, and indeed matter generally, could have a cordus
structure. The third re-conceptualised
entropy and showed why
interactions that were individually elastic at the atomic level nonetheless
created entropy at the level of the body as a whole. Those concepts are all
foundational to the present paper, particularly the models for the electron
and entropy.
50
Please address correspondence to Dr Dirk Pons, University of
Canterbury, Christchurch, New Zealand. Copyright D Pons 2011.
194
2
Superposition
Superposition from the perspective of Quantum mechanics (QM) is that a
particle occupies all possible quantum states simultaneously, and only
collapses to one when the variable is measured. According to QM it is only
probability that drives this, there is no underlying variable.
From the Cordus perspective, superposition is simply that the cordus
particuloid is actually physically oscillating between two positions. These
positions are the reactive ends at the end of the span. The cordus particle
(e.g. photon cordus) collapses to one of these ends when it is grounded
(L.2.2).
The QM and Cordus perspectives predict a similar overall effect, but their
explanations are very different. Cordus is particular about the type of
observation (L.3.5) and identifies this as an important variable.
Cordus does not support the concept of superposition in terms of
statistical indeterminacy as QM perceives it, but instead states that the
location of the particuloid alternates according to underlying deterministic
physical mechanics, and the probabilistic nature only emerges because the
observer inserts indeterminacy by selecting, even inadvertently, the
moment to make the measurement, and therefore the frequency state of
the cordus and ultimately the position at which it will be found.
Thus from the Cordus perspective, the perception of probability is only an
artefact caused by measurement-timing and epistemic uncertainty about
the underlying mechanisms. The underlying mechanisms are effectively
deterministic, and only look probabilistic because QM's mathematics only
go as far as averages. The probability is therefore not the reality, and
superposition is not a state in itself but simply a consequence of the
mathematics being unable to determine the state.
Furthermore, Cordus suggests that Superposition confounds two different
effects: positional and causal variability. Positional variability corresponds
to the cordus modes of the two reactive ends: there is positional
ambiguity in where the particuloid actually ‘is’ at any one moment.
However only one end is actually reactive, it is just that if the
measurement frequency is not high enough then it appears that the
particuloid is simultaneously in both positions. QM’s concept of
superposition strictly only applies to this positional variability, and even
then is only approximate as it’s statistical methods can only work with
average position.
Causal variability is multiple consequences in time, i.e. divergent system
states. Consider an event that has two possible outcomes, A or B. Once
either of these states occurs, then there are say two more outcomes: A1
or A2 for the A path of the tree, and B1 or B2 for the B branch. Thus after
time the system state has diverged into various outcomes, hence ‘causal
195
variability’. Quantum mechanics routinely assumes that causal variability
necessarily occurs with positional variability. Thus the QM thinking goes
something like this: ‘the particle is in two places at once, but the choice of
which has not yet been made. There are subsequent events <notice the
insertion of a time and causality premise here> the outcome of which will
depend on which location the particle chooses. Therefore those
subsequent events are also in superposition, i.e. exist simultaneously’.
Therefore the object or person <notice the insertion of a premise of
coherence here> in question will simultaneously be in several states, i.e. in
different futures.’
From there it is a very short logical step to the idea of a separate universe,
one for every causal outcome of every superposition states, hence the
‘many worlds’ theory. The combinatorial branching on that tree of
universes must be enormous if every superposition of every quark for all
of time, is to be accommodated. It is currently one of the favourite
contenders for a qualitative description of how QM works, but from a
logical perspective it creates more problems than it solves, and is hardly
parsimonious or even physical.
Cordus cuts this whole idea off at the root. It asserts that that causal
variability does not occur in the situation. According to cordus thinking,
quantum mechanics makes the mistake of assuming that causal variability
occurs with positional variability. Thus from the cordus perspective, a
particuloid that oscillates between two reactive ends (modes) does not
have dual futures. The confounding of these two types of variability drives
the paradox of Schrodinger’s Cat, as will be shown.
Thus superposition is an adequate mathematical representation of the
uncertain in average position of the reactive ends, but an unreliable
qualitative description of what is actually happening, and altogether not
applicable to causal variability. Consequently, cordus rejects the way
superposition is conceptualised in QM, and asserts that it does not occur
for macroscopic physical bodies, including cats.
The next section explains the fallacy of ‘easy coherence’, which is another
unreliable premise in QM, and commonly associated with the
superposition problem.
3
Coherence
From the QM perspective coherence is the ability for particles to interfere.
It is a fundamental requirement for many quantum effects, because it is
the premise that underpins superposition. If light or matter becomes
decoherent then interference is absent. However QM struggles to explain
why macroscopic objects are not coherent, and where classical behaviour
originates. Hence the scaling problem below.
The Cordus interpretation is different. First, Cordus rejects the
conventional concept of interference as a physical effect, though still
196
accepting it as a generally-adequate mathematical analogy. Cordus
suggests that separate particles, including photons, do not interfere or
cancel each other, and nor is interference is the mechanism for effects
such as fringes.
Body coherence
Coherence, from the Cordus perspective, is when all the cordus
particuloids, which may be photons, electrons, protons, and possibly
atoms & molecules, etc., have synchronised frequencies and phases
thereof, i.e. a form of complementary frequency state synchronisation
(CoFS). The bonds between any cordus particles are hyff and carry forces
that synchronise the cordus frequency and phase of particuloids, providing
the frequencies are compatible. We term this ‘body coherence’. For
photons in light beams, where the bonds are weak if they exist at all, the
coherence may be mainly temporal and coincidental.
Cordus predicts that body coherence requires a sufficiently stiff structure:
one where the bonds between particles and atoms are firm and able to
sustain the synchronicity. From this perspective coherence becomes
difficult to sustain when one part of the body goes in a different direction,
e.g. internal motion or flows. Internal inhomogeneity increases entropy.
Apparently it is not impossible to achieve synchronicity, as superfluidity
shows. However that effect occurs under constraints of homogeneity of
material and low temperature. Coherence is therefore not practical for
realistic every-day bodies: there is too much temperature (phonons) and
diversity of atomic composition.
Cordus predicts it will be impractical to achieve coherence for macroscopic
bodies at ambient conditions. It is particularly incompatible with living
creatures. These bodies cannot practically be put into coherence, nor for
that matter into superposition. Single cordus particles, such as electrons,
are self-coherent under any conditions. Assemblies such as atoms and
molecules are not necessarily self-coherent, but may be brought into
coherence (M.4.6).
Large-body matter-waves
A popular idea in conventional physics is that even large bodies, such as
motor cars, have a de Broglie frequency and should therefore be able to
diffract through a double-slit and form fringes. This arises from an
extrapolation of the QM wave-function idea. It is also a weird idea, i.e.
difficult to reconcile the prediction with the reality of every-day
experience. Cordus offers an explanation of what should be possible, and
not:
Small bodies: From the cordus perspective, sufficiently small
bodies, typically atoms and molecules, should be able to diffract,
form fringes through gaps, and pass through the double-slit
experiment with the usual outcomes, providing they are in bodycoherence. The Cordus explanation is that all the atoms in the
molecule translate in CoFS lock-step at the same time. So the
whole assembly effectively appears at one end of its span, and
197
then reappears at the other, generating hyff in each location, and
hence fringes. However smaller particuloids [higher mass] will
need closer spaced double-slits, and that will be a practical
limitation.
Large bodies: Macroscopic bodies cooled to near zero should be
able to be placed into coherent states of internal oscillation
(coherence), as a type of supersolid. Such bodies should be able to
diffract and form fringes through sufficiently large gaps (or at
edges), though the effects may be miniscule. Quite which mass
determines the span and frequency of an assembly in body
coherence is uncertain: the heaviest constituent particle, or the
body mass, or something else? Cordus suggests the last, and
makes two predictions. First, that for objects in body coherence it
is the Level of Assembly at which the coherence holds (see
reference [16] for elaboration of this concept) hence probably the
atomic mass. Second, large discoherent bodies like those that exist
at our level of reality will have no single frequency but instead a
spread of frequencies. Instead such bodies will have multiple
frequencies, analogous to white light. Discoherent bodies are
therefore predicted to diffract weakly if at all: any fringe effects
will be small and will be smudged. Even for a large coherent body
the diffraction effects are predicted to be small.
Furthermore, getting a large body into body-coherence is likely to be next
to practically impossible, especially for something like a motor car with
moving parts and fluid flows. The above applies to single gaps. This may
be a testable area for the cordus principle.
Cordus predicts that the double-slit experiment is infeasible for
macroscopic bodies, even if they are in body-coherence. This is because
the slit spacing (pitch to centrelines) will need to be similar to the span and
therefore very small. In contrast the slit widths will need to be large to
accommodate the macroscopic body, and will therefore delete the
medulla. The experiment will simply turn into a single large gap. Double
slit experiments are predicted to be feasible only where the outer limit of
size for the composite body (maximum material condition) is equal to or
smaller than the cordus span.
Cordus predicts that practically every object at ambient temperature and
visible with the naked eye is not going to form matter waves.
Quantum mechanics’ scaling problem
One of the puzzling features about QM has been why the effects it
predicts are only visible at sub-microscopic scale. For example, particles
seem to be able to appear in more than one place, and the act of
observing them influences their location. Yet macroscopic bodies show no
such tendency. Why does QM not scale up properly? If it is valid at
subatomic scale, what is preventing it from working at macroscopic scales?
Cordus shows why.
198
Cordus asserts that QM is only approximately accurate at the sub-atomic
scale (Cordus refutes the principle of superposition), and not at all at the
large scale. Briefly, the reason is that large bodies have too much internal
entropy (disorder) to have the necessary coherence to appear in more
than one location. Even if they did have body-coherence the results would
be miniscule (small span) and not as dramatic as popularly imagined. The
mathematics of QM are premised on coherence, and thus the explanations
of QM are unreliable where body-coherence fails. In most roomtemperature applications this is the atomic level. Quantum mechanics
therefore does not practically apply to large bodies, living creatures, or the
universe as a whole.
4
Superfluidity
Superfluidity occurs at low temperatures in materials such as helium, and
is characterised by unusual flow and thermal properties: the fluid can selfsiphon out of an open container; it has no viscosity (hence behaves
differently when rotated); and it has infinite heat capacity. It is known
that the superfluid properties of helium-4 and -3 are different, and
quantum mechanics offers specific theories for each: Bose–Einstein
statistics, and Cooper pairs respectively. Helium-4 has two protons and
two neutrons, and integer spin, and is therefore considered a boson. In
contrast helium-3 has only one neutron, ½ spin, and is therefore a
fermion. Fermionic condensed states require lower temperature. First two
electrons with opposite spin pair-up (Cooper pairs), and this creates an
integer spin assembly.
From the cordus perspective superfluidity is an application of
synchronisation (coherence), but between atoms not photons. The
current working model is that the interaction occurs through either the
electrons, or the vibrations (phonons) between the atoms (mediated by
electrons too).
Synchronisation of atomic forces
The
explanation
uses
electron-to-electron
complementary
synchronisation. This might be more relevant to fermionic condensed
states with ½ spin. The cordus explanation is that each electron is a cordus
and oscillates its appearance at its reactive ends. Thus two electrons from
different atoms may alternate their existences and thereby share the same
space. They achieve this by making complementary frequency state
synchronisations (CoFS), mediated through their hyff. The low
temperature is necessary to reduce vibrations of the electrons and atoms
(phonons).
Once the two electrons are entangled, they move together. So where
electron A goes, so does B, and the reciprocal. These correspond to the
conventional concept of Cooper pairs. The electrons themselves are
bonded into atoms, and those atoms also have other electrons. Those
electrons also become synchronised with other electrons in still other
atoms, either through entanglement, or phonons (see below). The result is
199
a connected network. The connecting force is from electron to electron,
through the nucleus and onwards through other electrons.
For helium-4, which is a boson with spin 1, the two electrons in the orbital
are already in a CoFS together, and this state is extended to neighbouring
atoms by the electron hyff. Spin in this case refers to the CoFS ability of
the atom as a whole, since both forms of helium have two electrons. The
hyff bump the neighbouring atoms, and push them into synchronous
frequency states. The low temperature is necessary to reduce the
background phonon noise. With bosons, many particuloids (e.g. atoms in
this case) may be in the same frequency state simultaneously, i.e.
‘complementary’ does not necessarily mean opposite in this case. One can
equally view the mechanism as synchronisation of phonons, because
phonons represent the dynamic nature of the electron bonds between
atoms.
Cordus suggests superfluidity will become compromised at relativistic
speeds. (See ‘Cordus in extremis’).
Fluid mechanics effects
Either way, mechanical movement of one atom takes others with it. Hence
the observed effect that a surface tension pulls a whole film along with it.
The whole body of liquid has complementary synchronised frequency
states. The body has some plasticity, presumably arising from both the
electron entanglement and in the orbital position of the electrons around
the nucleus. This plasticity means that individual atoms can move slightly
relative to their neighbours. The plasticity allows a film of fluid to be
flexible, and able to wet complex shapes, hence the observed Rollin film
and the self-siphoning behaviour.
A bowl of superfluid is known to rotate as a solid body at low speeds,
otherwise not at all at higher speeds. The Cordus explanation is that
rotation of the whole solid body occurs when the speed is sufficiently low
that imposed external shear forces (circumferential forces between bowl
and fluid due to surface tension) are lower than the capability of the hyffhyff forces at that location. The hyff forces can handle that level of shear
force, and therefore rigidly join the fluid to the container, and maintain
rigidity of the rest of the body of fluid.
At faster rotation the container rotates but the fluid stays still. The cordus
explanation is that the shear force between the container and the fluid is
too great for the hyff forces to cope with, so the fluid abandons that bond
with the container and instead preserves its own internal CoFS. This is a
natural consequence of the geometry: the radius of the bowl's surface
changes across the section, so if the fluid were to try and partially follow it,
then different velocities would be required at different radii, hence
internal turbulence, and this is incompatible with the CoFS coherence
condition.
There are three choices available to the fluid: (1) match the peripheral
velocities of the bowl and thereby generate internal vortices; (2) rotate as
200
a solid block with the bowl; or (3) decouple from the bowl by staying
stationary while the bowl rotates. Option (1) is the default for
conventional fluids, but for superfluids is prevented by the CoFS state.
Hence also the observed lack of viscosity of a superfluid. Only (2) and (3)
are available to a superfluid, and the choice depends on the relative
strength of the shear force at the wall compared to the hyff strength.
Cordus also explains phase effects in superfluids. The phase of the
superfluid refers to the CoFS state, i.e. the polarisation state of the
electrons. The phase may change slightly over distance, due to the
flexibility (above). But in a connected region it must, via any closed path
through the fluid, meet up at the same phase as before. This means that if
there is a hole in the fluid or a loop of fluid that reconnects, then the same
phase must be reached at the end of the loop, whichever path is taken.
However, it does not have to be exactly the same phase: a whole number
of phases different is also sufficient (but the total Berry phase effect must
be zero). Hence the known effect that the phase of a superfluid is
quantised. Hence also quantum vortices, these being loops where there is
an integer whole phase difference.
The cordus explanation for the rapid heat conduction of a superfluid is
that the state synchronisations and physical co-location of electrons mean
that the structure is stiff regarding phonon transmission. Phonons are the
mechanism of conductive heat transfer and the measurement of
temperature. Thus excess energy is rapidly dispersed through the fluid, by
phonons. This stiff direct coupling provides a wave-like propagation of the
energy, more similar to propagation of sound (hence 'second sound').
The speed is presumed finite due to the compliance in the electron
orbitals, and the ultimate limit is probably the cordus frequency of the
electron.
5
Superconductivity
Superconductivity is zero resistance to electrical current, and occurs in
some but not all materials, and below a critical temperature. The
temperature is dependent on the material properties. Denser isotopes
need lower temperatures to superconduct.
The existing explanation (BCS theory) is that electrons cause phonon
interactions that link electrons into pairs (Cooper pairs). The initial
attraction between electrons, which otherwise should repel, is held to be
caused by the interaction of the electron with the positive charges in the
lattice. These pairs then flow unimpeded by the material, whereas usually
the residual impurities would cause resistance.
CoFS network of orbitals
The Cordus explanation is that conventional resistive current flow involves
whole electrons hopping from one atom to the next, and having to get
past impurities, grain boundaries, and lattice imperfections on the way,
hence resistance. In the usual warm state the positions of each electron
201
(there are two, one at each end of the electron-cordus), are determined by
the medium, particularly the location of other hyff generators. Under
usual conditions the overall external hyff environment perceived by any
one electron is disorderly and over-prescribed. Therefore the electron is
forced to rapidly change its position. That electron also generates hyff and
contributes further to the disorderly regime. Note that the hyff range of an
electron is considerably larger than simply the immediate atom, so one
hyff affects multiple atoms, and this causes the over-prescription (see the
Principle of Wider locality). Individual electrons are forced to keep
changing their modes to accommodate the disorderly regime. These
modes are necessarily higher-energy states, i.e. with some tension along
the span, because the lower-energy resting states are non-accessible
solutions.51 Brownian motion results. This is what causes resistance in a
conventional conductor. The energy is partly dissipated in phonons during
these impacts.
Superconductivity arises from the electrons forming a network of
complementary frequency states (CoFS) across the entire body, i.e. any
one electron oscillates its modes of existence between two separate
atoms, and shares those positions with other electrons. When the
temperature is lowered, the phonons are reduced, and the number of
degrees of freedom within the material is thus reduced. The displacement
forces on the electron become calmer. Eventually, at the critical
temperature, the bulk hyff generators become synchronised so that the
electrons can start to appear in regular positions. The material properties
are such that those positions are also convenient for the electron. The
electron thus obtains regular modes. Moreover, these modes are
synchronised in a complementary manner across the entire bulk of the
material. This is a phase transition to a lower-energy phase.
From the perspective of an individual electron, the external hyff in the
bulk have moved into a complementary client state. Brownian motion
then ceases. As the electrons are in complementary states, and their
modes are at convenient and similar spans, the bulk becomes like a
network of orbitals. Individual electrons can readily move to a different
part of the network in response to flow of electrons (applied voltage).
Applying a voltage, which is the same as withdrawing electrons from one
side and injecting fresh ones at the other, then causes the existing
electrons in the bulk to index along in an orderly fashion (reminiscent of
the Jacob’s ladder falling-tile toy, except that the electrons do actually
move along). For an electron to adjust the next appearance of one of its
reactive-ends is effortless, so there is no resistance to that ‘movement’.
The reactive-end of one electron is guided to its next place of existence by
the surrounding hyff, which are in complementary states.
The nature of the current flow is then radically different. In usual
conduction the whole electron has to move through the bulk: and move its
reactive-ends (modes) while they are energised, which generates velocity
51
It is comparable to a rough sea, where the tops of the whipped-up waves
are higher than the average sea-level.
202
forces (i.e. magnetic fields).52 In superconduction the ‘movement’ takes
place while the electron-cordus is in the dormant state: the reactive-end
disappears as usual from one mode, and but when it reappears it is at a
different position, one in the CoFS network conveniently vacated by some
other electron. Thus the electron moves in stealth-mode (tunnelling). The
reactive-ends do not need to physically move while they are energised, so
they generate no magnetic field.
From the perspective of an individual electron, it finds that one of its
modes is already taken by an interloper electron, so it simply swaps into
one of the other equivalent modes available to it. This displaces the next
electron in the network, and the result is current-flow. If this explanation is
correct, the current should be quantised at the frequency of the electron.
This may be a testable cordus principle. Thus cordus suggests that there
is a form of environmentally induced coherence that takes hold when the
temperature [i.e. phonon effect] is sufficiently low.
The idea of a CoFS network accommodates loops of material with whole
phase differences around ‘holes’ within the network, hence vortices and
fluxons (see superfluidity for similar effects).
Meissner effect
The Meissner effect is that a weak externally-applied magnetic field is
expelled from the interior of the superconductor, the usual explanation
being that surface currents cancel the internal magnetic field, except in
the skin layer (hence London penetration depth). The Cordus explanation
is somewhat similar, but approaches it from a different direction.
In a normal conductor, an externally applied magnetic field displaces the
moving reactive-ends sideways, whereupon that moved electron
contributes further to interfering with other electrons and adds to the
disorder. In a superconductor the CoFS network provides lateral stiffness:
the hyff from neighbouring electrons lock the modes of the entire network
in place. Therefore an external magnetic field cannot displace the modes:
its effect is resisted, and the flux lines are denied passage so they go round
the wire instead. Surface currents arise as compensatory consequences of
the load on the CoFS network. If the external magnetic field is too strong,
then its forces on the modes overwhelm the CoFS force, and the network
degenerates: the superconductivity is lost. Thus an external magnetic field
can destroy superconductivity by breaking the network of orbitals
Temperature
In the superconducting state the material can still accommodate some
phonons, as seen in the fact that the critical temperature is not absolute
zero but rather a higher value. The Cordus explanation is that temperature
refers to the rate density of phonon production, and that superconductors
are able to accommodate a certain amount of phonons (hence
temperature) by small adjustments to orbitals and phase. However if the
52
The Cordus field theory states that magnetism arises from movement of
a reactive end while it is energised, i.e. curvature of the hyff (ref. ‘Cordus fields’).
203
rate density of phonons exceeds this basic carrying capacity, then phasedissonance arises and the superconductivity is lost.
Note in passing that the electron hyff extend some distance. This explains
why there is an ordering effect that takes hold at the critical temperature.
Cordus predicts that multiple domains of alignment may form at the
critical temperature for superconductivity, followed by a subsequent
coalescence into one single domain, i.e. the process of initiation of
superconduction may be marked by some interesting transitional states.
Related effects
Note also that the hyff may even extend through intervening material,
even an insulator. Thus electrons on the other side of a thin insulator may
also be recruited to the client state. More radically, Cordus states that an
individual electron may have one reactive-end in the one material, and the
second end in the other, with its fibril spanning the conductor, since the
fibril is non-reactive. Hence also the Josephson effect: current may cross a
thin insulating layer. See also the Casimir effect, which is a similar
spanning effect, according to Cordus.
6
Conclusions
The special states of matter are particularly interesting from a modelling
perspective because they show where the system variables are most
exposed. Superfluidity and superconductivity are two such situations.
Both are enigmatic to classical mechanics, and partly explained by
quantum mechanics. However the QM explanations cannot be said to be
intuitive, nor easy to comprehend: i.e. the descriptive power of QM is
inferior to its mathematical ability in these areas. On the other hand,
Cordus readily provides a description of the effects. The principle of
complementary frequency states (CoFS), which was established earlier in
the series, explains why and how superfluidity occurs, and likewise for
superconductivity. These are radically different explanations to those
provided by conventional physics, but are not necessarily in disagreement
about the mathematics. The primary difference is that Cordus suggests
different underlying mechanisms than are usually assumed to operate.
This situation arises because conventional physics has a paradigm that is
limited by its premises of zero-dimensional particles, whereas Cordus has a
two dimensional model for particuloids.
Critical analysis of superposition
Cordus makes the unorthodox assertion that superposition does not exist,
at least not the way QM conceives of a whole particle or body being fully
in two places at once. Cordus provides for positional variability: the two
reactive ends of a cordus are in different places, and extends that to larger
assemblies of matter only if such objects can be placed in full bodycoherence (which is rare). However Cordus rejects the QM superposition
concept of causal variability: the idea that the whole particle or body is
204
simultaneously in both and neither positions and therefore has two
futures before it, which can diverge. Cordus asserts this is a fallacy and a
potential flaw within quantum mechanics.
In the Cordus analysis the root cause is deficiency in the formulation of
superposition: a statistical average is fundamentally an unreliable
predictor of longitudinal future outcomes when the population is bimodal.
Quantum mechanics is built with a methodology that elected, at its
founding, to approach the problem as a cross-sectional statistical design
(single point in time). Therefore the mathematical representations that
QM developed are only applicable to average particle behaviour, because
that is all that a cross-sectional design is valid for. Quantum mechanics is
outside its base of validity when it tries to provide physical interpretations
for longitudinal effects (multiple consecutive points in time). Quantum
mechanic’s interpretations of what is happening in the double-slit device
are therefore irrelevant artefacts of its statistical methodology.
The weirdness of QM’s explanations is not because reality is weird, but
because QM is fundamentally wrong. Nonetheless QM’s mathematical
machinery is useful for small particles: it is not applicable for large objects,
nor for very small pieces of matter either.
The second error overlaid on that methodological root cause was QM’s
assumption that a whole macroscopic body should likewise be in
superposition. This is the fallacy of easy coherence, which is described
below. Cordus asserts it is generally impractical to create the level of
coherence required by QM, and therefore that QM does not apply to
objects in general.
The third flaw is the assumption that whole bodies therefore exist in two
places at once. In some interpretations of quantum mechanics this led to a
logical fourth assumption that any event in the whole universe had two
possible outcomes in time, i.e. the many-worlds interpretation. Cordus
rejects all those assumptions and asserts they are the consequence of the
flawed concept of superposition at the root of quantum mechanics.
Outcomes
Cordus re-conceptualises, or at least conceptually clarifies the concept of
‘coherence’, and describes why that state cannot be readily achieved. Thus
Cordus predicts what size bodies should and realistically cannot be made
into matter-waves. Thus the concept of large macroscopic objects, such as
motor-cars, being able to go through a double slit, is proposed to be a
fallacy. This also allows Cordus to explain why Quantum mechanics, which
seems to apply at the level of individual particles, does not scale up to
macroscopic bodies: something that QM itself has been unable to explain.
One of the major benefits of the Cordus approach is that its explanations
are coherent across a broad swath of physical phenomena. Thus the same
mechanisms that are used to explain the Meissner effect also explain
entropy, wave-particle duality, and indeed many other effects.
205
206
Special matter
207
Schrödinger’s Cat reconceptualised
Cordus matter: Part 3.5
Pons, D.J. , 53 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
Quantum mechanics is the dominant conceptual foundation for
fundamental physics. Nonetheless there are effects that it does not explain,
or explains only by reference to metaphysical effects. While many have
wondered whether there could be a more-complete explanation, the
solution has been elusive. Cordus suggests that the necessary deeper
mechanics is only accessible by abandoning the premise of ‘particle’, and
shows how to achieve this. The resulting Cordus mechanics provides a new
way of thinking and a radically different conceptual foundation. This paper
primarily contrasts Quantum and Cordus mechanics. In the process, Cordus
re-conceptualises Heisenberg’s uncertainty principle. It also provides an
explanation for the paradox of Schrödinger’s Cat, and shows it to be based
on unrealistic and unattainable premises.
Keywords: quantum mechanics; superposition; coherence; Schrödinger’s
cat; Heisenberg uncertainty principle; cordus; string theory
Revision 2.10 Minor edits of clarification
Document: Pons_Cordus_3.4SpecialMatter_E2.10.85.doc
1
Introduction
This is the last in a series of papers on the application of the Cordus
conjecture to matter. The first part created a novel explanation for
entanglement and proposed a new principle of locality. Part 2 described a
cordus model for the electron, its orbitals, and matter more generally.
Entropy was re-conceptualised in part 3, and this was used in part 4 to give
new explanations of superfluidity and superconductivity. That part also
came to surprising conclusions about some core concepts of quantum
mechanics (QM): that QM’s concept of superposition was flawed, and that
coherence is a special state that cannot be assumed to be applied to any
object. Thus it is appropriate that this final paper contrasts Cordus with
QM. In doing so it re-conceptualises the issues with Schrodinger’s Cat.
53
Please address correspondence to Dr Dirk Pons, University of
Canterbury, Christchurch, New Zealand. Copyright D Pons 2011.
208
2
Contrasting
mechanics
interpretations:
Quantum
and
Cordus
Quantum mechanics
Quantum mechanics originated with the idea that electrons can only take
up certain steps in energy, hence quanta. However with time QM has
come to mean more: that reality for particles is fundamentally
probabilistic; and that the wavefunction is the complete reality
(Copenhagen interpretation). QM is now a set of mathematics and beliefs
about reality, that include probabilistic origins, wave-particle duality,
wavefunction mathematics, and the uncertainty principle. QM views all
matter as discrete particles that may be made of still smaller particles. The
concept of 'particle' is generally one of zero-dimensional points, and this
becomes the implicit premise for many applications of QM including
photons. Bell's theorem is typically taken as sufficient evidence that there
is no underlying set of hidden variables, thus further confirming the belief
that the wavefunction is the complete reality.
At the same time the particles are understood to behave like waves. QM
offers a solution, first by positing that particles are wave-packets, second
by assuming that particles can be in multiple places at once (through
superposition or virtual twins), third by assuming that the state of a
particle can only be known as a probability, and fourth that the actual
position of the particle is only determined when it is observed, hence
collapsing the wave-function. Thus the QM mechanism for diffraction into
fringes is wave self-interference between the wavefunctions of the particle
and its virtual ghost particle.
As a mathematical method QM has impressive predictive power and
ability to quantify the outcomes. Unfortunately the qualitative
explanations rely on metaphysics, and this incongruence creates a
perception of weirdness. There are other problems too: the idea of
probabilities, e.g. path choice in interferometers, almost implies external
look-up tables, or someone assigning a probability to the outcome before
it takes place. This leads to observer paradoxes and causality conundrums,
or to the many worlds interpretation with its own metaphysical problems.
From QM perspective the weirdness is just a perception caused by our
inadequate human cognition.
Cordus
The Cordus interpretation is very different. First, Cordus proposes the
photon-cordus as a particuloid in place of the idea of a single small point
particle. It does not support the QM ‘particle’ view of light and matter, but
instead that the cordus can look like a particle (hence ‘particuloid’) from
further away. Cordus debunks Bell's theorem as being constructed on the
unnecessarily limiting premise of zero-dimensional particles, and therefore
cannot be used to rule out hidden-variable solutions. Second, Cordus
proposes that photons, and indeed all 'particles' are cordi that oscillate
into and out of existence across a finite span separation, and that
consequently the particuloid is effectively in two places at once. It does
not support the idea of the wavefunction (hence the Copenhagen
209
interpretation), nor of superposition (hence the many-worlds
interpretation), nor the probability-is-the-reality interpretation. From the
Cordus perspective these are all usefully convenient mathematical
analogies that are sufficient for predictive purposes, but are invalid
descriptors of reality. 54
Third, From the Cordus perspective the probabilities of a particle being in a
particular location arise simply and naturally as the cutting points on the
frequency. Stop the experiment with the photon in a different part of its
frequency cycle and the outcome may be different. The paradoxes
disappear, and there need be no violations of causality, providing one is
careful and does not confound the various types of observation. Cordus
proposes there are three different types of observation, with very
different outcomes for the photon.
3
Heisenberg uncertainty principle
Another area of difference is towards the Heisenberg uncertainty
principle, particularly the explanation thereof. For QM the explanation is
in the wave-packet, which represents the probability of finding the particle
in that place. The position of the particle is indeterminate as it could be
anywhere along the wave packet, and compressing the wave packet to
reduce that problem will change the wavelength and therefore the
momentum, and thus make the momentum indeterminate, and the
converse. The Uncertainty principle is typically expressed in terms of the
standard deviations of position and momentum, and the product thereof.
The Cordus perspective supports the principle, but not necessarily that
particular formulation. Heisenberg's statement was built on the standard
QM probabilistic premise: that variables are statistically distributed e.g.
with a normal distribution. In contrast, Cordus does not specifically require
that assumption, nor the product operation.
The Cordus explanation is that the free-flying cordus particuloid has no
sharply measureable position, because it is not a single point particle in
the first place. Position can be measured (reasonably precisely but not
absolutely) by arresting it, but then it is not a free-flying cordus particle
any longer, and the momentum is indeterminate. For a photon, the flight
and arrested states cannot occur at the same time, because they are
different stages in the life-cycle of the photon, and therefore cannot be
precisely measured at the same time.
54
For example, Cordus would disagree with just about everything in the following statement:
'When a photon's state is non-deterministically altered, such as interacting with a half-silvered mirror
where it non-deterministically passes through or is reflected, the photon undergoes quantum
superposition, whereby it takes on all possible states and can interact with itself. This phenomenon
continues until an observer interacts with it, causing the wave function to collapse and returning the
photon
to
a
deterministic
state.'
(Wikipedia,
http://en.wikipedia.org/wiki/Elitzur%E2%80%93Vaidman_bomb-tester
accessed 3 March 2011).
210
last
In the QM formulation there is a smooth trade-off between position and
momentum. However Cordus implies that the relationship is more
granular, and consists of two mutually exclusive sub-conditions: that
passing observation can measure momentum and mean position, and
intrusive measurement constrains position and measures force or energy.
Complementarity principle
QMs use a complementarity principle: that photons have multiple
properties that are contradictory. QM assumes that wave and particle
duality means that both are simultaneously in existence, that the photon
is truly a both a wave and a particle at any instant in time.
For Cordus the particuloid is neither a wave nor a particle but behaves as
either depending on the measuring method. The measurement method
unavoidably changes how the particle behaves, and this is particularly
pronounced with the photon. The Experimenter's choice of method
therefore limits the type of results that will be observed. Wave and
particle duality are only measuring artefacts, not the reality.
4
Schrödinger’s Cat
The thought-experiment
Schrödinger’s Cat is a thought-experiment in superposition: the basic idea
is that a cat is placed in a box with a radioactive sample rigged up so that
decay emits a particle which breaks a vial of poison that kills the cat. If the
box is closed and no-one can see inside, what state is the cat in?
This is an extension of an idea in quantum theory that a physical system
can be in multiple configurations (dead vs. alive), and therefore from the
quantum perspective is simultaneously in all those configurations until the
act of observation forces it to one particular configuration, i.e. collapses
the waveform. An extrapolation of the idea is that each of the other nonselected configurations does continue, but in another parallel universe,
hence the ‘many worlds’ theory.
While it might initially have been intended as a thought-experiment,
Schrödinger’s Cat has taken on a more mythical status, and is almost
considered fact. It has become the visible poster-child representative of
QM, particularly of superposition.
The cordus explanation is that Schrödinger’s Cat is only a conundrum
because of fallacious premises. First, note that there are several effects:
whether or not the radioactive material decays and emits a photon; the
dilemma about the state of the Cat before opening the box
(alive/dead/simultaneously alive and dead); and the Observer dilemma
about the effect of opening the box and looking.
211
Type of observation is critical
The Cordus Conjecture distinguishes between types of observation:
passive, passing and intrusive. Passive does nothing (L.3.1), passing can
change photons, but only intrusive detection collapses photons. Therefore
opening the lid on Schrödinger’s Cat and passively observing makes no
difference: it does not affect whether or not the radioactive material will
emit a photon. The photon will be emitted when it is emitted.
However there are some additional observer effects that could change the
emission, the first being that letting more light (external photons) into the
poison system could trigger radioactive decay. Second, if the Observer
changes to an intrusive mode, then the emission outcome can be affected
and even controlled. For example, intrusively detecting whether a photon
has been emitted will prevent it ever reaching the poison. Or,
interrogation of the radioactive material could force it to emit a photon or
prevent it from doing so: the Zeno effect. Passing measurement of already
flying photons will change their properties.
Then there is the matter of what the inside surface of the box was made
from. If mirrors, then there are multiple paths by which an emitted
photon’s reactive end could get to the poison vial. Opening the box and
thereby removing mirrors will deprive the photon of some path
opportunities: it could escape the box altogether. However these are all
complications, and simple passive observation, which is all the original
dilemma proposed, is inconsequential. Simply looking passively does not
change the cat’s fate.
No superposition of undead states
A simple act of passive observation does not affect the emission of a
photon nor the transmission thereof. Nor does it cause the Cat to suddenly
collapse to the dead or alive state. The Cat need not exist in any
superposition of undead states before the box was opened: it is simply
either alive or already dead, nothing else. In an inverted way, the cat
thought-experiment is often misunderstood as evidence that quantum
coherence applies to macroscopic objects. From the Cordus perspective
this is misplaced. The matter lemma states that superposition of states
only occurs for bodies that are internally coherent. Something as large and
internally dynamic (nerve impulses, flowing blood, etc.) as a Cat cannot
have that CoFS coherence in the first place: initially imposing the
coherence would deprive it of life. Only small, cold, inanimate things of
relatively homogeneous composition can be put into body coherence.
Nor does the presence of the passive Observer do anything. Hence
existential Observer dilemmas are void. Simply passively looking at the
universe does not cause it to change, nor necessitate creation of another
world.
Try Superposition of something smaller?
If Schrödinger’s Cat dilemma collapses because of lack of coherence of the
Cat, then what about replacing the Cat with an electron: something that
can generally be thought of as in ‘quantum superposition’? Will the
212
dilemma still be sustained then? Is the electron simultaneously blasted
and not-blasted by the radioactive decay? QM states that the electron
occupies all possible quantum states simultaneously, so the electron
should be in normal and high energy states simultaneously, and only
collapses to one when measured.
The answer, according to the Cordus Conjecture, is no. While an electron
does have two position modes, it does not occupy them simultaneously,
nor are these different energy levels. Consequently simple passive
observation does nothing to force the electron into one particular energy
level. Not-observing the electron makes no difference either.
As the previous discussion noted, superposition is merely a mathematical
representation of the uncertain in average position of the two reactive
ends, and cannot be applied to two different temporal causal outcomes
such as dead vs. alive. That’s an important point that tends to get
overlooked when QM is being interpreted, and is the fallacy at the core of
the many-worlds theory.
Hidden premises in the Box
To sum up, Schrödinger’s Cat thought-experiment is flawed in several
crucial areas. First, it confounds passive and intrusive observation to
suggest that the act of non-observation causes indeterminacy. A second
erroneous premise is that of superposition: that the cat's states are
simultaneously life and death. We do not see this in reality either, and
Cordus asserts this premise is invalid in any situation: QM’s superposition
is only a mathematical simplification of a deeper and different effect. The
third fallacious premise is that that the entire contents of the box,
including the cat, are in macroscopic quantum coherence (this being
necessary to support the superposition premise). This is not a particularly
practical premise, as we never see coherence at this level, only at atomic
and molecular scales, and Cordus explains why. Cordus also asserts that
coherence of a whole living cat will be next to impossible to achieve.
The Cordus conjecture implies that all three premises are wrong. The Cat is
either dead or alive, and opening the box (at least in the way originally
proposed) is inconsequential. Nor need there be other worlds in which the
Cat is in a different state. So for any one of these reasons on its own the
Cat experiment is not physically realisable. The lesson it teaches is that
superposition is strictly only a mathematical approximation for handling
positional uncertainty, not a real physical effect, and macroscopic physical
bodies cannot be assumed to be in body coherence just because some
atomic structures can be in the state.
Where the weirdness arises
Coming back to the starting point, which was the weirdness of existing
explanations of wave-particle duality, we can now identify why QM’s
descriptive explanations are weird. QM assumes that particles are points
(hence over-reliance on a single limited paradigm); QM assumes that
coherence effects at a particle level always generalise to whole bodies
(hence the conundrum of Schrodinger's Cat); QM extrapolates
213
mathematical solutions for the problem of indeterminacy, namely
superposition and wavefunction, to the physical reality. Cordus suggests
those premises are all unreliable. More than anything else, the premise of
zero-dimensional point particles pervades QM, and in a self-reinforcing
way Bell’s theorem has been influential in sustaining the belief that there
are no hidden-variable solutions, i.e. that the particle really is zerodimensional. Cordus cuts across that way of thinking: it unexpectedly
delivers a hidden-variable solution, debunks the zero-dimensional
premise, and expands the debate beyond the constraints of Bell’s
theorem.
5
Contrast: String Theory
The Cordus Conjecture relies on fibrils, and the obvious question is
whether there is an implication for string theory. The similarity, at least
for some versions of the Cordus conjecture, is in the idea that matter and
energy are made of oscillating lines (strings). Also, String Theory suggests
that the photon is an open string, as opposed to a closed loop. Most of the
cordus variants here are similar to a string, but include additional concepts
that are not necessarily string-like.
String theory is a mathematical rather than empirical approach. It requires
the universe to have multiple dimensions, most of which are presumed
hidden or too small to detect. It posits that variation in the properties of
the string give rise to different particles, e.g. photons and electrons, but is
not specific about what these situational variables might be or the
causality. It has many flavours and mathematical variations, and it is not
always easy to determine which describes our universe except by relying
on the anthropic principle. It is a theory of the structure of the universe,
rather than a predictor of sub-atomic structure.
The Cordus conjecture does not explicitly require String Theory, though it
does not preclude it either. The two approaches start from entirely
different premises, and use completely different methods. Despite some
apparent similarity in results -the prediction of string-like sub-structures –
there is considerable space between the two models and it would be
premature to consider them conceptually linked.
6
Discussion
Quid est atomos?
What is the atom made of? This work proposes that sub-atomic particles
have a cordus structure: two reactive ends joined by a fibril, with the
structure being energised at a high frequency and emitting one or more
hyff lines of force. They are not really particles at all.
Implications
The cordus concept was originally created to explain wave-particle duality
of the photon. It turns out to be much more adaptable and powerful, in a
214
descriptive way, than simply a solution for the photon. Cordus is a
conceptual solution that shows it is possible to conceive of internal
structures for the photon and other sub-atomic particles, without the
usual weird metaphysical explanations.
The conceptual contribution of this work is the demonstration that it is
indeed possible to create hidden-variable models, and that Bell's theorem
is not a limitation. It shows that the application of logic and semantic
inference to existing experimental observations can give interesting new
insights. The beauty of the Cordus Conjecture is that it provides an
explanation that is coherent across wave and particle effects, photons and
matter, ‘particles’ and macroscopic bodies. Perhaps the biggest
contribution is simply the intellectual stimulus to think differently about
topics that we think we already understand.
Cordus challenges the conventional idea of zero-dimensional points, and
the whole conceptual edifice built thereon. The concept that emerges here
is that ‘particles’ are not actually zero-dimensional points, neither are they
waves.
Instead ‘waves’ and ‘particles’ are simply the external
manifestations of hidden internal structures.
In this regard, Cordus suggests that Quantum Mechanics and Wave theory
are subsets of a deeper and simpler reality. Cordus also shows that reality
to be deterministic. It is not clear that ‘quantum’ is the best term to
describe such mechanics, and in some ways Cordus is more about
‘mechanics’ than QM ever was. From this perspective Quantum Mechanics
is of dubious validity as a descriptor of reality even if its mathematics is
sufficient for quantitative purposes. Now we finally understand why
quantum mechanics, which seems sufficiently accurate for individual
‘particles’, does not scale up to macroscopic bodies, something which QM
itself has been unable to explain.
At this stage Cordus is simply a conceptual model and some starting
mechanics that have been calibrated against several physical phenomena.
Cordus started from an intuitive conjecture, and through a set of lemmas
developed into a descriptive conceptual framework. What is needed next
is scrutiny: does this concept stack up to the reality of other observed
quantum and optical effects? Exploring this question may well require
further adjustments to the concept or show it to be an unworkable
conjecture. Thus the validity of the concept is an open question which is
put to the wider community of scholars.
7
Conclusions
The Cordus conjecture provides a radically new perspective on
fundamental particles. The conventional theories of electromagnetic wave
theory and quantum mechanics, are shown to be external simplifications
of the deeper set of hidden variables described by a cordus. Cordus is an
integrative theory: it provides a single coherent conceptual framework for
215
a wide range of physical effects both wave and particle. It provides natural
explanations of otherwise weird quantum phenomena.
Cordus does not follow the conventional method of physics, which is
derivation of beautiful mathematics and subsequent extrapolation to
explanation, but it is a logical theory nonetheless: that of creating a system
model by reverse-engineering known phenomena, adding conjectures and
intuitive material, and noting the necessary assumptions along the way.
There are many of these lemmas, and thus many potential flaws in the
cordus mechanics. Notwithstanding, if the cordus conjecture is even partly
correct, the consequences for conventional theories of matter are
profound. Cordus suggests there is a more fundamental and coherent
theory of reality than Quantum mechanics can provide. Perhaps
surprisingly, this deeper theory is deterministic.
Sub-atomic particles of matter exhibit strange behaviours such as
entanglement, superfluidity, and superconductivity. These effects are
usually explained by quantum mechanics (QM): at least the mathematics
are. This paper proposes an alternative explanation, based on the cordus
conjecture. In this concept, the basic structure to any ‘particle’ is a cordus:
a fibril connecting two reactive ends, with hyff force lines protruding from
the ends. This structure is used to explain matter waves and the waveparticle duality thereof, entanglement and interaction at a distance,
electron orbitals, coherence, superfluidity, and superconductivity. It is
shown that that a hidden-variable theory is indeed possible for the photon
and ‘particles’ in general. The limitations of conventional concepts of
‘particle’ are identified, and a counter argument is developed to Bell’s
theorem. A revised principle of wider locality is proposed. Mechanisms are
proposed for the absorption of the photon into matter, and the origins of
entropy on a sub-atomic scale. Cordus questions the validity of quantum
superposition, reinterprets coherence, and predicts what should be
achievable (or not) for macroscopic bodies. Schrodinger's Cat is explained
and shown to be based on unrealisable premises. Cordus also explains why
quantum mechanics, which seems applicable at the sub-atomic scale, fails
to scale up to macroscopic scales. Cordus offers a new conceptual
framework for a deeper internal mechanics for atoms and sub-atomic
particles. It provides an explanation that is coherent across multiple
physical effects. Perhaps unexpectedly, cordus suggests that the internal
mechanics for ‘particles’ is deterministic after all, and the probabilistic
nature as recognised by QM is only an artefact of the measurement
process.
216
21
7
Cordus
Conjecture
Part 4: Fields, forces, and fabric
Discrete
fields
(hyffons)
>
electrostatic forces >
magnetism
>
gravitation
>
unification of EMG >
fabric composition of
the
vacuum
>
interpretation
for
alpha > strong force
explained > quark
structure
>
explanation for time
21
219
Electromagnetism
Cordus in extremis: Part 4.1
Pons, D.J. , 55 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
The Cordus conjecture is extended to create a conceptual model for
electromagnetic fields. The resulting model shows how a cordus particuloid
generates small transient units of force at the sub-atomic level, thereby
creating the apparently smooth and continuous electric field that we more
commonly perceive. Cordus also reconceptualises how magnetism is
generated at the sub-atomic level, and likewise explains how the
granularity arises. It is shown that the electric field cannot be shielded, only
neutralised. Cordus electromagnetism is applied to explain the electric field
surrounding a wire carrying current, the locus of moving test charges in a
magnetic field, and the mechanism for how force arises in permanent
magnets. The contribution made by this paper is a description of
electromagnetism that goes to the next deeper level: it explains the
underlying mechanisms for how the forces arise. Also, it provides a
mechanism for fields to be granular and directional at the small scale, but
smooth and continuous at larger scale.
Keywords:
cordus;
electric;
field;
electrostatic;
electromagnetism; quantum field; hyff; particle
magnetism;
Revision 2.10 Minor edits
Document: Cordus_4Fields_E2.96.doc
1
Introduction
The Cordus conjecture provides a radically different interpretation of the
photon, and by extension, sub-atomic particles in general. Companion
papers have applied the Cordus concept to show that it provides a
conceptual resolution of wave-particle duality for the photon (ref: ‘Cordus
Conjecture’), explains optical effects (ref: ‘Cordus optics’), and explains
‘particle’ effects (ref: ‘Cordus matter’). This paper extends the concepts to
fields in general, and in doing so provides a reconceptualisation of
electromagnetism, gravitation, vacuum, mass, and quarks. The Cordus
conjecture offers some suggestions for thinking about these subjects,
though the treatment should be considered in extremis, i.e. a thoughtfulexperiment rather than a necessary core concept. This paper is the fourth
in the Cordus series, and itself consists of four parts. It is recommended
that these parts be read in the numbered series, since the concepts are
cumulative.
55
Please address correspondence to Dr Dirk Pons, University of
Canterbury, Christchurch, New Zealand. Copyright D Pons 2011.
220
Background: Cordus
The Cordus concept is that the photon and all massy ‘particles’ are not
zero-dimensional points as conventionally assumed, but consist of two
reactive ends (RE) connected together with a fibril. The reactive ends emit
hyper-fine fibrils (hyff), which are threads of transient force, see Figure 1.
The periodic renewal of the reactive ends corresponds to the frequency of
the photon or ‘particle’. In the case of the photon the hyff are extended
and withdrawn during each complete frequency cycle. The Cordus concept
has also been shown to be applicable to other so-called particles, e.g. the
electron (see ‘Cordus matter’). From the Cordus perspective there are no
such things as point particles, only small-span cordi that only appear to be
particles. Thus matter is made up of cordus particuloids. For matter cordi
like the electron, the electrostatic hyff (e-hyff) are not withdrawn at each
frequency cycle, but continue to propagate outwards. Each frequency
cycle sends a renewal-pulse down the hyff, so the force is transient and
quantised. This force makes up the electric field.
A companion paper (Cordus conjecture), describes the background to this
idea, applies it to path dilemmas in the double-slit device and MachZehnder interferometer, and uses it to explain fringes. It is shown that the
Cordus conjecture is conceptually able to resolve wave-particle duality for
the photon. Another paper (Cordus optics) shows that the idea is
applicable to conventional optical effects, such as refraction. That paper
also further develops the concept of frequency and the dynamic internal
states of the photon. A third paper (Cordus matter) applies those ideas to
matter generally and the electron specifically. It explains matter waves and
the wave-particle duality thereof, entanglement, locality (a revised
principle is proposed), electron orbitals, entropy, coherence, superfluidity,
and superconductivity. It also shows why quantum effects do not scale up
to the macroscopic world. We recommend that ‘Cordus conjecture’ and
‘Cordus matter’ be read first, as the present paper extends on concepts
described there.
One of the positive features of the Cordus idea is that it is coherent across
many physical effects, as shown in the companion papers. The
implications are that both electromagnetic Wave theory (WT) and
Quantum mechanics (QM) are only external manifestations and
measurements (respectively) of a deeper mechanics. Neither of them,
singularly or jointly, is the reality.
Purpose
The Cordus concept as a whole is conjectural, although the previous
papers have grounded the concepts by comparing them against wellknown physical phenomena. The present bracket of papers is less
cautious. The purpose here is to audaciously push the concept to see if it
has novel suggestions about deeper mechanisms, particularly the
propagation of light and fields in general.
Method
The approach taken is a continuation of that described in ‘Cordus
conjecture’, and not detailed here. The purpose is to synthesising a
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working-model that is sufficient to explain as much of the observed reality
as possible. The outcome is qualitative rather than mathematical, and is
termed a conceptual solution. Along the way the underlying assumptions
are notes as a series of lemmas. These we do not attempt to prove: they
are simply to make the premises explicit so that they can be evaluated
later. In the other papers the causality is relatively linear, but here the
concepts were found to depend on each other, and the process of
generating the conceptual solution was more iterative. The way the model
is presented is therefore for convenience of explanation rather than
necessarily descriptive of the method. Unavoidably, concepts are
sometimes mentioned at the start but only defined later. The lemmas
make up the central strand through the papers. L lemmas are in ‘Cordus
conjecture’, O in ‘Cordus Optics’, M in ‘Cordus matter’, and E in ‘Cordus in
extremis’.
The results follow, starting in part 1 with some basic preliminary
constructs for the electric field, then magnetism. Part 2 introduces a
concept for what the vacuum consists of, and why the speed of light is
finite. Gravitation, mass, and time are explored in Part 3 and new models
developed for each. Part 4 introduces a conceptual model for quarks and
the internal structure of the proton and neutron.
2
Field forces
The fundamental forces are electromagnetism (EM), strong and weak
nuclear forces, and gravity. Electromagnetism and gravitation are the only
forces with infinite range.
2.1
Quantum mechanics interpretation of fields
The QM explanation is that the forces arise between matter by the
exchange of gauge bosons. These bosons are the force-carriers, and the
photon is held to be the gauge boson for the electromagnetic force. The
other forces are carried by W & Z bosons (weak) and gluons (strong). The
force effects are described using bosons as virtual particles, which can only
be detected as forces not individual particles. Thus electromagnetism is
proposed to be carried by virtual photons, the strong interaction between
quarks by the gluon, and the weak interaction (e.g. quark flavour-changing
between left-handed fermions) by W and Z bosons. Thus the standard
explanation is that electromagnetic forces arise between matter when
they exchange virtual photons. These forces can cancel each other if the
bodies have both protons and electrons in equal numbers.
Gravity is the odd one out. All the others can be explained by QM.
Gravitons may be the force-carrier for gravity, though this is more
controversial and the particle has not been observed and detection is
generally expected to be difficult though perhaps feasible. The other
approach to gravity is general relativity, where gravity arises from the
warping of space time, i.e. the effect is a geometric one. However this
222
does not integrate very well with QM. The Cordus interpretation of fields
and bosons is very different, and is progressively developed in several
sections following.
2.2
Cordus electrostatics
The starting premise is that all fields are hyff, of one sort or another. The
following lemma sets out the assumptions more explicitly. \
Hyffon lemma
E.1 Hyffon lemma
E.1.1 All field forces are carried by hyff.
E.1.1.1 The hyff are persistent structures and each particuloid of matter
has a finite number of them.
E.1.2 Some hyff continue to propagate outwards (gravity,
electromagnetism) and hence have long range, whereas others are
withdrawn (photon hyff).
E.1.3 A hyff is a persistent structure even when not energised. Hyff are
in pairs: one part at each reactive end (RE) of the cordus.
E.1.4 A hyff line is directional but may be bent, e.g. by movement of the
basal generator.
E.1.5 The hyff carries a transient quantum of force (‘hyffon’) directed
back down the hyff towards its origin. Each re-energisation of the
reactive end sends another renewal-pulse of force down the hyff.
We term that pulse a hyffon since it is reminiscent of phonons and
plasmons in their distortion of the medium. The hyffon
corresponds approximately to ‘gauge bosons’.
E.1.6 Each hyffon renewal-pulse of hyff force has the ability to interact
with other ‘particles’ of matter that it meets. The force is transient
and is relinquished as the pulse decays, at least for the
electrostatic hyff (e-hyff).
E.1.7 The hyff propagate forward and the force is not consumed but
reapplied to the next most distal particuloid of matter.
E.1.8 Hyff penetrate everything. No field can be shielded.
E.1.9 Hyffon are force increments that propagate distally, and have a
sign. How that sign is interpreted depends on the recipient reactive end. If
the recipient is generating the same sign hyffons, then there is
competition for hyff emission directions (HEDs, see later) and repulsion.
Complementary HEDs results in attraction. So for like charges, e.g. two
electrons e.a and e.b, the first electron e.a emits hyffons with an outward
sign, and when these reach the second electron e.b they disrupt the
hyffon production of e.b, so that its reactive ends are forced to re-energise
a little further away, i.e. repulsion.
We nominally represent negative charge as a hyffon directed outwards,
and positive charge directed proximally, but this is only for convenience.
We show the hyffons by arrows but this does not indicate the direction of
the force but rather the sign. It is more convenient to think of the negative
223
charge as being hyffons that are propagated outwards, and positive charge
as those being drawn inwards.
Electrostatic attraction arises
Therefore hyff are directional force lines that extend out into space from
their basal particuloid, and where the force appears in pulses that travel
outwards along the line (hyffons), see Figure 1. The hyff themselves are
not being continuously created, but they are being energised by pulses
(hyffons) that travel down the line.
2.3
Electric field
Applying the lemma to the electric field, the Cordus interpretation is that
the charged cordus particuloid at the base emits an electric hyff (e-hyff) at
the moment of its creation, and that hyff continues to propagate outwards
with each pulse of renewal. This implies that charged particles created at
the birth of the universe will tend to have their hyff moored at the edge of
the expanding universe. Each electron is not necessarily bound to a single
proton somewhere else in the universe, so electric charges may be
monopoles, at least at the level that we perceive.
224
Figure 1: Cordus structure showing hyff and their periodic re-energisation
via hyffons emitted consecutively from the reactive ends. A fibril joins the
two reactive ends and perpetuates the frequency and the reciprocating
energisation of the reactive ends. Only one pair of hyff is shown. Later
works suggests that the proton and probably also the electron have three,
in orthogonal directions. Photons are thought to have only one pair of hyff,
but they are not persistent as shown here.
Thus fields consist of a rapid sequence of discrete impulses of transient
force, radiating out from a cordus at the centre. However we do not see
this granularity at our level of perception. Instead we perceive fields to be
smooth, continuous, and uniform in all directions. This is because of the
en-masse effect of many particuloids being involved, so the hyff lines are
numerous and in different directions, and the frequency is too high to
detect the individual pulses.
225
For a test charge in an electric field, the overall effect is a steady rain of
hyffons that are individually small transient units of force. The overall
effect is a smooth force. If the remote body has depth, then the incoming
hyffons apply force to the fore-most parts of the body, and then pass
through and apply force to the deeper layers.
Cordus predicts that the field will be granular at the frequency of the basal
charge, and not uniform quantum increments. Also, that the frequency
should depend on the level-of-assembly – for example a free electron will
have the same magnitude of field as one involved in a bond, but different
frequency. This may be a testable prediction.
Hyff lines for permanent charges like the electron are persistent, though
renewed periodically by hyffons. By comparison, the photon is odd, in that
it emits an electric field and then promptly withdraws it: the next pulse is
in the opposite direction.
Electrostatic Shielding
It is commonly known that an electric field can be shielded, whereas
gravitation cannot. For example, a Faraday cage is a container made of
conductive mesh, and is conventionally understood to block external
electrostatic fields from entering: no electric field is experienced inside.
However Cordus suggests that something different is happening, and
proposes a different principle.
Cordus predicts that hyff penetrate everything, and no field can be
shielded. In a Faraday cage the electric field only appears to be shielded.
That in turn is because electrons in the cage material, which has to be
conductive, have sufficient mobility to move rapidly to the other side of
the cage in response to the external field. There they set up own field
countering response fields, i.e. an induced voltage across the cage. The
external hyff (and field) still exist inside the cage, but the net force on a
test charge is zero because it is balanced by the induced voltage field
across the cage. The fineness of the cage-mesh determines the roughness
of that field, so better results are had from finer or continuous materials.
Electrons in the cage need to make this balancing at the frequency of the
externally applied field. For static electric fields this is straightforward, as
the electrons need to move into position only once, hence the
requirement that the cage be conductive. When the frequency of the
electric field is too high then the electrons cannot respond fast enough: in
which case the balancing fails and shielding is lost.
Note that it is the hyff that cannot be shielded. The electron or photon or
particuloid itself can be denied passage: shielded or reflected. Thus when
considering shielding or reflecting, it is important to note that the effects
are different for hyff and reactive-ends. Also, the effect is different for
photons because the do not have persistent hyff but rather extend and
then withdraw them. Photon hyff do not pass through everything, or at
226
least do not go far. Therefore the photon can be shielded against: it can be
absorbed. So light can have a shadow but not the electric field.
Applying this to reflection of radio-frequency photons, as the frequency
increases so the span of the photons decreases (see ‘Cordus conjecture’),
and the available current loops in the shield need to be correspondingly
smaller if the photon is to have a chance of meeting them: hence the
mesh-size of the reflector needs to be finer. As the frequency rises still
further, the required loops are of the order of atomic spacing, i.e. the
shield must be of a continuous material. For even greater frequencies the
electrons cannot counter the hyff so the photon passes straight through.
According to cordus the level of apparent electromagnetic shielding
achieved should be dependent on frequency of the field, the mobility of
the charge carriers in the shield material, and the geometry of the shield.
Further that shielding may be achievable for one species of charged
matter within a space, but not for much smaller charge species.
The hyff always go through everything, but the cordus particuloid itself,
represented by its REs, can be blocked, reflected, or collapsed. Once the
RE has been displaced, then the next hyffon is emitted from the new
location. So the inside of the Faraday cage appears to be free of electric
fields, whereas Cordus suggests the fields are not shielded but merely
balanced. The implication is that hyff penetrate everything, and no field
may be shielded, though some may be balanced (E.1.8). This is may seem a
trivial distinction, but is important in what follows regarding gravitation.
Virtual particles
The conventional perspective is that the virtual photon is the gauge boson
(force carrier) for the electromagnetic force. As shown above, the Cordus
interpretation is different: the electrostatic hyff carry the force and there
is no invisible additional particle per se. From the Cordus perspective
conventional references to ‘virtual particles’ of any kind can generally be
re-interpreted as a hyff effect (E.1.1). The hyff have a renewal frequency,
and travel as a hyffon pulse in the fabric of space (see part 4.2) A hyffon
only looks like ‘virtual particle’ because it involves transient disturbance of
the medium, and is not an identifiable real particle. Cordus suggests that
the term ‘virtual particle’ is misleading and confounds two very different
effects: the REs of the cordus particuloid, and the quantum hyff force
fields.
If this is true, then it means that seeking to find gravitons as the forcecarrier for gravity, can be re-interpreted as a search for hyffons. These can
be expected to be small disturbances in the fabric hyff (see Part 2), not
particles as such.
Cordus predicts that ‘virtual’ particles are fundamentally different to
normal ‘particles’, and should be massless. This includes any bosons for
gravitation.
227
Cordus suggests that hyff are permanent for matter. Assuming nominal
units of charge q- and q+, which are not necessarily those of the electron
and proton, then the q-hyff are outward propagating, whereas the q+hyff
are inward (a nominal sign convention). As the universe expands, so the
hyff get stretched out. Note that the hyff are not straight lines, but are
distorted into curves by the velocity and acceleration of their basal
particuloid.
2.4
Cordus magnetism
There are different perspectives on magnetism. The classical electrostatic
description is that static charged particles create only an electrostatic field,
whereas moving charged particles create a magnetic field too. The two
components are primarily related by change: when an electric field
changes or is moved it generates a magnetic field (and a changing
magnetic field creates an electric field). Thus a charged particle placed in
the fields will move accordingly under the Lorentz force, F = q(E + VxB)
where F is force, q is electric charge, E is electric field, V is velocity, B is
magnetic field, and x is the cross product using the right-hand-rule.56
From the perspective of special relativity, electric- and magnetic-fields are
part of the deeper phenomenon of electromagnetism. The two are
interchangeable depending on the frame of reference: what looks like a
magnetic field from one frame could be electrostatic in another. The
quantum perspective is that electromagnetism occurs by the transfer of
(virtual) photons. From the wave theory perspective, light is an
electromagnetic wave, with the electric and magnetic fields perpendicular
to each other.
Cordus provides a different explanation. Magnetic fields, from the Cordus
perspective, just represent the motion of the charge (basal generator) that
is emitting the e-hyff. This is based on the following assumptions.
Magnetism Lemma
E.2 Magnetism Lemma
E.2.1 Movement (velocity) of a charged reactive end causes magnetic
field. The mechanism is presumed to be bending of the hyff at the
basal emitter.
E.2.2 Curvature of e-hyff is magnetism. The hyff are bent when the base
charge moves, and this curvature is propagated out on the hyff by
the hyffon pulses.
E.2.3 The direction of magnetic field is perpendicular to the plane in
which the curvature occurs.
E.2.4 The electric field is the fundamental effect, and the magnetic field
is a derivative.
E.2.5 A remote particuloid responds to the hyffon pulses and the
curvature embedded therein.
56
Right-hand-rule: V along thumb, B on index, and then the force is in the
direction of the middle finger, for a positive charge
228
E.2.7
The mechanism for magnetic interaction is a yaw moment on the
remote moving particuloid. (Expanded below).
From the Cordus perspective, a static charge only generates an
electrostatic force, without magnetism, because the hyff are straight
outwards. However a moving charge causes bending of the e-hyff, and this
is what we perceive as magnetism, see Figure 2. The sharper the radius of
curvature the greater the magnetic field. Thus electrostatic forces are a
position effect, while magnetism is a velocity effect. However the same
basic structure, the hyff, is responsible for both.
Fields are granular directional effects
Cordus suggests that both the electrostatic and magnetic effects should be
directional for a single moving charge (the ‘base charge’), i.e. the force
should be orientated in a particular direction, and granular, at sufficiently
small scales. This is a consequence of the assumption that a single charge
has a limited number of hyff, and the effects travel out on the hyff. It is
easiest to understand as a single radial hyff, but that is a simplification for
convenience of explanation.
The emission direction of the hyff at the reactive end (proximal) can be
changed, but if the charge has existed for a long time, which will generally
be the case, then the far (distal) end of the hyff will be in another point in
space, and at a different orientation.
For a stationary base charge, the hyff lines are straight outwards. Thus any
small stationary test charge placed at some remote location along the hyff
will feel only the electrostatic force from the base charge. A granular
electrostatic force occurs when a hyffon reaches a remote test charge. The
force, which is momentary, is directed tangent to the hyff at that remote
location. The electrostatic effect is directional, so Cordus predicts that a
test charge should only feel the force if it happens to be sufficiently close
to the hyff line, and otherwise not. So the electric field is both granular
and directional, at small scales. However in most practical settings the
number of charges involved is large, they all point in different directions,
and the cordus frequency is high. These cause a smoothing effect, and
consequently the resulting field is continuous and uniform. So the overall
effect is not directional. The same smoothing applies to the magnetic field.
Generation of magnetism from a single moving charge
When the basal charge moves, then the hyff line is bent or displaced at the
proximal origin, see Figure 2. The resulting piece of curvature moves
outward with the hyffon pulses, reforming the mature line ('combing') as it
moves out to the distal end. Thus a remote test charge placed somewhere
on the hyff receives updates about where the basal charge is now located,
which means that the electrostatic force is more accurately aimed back at
the base. The test charge will also feel the magnetic force, depending on
its own velocity. The hyff process of propagating this information occurs at
light speed.
229
Figure 2: Magnetism is curvature of the hyff in the Cordus model. This
curvature creates a fragment of magnetic force, which moves outwards
with the hyffon.
In this particular working model,57 the magnetism effect is an impulse of
force that can act on a remote moving charge that gets in its way. The
directional hand58 of magnetism VxB ensures that the magnetic impulse is
in the opposite direction at the other reactive end. However it is not
sensible to speak of a magnetic field in this simple case of a single charge.
57
In a different model the magnetism corresponds to positive and negative
curvature of the hyff, in which case there is a looplet around each hyff. This is not
the currently preferred model, but at this relatively high level of conceptual
abstraction there is often not a lot to differentiate the models, so we have to be
open to the possibility that the model might need changing.
58
Why is the effect right-handed? What are the deeper variables that
cause this hand? E.6.11 suggests it is the way the quarks assemble into matter, i.e.
the way the hyff are orientated in the assembly of matter particuloids.
230
The overall field is generated by aggregation of the many small discrete
fragments of magnetism. Each moving charge creates part of a magnetic
looplet, not necessarily continuous, and the effect of multiple charges
moving together is to aggregate those into a what we perceive as a
continuous field.
Any moving mass generates curvature of the hyff, and these generate the
magnetic field, except that neutral-charge mass has no observable
magnetic field because it emits positive and negative hyff.
Cordus suggests that at a sufficient small scale neutral mass should show
magnetism, because the positive and negative basal generators are
separated slightly. This is a type of lack of parity.
Cordus predicts that the electric and magnetic forces apply
simultaneously, and with gravitation too. The curved path of the hyffon is
a discrete impulse of both electrostatism and magnetism. These forces
travel together, and as they move outward they are diluted across the
surface of an enlarging sphere, and thus the field effects becomes weaker.
This advancing front is an area effect (A = 4πr2), not a volume effect, which
is consistent with the observation that the electrostatic, magnetic and
gravity forces all reduce with radius squared (r2) rather than any other
power.
The faster the base charge moves, the greater the distortion of the hyff,
and the greater the magnetic impulse (so the force is not a fixed
quantum). Having more charges q moving in the same direction does not
increase the curvature but simply means that there are more hyffons
reaching the remote test charge, i.e. the effect is simply additive.
When the base charge stops moving, then the curvature of the hyff is
quickly (again at light speed) swept straight by the hyffons. The end-result
is a straight hyff line. So magnetism subsides and only the electrostatic
effect remains. Magnetism is thus only evident when the base charge has
velocity.
Thus one mechanism, the hyff, simultaneously transmits the electric and
magnetic forces. Thus Cordus accounts for all the terms in the Lorentz
force, F = q(E + VxB). The strengths of the two forces are not equal, being
determined by the electric constant (or vacuum permittivity) and the
magnetic constant (or vacuum permeability). Cordus explains this as
different efficacy of the two sub-mechanisms of the hyff.
Generation of magnetism in a wire
An electric current in a wire generates a magnetic field that wraps around
the wire (right-hand thumb rule). Cordus explains this as follows. When
electrons flow en-masse in a wire, they each emit a few hyff, and these
aggregate to create a smooth magnetic field. The component of any hyff
emitted axially forward or backward will neutralise with those of other
electrons, so the net result is hyff emitted radially. Thus the looplets (see
Figure 2) join to form the observed cylindrical field structure.
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Reaction of a remote moving charge to magnetic impulse
How does a curved hyffon create the magnetic force on the remote test
charge? If the remote test charge is stationary, then any curvature of the
incoming hyff (i.e. external magnetic field) only re-orients the direction of
the electrostatic force. However, if the test charge is also moving, and
encounters a magnetic field, then the magnetic force arises. The basic
principle is that the force tries to realign the moving test charge to the
same direction of motion as the basal charge. For example, if the magnetic
field is large and uniform, then the transecting moving test charge is
forced into a circular path: which is the same as the large basal current
required to make that magnetic field. The principle applies also when the
two moving charges are the same, except that they mutually influence
each other to try to become co-linear. Thus magnetism is one moving
charge attempting to force another to conform to the same direction of
motion: it is a type of synchronisation effect.
2.5
Magnetic interaction
The classical interpretation is that a test charge moving in a magnetic field
experiences a sideways Lorentz force that is perpendicular to its direction
of travel and the external magnetic field (i.e. excludes the magnetic field of
the test charge itself): F = qVxB. However the mechanism for how this
forces arises is obscure.
The following is a speculative model for the mechanism underlying cordus
magnetism. This is an explanation for Lemma E.2.7 which states ‘The
mechanism for magnetic interaction is a yaw moment on the remote
moving particuloid.’
Progressive model
The magnetism effect starts as an angular deflection of the emergent
hyffon at the basal charge (E.2.1), and this propagates outwards on the
hyff as a pulse of curvature (E.2.2), eventually reaching the remote
moving test charge (E.2.5). But how does the hyffon interact with the
remote charge in E.2.7? The following working model is suggested, though
it is speculative. The basic principle is that the pulse of magnetism
interferes with the re-energisation of the reactive ends of the remote test
charge, thereby encouraging that remote charge into a different position
than its momentum would usually have provided, and this is what is
experienced as the magnetic force.
Magnetic interaction lemma
The mechanism for magnetic interaction is a yaw moment on the remote
moving particuloid:
E.2.7
Magnetic interaction lemma
232
E.2.7.1 Velocity of any massy particuloid delays the re-energisation of its
reactive ends and thus the emergence of its hyffons.
E.2.7.2
Delay corresponds to energisation of the reactive end in a
geometrically retarded position on its locus, i.e. the fibril is
momentarily not perpendicular to the direction of motion.
The hyffon is emitted slightly rearwards, which
corresponds to a transient kink in the hyff.
E.2.7.3
All charged particuloids are assumed to have mass. The
momentum of the moving particuloid subsequently carries
the reactive end forward to where it should be in the
locus. Thus the retardation does not accumulate.
E.2.7.4
At the remote moving charge the process is
complementary.
E.2.7.5
Particuloids always line up their span to be perpendicular
to their direction of motion, and will adjust their spin to
achieve this. (However the roll angle is variable).
Cordus explanation
A somewhat fuller explanation follows. Within the basal moving charge,
the a1 reactive end is delayed slightly by the velocity (E.2.7.1), and the
need to emit the hyffon onto the fabric of space (see part 4.2). The a1
reactive end therefore energises in a geometrically retarded position on its
locus (E.2.7.2). Thus the fibril is rotated in yaw, momentarily, and the hyff
is temporarily bent as it is emitted. The momentum of the moving
particuloid resets the system by subsequently carrying the reactive end
forward to where it should be in the locus.
Cordus predicts a retardation of the frequency for the remote charge
during the operation of magnetism.
When the hyffon curvature pulse reaches the remote moving test charge,
it likewise interferes with the geometric location for the emergent reactive
end b1 of the moving test charge. Whether it delays or advances that
reactive ends depends on the sign of the magnetic field, i.e. the relative
direction of the velocity of the test charge. The pulse may prevent the b1
reactive end advancing forward as far as it usually might during a
frequency cycle, or it might push it forward. Recall that momentum
determines the nominal location on the locus where the reactive end is
expected to re-energise. Remember also that a reactive end will
preferentially re-energise in a location prepared for it by the external
environment. So the basal charge remotely interferes with the location of
re-energisation of other particuloids. This sets up a yaw moment across
the fibril, thereby adjusting the direction in which the remote charge is
moving.
The curvature pulse is not consumed but passes on outward to the other
RE b2. We assume that the effect is additive rather than being negated,
since the hand is reversed when it reaches that other reactive end.
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Particular cases
If the test charge is not moving, then the curvature pulse only interferes
with the spin of the test charge: it rotates it on the spot. This may be
testable.
If the test charge is moving in the same general direction as the base
charge, then the pulse yaws the cordus of the test charge towards the
direction of the basal charge. Of course the moving test charge is not
simply a passive participant, but also radiates its own hyff with electric and
magnetic effects. If the basal charge is of similar size, it will be affected in
turn by the magnetism of the test charge, and the two charges will
progressively synchronise their positions towards each other, i.e. the loci
converge, or the magnetic force is attractive.
The magnetism effect depends not simply on the speed of the charges, but
also their relative directions. This is economically explained in cordus by
adding lemma E.2.7.5: that particuloids always line up their span to be
perpendicular to their direction of motion. (However the roll angle is
variable). Thus magnetism only works in remote particuloids that already
have some degree of alignment with the velocity of the basal charge.
If the remote test charge is moving in some other deviant direction, then
the hyff it emits are orientated differently to that of the base charge. The
field of the base charge partly forces the remote test charge to comply.
This means that it will be forced to partly synchronise its hyff emission
with the base charge, (a weak form of CoFS in action) and in turn this
means that its reactive ends will have to energise in a different position
and orientation than their own momentum had originally intended. Thus
the general result of magnetism on two similarly sized moving charges, is
to redirect their trajectories towards each other.
Cordus predicts a tendency to mutual synchronisation of frequency for
identical moving charges.
The common case shown in physics texts is of a moving charge being
forced into a circular trajectory in the presence of a uniform magnetic
field. In this case the magnetic field dominates the interaction, and the
moving test charge tends to move into a circular or helical trajectory.
However the uniform field is not a particularly useful way of representing
magnetism because it obscures the important fact that creation of that
uniform field requires charges to be moving in a circular path too. Uniform
magnetic fields are a very special case and thus an artificial way to
approach magnetism, and it is the dance of two moving particuloids where
the more interesting mechanics becomes visible.
The implication of the E.2.7.5 lemma is profound, because it means that
any motion of a massy object results in all the internal particuloids
adjusting their spin. This sounds radical, and it may or not be valid.
Nonetheless there are several situations where we do see something
similar albeit with magnetism, namely permanent magnets, and magnetic
resonance imaging. In both these cases the spins of all the electrons in the
234
whole body are aligned, and in the latter case it is the human body which
is affected, to no obvious detriment.
Cordus suggests that particuloid orientation is affected by magnetism and
motion. This may be testable, but falsification would not be a serious
impediment to the cordus concept since this an extreme prediction.
To sum up the magnetism mechanism, the incoming hyffon interferes with
the intended re-energisation of the reactive ends, and changes the
preferred location. Thus there is a transient displacement effect that we
interpret as the magnetic force. Magnetism thus interferes with
momentum processes.59 Note that the force and displacement
perspectives for magnetism are equivalent. Thus the classical
interpretation of the Lorentz force F = qVxB and the cordus displacement
mechanism are different aspects of magnetism considered at different
scales.
Permanent magnets
A permanent ferro-magnet has a magnetic field, but no apparent electric
field. The usual explanation is that that the electron and nucleon spins are
aligned across a domain (region of atoms).
The Cordus interpretation extends this by saying that that the alignment of
the cordus (spin) of electrons and nucleons result in the hyff pointing in
the same direction. More accurately, that the hyff are orderly aligned
along the axis of the magnetic poles, but randomly orientated in the
transverse directions and there neutralised laterally. The electrostatic
force on an external test charge is balanced, because of the equal
contribution of positive and negative charges. So the magnet does not
appear to be charged or to emit an electric field. Nonetheless it emits hyff.
From the Cordus perspective, the magnetic domains are formed in the first
instance because electron hyff extend to neighbouring atoms and
encourage alignment: a complementary frequency state synchronisation
(CoFS). This is an important concept throughout the cordus mechanics,
and ‘Cordus matter’ describes the concept more fully. Within the magnetic
material the electrons themselves move, either through their unfilled
orbitals, or current flow within the sub-lattices of the material, and this
generates curvature of the hyff and thus magnetic fields. These curved
pieces of hyff propagate outwards to reach a remote magnetic material,
e.g. a piece of iron. At this point they induce the remote electrons and
atoms to align with the hyff and move with the direction of curvature, if
the atomic structure permits (paramagnetism). While the electrostatic
forces are balanced, the magnetic components are not, and the residual
component of force is attractive (or repulsive if the atomic response is
diamagnetic).
59
It should therefore not come as a surprise that cordus predicts a
coherent system behaviour across electricity, magnetism, momentum, mass, and
gravitation, as the following papers show.
235
How does the force itself arise? The piece of iron is attracted to the
magnet, and the hand must exert force to prevent it closing the gap. How
does this work? The explanation for this working model, is that the force is
a perception: the real effect is displacement at the sub-atomic cordus
level. The hyffons of the magnetic field put pressure on the electron
cordus in the iron test piece, and this encourages the reactive ends of the
electron to re-energise in a slightly closer position than they would
otherwise. These are lower-energy positions in the environment external
to the cordus, so the reactive ends naturally prefer to re-energise in these
locations. The REs can be prevented from doing so, but this requires a
force. For an electron deep inside the iron test piece, that force is carried
by the neighbouring electrons, and the stability of those bonds. The force
is therefore carried from electron to electron through the bulk of the iron
until it reaches the outside surfaces, where the pressure of the hand
provides (again through electron interactions between iron and tissue) the
force to resist the movement of the iron piece.
So, to answer the question, when holding two magnets apart, the force is
required to prevent the sub-atomic cordi (e.g. electrons) from inching
closer to the other body. If that force is not there, then the two bodies
accelerate towards each other.
Acceleration of a body in a field
If the hand is not there, or the biomechanics not strong enough, then the
REs of the electrons in the iron creep closer to the magnet, by a small
increment each frequency cycle. Once they start moving, the test piece of
iron obtains a body speed, and this with its mass creates momentum. In
turn the momentum predisposes the reactive end to re-energise ahead on
its locus, i.e. the velocity is maintained. The steady rain of magnetic
hyffons keep pulling the REs in the test piece even further ahead, and this
creates acceleration. The mechanism is similar for a body accelerating in
any field: electrostatic, magnetic, or gravitational.
Thus from the cordus perspective all three fundamental forces are caused,
at the sub-atomic level, by displacement effects of the reactive ends. The
fabric provides the medium that interlinks all these effects, see part 4.2.
Thus what we perceive as force is more fundamentally a constraineddisplacement effect. This is also why the speed of light is a common
limiting constraint on all the field effects. The three fundamental forces
electrostatic, magnetic, and gravitational, all use the same hyff, but just
different information channels thereon, see part 4.3.
3
Conclusions
A conceptual model has been shown for cordus electromagnetism. The
starting premise is that all fields are hyff, of one sort or another. Hyff are
directional force lines that extend out into space from their basal
particuloid, and where the force appears in pulses that travel outwards
along the line (hyffons). Thus fields consist of a rapid sequence of discrete
impulses of transient force, radiating out from a cordus at the centre.
236
However we do not see this granularity at our level of perception. Instead
we perceive fields to be smooth, continuous, and uniform in all directions.
This is because of the en-masse effect of many particuloids being involved.
For a test charge in an electric field, the overall effect is a steady rain of
hyffons that are individually small transient units of force. The overall
effect is a smooth force. From the Cordus perspective, a static charge only
generates an electrostatic force, without magnetism, because the hyff are
straight outwards. However a moving charge causes bending of the e-hyff,
and this is what we perceive as magnetism. Any moving mass generates
curvature of the hyff, and these generate the magnetic field, except that
neutral-charge mass has no observable magnetic field because it emits
positive and negative hyff. Thus electrostatic forces are a position effect,
while magnetism is a velocity effect. However the same basic structure,
the hyff, is responsible for both.
Cordus electromagnetism is applied to explain the electric field
surrounding a wire carrying current, the locus of moving test charges in a
magnetic field, and the mechanism for how force arises in permanent
magnets.
The contribution made by this paper is a description of electromagnetism
that goes to the next deeper level: it can explain the underlying
mechanisms for how the forces arise, where conventional theories do not
go. Also, it provides a mechanism for fields to be granular and directional
at the small scale, but smooth and continuous at larger scale. What is
particularly valuable is that the overall coherency of the cordus concept, in
that the same mechanics that resolve wave-particle duality can also be
used to explain fields, i.e. the creation of a consistent conceptual
framework.
The cordus explanation for electromagnetism is unorthodox in several
areas. First, it dispenses with the need for additional particles, and
conventional references to ‘virtual particles’ of any kind are thus reinterpreted as a hyff effect. Second, conventional theories tend to portray
electric fields and magnetic fields with equal standing: they are
interchangeable concepts. By contrast, Cordus suggests that the electric
field is the fundamental effect, and the magnetic field is a derivative. Thus
electrostatics is a reactive end position effect, magnetism a RE-movement
phenomenon, and (yet to be shown) gravitation a RE-acceleration effect.
Third, Cordus is unconventional in asserting that the electric field cannot
be shielded, and that what looks like shielding is only localised
neutralisation.
The results show that the Cordus conjecture can be extended to
electromagnetic fields. Doing so permits novel re-conceptualisation of
some fundamental paradigms of conventional physics. In particular,
Cordus shows that it is conceptually easy to explain how granularity of the
electromagnetic field arises at a sub-atomic level, and also how the
macroscopic perception arises of fields being smooth. Furthermore, the
cordus concepts of fields are important in what follows, when the
237
composition of the vacuum is considered and gravitation is added to the
model.
238
239
Fabric of the universe
Cordus in extremis: Part 4.2
Pons, D.J. , 60 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
The concept of the vacuum is problematic for conventional physics.
Electromagnetic wave theory models it as consisting of nothing at all, but
yet paradoxically having finite electric and magnetic constants. Quantum
mechanics models it as consisting of temporary particles, but no average
substance. General Relativity theory includes a spacetime medium,
without describing the composition. In all cases the underlying physical
mechanisms are obscure. Furthermore, these existing perspectives conflict
in their expectations, so the integration is poor. The treatment is not
always logical either: conventional theories find the idea of the matterbased aether thoroughly unacceptable, yet ironically all include something
that looks conceptually much like a medium. The Cordus conjecture
provides a conceptual solution for the composition of the vacuum: it
provides a fabric that is granular (similar to quantised) at the smallest
scale, scales up to a continuum, provides a medium for propagation of
disturbances and waves, provides a medium for electromagnetism and
gravitation, is relativistic, is not a matter aether, and includes a time
signal. In the cordus solution the vacuum is made of tangled hyff (force
lines) from all the surrounding matter particuloids. This cordus fabric
concept also provides a descriptive explanation as to why the speed of light
is a finite value. The fine structure constant is given a physical
interpretation, as a measure of the transmission efficacy of the fabric.
Cordus also distinguishes between the fabric that makes up the vacuum of
space, as opposed to the void which has neither fabric nor time as we
perceive it. This model is radically unorthodox in suggesting that the speed
of light is relativistic but not invariant; that it depends fundamentally on
the fabric density and hence the accessible mass density of the universe at
that locality.
Keywords: cordus; vacuum; void; quantum fluctuations; magnetic
constant; aether; relativity; spacetime; speed of light; fine structure
constant
Revision 2.10 Minor edits
Document: Pons_Cordus_4.1Fabric_E2.10.98.doc
1
Introduction
There is a finite limit to the speed of light in a vacuum, but it is not known
what determines the value. Wave theory defines light as a selfpropagating field disturbance. From that perspective the speed of light is
determined by the electric constant and magnetic constant. This of course
60
Please address correspondence to Dr Dirk Pons, University of
Canterbury, Christchurch, New Zealand. Copyright D Pons 2011.
240
begs the question of what determines those constants. Why should a
region of space, with nothing in it, have a resistance to the growth of
electric and magnetic fields?
Answers to these questions are not needed to explain the double-slit and
other quantum effects. Nonetheless the Cordus conjecture offers some
suggestions for thinking about the questions, though these should be
considered in extremis, i.e. a thought-experiment rather than a necessary
core concept.
This paper is the second in a set of four. The first extended the Cordus
conjecture to create a conceptual model for electromagnetic fields. The
resulting model showed how a cordus particuloid could generate small
transient units of force at the sub-atomic level, thereby creating the
apparently smooth and continuous electric field that we more commonly
perceive. That paper also reconceptualised how magnetism is generated at
the sub-atomic level, and likewise explained how the granularity arises. It
showed that the electric field is not shielded, only neutralised.
The present paper builds the concept further by creating a working model
for how the vacuum operates. This is termed the ‘fabric’. The concept is
used to explain why light has a finite speed in the vacuum. This has
interesting implications for distinguishing between the ‘vacuum’ of space
and what we call the ‘void’ beyond the vacuum, and it also suggests a
physical interpretation for the fine structure constant. The concept of
fabric is important in the parts that follow, in that the fabric is proposed to
be a core element in the unification of gravitation with electromagnetism,
and it provides an explanation for time.
2
Temporal capacitance
The photon is unusual in that it emits and then withdraws its hyff, unlike
the electron and proton (E.1.2). Therefore it is more self-contained than
other particuloids. Light slows down in denser media because the cordus,
through its hyff, exerts forces on nearby charged particles (particularly
electrons). This takes time because the electrons have to move, hence
plasmons, and their mass resists that. The photon has to delay while this
happens - it cannot race ahead – because the hyff of the photon and
electron are momentarily joined. This is the same as saying that the
reactive-ends have to increase their lateral deviation zig-zag through the
material and thus take a longer path. Note that the whole process is elastic
and there are no losses: even though the photon slows down, it does not
lose energy. (This counter-intuitive fact is useful in what follows.) For
example, when it leaves a glass medium and goes back into air, it speeds
up again. The glass does not provide resistance per se, instead it simply
wastes the photon’s time, and we call this temporal capacitance.
That explanation is fine for light passing through matter, but what about a
vacuum, where there is no matter or charged particles? What provides the
temporal capacitance? Saying it is the electric and magnetic constant is
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simply circular reasoning. The logical explanation is that there is some kind
of invisible medium, perhaps matter-based, that provides temporal
capacitance and keeps the photon’s speed down. What could that
substance be made of?
One candidate might be quantum vacuum fluctuations: particles and
antiparticles that pop into existence and almost immediately interact and
then disappear. If so, this suggests that the speed of light would be
determined by the rate density at which electron quantum fluctuations
occur. For that to be a workable solution would require a uniform
distribution of electron energies, so that the speed was the same for all
energies of photons. Nor is that the only limitation. Why should the
vacuum need to fluctuate in the first place? The conventional explanation
is that it is an outcome of the probabilistic nature of the wave-function.
However Cordus does not accept the wave-function as the reality (see
‘Cordus matter’), so cannot accept that explanation either.
What about the concept of aether: that there is a fluid of otherwise
undetectable particles through which light travels? That is an ancient
concept, first disproved by the Michelson-Morley experiment, and now
thoroughly discredited by modern physics. Yet the Michelson-Morley
experiment merely disproved the concept of a static or moving-matter
aether through which the Earth was moving – the wind. Is it possible to
conceive of a different type of aether that is invariant to velocity, a
relativistic aether? After all, c is invariant to Observer speed. This leads us
to the fabric conjecture.
3
Cordus Fabric-of-the-universe conjecture
The fabric conjecture is based on the following assumptions.
E.3 Fabric hyff Lemma
E.3.1
E.3.2
E.3.3
E.3.4
E.3.5
E.3.6
The fabric of the universe is made of the hyff of all the other
massy particuloids in the universe.
All ‘virtual particles’ are actually hyffons.
There is only one type of hyff, which is electrical, and is created by
charged particuloids, but the frequency varies. The low frequency
hyff generated by electrons are termed e-hyff, whereas high
frequency hyff from quarks are termed q hyff, but they are
otherwise all the same.
The frequency of the basal generator determines the spacing of
the hyffons. Therefore the frequency of the hyff varies for
different types of cordus particuloids. There is a spectrum.
The density of the hyff in the vacuum determines the temporal
capacitance and therefore the propagation speed through the
vacuum. We term this the saturated speed of the fabric. This is the
speed of light in the vacuum.
Propagation of light through matter, e.g. glass, involves additional
hyff generated by the matter of the medium. This increases the
hyff density and lowers the speed of light.
242
While we use the term ‘fabric’, this should not be taken to mean a 2D
structure, nor a regular lattice like cloth. Instead the fabric weave a
complex and disorderly mesh of 3D force lines, more like a bowl of
spaghetti.
Speed of light explanation
Cordus suggests that light has a finite speed in a vacuum because the
cordus has to interact with the fabric of the vacuum.
Origins of the fabric hyff
All the positive and negative charged particuloids in the universe, even
those in neutral matter, contribute to the fabric hyff. The relatively low
frequency hyff (e-hyff) from unit charges (electrons and protons) create
electric fields which travel through everything. These low frequency hyff
exert the electrostatic force on other charged particuloids of comparable
frequency, i.e. on other protons and electrons. The e-hyff are also
compatible with some energies of photons, and therefore electron
mobility is important in many optical phenomena: it is no coincidence that
polished metal reflects light. These e-hyff can apparently be shielded, by
electrons in a Faraday cage setting up a counter field that balances the
electrostatic force. However the original hyff are still there.
Deeper particuloids, e.g. quarks, also emit hyff. These particuloids have
short span and high frequency, and their hyff have corresponding high
frequency (q hyff). These hyff penetrate everything, but do not react with
nominally charged particuloids like the electron and proton. These q hyff
correspond to the gluons in QM. It is important to note that these q hyff
are the same effect as the electrostatic hyff: just different frequency.
The hyff are weak at vast distances, but still finite. And they never expire,
unlike those of the photon. All the positive and negative charges in the
universe contribute to the hyff fabric. The electromagnetic force may
seem to be zero at any one point, but this is merely because the hyff fields
balance: the underlying hyff still exist. At sufficiently small scale there
should still be electric fields even if there is no field at macroscopic level.
These fabric hyff are themselves propagating outwards. These fabric hyff
interact weakly with each other in passing, providing temporal
capacitance. The interactions mean that the whole fabric operates at a
certain saturated speed, c, and this also applies to the temporary hyff of
any photons trying to move through. Since the whole hyff fabric operates
at c, this provides the invariance to the observer’s speed. It is not an
‘aether’ because it is not made up of particles, 61 but it is relativistic. So
everything that travels in the fabric of the universe is limited to a finite
saturated speed, which is the speed of light in the vacuum.
61
However if one wished to use the nomenclature of QM, one could say
that the fabric was composed of virtual bosons.
243
In this model, the fabric itself provides the temporal capacitance: it uses
up the time of photons and other particuloids that travel through it. The
mechanism for using up time becomes apparent later in the gravitation
and time paper (part 4.3), as interference by the fabric with the reenergisation of reactive ends. Thus the vacuum is not empty, but contains
a tangle of moving hyff lines, each propagating hyffon pulses down its
length at high refresh frequencies, so that the overall effect is a busy
congested and dynamic network. The photon has to fight its way, albeit
elastically, through this fabric, and this slows it down to the speed that we
know as the speed of light in the vacuum. Thus the fabric itself contributes
to entropy in that it delays the redistribution of radiant energy by photons.
Cordus also suggests that, by contrast, there is something emptier than
the vacuum: something where the tangle of hyff has never been, and time
perhaps has not yet existed. We term this the void. Conventional theories,
including wave theory and quantum mechanics, do not have this concept.
Instead they perceive of the vacuum as containing either nothing at all, or
a sea of transitory particles (which is effectively also nothing on average).
The electric and magnetic constants of the vacuum become much easier to
comprehend when the concept of the fabric is included.
As a lemma in the previous paper noted (E.2.4), the electric field is the
fundamental effect, and the magnetic field is a derivative. The fabric
model derived here is consistent, in that it proposes that the fabric is
fundamentally constructed of plain electric hyff. That does not need to
stop it also transmitting magnetism, and as we shall see, gravitation too,
but the fabric itself is electric. This is also consistent with the known fact
that the vacuum has an ‘impedance of free space’, which is in units of
electrical resistance (approx. 376Ω). Those units are unfortunate, because
from the cordus perspective it is better to think about the fabric in terms
of 3E-09 sec time lost per metre travelled, because that emphasises that
the impedance is not loss of energy in drag or resistance, but rather the
loss of time in transit.62
The fabric as a whole is charge-neutral, because it consists of hyff from
positive and negative charges. Thus the electromagnetic force on a
stationary test charge seems to be zero at any one point, and it does not
get moved by the fabric. This is merely because the hyff fabric-forces
balance: the underlying fabric hyff still exist. In addition, the
electromagnetic force only looks like a photon-effect, hence QM’s ‘virtual
photon’, because the hyffons create transient disturbances in the fabric
hyff and these have a similar signature to a photon.
Quantum vacuum fluctuations
The fabric is granular at sufficiently small scales. It will also appear as
noise, since there are q+ and q- hyffons to the fabric. Thus it can look like
short-lived particles of electrons and positrons suddenly appearing and
then disappearing.
62
Both electrical capacitance and inductance are time effects, and lossless
regarding energy.
244
Cordus suggests that what QM perceives as quantum vacuum fluctuations
are the passage, past the Observer, of disorderly hyffons, not real
particuloids of matter. Thus cordus predicts that 'virtual particles' should
be massless.
Gravitational bending of light
If the above conjecture were true, then it has some other implications. The
first concerns nearby masses. What happens when light goes close to a big
lump of matter – won’t that change the strength of the fabric hyff? Yes,
and that is what we interpret as gravitational bending of light. In this idea,
it's not so much the mass that the photon is responding to, but the
charges within that mass. The bending of the locus would be caused by
more fabric-hyff leading towards the mass. Note that hyff are force lines,
and while the general background fabric-hyff apply a balanced force on
any particuloid, the hyff from the local mass are strongly directional.
Therefore the fabric in the vicinity of a mass will have a preferred
direction, i.e. it is a vector field not a scalar field.
Fine structure constant
One implication of the hyff fabric concept is that the density of the
universe affects the speed of light. The fine structure constant α appears
in several places in physics, and thus can be explained in various ways.
From the Cordus perspective α is a measure of the transmission efficacy of
the hyff-fabric, i.e. it determines the relationship between the electric
constant of the vacuum fabric, and the speed of propagation c through the
fabric. To explain this another way, the fabric is made of electrical hyff,
and the saturation thereof crates the temporal capacitance, which in turn
results in the electric constant and limits the speed of light to a certain
finite value. Thus Cordus suggests that the dependent variable in the
equation is the velocity of light c. Thus:
e 2e 2
cc == (4π hα )ε o
(4π hα )ε o
where e is electric charge; ħ is reduced Planck’s constant; α fine structure
constant; εo electrical constant of the vacuum. Assuming all of these are
constant bar the last, then the speed of light depends on εo, the electrical
constant of the vacuum. Cordus suggests that εo represents the density of
the fabric hyff, and thus depends on the mass density of the universe.
Thus the speed of light in the vacuum depends on the mass of the universe
and the local density of the fabric hyff.
Thus the Cordus perspective is that the fine structure constant α refers to
the relationship between electrical hyff and the speed of propagation of
hyffons. Thus it is to be expected that α will appear wherever electrical
hyff and propagation of fields occur, and this includes the cases covered by
CoFS such as electron bonding.
245
If this is correct then the speed of light in the vacuum should be locally but
not temporally invariant, even if it is always relativistic. Perhaps this is
testable? Light may have been faster in the very first moments of the
universe when there was not much matter about, hence driving inflation,
then slower when matter formed and the universe was much denser than
now. Finally it could be increasingly faster as the universe expanded and
the mass density dropped. The speed of light may not even be
directionally invariant. These are unorthodox predictions of cordus in
extremis, and there may be other factors to consider. But if true then the
structural implications would be large: it would imply that many of the
supposedly fundamental physical constants may not be as exact as
thought. On the bright side, the differences are likely to be negligibly
small, at least for engineers who need to make things work in this present
epoch and local region of space.
Vacuum vs. void
In conventional electromagnetic wave theory there is no aether and EM
waves can propagate through nothingness. However Cordus in extremis
differentiates between the vacuum of space and the void. The vacuum is
that region of space in which the hyff-fabric has become established, but
where there is not-yet any matter. As later extensions of the idea show,
the fabric is also where time, as we perceive it, exists. By contrast the void
is beyond the universe and has neither fabric nor time as we perceive it.
The fabric expands into the void and colonises it.
The fabric concept is that the hyff expand space into the void, and that
gravitational attraction is carried by the fabric. The expansion might not
occur at the outer edge of a spherical universe, but throughout the space
of the universe, in which case space is also expanded, and matter
accelerates outwards (the expanding universe). It is also possible that the
fabric simultaneously carries the hyffon pulses that create specific
gravitational attraction between bodies, while the fabric itself exerts a
repulsive force on space (‘dark energy’).
If matter continues to accelerate outwards, and were to approach
relativistic speeds, then parts of the fabric might become disconnected
from each other and the hyff Lorentz-compromised (see part 4.3) in the
radial direction. In this speculative model, the eventual physical fate of the
universe should be a 2D shell, or rather a set of disconnected shells like an
onion, where the only possible interaction was laterally.
4
Conclusions
Conventional theories of physics model the vacuum in one of two ways.
Electromagnetic wave theory models it as consisting of nothing at all but
yet paradoxically having finite electric and magnetic constants. Quantum
mechanics models it as consisting of particles that randomly pop in and
out of existence, though the underlying physical mechanisms are obscure.
General Relativity theory also has a fabric, in this case of spacetime, but
246
likewise is not specific as to what that contains, though by implication it is
smooth rather than granular. Even more problematic, the existing
perspectives do not integrate together, and thus are part of the wider
discontinuity that is ‘wave-particle duality’. Gravitation has been
particularly difficult to integrate into the particle paradigm of conventional
quantum mechanics. This is because relativity has a smooth spacetime,
whereas QM expects gravitation to be quantised to particles.
Existing theories implicitly require that there is something in the vacuum:
something that is a medium for the propagation of waves, or provides the
random fluctuations required by QM, or carries the spacetime curvature
for relativity. While conventional theories find the idea of the matterbased aether thoroughly unacceptable, they ironically all include
something that looks conceptually much like a medium, though none are
specific about its composition.
Cordus provides a solution that does provide an integrated solution for the
composition of the vacuum: it provides a fabric that is granular63 at the
smallest scale, scales up to a continuum, provides a medium for
propagation of disturbances and waves, provides a medium for
electromagnetism and gravitation, is relativistic, is not a matter aether,
and includes a time signal. Cordus is a radically different theory to the
conventional physics of wave theory, quantum mechanics, and general
relativity, and was not derived from any of them. Yet the fabric that it
predicts still includes features that are recognisable, even if subtly
different, to those other theories.
In the cordus solution the vacuum is made of tangled hyff (force lines)
from all the surrounding matter particuloids. This cordus fabric concept
also provides a descriptive explanation as to why the speed of light is a
finite value. The fine structure constant is given a physical interpretation,
as a measure of the transmission efficacy of the fabric. Cordus also
distinguishes between the fabric that makes up the vacuum of space, as
opposed to the void which has neither fabric nor time as we perceive it.
This model is radically unorthodox in suggesting that the speed of light is
relativistic but not invariant; that it depends fundamentally on the fabric
density and hence the accessible mass density of the universe at that
locality.
The Cordus fabric concept is a useful component in the next level of
exploration, which is the creation of a model for mass and gravitation, and
for time, see Part 4.3.
63
Granular, not quantised, as the fabric is not composed of uniform
increments as the term ‘quantum’ suggests.
247
248
Gravitation, Mass and Time
Cordus in extremis: Part 4.3
Pons, D.J. , 64 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
Gravitation is conceptually problematic to General Relativity and Quantum
mechanics in that the fundamental mechanisms are unknown to both, and
the theories have different requirements that are difficult to reconcile into
a single model. Cordus gravitation offers a solution to the problem. It
provides a mechanism whereby gravitation is not continuous but in
discrete force (or displacement) increments similar to quanta (but not
uniform increments). Also, the closing force between two masses is
transient. In this idea, gravitation, and therefore also mass, is a
discontinuous property: i.e. a particuloid emits gravity (has mass) at some
moments but not others. Thus gravitation is an effect that a mass does to
the whole universe, not to targeted other bodies, and in this regard Cordus
is consistent with General relativity. Both QM and Cordus agree that
gravitation is quantised. Cordus conceptually integrates the different
effects of mass: Gravitation is a particuloid contributing hyff to the fabric;
Newtonian mass is resistance of the reactive ends to unexpected
displacement; Relativistic mass is decreasing efficacy of hyff engagement
with the fabric as velocity of the reactive end increases; Momentum is a
frequency mechanism that ensures the reactive end re-energises on-time
and in-place; particuloids like nucleons have mass to the extent that they
have frequency. Furthermore, Cordus offers an explanation of how time
arises at a sub-atomic level by the cordus frequency, and how this
aggregates to the sense of time that we perceive biologically. Thus Cordus
offers a radically new way of thinking about the problem of gravitation,
mass and time that is quite unlike conventional physics, yet includes
concepts that might be recognisable to those other physics.
Keywords: cordus; hyff; gravitation; mass,; time; spacetime; sense of time;
fundamental physics; Lorentz; fabric; time dilation
Revision 2.10 Minor edits
Document: Pons_Cordus_4.3GravMassTime_E2.10.98xxx.doc
1
Introduction
Existing approaches to gravitation are primarily space-time of general
relativity, and gravitons of quantum mechanics. However neither explain
how the underlying mechanisms work. This paper extends the Cordus
principles to gravitation and mass as an in-extremis development, i.e. as a
conceptual exploration.
64
Please address correspondence to Dr Dirk Pons, University of
Canterbury, Christchurch, New Zealand. Copyright D Pons 2011.
249
Mass is strange because it is the coupling for effects that otherwise might
be independent:
Gravitation: two masses attract each other. The gravitation force
(or interaction) has an unusual set of properties compared to the
other forces: (1) it only acts on matter with mass; (2) it always
attracts, never repels; (3) it has infinite range; and (4) it cannot be
redirected or shielded. Mass is the fundamental strength variable
for gravitation.
Resistance to acceleration (Newtonian mass): the greater the
acceleration a or mass m of a body, the greater the force required
to change its speed v, F=m.a or more generally F = d(m.v)/dt
Relativistic mass: as the speed v of a body of rest mass mo
approaches that of light, so the effective mass tends to infinity, or
at least the resistance to acceleration does, m = mo (1-v2/C2) 0.5.
This effect applies even if there is no acceleration.
From the perspective of relativity, momentum is a separate
property to mass and the full energy-momentum formula is
E = [ (p.c)2 + (mo.c2)2 ]0.5
In that case, what physical structure carries the momentum, and
what carries the mass?
Mass originates with particles, e.g. protons and neutrons (among
others), hence atomic number.
This paper is the third in a set of four that extrapolate cordus ideas to the
extremes. The first paper covers the electric and magnetic fields and
shows conceptually how they are formed by hyff from cordus particuloids.
The second creates a working model for the composition of the vacuum,
and shows how this fabric is made of the hyff of all the other particuloids
in the universe. It also shows how this fabric limits the speed of light to a
finite value that is relativistic but not necessarily invariant. This third paper
applies the Cordus concepts in extremis to create a conceptual model for
gravitation. This model uses the hyff and fabric concepts from the previous
papers, and offers an integration between electromagnetism and
gravitation. It also provides a working model for mass. Finally, it creates a
Cordus model for time, and shows how that integrates with gravitation
and the fabric.
2
Cordus Gravitation
We suggest that gravity is a hyff effect, and simply an extension of
electromagnetism. There are several variants of this idea. In the first
variant, which is not the preferred working model, each massy particle
sends out a specialised gravity hyff in addition to any electrostatic hyff.
The difficulty with this idea is that it requires extra hyff (is not
parsimonious) and it is not immediately apparent why a different
mechanism should also be subject to c.65
65
Also, it suggests by analogy with the electrostatic case that there should
be another force for movement of the basal generator, like magnetism is for
electrostatic. But there is no obvious missing force.
250
Why is c involved in mass? Variable c is the flight speed of the photon, not
an atomic variable. From the Cordus perspective c is the propagation
speed of hyff in general. This leads to the second and preferred model:
that there is only one type of hyff (E.3.3), and gravitation is therefore
carried by the hyff of the fabric. The following lemma sets out the
assumptions.
E.4
Gravitation and mass Lemma
E.4.1 All sub-atomic particles, including quarks, are cordi.
E.4.2 All massy cordus particuloids emit hyff.
E.4.2.1
All hyff are the electric field type hyff, but smaller
particuloids emit higher frequency hyff (q hyff).
E.4.2.2
The hyff of quarks are much higher frequency than the
electric field of the electron, because the cordus frequency
is higher for a quark, in turn due to shorter span.
E.4.3 Gravitation is carried by the hyff.
E.4.3.1
The current working model is that the hyffon carries a
torsional twist down the fibril.
E.4.3.2
The transmission of gravitation is therefore at the
saturated speed of the fabric, c.
E.4.4 Gravitation is attractive.
E.4.4.1
The current working model is that remote particuloids
respond in the same way to the hyffon twist, regardless of
the particuloid charge and other properties.
E.4.5 Higher cordus frequencies result in more frequent hyffons, and
hence greater mass and gravitation effects.
E.4.6 continued below
Cordus proposes that the hyff of particuloids, including quarks and any
free sub-quark cordi, carry gravitation. More specifically, even when the
quark is stationary, it still oscillates at the cordus frequency. The frequency
also relates to ‘spin’.
In the Cordus gravitation working model hyff do not create gravitation by a
direct pull, because that is the electrostatic force itself. Instead the force
of gravitation on the remote matter particuloid is caused by the
interaction of that particuloid with the hyffon spin: the re-energising
reactive end of the particuloid is pulled closer, which is equivalent to
saying it is constrained to re-energise in a closer position. This is similar to
the magnetism mechanism. The mechanism is elaborated below.
2.1
Mechanism for gravitational interaction force
It is an open question as to how the oscillation of the quark emits the
gravitation effect at the basal mass, how that effect is carried on the
emitted hyff, and how it interacts with the remote test mass to create
gravitational attraction.
251
It is tempting to say that whatever mechanism is behind the known strongforce phenomenon of quarks always attracting each other, is also that for
gravitation. However that will not do, as the later work on quarks
identifies the mechanism for the strong force and it is not obviously also a
mechanism for gravitation. Thus gravitation does not correspond to what
QM might call a gluon field.
The preferred candidate is the hyff twist idea. This model has the hyffon
carrying a torsional twist down the fibril. According to this model, all
massy matter comprises charged particuloids, and thus there is
electromagnetism to consider. Consider a basal mass of a single
particuloid, and the a1 reactive end thereof. Assume a single radial hyff in
the <r> direction. As a1 re-energises, it emits a hyffon that carries the
electrostatic direct-force fragment, as well as magnetism curvature, and
gravitational twist. The process of re-energisation of a reactive end, i.e. the
hyffon emission, involves a 3D interaction, driven by the underlying righthand rule (E.6.11, see part 4.4): the emission of the electrostatic
component causes the reactive end to displace radially δr in the <r>
direction as per E.7.8 (see part 4.4), there is a linked displacement δa in
the <a> direction due to magnetism,66 and a coupled displacement δt in
the orthogonal <t> direction. The combined effect is that the RE describes
a localised spiral motion at the moment of re-energisation, and the
corresponding hyffon that propagates outwards on the hyff is likewise a
spiral pulse.67 The reasons for the chirality of matter are not evident at this
level.
Assuming such a spiral hyffon, this twist is transmitted out along the hyff,
and gravitation is the response of other particles to that twist.
Remote particuloids should be able to affect each other’s spin through
gravitational interaction, though it would only be evident when both
bodies were in (separate) full body-coherence. The usual massy bodies of
the universe do not have such a degree of coherence, (see ‘Cordus
matter’).
Emission of the hyff occurs as part of the frequency cycle for the
particuloid. Outward propagation of the hyffon occurs at velocity c, and
does not consume energy. The above explanation was for a single hyff.
There is reason to think that massy particuloids have three pairs of hyff:
one in each of the three orthogonal directions (E.6.2 in part 4.4). Therefore
there is always a component of the hyff that is oriented in such a way to
interact with another particuloid, regardless of the orientation of that
particuloid, at least at macroscopic level if not for individual particuloids.
When this torsional pulse reaches a remote test mass comprising cordus b,
with reactive end b1, the handedness of matter ensures similar reactive
forces along the hyff of b1. These forces correspond to lengthening the
66
The magnetic curvature effect, which exists even for a nominally
stationary particuloid because it still has spin angular momentum, causes and is
caused by a displacement δa in the <a> direction (which is tangential to the spin).
67
The chirality of matter could be an interesting area for further research.
252
span of the b cordus. Since there three pairs of hyff, the net effect is a
motion of the b1 reactive end directly towards that of a1. Note also that
the emission process at a1 also moved that reactive end outward. So the
overall effect is that the two reactive ends move closer together, if these
are the only two masses operating. We term this effect geometrically
constrained re-energisation, and suggest it is the deeper mechanism for
force (see E.6).
The hyffon twist-pulse moves on further outwards and encounters the
second reactive end b2. However the hand is conserved across the span
(E.6.7, part 4.4) and the hyffon is approaching from the opposite direction
so the force also moves this reactive end closer. The net result is that the
whole of cordus b shuffles one increment closer to that of a. Thus
gravitation is attractive.68 In the meantime, cordus b also exerts a similar
gravitational effect on cordus a.
At small scales gravitation should be dependent on the directional
alignment of the particuloids, similar to magnetism.
We also speculate that the work that can be extracted from gravitational
interaction arises from the changed spans of the cordi involved. Recall that
the gravitational twist hyffon first encountered reactive end b1, and
moved it outwards, i.e. increased the span. The pulse then moved outward
and moved reactive end b2 towards a1, i.e. shortened the span again.
However in the intervening distance the overall gravitational field, which is
made up of many such hyffons, is diluted because it propagates across the
surface of an expanding sphere. Thus on average reactive end b2 will not
be moved quite as much as b1, i.e. the span will be increased. This
corresponds to lower frequency and lower energy stored in the fibril. Thus
there is more energy in the hyff field component.
As two bodies move closer together under gravitational attraction, so they
release energy for other purposes, and their frequency and mass should
decrease slightly, according to this model.
The concepts of force and displacement are complementary in this model.
This is similar to the magnetism model. Thus force is the high-level effect,
whereas the effect at the deeper level is constrained displacement of
reactive ends.
We acknowledge that the mechanics of all this at the next level deeper are
indistinct, so the mechanism should be considered simply a speculative
working model.
68
If this explanation is correct then the handedness of matter is
responsible for gravitation being only attractive. Therefore the logical implication
is that if one particuloid was left handed then gravitation would be repulsive.
253
2.2
Features of cordus gravitation
Why can gravity not be shielded?
The above lemmas explain why gravity cannot be shielded: the hyff
penetrate everything, and there is no mobile particuloid that can set up a
counter field, as the electron does in the Faraday cage for the electric field.
Quarks are locked into atoms and are consequently not mobile enough to
create such a cage, and even a quark plasma would be insufficient (unless
quarks can repel). Only the electric field can be apparently shielded (more
accurately neutralised), because the electron is the smallest particuloid
that is freely mobile: anything smaller is only available in higher levels of
assembly (see part 4.4).
Operation of Cordus gravitation
Cordus suggests that gravitation is not continuous but in discrete force (or
displacement) increments (similar to quanta but not uniform). Also, the
closing force between two masses is transient. The hyff is not consumed in
the process, but momentarily exerts the closing force, then relinquishes it
as the particuloid phases back into the de-energised state, and the hyffon
moves on outwards. It passes through like a wave to react with other
particuloids and even bodies beyond the first. A following renewal pulse
along the hyff renews the force. What is perceived as gravitational
attraction is the sum of many repeated interactions from different hyff.
Thus gravity propagates outwards in a granular manner from sub-atomic
particles. The gravitational field of a particuloid therefore consists of a
series of discrete forces. The hyff have infinite range, and are not
retracted as in the case of the hyff of the photon. They maintain a
connection thread to their base particuloid even at large range. As the
particuloid moves, even spins on-the-spot, the subsequent hyff of the next
frequency cycle may be released in a different direction. This frequency is
very high, and there is an en-masse effect of multiple asynchronised
particles, so the overall effect is what we perceive as a smooth field.69
In this idea, gravitation, and therefore also mass, is a discontinuous
property: i.e. a particuloid emits gravity (has mass) at some moments but
not others.
Comparison
The Cordus perspective of gravitation emerges as being similar but also
different to General relativity (GR). In that other perspective gravitation
arises from the curvature of spacetime, and is not so much a force as a
geometric interaction of the moving body with that curvature. GR does not
explain what makes up spacetime. By comparison Cordus also includes a
concept that there is something in the vacuum (fabric), and is more
specific about what is in there (tangled hyff). Cordus uses a quantised
69
To even measure the hyffons will require having an ‘instrument’
particuloid with smaller span (higher frequency) than the particuloid that
generates them. A free quark could be a good start, though not without practical
difficulties.
254
force (hyffons) as the mechanism rather than geometric curvature. Both
perspectives agree that gravitation is an effect that a mass does to the
whole universe, not to targeted other bodies.
Plain Quantum mechanics does not have much of an explanation for
gravitation, but Loop quantum gravity does: it proposes the mathematical
concept that the fabric consists of spin networks. A region of Cordus
fabric contains multiple hyff, and conceptually these momentarily define
small dynamic domains: perhaps these correspond to spin networks?
However from the Cordus perspective the underlying mechanism is force
lines and force pulses, and loops in the fabric are likely to be only
transient, and artefacts rather than the mechanism itself. Both QM and
Cordus agree that gravitation is quantised.
3
Mass
The Cordus explanation for gravitation involves hyff: the same hyff as
transmit electrostaticism and magnetism. This gravitation force only acts
on matter with mass, always attracts, has infinite range, and cannot be
shielded. We now need to show how mass arises, and why it is affected by
motion.
The difficulty is integrating mass and gravitation. If an object is just
stationary in space, then it is impossible to determine its mass, other than
through measuring its gravity. What we perceive as mass only becomes
apparent when we try to move the body. So mass is resistance to
acceleration, or force required to accelerate the body. Yet the same body
just sitting there, also creates gravity, and mass is the common variable.
Another complication is that mass increases as velocity approaches the
speed of light. How can we integrate all these disjoint concepts?
Cordus model for mass
Additional lemmas are required to integrate mass and gravitation:
E.4
Additional lemmas continued
E.4.6
The mass effect is created at the level of the cordus particuloid by
acceleration of energised reactive ends.
E.4.6.1
The reactive ends do not energise and de-energise
instantly, so ‘energised’ above includes partially energised
states.
E.4.7 Momentum provides the cordus with the ability to accommodate
translational velocity in the position at which the reactive ends reenergise, i.e. there is an interaction between momentum and the
frequency process.
Why is mass a motion effect? From an in-extremis perspective, the reason
velocity and acceleration are linked to mass, is because what we perceive
as ‘mass’ is the resistance to acceleration of the basal reactive end while it
is energised (E.4.6). The hyff are force threads into the external
environment, all attached to the reactive end. They maintain that force
255
connection even when they are extended far, and they never expire: they
just keep propagating outwards, and the force quanta are periodically
renewed by new hyffons travelling down the hyff.
Velocity can be accommodated
The hyff are able to accommodate velocity of the basal mass (E.4.7).
Velocity generates curvature of the hyff, and thus magnetic fields. At
constant velocity the hyffons propagate the new curvature out towards
the extremities, i.e. a combing effect. Thus for a stationary particuloid the
curvature will eventually be combed out: there will be no magnetic field,
and the hyff lines will simply travel radially outwards. The magnetism
process does not consume energy per se. So once a velocity is established
for the mass or charge, then it can continue moving indefinitely if there is
no external resistance: the velocity does not expire. This property is
momentum.
Thus the reactive ends resist a change in velocity. The greater the
acceleration a or mass m of a body, the greater the force F required to
constrain the reactive ends of its particuloids into positions they would not
naturally take. Thus F = d(m.v)/dt or F = m.a.
Thus a Cordus model offers explanations for the resistance to acceleration
(Newtonian mass).
Relativistic mass and the Lorentz
It is known that as the speed v of a body of rest mass mo approaches that
of light c, so the effective mass tends to infinity, or at least the resistance
to acceleration does, m = mo (1-v2/c2) 0.5. Thus the mass of a body appears
heavier when it travels at higher velocity. This effect does not slow the
velocity, so the body can continue at this speed indefinitely, but it does
mean that disproportionately more force will be required to further
accelerate it.
The Cordus explanation is that process of the hyff engaging with the fabric
becomes progressively less effective as the velocity of the mass also
approaches c. Thus from the Cordus perspective the concept of ‘relativistic
mass’ is incorrect: the mass does not increase as the velocity approaches
the speed of light, nor does the mass grow more hyff. Instead the
mechanism of communicating with the distal regions of the hyff becomes
compromised. Another perspective is that the fabric cannot be informed
as easily of the changes, so the moving mass clashes more with the fabric.
But the fabric is immense, being backed by the rest of the universe, and
resists. To an observer it looks like the mass is increasing.
A partial quantitative explanation is also available, see Figure 1. In one unit
of time, as the mass moves forward at v, so the hyff length has to maintain
range c. The range contracts to B whereas usually it would be A. Then γ =
c/b is the ratio of contraction of the hyff in the direction perpendicular to
the motion, and is the degree to which the hyff are compromised in their
interaction with the fabric. By simple trigonometry b = (c2-v2)1/2 and hence
after rearrangement γ = (1 – v2/c2)0.5, which is the Lorentz.
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Figure 1: Degree to which hyff engagement with fabric is compromised as
velocity of particuloid increases.
Thus greater force is required to accelerate a mass that is already at higher
velocity, than slower. As the velocity approaches c, so the efficacy of the
hyff compensatory mechanism tends to zero, and therefore the inertial
resistance to further acceleration becomes infinite. From the Cordus
perspective, mass is invariant (well, approximately): it is the number of
hyff a body emits and the frequency thereof. From this perspective the
mass only appears to increase at relativistic speeds because another force
is acting that happens to look like mass.70
Momentum mechanism
Everyday experience, and classical mechanics, suggests that a body needs
to have mass to have momentum, and therefore if the photon has
momentum it should have mass. However, relativity states that mass and
momentum are separate properties, related to energy through the energymomentum formula:
E = [ (p.c)2 + (mo.c2)2 ]0.5
In that case, what physical structure carries the momentum, and what
carries the mass? Cordus suggests that a frequency effect at the fibril level
drives both mass and momentum. The working model is that a moving
cordus has a persistent gait for its reactive ends: at constant velocity the
70
On the other hand, we are open to the possibility that at higher speeds
the interaction with the fabric makes the reactive ends re-energise sooner than
they would have. Thus the frequency of the particuloid may increase with speed,
and hence the mass too. So perhaps the two views are complementary after all. If
we could measure the frequency of a particuloid at speed, we might know.
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momentum gives the cordus frequency mechanism the required position
of the RE that will energise next (E.4.7). Change in velocity interferes with
the location, determined by momentum, where the reactive end was due
to re-energise. Thus the reactive end re-energises later or sooner than it
should have, which affects the frequency of the whole cordus including
the hyffons. The engagement of hyff with the fabric becomes less
effective. We cannot answer the question of momentum as clearly as we
would like, and it looks to be an interestingly open question for future
research. The place to start looking for a better understanding is probably
the photon.
Relativity has no issue with a particle having momentum but no mass, and
the photon is usually considered such an example. The photon is
conventionally thought to be massless at rest, and in flight to be massless
but with momentum. Several effects are known: its trajectory is affected
by gravity, as is the frequency. Compton scattering, whereby an incident
photon is deflected by an electron and changes energy, is explainable
assuming conservation of energy and momentum, with the photon having
momentum p=hf/c.
Cordus suggests the issue may need reconsideration, for several reasons.
The first is that it is not sensible to speak of a stationary photon (see
Cordus conjecture), so what it appears to be at rest is totally irrelevant to
flight, since they are different forms. Furthermore, Cordus suggests that
mass is a transient phenomenon, not the enduringly stable property
conventionally assumed. Specifically, the Cordus construct is that mass is
created by acceleration of energised reactive ends (E.4.7). Since the
photon meets that criterion, and there is no other lemma preventing it, we
have to logically assume that there is a possibility that the photon has
dynamically transient mass during flight. If this were to be true, then the
conventional partition of mass and momentum might need to be
reconsidered too.
Integration of gravitation and mass
Cordus conceptually integrates the different effects of mass: Gravitation is
a particuloid contributing hyff to the fabric; Newtonian mass is resistance
of the reactive ends to unexpected displacement; Relativistic mass is
decreasing efficacy of hyff engagement with the fabric as velocity of the
reactive end increases; Momentum is a frequency mechanism (as yet
incompletely described) that ensures the reactive end re-energises ontime and in-place; particuloids have mass to the extent that they have
frequency; mass arises from particuloids like the proton and neutron.
Thus a stationary object floating in space contains particuloids that are
oscillating cordi, and these engage with the fabric. They contribute to the
fabric and thus gravitation, and are constrained by the fabric hence the
mass effects. The Cordus mass model is therefore consistent with that for
gravitation, and both depend on the concept of cordus frequency. What
the model has not yet explained is gravitational time dilation. That comes
at the end of the next section on time.
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4
Cordus Time
The following is a Cordus model for time. Cordus offers an explanation
whereby time is determined at a sub-atomic level by the cordus frequency,
and this aggregates to the sense of time that we perceive biologically.
E.5
Time Lemma
E.5.1
The cordus frequency for a particuloid determines its time unit
(tick). Time is determined at the sub-atomic level by the reenergisation of the reactive ends at the cordus frequency. The
cordus frequency is therefore the minimum time unit for that
particuloid. Each particuloid has its own tick, which is determined
by its span (E.5.6).
Anything that delays or interferes with re-energisation of a
reactive end, changes time for that cordus particuloid. This is the
Principle of delayed re-energisation.
The fabric, to which every matter particuloid contributes,
transmits information about the phase of other particuloids, and
provides an opportunity for a degree of disorderly synchronisation
between particuloids and atoms. (Not necessarily full body
coherence).
Interactions between atoms are not temporally continuous but
occur when the particuloids are energised.
Biological sense of time is a neurological perception overlaid on
the molecular time units.
The smaller the span of the cordus particuloid the higher the
frequency.
The higher the cordus frequency the greater the contribution to
the fabric, and the greater the mass of the particuloid.
Assembly of particuloids into structures may cause the spans of
some to change to accommodate the others. This changes the
frequency of the particuloid and also its mass.
E.5.2
E.5.3
E.5.4
E.5.5
E.5.6
E.5.7
E.5.8
Tick of time for the particuloid
The Cordus perspective is that time, or at least the tick (time unit) thereof
if not the flow, is determined at the sub-atomic level by the reenergisation of the reactive ends at the cordus frequency (E.5.1). Each half
cycle of frequency is the tick of that particular particuloid. It eventually
becomes the time unit for the rest of the local environment: that
particuloid interacts with the rest of the atom, and in turn is influenced by
the other particuloids in the atom. That atom is linked to others to form
molecules (E.5.3).The maximum speed that an effect can occur within that
molecule, e.g. the making or breaking of a bond, is one tick of the involved
particuloids.
Therefore the frequency of the cordus becomes time for the particuloid: if
for any reason the cordus was prevented or delayed in its re-energisation
of a reactive end, then time for that cordus is likewise stopped or delayed
(E.5.2). We term this the Principle of delayed re-energisation.
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The degree of synchronisation of re-energisation (CoFS) is very strong
within one electron orbital (see ‘Cordus matter’), and between the quarks.
It can be strong between atoms, as superfluidity shows, but is not always
dominant like that. In everyday materials the CoFS is not strong, but we
assume that some degree of loose co-ordination exists between the
matter particuloids (E.5.3). We conceptualise it as radiating out from each
particuloid in the form of the hyffons in the fabric, that encourage but not
prescribe other particuloids to synchronisation. So the fabric provides a
relativistic, dynamic and flexible partly-synchronised fuzzy-tick for the
universe.
Irreversibility of time
Thus ‘spacetime’ is an apt descriptive term for the fabric: it encapsulates
space, and it includes a universal (if disorderly) time synchronisation
signal. The fabric guides reactive ends to reform in accessible locations, by
interacting with the hyff emerging from the RE as it phases into existence.
The fabric is a mechanism for all matter in the universe to influence all
other matter. The one-way irreversibility arrow of time is then the
internal continuity of the cordus that ensures that the opposite reactive
end will re-energise, but where it does is influenced by the fabric hyff
(E.5.3). Given the fine and disorderly nature of the fabric, and that every
particuloid (including the one under consideration) contributes to that
fabric, no cordus will necessarily re-energise in exactly the same place as
previously. So there is an irreversibility of geometric position, and that
contributes to the irreversibility of time too. The actual mechanism for
controlling the frequency is then time itself, from this perspective, the
cordus provides the tick or quantisation of time, and the fabric of the
universe provides the irreversibility.
It is important to note that the span of the cordus particuloid is a
fundamental driver of the irreversibility. If matter was a zero-dimensional
point particle, then there would be no irreversibility in time, because the
second reactive event would be exactly where the first was located. The
fact that the REs are in different places provides a small increment of time
in which the universe can partially re-arrange itself in response to what the
first RE did in the previous time unit. Larger particuloids like the proton are
buffeted by the higher-frequency of the fabric hyff. Thus the fabric, with
its higher frequency, has plenty of time to respond to the first RE. Thus the
irreversibility of time becomes stronger as the level of assembly of the
system becomes higher, i.e. tending towards larger bodies. There is also
entropy in those bodies (see 'Cordus Matter'). The corollary is that the
observed CP violation is also due to cordus span. As Cordus Matter
concluded, the zero-dimensional point paradigm of conventional physics is
an unreliable premise and the cause of many unnecessary problems.
Sense of time
Our biological perception of time is apparently smooth and continuous.
We think, and move our hand; our fingers touch the paper; we feel the
sensation of touch; we pull the book towards us; the book does actually
move; we see the letters on the page; we comprehend. The whole of the
physical reality is apparently consistent. We do not perceive the
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underlying individual atomic interactions, the agitation of the electrons
throughout both bodies, the chemical bonds being changed. But they are
there, happening faster than our senses can detect.
Our perception of time is at that higher level of squishy biology. We see
physical cause and effect around us, and we can participate in moving
objects and interacting with the rest of the world – and enjoy the world
interacting with ourself, like the touch of another or the simple pleasure
of the fresh air on our face. Each quark has a unique personal time
determined by the fabric of the universe in its location. But that frequency
is so high that it really does not matter at our level of perception, since the
effects are averaged out. The brain constructs a personal sense of time out
of the neurological events, which in turn are based on physiology, which in
turn is based on chemistry, which in turn is based on atomic physics, which
in turn is based on the frequency of cordi. That biological sense of time is
subjective and sufficient rather than necessarily accurate.
When we look at atomic clocks then we see closer to the sub-atomic level
of time. The electrons in that clock change energy levels at a higher
frequency than we can perceive biologically. That clock frequency in turn
depends on the cordus frequency for the electron (E.5.4). The atoms in our
own body likewise react at a cordus frequency to create bodily functions,
so our sense of time is a neurological phenomenon overlaid on a physical
foundation.
Matter, fabric, and time
The above interpretation of time is at the level of particuloid physics, and
thus closer to the quantum mechanics perspective. Conventionally the QM
and general relativity perspectives of time do not integrate well. With
Cordus the integration is conceptually straightforward: cordus frequency
determines local time for matter particuloids, and simultaneously all the
matter particuloids in the universe contribute hyffons to the fabric and
thereby affect local time everywhere: a causal arrow.
So all of the universe, including the vacuum, has a time signature. At any
one point in space these hyffons might conflict with each other, so the
signature might not be clear, but it exists nonetheless and it is relativistic.
Thus spacetime does have a time signature, though Cordus does not
conceptualise time as a fourth dimension.
If this is correct, then the fabric itself carries the time signature for the
whole universe. If we accept that the unit of time exists at the sub-atomic
level, and that sub-atomic mechanisms create the irreversibility, then
philosophically the next deeper question to ask is, ‘Why does the cordus
fibril have a frequency?’ Even so, if we accept that time is fundamentally
an effect whereby cordi interact with the fabric, then it suggests that time
only exists where the fabric exists.71
71
Thus the void is timeless. A universe of fabric and time expands into the
void. The universe is granular and therefore the void is also within the universe. A
time-full universe is overlaid on a time-less void.
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The Cordus concept of time therefore explains time at the ‘particle’ level,
biological level, and for general relativity.
Spacetime metric
The spacetime metric is the mathematical formalism conventionally used
to describe the relationship between the three dimensions of space and
that of time (x,y,z,t). Cordus does not support that specific formalism
because it does not support the concept of time as another continuous
dimension. Instead the causal relationships between geometry (x,y,z) and
time (t) are more complex, and time is assembled from the local
interactions of the participating matter. Thus the nature of the assembly
of matter determines time, which is to say the bonding relationships and
interaction between particuloids.
So cordus would suggest a totally different causal structure, i.e. that the
spacetime metric needs separate partitions for the Euclidian (x,y,z) and
Temporal components (t). To put it another way, cordus suggests that the
assumption of connectedness, which underlies most formalisations of
spacetime, only applies to the Euclidian component (x,y,z), and the sense
of temporal connectedness arises through a more complex causality.
Granted, there is a sense of connectedness about time, i.e. that you and I
both share the same universe and can experience the same things at the
same time but from different perspectives. However cordus suggests this
is fabricated by the contribution of all matter (via the hyff) to the fabric,
and the fabric thereby providing a degree of temporal connectedness
between remote patches of matter.
For most of the matter in the universe, the bonding and
interconnectedness between matter is disorderly, and the interactions are
accomplished by relatively many frequency cycles of the participating
particuloids. Time -in the sense of the rate of events- runs slowly in these
cases. However in some cases the interaction between particuloids is
faster, and events can be accomplished quickly or instantly. This occurs
when the particuloids are in body coherence. In turn this either occurs for
very simple assemblies, e.g. two entangled electrons, or for very cold
assemblies, e.g. superfluids, superconductors. This is another explanation
as to why entanglement, which is a special state of assembly, is
superluminal in its effects.
Time dilation
Time dilation (slowing of clocks) is known to occur for bodies that are
accelerating or in higher gravity. Cordus explains this as the reactive ends
of the particuloids in the body encounter the fabric at a greater rate or
density (respectively). This compromises the hyff emission process (see
the Lorentz above) and the re-energisation of the reactive ends, which
then slows the frequency of the cordus. This applies also to a body
travelling at relativistic velocity.
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5
Force and the Principle of Geometrically Constrained reenergisation
The above conceptual exploration has identified the action of forces in
several contexts. The concepts of force and displacement are
complementary: force is the high-level effect, whereas the deeper
mechanism is constrained displacement of reactive ends. For convenience
these scattered ideas are collected together and summarised in the
following force lemma.
E.6
Force Lemma
E.6.1
The three fundamental forces are electrostatic, magnetism, and
gravitation.
These forces are all transient pulses. In this working model they
are carried by hyffons.
These forces are all directional at sufficiently small scales. They
aggregate to apparently smooth and continuous fields at
macroscopic scales and when many particuloids are involved.
None of these fundamental forces may be shielded.
The deeper mechanism for force is prescribed geometric location:
that the reactive end of the affected particuloid is geometrically
constrained to re-energise closer (or further) to the body doing the
forcing.
E.6.1
E.6.2
E.6.3
E.6.4
Thus we identify a Principle of Geometrically constrained re-energisation,
underpinning force. Note that time also operates on the re-energisation
frequency. Anything that delays the re-energisation changes time for that
particuloid; the Principle of Delayed re-energisation. Thus there is a
relationship between force and time at the deeper level, through the
common concept of frequency. If cordus is the fourth mechanics, after
classical mechanics, electromagnetic wave theory, and quantum
mechanics, then the fifth mechanics would seem to be the mechanisms
that drive frequency.
Cordus predicts that knowing the mechanisms for particuloid frequency
should significantly enhance our understanding of momentum, time, and
force.
6
Conclusions
Gravitation is conceptually problematic to conventional theories of physics
in that the fundamental mechanisms are unknown, and the theories have
different requirements that are difficult to reconcile.
Cordus gravitation offers a solution to the problem. It provides a
mechanism whereby gravitation is not continuous but in discrete force (or
displacement) increments (quanta). Also, the closing force between two
masses is transient. In this idea, gravitation, and therefore also mass, is a
discontinuous property: i.e. a particuloid emits gravity (has mass) at some
263
moments but not others. Thus gravitation is an effect that a mass does to
the whole universe, not to targeted other bodies, and in this regard
Cordus is consistent with General relativity. Both QM and Cordus agree
that gravitation is quantised, though Cordus diverges in suggesting that
the effect is granulation rather than uniform indivisible increments.
From the Cordus perspective ‘mass’ is the resistance to acceleration of the
basal reactive end while it is energised. Cordus conceptually integrates the
different effects of mass: Gravitation is a particuloid contributing hyff to
the fabric; Newtonian mass is resistance of the reactive ends to
unexpected displacement; Relativistic mass is decreasing efficacy of hyff
engagement with the fabric as velocity of the reactive end increases;
Momentum is a frequency mechanism (as yet incompletely described)
that ensures the reactive end re-energises on-time and in-place;
particuloids have mass to the extent that they have frequency.
Furthermore, Cordus offers an explanation of how time arises. It is
proposed that time is determined at a sub-atomic level by the cordus
frequency, and this aggregates to the sense of time that we perceive
biologically. The fabric therefore carries an elemental time signature,
though it is not a fixed quantised system. The concept of time is
conceptually consistent with General relativity’s spacetime, and with the
QM expectation that time is quantised. Thus Cordus offers a solution to
reconcile those competing perspectives into a new way of thinking.
264
265
Cordus Quarks
Cordus in extremis: Part 4.4
Pons, D.J. , 72 Pons, A.D., Pons, A.M., Pons, A.J.
Abstract
A conceptual model is created for the composition of quarks and the
internal structure of the proton and neutron. In this model the charge of a
quark indicates the number of hyff (force lines) it emits. Cordus also
explains the colour and provides a mechanism for the strong interaction
(both the attraction and repulsive components). The model also explains
why parity violation occurs. A new concept of the ‘level of assembly’ is
introduced and used to explain mass excess and why smaller particuloids
have greater mass. Cordus also predicts non-conservation of mass.
Keywords: cordus; quark; colour; spin; proton; neutron; parity violation;
strong interaction; weak interaction; fundamental forces; unification;
Revision 2.10 Minor edits
Document: Pons_Cordus_4.4Quarks_E2.10.99.doc
1
Introduction
It may seem strange to addresses the structure of quarks when describing
fields and cosmological effects of the wider universe, but the two are
linked. The connecting effect is the fabric (see part 4.2), because this
determines the macroscopic features of the universe, as well as the
locations at which the quarks can exist, and therefore the stability of
matter. And in the reciprocal direction the existence of the quarks creates
the fabric hyff. So the systems are co-determined.
This paper, which is fourth in a set that applies the Cordus concept to the
extremes. The first paper covers the electric and magnetic fields and
shows conceptually how they are formed by hyff from cordus particuloids.
The cordus concept itself is described in a companion set of papers (ref.
‘Cordus Conjecture’, ‘Cordus matter’). The second part creates a working
model for the composition of the vacuum, and shows how this fabric is
made of the hyff of all the other particuloids in the universe. It also shows
how this fabric limits the speed of light to a finite value that is relativistic.
The third paper creates a conceptual model for gravitation that is
integrated with electromagnetism, and a model for time. The present
paper applies elements of those previous concepts to predict the basic
structure of the quarks within protons and neutrons, and creates a model
for the strong interaction, thereby reconciling another of the fundamental
interactions.
72
Please address correspondence to Dr Dirk Pons, University of
Canterbury, Christchurch, New Zealand. Copyright D Pons 2011.
266
2
Existing interpretations for the strong interaction
The nuclear force, or strong interaction, holds neutrons and protons
together in the nucleus, overpowering the electrical repulsion. The nuclear
force, by extending a short distance beyond the nucleus, is also
understood to give rise to van der Waals forces. The same effect holds the
quarks together within the proton and neutron.
The Quantum mechanics (QM) interpretation is that the force is
transmitted by the exchange of particles called gluons between quarks. It
is generally accepted that quarks attract each other (strong force): this
creates the force binding quarks together inside the proton and neutron,
and holds the protons in the nucleus despite their same electric charge.
Quarks have six types (flavours): down, strange and bottom; up, charm,
and top, with the first three having -1/3 charge and the latter +2/3 charge.
Of these, up (U) and down (D) are lightest and most stable, hence
abundant. Quarks also have spin (+- ½) and colour charge (RBG). Quarks
can transform into other types. Protons consist of UUD, and neutrons of
UDD. It is believed that the strong interaction is repulsive at small
separations, and that this maintains the spacing of protons and neutrons.
QM does not provide physical explanations for these parameters: it
portrays them as intrinsic variables devoid of physical meaning.
3
Cordus quark mechanics
The Cordus interpretation is that quarks are also cordi, not particles. It is
then relatively easy to assign physical interpretations to the various
properties. The spin refers to the frequency state: there are two reactive
ends for each quark, only one is active at any one time, and two quarks
may share space if their frequency states are opposite (+- ½), as per
lemmas provided previously (ref. ‘Cordus Matter’). Several additional
assumptions, as follow, are required to build a working model for the
quark.
Lemma
E.6
E.6.1
Quark lemma
Quarks are cordi and alternately energise their reactive ends at
the cordus frequency
E.6.2 The magnitude of the charge of a quark refers to the number of
hyff emitted at a reactive end, out of three possible directions, i.e.
the arrangement is 3D geometric.
E.6.2.1
We term these hyff emission directions (HEDs).
E.6.2.2
Particuloids with unit charge have one hyff in each of
three orthogonal directions.
E.6.3 The colour (red, blue, green) refers to the arrangement of the hyff
in the orthogonal 3 axes of the HEDs.
267
E.6.3.1
E.6.3.2
E.6.3.3
E.6.4
E.6.5
E.6.6
E.6.7
E.6.7.1
E.6.7.2
E.6.8
E.6.9
E.6.10
E.6.11
The axes are named (r) radial outwards co-linear with the
span, (a) and (t) perpendicular to the span and to each
other.
A single hyff (e.g. D -1/3) may be arranged in one of three
ways: (a), (r), or (t).
A double hyff (e.g. U +2/3) may be arranged in one of
three ways: (a, r), (a, t), (r, t)
The operative principle governing the sharing of hyff spaces is
Complementary frequency state synchronisation
(CoFS). A
maximum of all three directions (a, r, t) may be filled with hyff, i.e.
a synchronous hyff emission direction structure (SHEDS) is
created.
Opposed charge hyff may be considered to cancel each other’s use
of the hyff emission directions. However they do not cancel the
contribution to the fabric.
A hyff can change to a different HED. This corresponds to a colour
change.
Hyff come in pairs, one at each end of the span, and the emission
directions at the two reactive ends are complementary (parallel
but opposite directions).
The hand of the hyff at one RE is consistent with that at
the other RE, i.e. colour is conserved across the span.
The span of the particuloid provides a small offset
between the two hyff of any pair, i.e. the hyff are not colinear. At higher frequencies the span decreases and this
lack of parity also decreases.
Charge is reversed for antiquarks: hyff go in the opposite
direction.73 Later work clarifies that the hyffon propagate
outwards, but the direction of their force may be inwards (positive
charge) or outwards (negative charge).
The SHED alignment force locks hyff into synchronisation, and is
also repulsive to intrusion.
A particuloid becomes unstable and decays to a photon or
alternative structure when there is no place for its reactive end to
form, i.e. the external constraints of the fabric and the hyff of the
immediate environment dominate and preclude the emergence of
the particuloids’s hyff.
The nature of the SHED process within a nucleon creates the
handedness (chirality) of matter, e.g. the right-hand rule of the
Lorentz magnetic force.
Note that the Pauli exclusion principle does not apply here. That principle
applies only where the hyff emission directions are already all fully
occupied, which happens in the electron. In the more general case of the
quark there are three HEDS which may be filled in three ways. The more
universal principle, that subsumes the Pauli principle and covers several
other effects (see Cordus matter) is the complementary frequency state
synchronisation (CoFS).
73
This is a simplification. See later work for further development.
268
4
Quark structures
What is the structure of a quark?
Thus Cordus proposes that quarks like D have a single hyff giving a -1/3
charge and three hyff emission directions available for that single hyff,
hence three colours. Quarks like U have two hyff, energised in turn at
each of two reactive ends. There are three ways of arranging these hyff
across three HEDs. The conceptual layout for an isolated U quark is shown
in Figure 1.
Figure 1: Hyff arrangement for a U quark, with +2/3 charge. The reactive
ends are Ua1 and Ua2, and the former is energised in this diagram. The
arrow shows that the hand is consistent across the span (E.6.7). The hyff
emission directions are presumed to be orthogonal.
The implication of this lemma is that while the current working model for
the photon has only one hyff at each reactive-end, in the (r) axis, this is not
a universal limitation. Thus the quark lemma provides for the proton, and
by implication probably also the electron, to have three pairs of hyff, one
in each HED. The corollary is that that the fundamental electric charge of 1 for the electron is actually not the base unit of charge: instead that is a
single hyff of -1/3 (except that separate quarks do not exist naturally).
Note that whereas the photon emits and recalls its hyff, the quarks have
permanent hyff.
Cordus predicts that the proton and probably the electron have three pairs
of hyff, in orthogonal directions, but the pairs are offset across a small
span.
Internal structure of the proton
A proton and neutron each have three quarks: UUD and UDD respectively.
This gives +1 charge to the proton and nil charge to the neutron. It is now
straightforward to propose a model for the internal quark structure of the
proton for example. Each subatomic baryon particuloid is known to have
three quarks. Cordus requires that these must be arranged without their
hyff being superimposed so that slots in all axes are filled: the E.6.4 CoFS
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exclusion principle, with the E.6.5 concession. This means that the local
axes of some the quarks will have to rotate relative to the others (change
colour), thereby accessing the slots in 3D. Three colours (RBG) for three
rotations.
The previous figure showed what a single free quark might look like.
However, when the quarks condense into the proton, their hyff mutually
influence each other to rotate, synchronise, and snap into the available
emission directions, i.e. SHEDS. Once they are in, they are locked in by the
high degree of CoFS.74 Thus the arrangement of the quarks inside the
proton is proposed as per Figure 2.
Figure 2: Proposed components of the proton. Two up quarks (U) and a
down (D) quark align themselves to fill all three orthogonal hyff emission
directions. They also synchronise their three frequencies, polarisations of
their spans, and phases of their frequencies. This high degree of
complementary frequency state synchronisation gives the assembly high
stability against perturbations in the fabric.
All the above comments apply also to the neutron, and the structure of
that particuloid is a simple adaptation of the proton but with a UDD
structure such that all the hyff are cancelled out, so there is no net electric
charge. However, that does not mean that there are no hyff emitted, only
that they are balanced (E.6.5).
Cordus predicts that the quarks should be arranged in a co-linear manner.
74
One could say that there is a high degree of ‘coherence’ across the
structure. However we avoid that term, because it is so mixed up with multiple
other meanings in QM, that it is a cognitively ambiguous concept and therefore
semantically unreliable. We deliberately use ‘CoFS’ because it does not come with
prior connotations.
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Stability through SHEDS
An individual quark is known to be unstable. Cordus suggests the reason is
the fabric locally disrupts the hyff differently at the two reactive ends, so
that the hand or colour cannot be conserved across the span (E.6.7), hence
instability of the RE. The quark may be intrinsically stable, but no quark
exists in a void of its own. The combination of three quarks creates a
structure that also has external stability. The hyff of the three quarks guide
each other to persistently stable locations (hence emission directions).
This is consistent with the QM perspective that quarks of different colour
are ‘attracted’ to each other. The whole structure is in a CoFs state. The
hyff support each other, and this reduces their vulnerability to the fabric
variability, and hence increases stability.
Cordus suggests that if the localised gradients in the fabric were too high,
then the proton structure could disintegrate.
Decay model
We anticipate a general mechanism for decay in E.6.10.
Cordus suggests that a particuloid becomes unstable and decays when
there is no place for its reactive end to form, i.e. the external constraints
of the fabric and the hyff of the immediate environment dominate and
preclude the emergence of the particuloids’s hyff. This prevents reenergisation of the RE. We further speculate that the particuloid escapes
this untenable situation by converting to a photon and transmitting away,
and/or changing its internal structure and level of assembly. This decay
model may be a testable cordus principle. This principle may also underpin
the absorption of photons into matter.
Parity violation
The reason parity is not conserved by quark interactions is a geometric
consequence of E.6.7: that the arrangement of the hyff is conserved
across the span, but the span is a finite length of separation. Therefore the
particuloid has an orientation of its span, and is not a simple zerodimensional point. Thus a mirror image of quark Ub in the above figure is
not identical to Ub itself, about every mirror plane. If quarks were points,
which is the conventional QM paradigm, then they would be. At a high
enough level of abstraction the cordi can effectively be considered
particles, hence parity violation only occurs at small scales.
Comparison with QM
What then of QM’s gluons? Cordus suggests there are no such zerodimensional particles, but that instead the interaction is mediated by the
CoFS interlocking of hyff. The nearest match to a ‘gluon’ is therefore a
single hyff, or perhaps the hyff renewal pulses (hyffons), but this is not a
particularly apt or useful concept. Cordus suggests it is better to abandon
the ‘particle’ view altogether, and not try to translate the concepts back
into Quantum mechanics. The glue is in the SHEDS, not the particles.
271
What is the strong interaction (force)?
Cordus suggests that the strong interaction is simply an application of the
CoFS principle to three axes. Thus the force that bonds quarks together is
the positional convenience of their interlocked hyff, i.e. SHEDS. The hyff
themselves are the same as those that create the electrostatic force, but it
is not electrostatic attraction that does the bonding in this case. Thus the
‘strong’ force is not a fundamental force, but rather an interaction. It is the
same class of effect as electron orbitals and bonds between atoms.
What is the weak interaction (force)?
The ‘weak’ interaction is the activity whereby quarks can change flavour
and emit/absorb electrons. It apparently involves short-lived particles, the
W and Z bosons, that carry away charge, spin, or momentum etc., and
thereby change the properties of quarks, before decaying into a
conventional particle and a photon.
Cordus suggests the weak interaction is not a fundamental force or
interaction, but rather an effect: a transitory form in the decay of matter.
It is the same class of effect as electrons emitting/absorbing photons to
change energy shells. From a Cordus perspective it is likely that there are
still deeper internal variables driving those behaviours, but it is not a
different category of force.
Fundamental forces
Thus, from the Cordus perspective, there are only three fundamental
forces: electrostatics, magnetism, and gravitation. There are also several
different ways that hyff interact, including electron orbitals and a
predicted synchronous hyff emission for the quark.
5
Level of assembly
The concept of mass developed above (part 4.3) is not what it seems at
the everyday level of our existence. Mass is not a permanent property of
matter, but a dynamic consequence of the frequency of the cordus, and
the interaction thereof with the fabric (part 2). If true, this has some
interesting implications regarding the absoluteness of mass.
The atom is known to have a ‘mass excess’, whereby the assembled
nucleus is lighter [‘mass deficit’] than the individual masses of the protons
and neutrons. From the Cordus perspective the reason for mass excess is
that smaller-span cordi have greater frequency. This means, in a counterintuitive way, that smaller-span particuloids have more mass. By
implication any particuloids that exist within the quarks will have shorter
span and hence greater mass: at least for particuloids that are isolated.
However the distinction between assembled and isolated particuloids is an
important one. The process of aggregating particuloids into a higher
assembly results in less mass than the separate particuloids. This means
that mass is not conserved at assembly/disassembly. The Cordus
explanation is the spans of the assembled particuloids are longer than
272
their free spans, and therefore their frequencies are higher and their mass
lighter.
When particuloids are assembled into CoFS states, e.g. the SHEDS of the
quarks in the proton and neutron, then their spans are stretched to
accommodate the standard gauge of the assembly. Thus the span of the
assembly determines the mass of the assembled particuloid, not the
masses of the individual parts. This applies within the nucleons, within the
nucleus, within atoms, and within molecules.
Conservation of mass – or not
Why then is there a conservation of mass in physics and mechanics?
Cordus suggests that the conservation exists in our everyday living,
because the interactions of matter generally do not deconstruct the body
very much. However, when the interaction has sufficient energy to break
the protons apart, then the fragments have the potential to have greater
mass than the assembly.
The conventional interpretation is that the energy is converted into mass,
i.e. E = mc2 mass–energy equivalence. Cordus does not disagree with that,
but merely shows there is another way to look at it: that mass depends on
the ‘level of assembly’. Thus changing the level of assembly exposes or
incorporates more mass. It involves energy to change the assembly level.
So mass is the dependent variable: m = E/c2.
The level of assembly concept suggests that at smaller scales the
relationship between mass and energy is not smooth but should become
granular as whole assemblies are changed. This applies also to electron
bonding, and the effects are visible even at room temperature, e.g. the
specific heat capacity of matter and latent heat.
According to Cordus Matter does not have an invariant mass: it depends
on the level of assembly. Conservation of mass therefore only applies
when the masses do not change assembly level. Even then the
conservation is only approximate, because even changes to electron bonds
change the mass of the assembly, albeit small.
Another implication concerns the binding energy required to disassemble
a molecule or atom.
Cordus interprets a positive binding energy as meaning that the span of
the assembly should be greater than the parts. This is somewhat counter
intuitive as we tend to think of molecular assemblies as bonds that pull the
atoms closer.
Mass, span and Level of Assembly are related
Thus the mass of a particuloid depends on the span that the external
environment requires it to adopt. For a quark in a proton, that constraint
on span is determined by the other quarks in the assembly in a negotiation
process of exchanged constraints, and we term this the ‘Assembly gauge’.
For an electron in a bond, the constraint on span is determined by the
273
joint structures of the two atoms. For a free electron in space, the spanconstraint arises from the fabric.
The assembly gauge concept suggests that a coherent body will have only
one frequency, not many.
Coupling between mass and field
That suggests another interesting conceptual development. We call this
the Principle of mass-field coupling, and note it with lemma E.7.8. The
Cordus mechanics already provides that the hyff and the fibril are coupled.
So if a free cordus particuloid, say a free electron, is forced by the fabric to
take a different span, say shorter, and therefore increase its frequency,
then there is a consequence for the hyff (read ‘field’ in conventional
physics). The increase in frequency causes the mass of the electron to
increase too. In conventional physics this would be called the mass of the
‘shell’, but of course Cordus does not hold with that notion of spherical
particles. If the situation is adiabatic, i.e. the electron has not been given
additional energy or absorbed a photon, and assuming conservation of
energy, then by implication the electron has to withdraw energy from the
hyff system to support the increase in its mass.
It is to be expected that the hyff system will resist this. Consequently there
will be an element of stability for the cordus system as a whole (fibril,
span, frequency generator, reactive-ends, hyff, hyffons). Thus the cordus
particuloid can adjust its frequency and span in response to sufficiently
strong external demand, but it has internal stability mechanisms that
moderate the changes.
It may be that this is what the photon is doing. In other words, this might
explain why the photon emits and withdraws its hyff, a feature of Cordus
that has been commented on above.
It also means that the span is not constant, though it has a mean. The
reactive end moves inwards and outwards as it energises and re-energises.
So the precise span of a cordus particuloid at any one instant changes. It
may be for the photon that in a sense, the reactive end dilutes itself and
becomes the hyffon at the extreme of the span, so that the outer extreme
of the span is very great, but also very rare. So some photons will pass
through both slits of the double-slit device, regardless of the spacing. We
have noted this as Lemma L.5.7 [1].
Singularities
One of the problems in conventional physics including quantum field
theory is the singularities that arise when diameters of ‘particles’ are
condensed to zero. The resulting infinities have to be treated with
‘renormalisation’ processes which seem to work even if of dubious
fundamental validity.
Cordus offers a totally different way to view the problem: matter is not
points in the first place, and the smallest size of a particuloid is not zero
but the span of its cordus. The inertia of an electron is not infinite, because
274
it never is a point. Nor do interactions become infinitely strong at shorter
distances: the particuloid is not always energised to be able to react. There
are no actual singularities: those only appear in physics as artefacts of the
zero-dimensional point premise. Thus the appearance of a singularity in
physics implies that the mechanics and its mathematics are deficient and
unable to be applied to the next level down: they only apply on-average to
the next higher level of assembly. That is why quantum mechanics is only
applicable, and only on-average, to larger aggregates of particuloids, and
starts to break down at the level of the double-slit device where individual
particuloids become involved.
Cordus thus asserts that we cannot
complacently accept ‘renormalisation’ as a self-consistent process, but
instead need to recognise it as a warning sign that the limits of validity for
that theory have been reached and that a fundamental reconceptualisation may be required in that area, with a switch to a deeper
mechanics with a different mathematics, if the next deeper level of reality
is to be accessed.
Nucleon masses
The interconnectedness of mass, span and Level of Assembly also allows
an explanation of the mass difference between the proton and neutron.
The neutron is known to be heavier. The Cordus explanation is that the
natural span of the D quark is smaller than that of U, for reasons
uncertain.75 Thus a proton of UUD causes the D to be stretched, hence
lowering its mass, because the UU dominate the outcome. The neutron of
UDD causes the U span to be compressed, increasing its mass. True, the
DD will be stretched slightly, decreasing their mass, but there are two of
them so the effect is disproportionally smaller. The overall effect is that
the neutron is slightly heavier.
Thus considerations of cordus span and frequency could be useful in
understanding the mass differences in other sub-atomic assemblies.
Cordus suggests that mass is determined by the frequency of the
assembly. This may be testable.
We summarise the above with the following lemma.
Level-of-assembly lemma
E.7 Level-of-assembly lemma
E.7.1 Higher frequency (smaller) particuloids have more mass.
E.7.2 Mass is not conserved at assembly/disassembly.
E.7.3 Particuloids that have their span stretched at assembly into atomic
structures reduce mass, and the converse.
E.7.4 The span of the assembly as a whole (assembly gauge) determines
the mass of the assembled particuloid, not the masses of the
individual parts.
E.7.5 Matter does not have an invariant mass: it depends on the level of
assembly.
75
Probably the U quark is an assembly of smaller cordi, and the assembly
gauge is thus stretched (E.7.3).
275
E.7.6
E.7.8
Span (assembly gauge) tends to increase at higher levels of
assembly. Hence higher levels of assembly are lighter.
Principle of mass-field coupling: In adiabatic conditions a
conservation of energy applies between the fibril energy and the
hyff energy of a cordus matter particuloid. Thus the emission of a
hyffon momentarily extracts energy from the fibril, which causes
the span to increase (reactive end to move radially outward).
Atoms in SHEDS
Previously, in ‘Cordus Matter’, it was suggested that the electron in a shell
was influenced by the hyff arrangements of the inner shells, and those
inner shells in turn by the outer shells. Presumably something similar
applies to the nucleus. The hyff that protrude from the three quarks inside
the proton will interact with those from other protons and neutrons.
The whole nucleus is therefore an extended SHED structure. The protons
and neutrons have to fit their hyff around each other. The electrons also:
they cannot simply go anywhere, but have to fit around the hyff from the
nucleus and the other electrons, hence the orbitals. The addition of more
electrons neutralises some of the proton hyff, and thus allows more
protons to be added to the assembly. The whole atom is therefore very
much more than simply an electrostatic interaction between electrons and
protons.
Thus we have provided a model for the inside of a proton, and
conceptually identified the possible structural principle for the larger
nucleus and the atom itself, but the details remain an open question. This
might be a good place for a mathematically based optimisation method to
make a contribution, because intuitive the structure of a large atom is
going to be complex and beyond the power of the simple logically
descriptive method used here.
According to cordus, the mass of any particuloid should depend on the
level of assembly.
6
Conclusions
By pushing Cordus to the extremes, a conceptual model has been created
for quarks and the internal structure of the proton and neutron. In this
model the charge of a quark indicates the number of hyff (force lines) it
emits. Cordus also explains the colour and provides a mechanism for the
strong interaction (both the attraction and repulsive components). The
model also explains why parity violation occurs. A new concept of the
‘level of assembly’ is introduced and used to explain mass excess and why
smaller particuloids have greater mass. Cordus also makes some more
radical predictions, such as non-conservation of mass.
Fundamental forces
In this extrapolation of the Cordus conjecture, gravitation is caused by
acceleration of the basal cordus particuloid, magnetism by velocity of the
276
reactive ends, and electrostatic force by position thereof. These are the
only three fundamental forces: the strong and the weak ‘forces’ are aptly
named ‘interactions’ and in the same categories as orbitals and photon
emission respectively, i.e. not fundamental forces.
The important concept here is that one mechanism, the emission of hyff,
provides the underlying mechanism for electrostatics, magnetism, and
gravitation. These forces are intrinsically unified. In contrast, QM
perceives these forces, together with the strong and weak nuclear
interactions, as mediated by virtual particles and tries to unify them on
that basis. Cordus suggests the so called virtual particles are simply
different measurement artefacts of the hyff, not the real interactions.
Comment
The macroscopic world is very beautiful. Despite the large gaps at the subatomic level, and the dynamic turmoil within even the simplest atom, the
overall effect at our level of being is of a reliable, smooth, persistent
world. The paint on the aircraft is durable and behaves the same, day after
day, despite what is happening in its sub-atomic structure. The
macroscopic stability of matter is all the more surprising. It is also beautiful
because it creates the world in which our bodies can exist.
7
Closing summary
This series of papers is an extrapolation of the basic Cordus concept to the
extremes. We are not saying that the resulting concepts are necessarily
true, only that they are challenging ideas that are worth considering.
What has been achieved here?
Cordus in extremis offers novel concepts for several effects, starting with
fields. It proposes a mechanism for granular field-forces that aggregate to
the apparently smooth field at our level of everyday perception. The hyff
carries a transient quantum of force (‘hyffon’) directed back down the hyff
towards its origin. Each re-energisation of the reactive end sends another
renewal-pulse of force down the hyff. Therefore hyff are directional force
lines that extend out into space from their basal particuloid, and where
the force appears in pulses that travel outwards along the line (hyffons).
For a test charge in an electric field, the overall effect is a steady rain of
hyffons that are individually small transient units of force. The overall
effect is a smooth force.
Cordus proposes that the electric field cannot actually be shielded, only
locally neutralised, and it provides a new way to conceive of the
connection between electrostatics and magnetism. Cordus does not
consider electromagnetism as equivalent concepts, but suggests they are
quite different physical effects and that electrostatics is the more
fundamental and magnetism the derivative.
Unconventionally, Cordus predicts a fabric to the universe: a type of
massless relativistic aether, but made of tangled hyff force lines not
277
particles. The fabric is made of the hyff of all the other massy particuloids
in the accessible universe. This fabric limits the speed of light to a finite
value. An even more drastic proposal is that the speed of light is not
invariant, even if it is relativistic.
Another radical outcome is that Cordus proposes an integration with
gravitation through the same hyff mechanism underlying electrostatics
and magnetism. The important concept here is that one mechanism, the
emission of hyff, provides the underlying mechanism for electrostatics,
magnetism, and gravitation. It is proposed that these are the only
fundamental forces and are intrinsically unified. The hyff provide a
mechanism whereby gravitation is not continuous but in discrete force (or
displacement) increments, and the closing force between two masses is
transient. In this idea, gravitation, and therefore also mass, is a
discontinuous property: i.e. a particuloid emits gravity (has mass) at some
moments but not others. Thus gravitation is an effect that a mass does to
the whole universe, not to targeted other bodies. Cordus conceptually
integrates the different effects of mass: Gravitation is a particuloid
contributing hyff to the fabric; Newtonian mass is resistance of the
reactive ends to unexpected displacement; Relativistic mass is decreasing
efficacy of hyff engagement with the fabric as velocity of the reactive end
increases; Momentum is a frequency mechanism (as yet incompletely
described) that ensures the reactive end re-energises on-time and inplace; particuloids have mass to the extent that they have frequency.
Less radical, but nonetheless a useful integration, Cordus offers an
explanation of how time arises at a sub-atomic level by the cordus
frequency, and how this aggregates to the sense of time that we perceive
biologically. Thus time is carried in the fabric, and this is a similar concept
to spacetime in General relativity, though Cordus does not see time as a
fourth dimension.
The fabric itself is proposed to be made from the hyff of sub-atomic
particles, including the quarks. Cordus goes on to suggest a composition
for quarks, and the structure of the proton and neutron. The fractional
charge of the quark is explained in terms of hyff, and the colour by the
combinations of hyff emission directions. The strong interaction then
emerges as a hyff interaction effect, not a fundamental force as such.
Cordus suggests the weak interaction is not a fundamental force either,
but rather an effect: a transitory form in the decay of matter. Thus Cordus
proposes that there are only three fundamental forces: electrostatics,
magnetism, and gravitation, and they are all carried by the same hyff.
Those same hyff also contribute to the fabric and to time, so the concepts
are interlinked. As a by-product, an explanation emerges for why parity is
violated by quark interactions: this is explained as a geometric
consequence the cordus having a finite span.
Cordus is unconventional in suggesting that mass is not generally. Instead
it is proposed that matter does not have an invariant mass. Mass depends
on the level of assembly of the particuloid into sub-atomic, atomic and
molecular structures. It predicts that mass is determined by frequency,
278
which in turn is related to cordus span, hence size of particuloid and the
way it is bonded into other assemblies.
Thus Cordus in extremis provides a coherent explanation across a wide
variety of phenomena that otherwise are only partially explained by
conventional theories of physics, see Figure 3. Compared to the
conventional theories, Cordus offers greater explanatory power, greater
coherence with less reliance on metaphysical explanations, and greater
integration across a broader range of phenomena. This is particularly
evident when considering the effects also described in the companion
papers, which resolve many of the paradoxes of wave-particle duality and
provide explanations where conventional theories are limited to abstract
mathematical interpretations or reliant on metaphysical effects.
279
Figure 3: The core idea of the cordus conjecture is that all ‘particles’ have a
two-ended cordus structure. This basic idea may be extended to create a
conceptual framework that provides a logically consistent description
across a variety of effects. The result is a high-level descriptive integration
across fundamental physics, and the emergence of a deeper mechanics.
The purpose of this paper was to push the Cordus mechanics into extreme
predictions, out of curiosity for any new concepts that it might suggest.
The original Cordus concept was created to explain wave-particle duality
of the photon in the double-slit device. When applied to the extremes, the
concept has yielded unexpected new insights, novel re-thinking of things
we thought we already knew, explanations for things that were paradoxes,
and some unconventional contrary predictions. Cordus provides a radical
re-conceptualisation of several areas of fundamental physics.
Cordus is fundamentally different to conventional thinking. It departs
radically from both quantum mechanics and general relativity in its
suggestions of the underlying mechanisms. Yet in many cases it offers
concepts that will be recognisable to those other areas.
280
The primary contribution of the Cordus work as a whole is that it provides
a new conceptual framework for thinking about fundamental physics.
Cordus may or may not be a robust solution, but it does show that there
are other ways of thinking about the issues, and we do not need to be
discouraged by the staleness of the debates about wave-particle duality,
nor stuck in the fixed paradigms of existing theories, nor perplexed by the
weirdness of quantum mechanics. Even if Cordus is not the deeper
mechanics, there can now be no doubt that a deeper mechanics does
exist.
References
1.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J. (2011)
Explanation of fringes. Cordus Conjecture: Part 1.3 viXra 1104.0018, 1-18
DOI: vixra.org/abs/1104.0018.
281
282
Cordus
Conjecture
Part 5: Matter and antimatter
Concept
of
handedness (ma) of
fields > matter and
antimatter
differentiated
by
mirrored hand of
hyffons > structure of
antimatter proposed
>
annihilation
process explained >
different behaviour
of
the
two
positroniums
explained > new
process diagrams and
HED
notation
introduced
283
Mirror images: Matter and Antimatter
Pons, D.J. 76
Abstract
Existing theories of physics struggle to explain the difference between
matter and antimatter in ways that make physical sense. This paper offers
a reconceptualisation based on the cordus conjecture. We create a new
concept of handedness, called ma, and an operational definition based on
the energisation sequence of the cordus reactive-ends. Each reactive end
for a stable matter particuloid, e.g. the electron, has three orthogonal
hyff. The hand of these is held to be the same for all matter particuloids,
whether positive or negative charge. For all antimatter particuloids the
hand is inverted. The inversion also changes the direction of the hyff, and
thus reverses the charge, but this is a secondary effect. This cordus concept
permits models to be created differentiating between the electron, proton,
and antielectron (positron). This explains why the antielectron is very
different to the proton despite the same charge, and why the photon does
not have an antiparticle. It also allows the wider integration of bonding
and annihilation as manifestations of a single deeper mechanics.
Keywords: antimatter, hand, chirality, fundamental physics
Edition 1.1 Minor edits > Date: Saturday, 11 February 2012 > Document:
Pons_Cordus_5.1_MirrorImages_MatterAntiMatter_E1.1.16.doc
1
Introduction
Reality is concrete enough, at least at our level of experience, but what
exactly is all that matter made of? What is antimatter (aM) and how does
it differ from matter? Why and how do the two annihilate? Why does the
universe contain so little antimatter compared to matter? Those questions
are difficult to answer with current fundamental physics.
Part of the problem is that conventional physics does not really know what
matter is. We think that matter is made of particles, and we think they are
only points with no internal structure (other than assemblies of more
points), but we don't know what makes up the point. We also think that
particles are waves, but other than being able to describe their
mathematical behaviour as a wave, we really do not know what that wave
comprises either. We think that particles are in two positions at once, i.e.
superposition and can represent that with the wavefunction – indeed we
76
Please address correspondence to Dr Dirk Pons, University of Canterbury,
Christchurch, New Zealand. Copyright D Pons 2011.
284
see confirming empirical evidence at the microscopic scale: but not at the
macroscopic, which is perplexing. We don't really know what matter is.
Naturally that also means we don't know antimatter to the level that we
would like. The dominant explanation for antimatter is quantum
mechanics. However QM cannot explain the structure of antimatter, and
has practically nothing to say about the process of annihilation.
This paper shows how antimatter can be conceptualised from the cordus
conjecture [1]. Doing this provides a better explanation of the difference
between matter and antimatter in ways that make physical sense.
2
The conventional perspective of antimatter
Antimatter: content and formation
The most abundant type of antimatter is antielectrons (e, positrons), but
antiprotons (p) and antineutrons (n) have also been synthesised. Note that
we use the underscore to denote antimatter.77
The E=mc2 relation superficially suggests that energy can be converted into
matter (or the inverse). However that is only half the story, because
antimatter is always created when matter is created: the formation of only
matter particles has not been observed. Energy always transforms into a
particle and its antiparticle.
Antimatter particles are regularly produced by natural phenomena, e.g.
cosmic rays striking the atmosphere, and radioactive decay. They are also
produced artificially, e.g. in colliders. Whole antimatter atoms have also
been produced, currently limited in size to the smaller assemblies:
antihydrogen, antideuterium, antihelium (-3 & -4).
Existing theories of antimatter
The common idea is that antimatter is simply opposite charge. On its own
that cannot be correct as it suggests that the electron and proton should
also annihilate, which doesn’t happen.78 Also, it is not immediately clear
why neutral particles, e.g. neutrons, have antiparticles too.
From the perspective of quantum mechanics, antimatter is opposite
charge and opposite quantum numbers. This concept of antimatter as
opposite chirality is a more thoughtful approach, but chirality is an
77
Conventionally the antielectron is given a special name, the positron, since it was first
discovered, whereas other antiparticles do not have special names. Here we simply stay
with ‘antielectron’, because it is a better cognitive reminder about the special
complementary features of antimatter in the cordus model. Our notation also departs
regarding the abbreviated representations, which conventionally have a signed superscript
+
(positron: e , antiproton: p ) or an overprinted bar (antiparticle: ā). We avoid the former
because our model shows that the antimatter effect is not simply a matter of opposite
charge. Instead we use an underscore, as in antiparticle a, to signal the cognitive break
with conventional ideas of antimatter, but yet the retention of some of the conventional
constructs.
78
That is usually popularly explained away as the electron orbiting too fast around the
nucleus, though that too is a superficial explanation as orbitals are not orbits.
285
incompletely defined physical concept in physics: it is variably related to
helicity and spin. It is mostly a mathematical abstraction rather than a
physical effect, though that is a feature of many of the other intrinsic
variables of QM. Thus there is no clear explanation from conventional
physics as to what chirality corresponds to in a ‘particle’, and how it
contributes to annihilation.
The concept of quantum numbers is also helpful, but there is no universal
set of quantum numbers. Instead the number of these variables depends
on the particle situation under examination. At a deeper level one has to
question the QM premise that antimatter is opposite quantum numbers,
because realistically the main quantum numbers for fermions are charge
and spin, but these are common throughout any one generation. This
does not explain why particles from dissimilar generations do not directly
annihilate. Instead annihilation is primarily a process between a particle
and its exact opposite antiparticle, not a different type of antiparticle. The
logical conclusion is that there may be additional quantum numbers, or
more accurately additional variables or qualitative factors that govern the
annihilation behaviour. What are those? Whatever they are, they do seem
to be hidden to QM. So we have to be open to the possibility that there
might be additional hidden variables involved in the matter-antimatter
definition.
There are other theories of physics, the most complete of, and almost at
the state of mainstream acceptance, is string theory and the related Mtheory [2]. However the focus there is on cosmology,79 and while it does
not conceptually preclude antimatter, nor is the idea particularly advanced
either. So all the mainstream theories have an incomplete explanation of
antimatter.
3
Background: Cordus conjecture
The cordus conjecture is a novel alternative theory of fundamental
physics, and has been shown to provide radically different interpretations
of many physical effects. It is a different way of thinking, both about the
subject of ‘particles’, and also in the cognitive approach. It is primarily a
qualitative conceptual method as opposed to the quantitative
mathematical method of conventional physics. It is a type of hidden
variable solution that circumvents the limitations of Bell’s theorem [3].
79
In String theory all particles are one-dimensional oscillating lines, and this requires that
the universe have additional dimensions that we cannot see. There are several variants of
the theory, with different prescriptions for the required dimensions. It is believed that the
variants are all subsets of M-theory, with its 11 dimensions. There is hope that string theory
may unify gravitation with electromagnetism, and describe the fundamental reality of
nature, but it is not yet capable of that. It is a mathematical approach, but even so has not
made quantitative predictions that can be verified one way or the other. Also, it has many
formulations, and it is difficult to know which applies to the real world, i.e. it is still abstract
rather than concrete. It is a class of theories, and a work in progress rather than a complete
solution.
286
The conjecture states that all 'particles', e.g. photons of light, electrons,
and the protons in the nucleus of the atom, are not one-dimensional
points, but have a specific internal structure called a 'cordus'. The cordus
consists of two ‘reactive ends’, which are a small finite distance apart
(‘span’), and each behave like a particle in their interaction with the
external environment. A ‘fibril’ joins the reactive ends, and is a persistent
and dynamic structure but does not interact with matter [4]. The reactive
ends are energised (typically in turn) at a frequency [5]. The reactive ends
emit one or more force lines called ‘hyperfine fibrils’ (hyff) into space, and
when the reactive end is energised it sends a transient force pulse
(‘hyffon’) outwards along the hyff curve [6]. This makes up the field, which
is thus also discretised. Various features of the hyff and hyffon carry the
electrostatic field, magnetism, and gravitation simultaneously. In this
model the photon has a single radial hyff which it periodically extends and
withdraws, see Figure 1 [4].
By comparison all massy particuloids, including neutral particuloids like the
neutron, have permanent hyff [6]. Electric charge is carried at 1/3 charge
per hyff, so stable particuloids like the electron are surmised to have three
hyff, and these are presumed to be arranged orthogonally [7]. The hyff
around massy particuloids compete for emission directions and may
synchronise their emissions to access those spaces -the cordus concept of
synchronous hyff emission directions (SHED) [7]. Thus there is an element
of mutual negotiation, based on shared geometric timing constraints[7].
Figure 1: Cordus model of the photon. It is proposed that the photon
probably only has a single radial hyff at each reactive end, whereas the
electron has three, but the fundamental structural concept is similar.
Image is in the common domain
http://en.wikipedia.org/wiki/File:CordusConjecture2.21_PhotonCordus.png
The core concept in the cordus conjecture is thus a particular bipolar
internal structure for the photon and indeed all ‘particles’. We term this a
cordus, and emphasise that it is the internal structure of what is otherwise
called a ‘particle’, and is not the same as a ‘dipole’ (separation of negative
287
and positive charges) which is an external structure of multiple charges.
Nor is it appropriate to call this a ‘particle’, because it is not a zerodimensional point. The idea of a cordus allows many puzzling phenomena
to be explained at a conceptual level, such as wave-particle duality [8],
why quantum mechanics does not scale up to macroscopic objects [9],
among other lesser conundrums of fundamental physics like Casimir effect
superfluidity, local realism, entanglement, strong force, etc.
We now apply the cordus concept to differentiate matter and antimatter.
This novel explanation is an important part in eventually explaining the
annihilation process itself.
4
Cordus model for matter and antimatter
The cordus model for antimatter builds on some of the previous work on
quarks, and is briefly summarised below.
4.1
Consolidating existing principles
The basic HEDs
The core idea, which also differentiates the cordus M-aM model from
conventional perspectives, is that of hyff emission directions (HED) [7].
Each reactive end of a massy particuloid emits three hyff: one in each of
three orthogonal directions, here named [r,a,t], hence hyff emission
directions. Each HED carries a 1/3 charge, so the overall charge of the
particuloid depends on how many HED are active.
These concepts were already anticipated and encapsulated in the Quark
lemmas (E.6) [7]:
E.6.2
E.6.2.1
E.6.2.2
E.6.3
E.6.3.1
E.6.3.2
E.6.3.3
E.6.4
E.6.5
The magnitude of the charge of a quark refers to the number of hyff emitted at a
reactive end, out of three possible directions, i.e. the arrangement is 3D
geometric.
We term these hyff emission directions (HEDs).
Particuloids with unit charge have one hyff in each of three orthogonal
directions.
The colour (red, blue, green) refers to the arrangement of the hyff in the
orthogonal 3 axes of the HEDs.
The axes are named [r] radial outwards co-linear with the span, [a] and
[t] perpendicular to the span and to each other.
A single hyff (e.g. D -1/3) may be arranged in one of three ways: [a], [r],
or [t].
A double hyff (e.g. U +2/3) may be arranged in one of three ways: [a, r],
[a, t], [r, t]
The operative principle governing the sharing of hyff spaces is Complementary
frequency state synchronisation (CoFS). A maximum of all three directions [a, r, t]
may be filled with hyff, i.e. a synchronous hyff emission direction structure
(SHEDS) is created.
Opposed charge hyff may be considered to cancel each other’s use of the hyff
emission directions. However they do not cancel the contribution to the fabric.
288
Structure of the electron
We consolidate these concepts by providing a cordus model of the
electron, see Figure 2.
[r]
[t]
Three hyff,
(-1/3) each, one
in each of three
HED
a1
reactive end
a2
reactive end
currently dormant
Note hand (colour)
preserved across span
[a]
Co-ordinate system for
a1 reactive end
Energisation
sequence, e.g. [r,a,t]
contributes to hand
[r]
[t]
[a]
e
electron
structure
e
simplified
structure
[a]
[t]
[r]
Note that coordinate
system is not
absolute but relative
to reactive end
Figure 2: Cordus model of the electron. It is proposed that the particuloid
has three orthogonal hyff, energised in turn at each reactive end.
At this point we are not too concerned about the further divisibility or not
of the electron.80 However for the present we can treat the three hyff as a
unit, albeit one that energises in some sequence such as [r, a, t]. Nor are
we concerned about the mechanisms that sustain the reactive ends, hyff,
hyffons, or fibril: we acknowledge those as the next deeper level in the
mechanics.
4.2
Cordus hand: ma
Handedness of matter
In the cordus model, we have already encountered a handedness effect, in
Lemma E6 [7], as follows.
E.6.11
The nature of the SHED process within a nucleon creates the handedness
(chirality) of matter, e.g. the right-hand rule of the Lorentz magnetic force.
Now we extend this idea to build the concept of hand (‘ma’) and thence
to an operational definition of matter and antimatter. The cordus concept
is very different to the quantum mechanics concepts of ‘hand’ and
‘chirality’, so it is important to differentiate the terminology and introduce
new concepts.
80
We anticipate that the hyff might be separable at higher energies into endogenous
elements, like the quarks make up the baryons.
289
The cordus interpretation is that all matter and antimatter particuloids
have three orthogonal hyff emission directions (HEDs) at their reactive
ends, as per the above model for the electron. The arrangement of the
three hyff around the reactive end has a hand, which we call ma. We use
this different term to differentiate the constructs from QM.81
Handedness in QM refers to the direction of spin of the particle relative to
its linear motion [10]. When the spin is in the same direction as the
momentum, then it is termed right-handed. The particles of QM may have
either right or left spin-hand, and this spin-hand inverts for antiparticles.
From the cordus perspective this is a spin effect, which for convenience
we refer to as ‘spin-hand’. It is not the same as the ma hand. However the
concepts are possibly related at a deeper level of mechanics.
For convenience and consistency with our previous nomenclature for the
photon, we name the three orthogonal HEDs the radial [r], axial [a], and
tangential [t] hyff. We acknowledge that the directions may be ambiguous
as they imply motion. It is assumed that all particuloids have at least a
momentary motion-on-the-spot of their reactive ends, even if the particle
as a whole is stationary. (We note this as a lemma at the end).
We have two candidates for the origin of the handedness. One is that it is
built into the structure of the fabric, and is thus a deeper level of
mechanics than the cordus structure. The other, and the current working
model, is that the handedness arises because of the sequence of activation
of the hyff, e.g. [r], then [a], then [t] at the first reactive end, followed by ra-t at the other, as the particuloid oscillates at its frequency.
The ma mechanism ensures that the three hyff, [r, a, t] are consistently
arranged in the same way relative to each other. Further, it is assumed
that this handedness is set at the point in time when the particuloid is
created and cannot be subsequently changed while the assembly remains.
The ma requirement might seem artificial, but is not unreasonable
because something similar already exists in all the other models of physics:
classical physics already has the right-hand-rule for electromagnetism, and
quantum theory has chirality. And even the basic QM concept of spin
suggests that there is some directionality to a zero-dimensional stationary
particle. None of these are well explained: Why does the right-hand-rule
exist? How can a 0D point (or a wave) have spin and directionality? Cordus
provides a more substantial concept for handedness than any of these
other models. Having created a concept for ma hand, we now apply it to
differentiate matter from antimatter.
4.3
Cordus matter and antimatter
81
The concept of chirality is known in QM, but in a different theoretical formulation, e.g.
chiral perturbation theory in quantum chromodynamics. Here we reconceptualise it, and
therefore use a different term, ma, to distinguish the cordus concept.
290
From the cordus perspective all stable matter particles, including the
electron and the proton, have three orthogonal hyff at each reactive end,
and these are all of the same hand, for convenience called forma (right
hand). Note that the hand is the same for all matter particuloid, whatever
their charge. The difference made by charge is simply that the negative
hyff (e.g. for the electron) are all propagating outwards (a cordus sign
convention), whereas those for positive charges are inwards-directed.
Inversion of hand
The cordus interpretation for antimatter is that antiparticuloids have
opposite hand, i.e. the sequence of energisation of the hyff is spatially
inverted (mirrored). The inversion is about the long axis of the fibril, so the
[r] axis is preserved – though it changes sign, see Figure 3. We term the
inverted hand hyarma (left-hand - since this hand was left-behind at the
genesis of the universe). Importantly, note that inversion of the hand also
changes the sign of the charge.82
Cordus thus conceptualises the inversion of hand in terms of the
functional geometry of the cordus structure. Thus it provides a physically
natural (‘ordinary’) interpretation for antimatter. Note that the inversion is
about the fibril axis. Thus the [r] axis is conserved in both hands, though
the sign changes.
There is a subtle, but important distinction between this cordus definition
and that of quantum mechanics. First, cordus creates an operational
definition out of handedness, which QM with its premise of zerodimensional points (alternatively waves) does not, and cannot. Second,
cordus states that that the difference between matter and antimatter is
primarily in the hand, and the changed sign of the charge is a secondary
effect and dependent on the first. By comparison QM conceptualises
antimatter in terms of opposite charge and opposite spin, as independent
variables, and does not define the relationship between the two.
(Obviously there must be a relationship between the two, since there are
not four species of matter).
Thus it is hand AND charge that is important in cordus. Incidentally, this
definition also makes it easier to understand why a neutral particuloid like
the neutron does have an antineutron. In the cordus model the neutron
has internal charges but these neutralise so that there is no net external
charge: but nonetheless hyffons are propagated on the forma hand, hence
gravitation and mass [7]. An antineutron is easily explained as having
inverted hand and therefore charge, i.e. is still charge-neutral externally,
but has the hyarma hand. By comparison, it is not intuitive in quantum
mechanics why neutral particles should have antiparticles. By comparison
cordus readily accommodates a neutral particuloid having an
antiparticuloid: the hands are different, even if the changed sign of the
charges is still neutral.
82
It is not so much that the charge reverses, but its direction relative to the reactive end is
inverted, and thus the sign changes. Note that in cordus the sign of the charge is simply the
direction of action of the hyffon relative to the reactive end.
291
Note that the cordus model states that all matter (and antimatter)
comprises charged particuloids, it is just that sometimes the positive and
negative are balanced. Thus neutral matter particuloids, e.g. neutron, still
have internal charges, and hence there is no conceptual difficulty with
these charges changing sign (i.e. hyff changing directions) for antimatter.
Comparison of electron, proton, and antielectron
One of the paradoxes of conventional theories of antimatter is that it is
not immediately clear what the difference is between the proton and the
positron. After all, they both have charge +1. Why then does the electron
not annihilate with the proton, but does with the positron? Why do the
proton and positron have such difference masses, given that their charge
is the same?
With the cordus concept of ma hand, the explanation is easy. The
structures for these three particuloids, as proposed by cordus, are shown
in Figure 3. Note that we deliberately prefer the term ‘antielectron’ and
avoid ‘positron’: this is because antielectron is a much truer
representation of the structure. The word ‘anti-‘ refers in cordus to
inverted hand, and this feature is much more important in understanding
what is happening than the charge perspective. Thus the electron is a
structure with forma hand and outgoing hyffons, the proton is forma with
incoming hyffons, and the antielectron is hyarma (anti-forma) with
incoming hyffons.
292
Figure 3: Models for the electron, proton, and antielectron. Note that the
electron and proton have the same hand (forma) but the hyff are reversed,
hence the reversion of charge. The proton is also a different type of
assembly, being a composite of quarks at this level, whereas the electron is
a unified structure at this same level. The difference between the electron
and antielectron is inversion of hand: the electron is forma, and the
antielectron hyarma. The inversion is about the fibril axis [r] and this also
inverts all the hyff, hence reversing of charge.
We will stop this development here, having established the basic principle
of ma hand, and leave its further development, such as the process of
annihilation itself, to companions papers. But before we go, we
consolidate the current assumptions into the following lemma.
4.4
Lemma
The following lemma summarises the assumptions in this antimatter
model, and the principles involved.
Ma.1 Matter and antimatter lemma
Ma.1.1 All matter and antimatter particuloids have three orthogonal hyff
emission directions (HEDs) at their reactive ends: [r,a,t].
Ma.1.2 It is assumed that all particuloids have at least a momentary
motion-on-the-spot of their reactive ends, even if the particle as a
whole is stationary, which gives a direction to the [r,a,t] axes.
Ma.1.3 The arrangement of the three hyff around the reactive end has a
hand, which we call ma.
Ma.1.4 Mechanism for ma hand: The current working model is that the
handedness arises because of the sequence of activation of the
293
hyff, e.g. [r], then [a], then [t] at the first reactive end, followed by
the same at the other, as the particuloid oscillates at its frequency.
Ma.1.5 This handedness is set at the point in time when the particuloid is
created.
Ma.1.6 Cordus assumes that all particuloids (except the photon) have a
hand.
Ma.1.6
The hand differentiates matter from antimatter.
Ma.1.6.1
All matter particuloids, e.g. electron and proton, are of
the same hand, forma, regardless of charge. (Charge refers
instead to the direction of propagation of the hyffons:
outwards for negative charge, inwards for positive. A sign
convention).
Ma.1.6.2
All antimatter has the inverted ma hand, termed hyarma.
The inversion is about the long axis of the fibril.
5
Discussion
Cordus has a radically different conceptual foundation to other theories of
fundamental physics. It also differs in being a qualitative approach as
opposed to the mathematical modelling that otherwise dominates
theoretical developments in physics. These large differences mean that
cordus is able to provide a fresh perspective on an old subject.
5.1
Outcomes: what has been achieved?
An operational model of handedness and matter-antimatter
Using the cordus conjecture, a model has been created for the ma
handedness of matter, and this becomes the primary differentiating factor
between matter and antimatter. This has been used to create models of
the electron, proton, and positron, as representative of the two species. It
is proposed that the quarks and other leptons follow the same pattern,
though in the case of the quarks not all the hyff emission directions [r,a,t]
are filled (hence their fractional charge).
Note that in this model the antielectron is very different to the proton.
They are dissimilar regarding mass, span, frequency, and ma. The only
thing that is common is that they both show positive-charge behaviour.83
83
This dissimilarity is why we prefer not to use the word ‘positron’. The term is too
conceptually limiting as it implies a similarity with the proton. Also, it reinforces the
impression that antimatter is merely about reversed charge, which cordus refutes. The
orthodox theories of antimatter are charge-centric. Cordus suggests instead that the main
factor is ma (hand), and the reversion of charge is a secondary effect. Thus the annihilation
energy is due to the hand, not the charge. This should not be surprising, because the
electron and proton do not annihilate despite their opposite charges (cordus can also
explain why this should be – the hands are the same). So evidently opposite charge is not
the main factor for annihilation, and therefore cannot be the main factor that differentiates
matter and antimatter either.
294
From the cordus perspective it is a fallacy to think of antimatter as being
primarily characterised by opposite charge.
A different method
Another unusual feature about this cordus model is the methodology. It
has been noted that strategies based on mathematical hypotheses have
generally not delivered interpretations that make physical sense [11].
Cordus takes a different path, one of engineering design synthesis towards
a solution. It is a qualitative approach, and while it does not (yet) have the
mathematics embedded, of its very nature it provides explanations that
make physical sense. We have managed to create a novel model of
antimatter, using concepts and without needing mathematical analogies
or fomalism. That on its own makes cordus stand out as a radically
different methodology.
With the addition of this latest explanation for the two species of matter,
cordus can now offer a coherent explanation for effects ranging from
wave-particle duality through to the antimatter problems considered here.
That of itself does not constitute validity, but it is a reassuring feature
since it is what would be expected of a deeper mechanics.
5.2
What are the implications?
The cordus model also explains why the photon does not have an
antiparticle: it does not have a hand. The photon is a single hyff, and a
fibrillating one too.
The differentiation by ma hand is very important in what follows because
we subsequently show that both electron-proton bonding and electronantielectron annihilation have the same underlying mechanism:
complementary frequency synchronisation (CoFS) [12]. Thus CoFS is the
deeper mechanism for holding the nucleus together (strong force), the
electron orbitals, the filling of orbitals (Pauli exclusion principle), bonding
between atoms, superfluidity, superconductivity, entanglement.
What is positive charge in the hyffon model?
The cordus model for the electron has the reactive end producing a new
set of hyffons (EMG force pulses, see below) at each re-energisation, and
the outward propagation of these distally down the hyff, at the speed of
light.
The positive charge is shown as hyffons moving proximally: being drawn
inwards. What is the physical interpretation? We offer some suggestions.
The first is that the positive hyffons are indeed extracted from the remote
hinterland. A second and related idea is that all positive hyff connect up
the corresponding negative hyff from their lepto/baryogenesis twin, or
network thereof, like magnetic poles. Another, and the currently preferred
working model is that the positive hyffon are force increments directed
295
proximally, but they themselves propagate distally. In other words that the
action is directed medially. We acknowledge that we have not
satisfactorily explained exactly what a hyffon is, or how its underlying
mechanisms operate regarding its propagation and exertion of force – we
leave such matters to the next deeper level of conceptualisation.
Later we change the working model for hyffons to state that they are
extracted from or generated into the fabric.
What about gravitation?
The cordus model for the unity of electro-magneto-gravito (EMG) force
uses a speculative mechanism whereby the gravitation component is the
torsion in the hyffon, and this is identical to the hand [13].
An analogy for our working model for EMG force is that the hyffon is like a
nut spinning off a screw, and then engaging with another remote screw,
pulling it closer. The hand of the hyffon is thus a similar concept to the
hand of a thread. If this analogy is correct, then there exists the possibility
that matter and antimatter may not interact gravitationally (which of
course is not the same as repulsion), though they will electrostatically and
magnetically. However this is highly speculative and uncertain.84
The cordus model for gravitation is that the hyffon have a hand – which is
minted by the emitting reactive end, and that engages with the reactive
end of the remote particuloid, thereby forcing it to re-energise a little
closer to the calling particuloid. Force in the cordus model is therefore a
positional constraint on re-energisation, i.e. a fundamentally a
displacement effect.
Comparison with quantum mechanics
Quantum mechanics explains antimatter in terms of quantum numbers. It
has no physical meaning for these, and instead considers them to be
‘intrinsic’: properties that are disembodied from any physical structure. At
the same time, the conventional interpretations of QM generally take
Bell’s theorem to mean that particles like the photon and electron cannot
84
The interesting issue with this idea is that it could have the side-effect of decoupling
mass (velocity, acceleration effects) and gravitation across the M-aM divide. This is because
cordus provides different mechanisms for the generation of the different forms of mass.
Thus in the cordus model, mass-as-resistance-to-acceleration arises from the embedment
of the particuloids hyff in the surrounding moving-fabric. In contrast, mass-as-gravitation
arises from the handedness of the emitted hyffons. Thus cordus suggests that there is one
underlying mechanism – the emission of hyffon along the hyff, that unites the two aspects
of mass. But mass as we experience it is an output behaviour, not the fundamental effect.
Thus it is conceivable that the acceleration and gravitational components of mass might not
always be evidenced together, and antimatter might show this. Antimatter is known to
have mass, since it appears in the pions and kaons (matter-antimatter chimera
particuloids). Note also that these structures have greater mass than the individual quarks:
the mass-excess problem has in general already been explained by cordus. However the
observed mass is most likely acceleration-mass, since it is measured as momentum, i.e.
resistance to change in direction. It is possible that the gravitational response could be
different, even absent. For example, the pions and kaons might have different responses to
acceleration and gravitation.
296
have any internal structure, i.e. no ‘hidden variables’. The logical
inconsistency of this approach is worth remarking on: to believe in internal
variables yet deny their physical existence. What really is the difference
between an intrinsic variable (which QM accepts) and a hidden one (which
QM denies)? QM deals with this dissonance by its choice of methodology:
mathematical modelling. Doing so neatly obviates the need to ground the
results in physical interpretations. QM has thereby inured itself from the
dissonance. But the consequences of this expediency is that the
methodology of QM is disconnected from the fundamental premise of
science: that observed physical effects have rational and physical
underlying causes.
In contrast, cordus takes the perspective that any output functionality of a
system, i.e. observed behaviour, MUST arise from some physical internal
substructure, and that internal mechanisms MUST exist (relationships of
causality) that generate the observed external behaviour. That is our
premise in constructing the cordus conjecture, and it is very radically
different to that of quantum mechanics. QM is undoubtedly the dominant
paradigm for fundamental physics, but we would argue that our method is
truer to the scientific method. Our criticism is not so much of the
machinery of QM but of the conceptual complacency of the method,
particularly the lack of coherence in the conceptual foundations, and the
compromised logic of intrinsic/hidden variables.
By taking a different approach using intuitive creative thinking from the
engineering methods, we have synthesised an alternative model for
matter and antimatter. This immediately opens up new possibilities, both
for the interpretation of the structure of matter, and further conceptual
advance. We are not saying that these concepts are necessarily valid, but
rather that the generation of alternative concepts is a worthwhile activity
in its own right.85
5.3
What are the limitations and implications for further
research?
Uncertain validity
We acknowledge that the validity of the cordus conjecture is untested. It
therefore needs to be treated as a conjecture and its mechanics as
speculative. The explanation uses the idea of ma hand, and the underlying
mechanism for this is only tentatively identified as energisation sequence
of the HEDs, linked to the also tentative idea of the three [r,a,t] HEDS
having a motion-induced sense of orientation. So this is a specific area of
potential weakness in the current model.
85
In conceptual design there are no bad concepts, only more or less useful concepts.
Innovation is a cognitive process of creating intuitive associations between existing ideas to
create a successful solution. The more ideas, the more novel, and the more diverse, the
better: we accept that some may not be workable.
297
Cordus is a very radically different way of conceptualising fundamental
physics and conflicts with QM – to the point of asserting that most of the
conceptual premises of QM are fallacious [9]. However in this particular
area its explanations of antimatter are broadly consistent with quantum
mechanics, though it takes the handedness concept further.
If the cordus model for antimatter is valid, then there would be significant
implications for further research, because of the deeper mechanics that
cordus starts to expose, including the potential to explain the process of
annihilation itself.
6
Conclusions
The main difference between matter and antimatter (M-aM), according to
cordus, is that the ma hand is inverted. Each reactive end for a stable
matter particuloid, e.g. the electron, has three orthogonal hyff, in the axes
[r,a,t]. The hand of these is held to be the same for all matter particuloids,
whether positive or negative charge, and nominated as forma. The hand is
presumably created by the sequence of energisation of the hyff. For all
antimatter particuloids the hand is inverted, and is termed hyarma. The
inversion of the hand changes the direction of the hyff, and thus reverses
the charge, but this is a secondary effect. Thus from the cordus
perspective positive and negative charges (of like ma hand) do not destroy
each other but instead bond through complementary frequency
synchronisation (CoFS). This cordus concept permits models to be created
differentiating between the electron, proton, and antielectron (positron).
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1104.0016. Available from: http://vixra.org/abs/1104.0016.
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Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus optics: Part 2.1 Frequency. vixra, 2011, v. 1104.0019.
Available from: http://vixra.org/abs/1104.0019.
298
6.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus in extremis: Part 4.1 Electromagnetism. vixra, 2011, v.
1104.0027. Available from: http://vixra.org/abs/1104.0027.
7.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus in extremis: Part 4.4 Quarks. vixra, 2011, v. 1104.0030.
Available from: http://vixra.org/abs/1104.0030.
8.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: WaveParticle Duality: a Proposed Resolution. vixra, 2011, v. 1106.0027.
Available from: http://vixra.org/abs/1106.0027.
9.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Why
does quantum mechanics not scale up? vixra, 2011, v. 1107.0019.
Available from: http://vixra.org/abs/1107.0019.
10.
Murayama, H.: Origin of Neutrino mass. Physics World, 2002,
May:
p.
35-39.
http://hitoshi.berkeley.edu/neutrino/PhysicsWorld.pdf.
11.
Mrozek, J.: The role of mathematical analogies in creating physical
theories. Physics Essays, 2011, 24(2): p. 192-195.
12.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus matter: Part 3.4 Special states of matter. vixra, 2011, v.
1104.0025. Available from: http://vixra.org/abs/1104.0025.
13.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.:
Cordus in extremis: Part 4.3 Gravitation, Mass and Time. vixra,
2011,
v.
1104.0029.
Available
from:
http://vixra.org/abs/1104.0029.
299
Contrasting internal structures: Photon and
electron
Pons, D.J. 86
Abstract
We develop a conceptual model for the internal structures of the photon
and electron, based on the cordus model. The main differentiating feature
between the photon and electron is identified as the way it deals with its
field structures or hyff. The photon has a fibrillating relationship with its
field, whereas the electron is a pulsating field-pump. The resulting model
permits an explanation of the discrete (approximately quantised)
electrostatic force, the propulsion mechanism for the speed of light, and
the gravitational bending of light. These are side-effects and the larger
advantage of this model is the potential to explain photon-electron
interactions generally.
Keywords: photon, electron, field, hidden variable solution
Edition 1.1 > Clarified superluminal fibril > Date: Saturday, 11 February 2012 > Document:
Pons_Cordus_5.2_ElectronPhoton_E1.1.12.doc
1
Introduction
The root assumption of orthodox physics is the premise that particles are
merely zero-dimensional points. Consequently the conventional physics,
including quantum mechanics (QM), sees no internal structure to the
photon and electron. These fundamental particles are held to be simple
points, and Bell's theorem is typically taken as confirming this
interpretation. However, 'simple' might not be an apt term, since QM
nonetheless and paradoxically believes the particles have certain
properties, such as frequency, spin, and polarisation. QM calls these
'intrinsic' variables and denies that there is any internal structure that
carries these variables. Hence QM denies the legitimacy of what are called
hidden variable solutions.
Purpose
Thus the purpose of the present paper, which is to describe the internal
structure of the photon and electron, is totally irrelevant to orthodox
physics. We take the position of physical realism: that externally manifest
physical properties logically require some sort of internal physical
substructure to carry the mechanisms. Our aim is to identify what that
internal structure might look like, and put forward some conceptual
models. Ultimately we wish to get closer to answering the deeper
questions of physics: how does annihilation actually work?; how is a
photon emitted? To do this requires a model of the internal structures,
86
Please address correspondence to Dr Dirk Pons, University of Canterbury, Christchurch, New
Zealand. Copyright D Pons 2011.
300
because asking how an electron emits a photon is a meaningless question
from the point perspective.
So we need a different way of thinking if we are going to make any
progress towards these fundamental questions. Quantum mechanics
simply is not up to the task of giving us physical interpretations of
processes between substructures that it denies even exist. So the new
paradigm will have to be radically different to QM [14]. However it is
undeniable that QM is massively successful as a mathematical model, and
thus we can reasonably expect that a new paradigm will also need to be
consistent with QM's mathematical models.
There is reason to believe that there may be a better theory than QM. In
particular, a case may be made that Bell’s theorem is fundamentally
wrong, being only an artefact of circular logic [3, 9]. If Bell's theorem is put
aside, then QM's point construct also fails. Thus it is possible to conceive
of internal structures for particles, as the cordus conjecture shows [4].
Previously we have predicted some of the internal structures for the
photon [4-5], quarks [7], and electron [15]. Now we consolidate these
ideas into more specific models, focussing on the photon and electron.
We are particularly interested in these two 'particules', as a better
understanding of their internal mechanics has the potential to unlock
other effects such as annihilation.
Background: Cordus conjecture
The cordus model [4] is used as the starting point. This perspective refutes
the premise of the point particle, and instead replaces it with the idea of
the 'cordus particule', consisting of two ‘reactive ends’ a small distance
apart (‘span’) and joined by a ‘fibril’. The reactive ends are energised at a
frequency [5], during which time they emit one or more transient force
pulses (‘hyffons’) into space along lines called ‘hyperfine fibrils’ (hyff) [6].
This makes up the electrostatic, magnetic, and gravitation (EMG) fields,
which are thus also discretised.
2
Structural differences between photon and electron
We need to have a clear model of the difference between the photon and
electron particules, because we expect those differences will support the
process, which in turn give rise to emission, absorption, annihilation, etc.
We have separately created a model that differentiates between matter
and antimatter (M-aM) [15]. This novel explanation is made in terms of the
arrangement of hyff, and these considerations are again important here.
Thus we distinguish the photon and electron by the way their hyff behave,
particularly the handedness thereof, which we call ma.
301
2.1
Photon as a fibrillating hyff-pump
The cordus model identifies that the field structures (hyff) of the photon
have some peculiar characteristics. Specifically, the photon is a fibrillating
hyff-pump, whereas the electron and indeed all other matter and
antimatter is a pulsating pump. The photon reactive end pumps out a
hyffon, and then promptly withdraws it, and reverses the direction, see
Figure 1. The photon never releases its hyffon.
The outward hyffon motion corresponds to negative charge, and inward to
positive (a cordus convention). Thus the photon changes sign, hence the
observed reality that the electric field of the photon reverses sign. The
frequency model for the photon is set out in a companion paper [5] and
describes the internal structures and how their mechanics delivers the
externally observed effects.
Figure 1: Models for the photon and electron, showing the different
characteristics of their pumps. The photon has a fibrillating pump that only
shuttles energy outwards and then immediately afterwards brings it back
inwards, whereas the electron consistently pushes hyffon force fragments
outwards in a pulsating manner. Both cordi therefore have a frequency,
but the difference is what they do with it. All other matter and antimatter
behaves like the electron, though the direction of pumping is reverse for
positive charge.
The fibrillating nature of the photon arises because of a close coupling
between the field and the fibril: the energy bounces between the two.
302
2.2
Electron as a pulsating hyff-pump
The electron, and all M-aM, pushes a hyffon outwards along a persistent
hyff – or pulls inwards in the case of positive charge).87 The hyff is
enduring, and the direction of propagation of the hyffons is consistently
outwards (or inwards as the case may be), see Figure 1. Hence we call this
a pulsating pump, as opposed to the fibrillating pump of the photon.
The electron releases its hyffon into the wild, and then manufactures a
new one.
The fibril is an instantaneous (superluminal) communication device. The
hyffon is emitted at one reactive end, with its strength perhaps varying like
one half of a sine curve. When it is finished, the other reactive end
immediately starts to spool out its hyffon: there is no delay. When viewed
at a coarser scale, such that the span is not evident and it looks like a
point, the field system looks smooth. The same feature of the fibril
provides for the superluminal effects of entanglement.
2.3
Explanation of various effects
The main differentiating features between the photon and the electron
are shown in Table 1.
Photon
Electron
one pair
three pairs
Fibrillating
(retains Pulsating
(releases
hyffon)
new hyffon)
Sign of charge
Alternating: +- 1/3
Constant: 3x(-1/3)
Table 1: Main differentiating features between the photon and the electron
Number of hyff
Nature of the pump
This permits us to explain various effects.
Range of the electric fields
The photon has only a short range for its electromagnetic (EM) fields: their
strength drops off very quickly with distance.88 The electron has a much
greater range for its EM fields – potentially infinite – and though they do
drop off with radius it is not as quickly as the photon’s. This is explained by
the Nature of the pump: the photon does not release its hyffons and
therefore has a short range, whereas the electron can reach infinite range
87
What is the hyff made of, and what are its mechanisms? We acknowledge that
the deeper mechanics of this have not been addressed. However we suggest that
perhaps the hyffons themselves are daisy-chained together to form the hyff, or
that the hyffon is simply a disturbance on the linear structure of the hyff.
88
Cordus suggests, as a rough rule, whenever one sees an EM field drop off as an
exponential function, then suspect a fibrillating hyff effect. For example, cordus
interprets the evanescent wave as such a hyff effect.
303
with time because it relinquishes its hyffons (though its hyffons are diluted
by the volume of space).
Correction to positive charge model
One of the implications of the present work is how the hyff interact. In the
immediate previous paper [15] we suggested several physical
interpretations for the positive and negative hyffons. The preferred model
at that time was that ‘the positive hyffon are force increments directed
proximally, but they themselves propagate distally. In other words that the
action is directed medially.’ We now have cause to reject that, because it
cannot explain electrostatic attraction and repulsion without adding more
phenomena (which we are reluctant to do unless they are also required
elsewhere). Instead we adopt one of the other suggestions.
So now we explain negative charge as hyffons that move outwards from
the reactive end (a sign convention) and positive charge as hyffons that
move inwards. We suggest that the positive hyffons are indeed extracted
from the remote hinterland, which we now specifically identify as the
fabric [7], i.e. the mesh of all the other hyffons from all the other
particules in the universe.
Electrostatic attraction therefore arises because dissimilar signed hyffons
can share hyff emission directions (HEDs), and this causes the discrete
force of the hyffon to draw the bodies together. Electrostatic repulsion is
thus conflict within similar signed hyff systems, such that there is oversubscription of the HEDs. This causes the particules to seek to re-energise
further away from each other if they can, i.e. a repulsive force for like
charges. This means that the electrostatic force is the same basic
mechanisms as the strong force, albeit at a larger range. Force, as we have
elsewhere stated, is nothing more than a geometric constraint on the
position of re-energisation of a reactive end.
Genesis and charge
It is generally accepted by physics that leptogenesis and baryogenesis
converted photons into matter, though the precise mechanisms are still
unknown.
The cordus interpretation is that the creation of matter also created the
hyffon system, of which the electron system shown here is representative.
So the working model here is that the mesh of hyffons between matter
particules did create, and continues to replenish, the fabric. The matter
particules continue to supply and withdraw hyffons from that fabric. So in
a sense all positive hyff connect up to negative hyff, but not necessarily to
a specific other particule formed at genesis but rather to the network of
hyffons that makes up the fabric. The photon however, does not
contribute to the fabric, because it does not release its hyffon.
The presence of matter particules therefore withdraws and contributes to
the immediate fabric, and thus shapes and warps the fabric. This concept
is therefore similar to the idea of space-time being warped by large
304
masses. Though there is a basic compatibility between the cordus concept
of fabric and the space-time of general relativity, the proposed underlying
mechanisms are very different.
In addition, this implies that electric charge is somewhat like magnetic
poles: there are no monopoles, at least not on average across the
universe.
Speed of light: the propulsion mechanism
This change to the hyffon working model also permits the further
development of the cordus concept for the photon [4]. The photon only
has a single pair of radial hyff (one from each reactive end). By contrast
the fabric of the universe has forma hand [15]. Thus the photon has one
hyff emission direction (HED) [7] whereas its surrounding has three. We
suspect that this mismatch is what causes the photon to travel at the
speed of light. Since it does not have hyff in the other directions, it has to
move at the speed of the hyffons making up the fabric, i.e. speed is a
compensatory mechanism. (We acknowledge we have not fully defined
this mechanism.) Thus the photon is propelled through space by the fabric,
and takes its speed from the fabric. Thus the speed of light is a secondary
variable: the deeper variable is the density of the hyff in the fabric. This
model is consistent with our earlier model [16] for light, but explains the
propagation slightly better.
Gravitational bending of light
This also offers an explanation for the gravitational effect on light. Light is
known to be deflected slightly by gravity, but whether light itself has mass
is uncertain to conventional physics. It is known to have momentum
though, at least when arrested.
The cordus explanation is that light probably does not have mass, because
it only emits a single [r] hyff. Mass is otherwise the interaction of the
torsion [r,a,t] hyffon [13] with the fabric: a torsion hyffon requires a hand
at emission, which the photon does not have.
The gravitational bending of light is instead explained by cordus as due to
the gradient in the fabric density near a large mass. On the side of the
photon nearest the mass, the fabric is slightly denser so a frequency cycle
of the photon on that side accomplishes a slightly lesser displacement, i.e.
the speed of light is slightly slower, thus bending the trajectory. If this
explanation is really correct, then we would expect to see the gravitational
bending of light being dependent on its polarisation, and possibly this is
testable.
3
Discussion
What has been achieved?
We propose a model wherein the fundamental differentiating factor
between the photon and electron is the behaviour of their internal
structures, particularly the hyff. This is a novel accomplishment in itself –if
305
it is valid- as even the internal structures of these particles are unknown to
orthodox physics, let alone their behaviours.
We have inferred these internal structures from basic logic and design
synthesis applied to the prior cordus models. Most of the precursor ideas
already exist elsewhere in the cordus work, but the contribution here is
putting them together so that the two structures can be directly compared
and contrasted. This is a key development as it permits further advances.
With models of the photon and electron in hand, we now have the
capability to infer their interaction processes. There are several processes
of interest, including annihilation, photon absorption, photon emission,
and leptogenesis.
The photon’s purpose in the universe
There is significance, from the cordus perspective, in the peculiar
fibrillating field of the photon: it makes the photon a universal energy
carrier.
The photon is not out to create an electro-magnetic-gravitational (EMG)
empire for itself, like the matter and antimatter particuloids. Instead it is
the unit of energy currency between assemblies of matter. The photon
transfers spare energy around the place. It is an escapement mechanism
whereby particuloids that are over-prescribed (in terms of positional
constraints on re-energisation) can get rid of that energy [17].
The photon is not quantised, but flexible in its ability to contain whatever
energy it is given: like an expandable container. Yet it is sufficiently like a
matter particuloid to be able to interact with matter. Further, it has no ma
hand and is therefore able to freely interact with, and transfer energy
between, both matter and antimatter – it appears to be the only
mechanism for this. It is the slim bridge between the world of matter
particuloids, and the antiworld. The photon is therefore a key component
in the formation of matter, hence annihilation and leptogenesis.
Lemma on hyff pumps
We summarise the above assumptions in these lemmas:
Ma.2 Hyff pumps
Ma.2.1 The photon is a fibrillating hyff-pump: the reactive end pumps out
a hyffon, and then promptly withdraws it, and reverses the
direction. The photon never releases its hyffon.
Ma.2.2 Matter and antimatter particules, e.g. electron, have a pulsating
pump that for negative charge pushes a hyffon outwards along a
persistent hyff – or pulls inwards in the case of positive charge.
The hyff is enduring, and the direction of propagation of the
hyffons is consistent.
Ma.2.3 The outward hyffon motion corresponds to negative charge, and
inward to positive (a cordus convention). As a working model we
suggest that the positive hyffons are extracted from the remote
hinterland, which we specifically identify as the fabric, i.e. the
306
mesh of all the other hyffons from all the other particules in the
universe.
Ma.2.4 Electrostatic force arises because dissimilar directioned hyffons can
share hyff emission directions (HEDs), and this causes the discrete
force of the hyffon to draw the bodies together. Similarly similar
charges compete for HEDs and thus repel eath other.
Ma.2.5 The fabric of the universe is created by the matter particules of the
universe.
Ma.2.6 The propulsion mechanism for the speed of light is the imbalance
between the single hyffon pair of the photon, and the three HEDS
of the fabric.
Ma.2.7 The photon moves at the local speed of the fabric, which in turn
depends on the mass distribution. The photon trajectory may be
bent by gradients in the fabric density.
Conclusions
Returning to the original purpose of this paper, we now have a hidden
variable solution: a description of the internal structures of the photon and
electron. This is a radical break from orthodox physics, and a potentially
significant development in fundamental physics. We have got past the
limitations of the point-premise, which arguably has stifled progress in
physics, and have shown that it is indeed possible to create a working
model of the internal structure of light and matter. We do not claim that
this model is necessary valid, because that has not yet been tested. There
is no fundamental incompatibility between our cordus model and the
mathematical models of quantum mechanics, but we acknowledge that
the conceptual differences are large, and that the orthodoxy might have
issues. We have broken Bell's theorem to get here, so we encourage
critical evaluation of how we did that [3].
If one wishes to take the prior position that photon and electron must be
points, then the present paper may seem irrelevant. However we can see
potential to expand this model to annihilation and other photon-electron
interactions. There is now a reasonable chance that we might indeed be
able get closer to answering the deeper questions of physics, like 'how
does annihilation actually work?'
References
1.
Kuhn, T.S.: The Structure of Scientific Revolutions. 1996, 3 ed., Chicago,
IL: University of Chicago Press.
2.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Cordus
matter: Part 3.1 Wider Locality. vixra, 2011, v. 1104.0022. Available
from: http://vixra.org/abs/1104.0022.
3.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Why does
quantum mechanics not scale up? vixra, 2011, v. 1107.0019. Available
from: http://vixra.org/abs/1107.0019.
4.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Cordus
Conjecture: Part 1.1 Quis es tu photon? . vixra, 2011, v. 1104.0016.
Available from: http://vixra.org/abs/1104.0016.
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5.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Cordus
optics: Part 2.1 Frequency. vixra, 2011, v. 1104.0019. Available from:
http://vixra.org/abs/1104.0019.
6.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Cordus in
extremis: Part 4.4 Quarks. vixra, 2011, v. 1104.0030. Available from:
http://vixra.org/abs/1104.0030.
7.
Pons, D.J.: Mirror images: Cordus reconceptualisation of Matter and
Antimatter. Vixra, 2011, v. 1109.0009.
Available from:
http://vixra.org/abs/1109.0009.
8.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Cordus in
extremis: Part 4.1 Electromagnetism. vixra, 2011, v. 1104.0027. Available
from: http://vixra.org/abs/1104.0027.
9.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Cordus in
extremis: Part 4.2 Fabric of the universe. vixra, 2011, v. 1104.0028.
Available from: http://vixra.org/abs/1104.0028.
10.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Cordus in
extremis: Part 4.3 Gravitation, Mass and Time. vixra, 2011, v. 1104.0029.
Available from: http://vixra.org/abs/1104.0029.
11.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Cordus
matter: Part 3.3 Energy cycles within matter. vixra, 2011, v. 1104.0024.
Available from: http://vixra.org/abs/1104.0024.
308
Annihilation mechanisms: Intermediate
processes in the conversion of electron and
antielectron into photons
Pons, D.J. 89
Abstract
The outcomes of annihilation are known, including some of the
intermediary products, and the process can be represented by Feynman
diagrams and modelled mathematically. However the mechanisms of
annihilation at a deeper fundamental level are unknown. How exactly does
matter and antimatter convert into photons? How does mass change into
energy? This paper develops an answer by providing a theory for the
annihilation process based on mechanics derived from the cordus
conjecture. The particular area under examination is the annihilation of an
electron and antielectron (positron) to gamma photons. In this model
matter and antimatter annihilate by transforming their field structures called hyff - into those of the photon. The process is more one of
remanufacture than destruction. The model proposes the stages of
annihilation and identifies the mechanisms for each. The reverse of the
process gives a physical description of pair-creation: the creation of
separate electron and antielectron particules out of two initial photons. It
also explains why the proton and electron do not annihilate. We show that
a deeper common mechanism exists for annihilation, pair-creation, and
bonding.
Keywords: annihilation, fundamental physics, positronium, QCD, paircreation
Edition 1 > Initial release > Date: Saturday, 11 February 2012 > Document:
Pons_Cordus_5.3_Annihilation_E1.0.28.doc
1
Introduction
How do matter (M) and antimatter (aM) annihilate? Why does it happen at
all? Unfortunately these questions are at the edge of, or even beyond, our
conventional theories of physics. We do not know the mechanisms of
annihilation, though the outcomes and some of the intermediary products
are known.
89
Please address correspondence to Dr Dirk Pons, University of Canterbury, Christchurch, New
Zealand. Copyright D Pons 2011.
309
Existing models of annihilation
The dominant explanation for antimatter is quantum mechanics (QM).
However QM cannot explain the structure of antimatter to the extent that
we would like, and has practically nothing to say about the process of
annihilation. That annihilation occurs is not a problem to QM, and the
process can even be represented, by Feynman diagrams, albeit at a high
level of abstraction, see Figure 1. However the details are not understood
nor the deeper question of why it should occur at all.
Figure 1: Feynman diagram for electron-antielectron annihilation to two
gamma photons. The inputs are on the left and comprise an electron e and
an antielectron e (with reversed arrow). These two interact, in ways
uncertain, to produce two output photons y.
Feynman diagrams do not represent the underlying mechanisms at the
deeper level, nor all the intermediate structures. In this way at least, the
diagrams are consistent with empirical observed tracks where certain
intermediates are not detected until a transformation to another particle
occurs, i.e. there are gaps in the tracks. The diagrams encapsulate the idea
that these unobservable structures are ‘virtual’ particles. Thus we have
various virtual bosons identified as part of the deconstruction process, and
even the photon is repurposed as a virtual photon for the electromagnetic
effect.
Existing approaches to understand annihilation are primarily the
refinement of mathematical models such as quantum chromodynamics
(QCD) to accommodate the diversity of observed results. Most of the focus
is on the combinations of outcomes and the conditions under which they
arise [18], or the characteristics thereof [19], hence ‘production channels’
[20]. A common approach is the fitting of mathematical models to
empirical observations, e.g. size of jet width [21], or the environmental
conditions [22], or energies involved [23], or the output characteristics
[24-25].
Mathematical models have been constructed to account for production
rates under various types of annihilation, e.g. for e+e- into photons [9-11],
310
leptons or muons [26-27]. There is also work on hadrons [28-30],
positronium output states [31], or hydrogen-antihydrogen annihilation
[32]. These approaches are sometimes called ‘descriptions’ of the process,
but they are better understood as mathematical models seeking to find
factors and coefficients [18, 19] or statistical fit [33-34] to empirical data.
In general these require
adjustment factors to fit to empirical
observations.
Overall, the resulting aggregation of mathematical methods has
empowered the QCD model with good fit to the data. The ultimate hope
with this particular modelling line of enquiry is that it ‘may provide insight
into the hadron production mechanism’ [28](p45). Indeed the models
may be applied in the inverse direction, back to other observations, e.g.
astronomical emission, to infer the environmental conditions at the source
[35]. However the production mechanisms themselves remain obscure,
even if the outputs can be predicted and modelled accurately.
The practical measurement of annihilation data often involves smashing
particles together in colliders, and this introduces additional complexity
into the process. For a start, the input particles are not always pure
electrons and antielectrons. Instead they may be proton vs. proton.
Secondly, the input particles have considerable kinetic energy. Thus
experiments in high energy physics may produce complex showers of
various short-lived particles and antiparticles that further decay into other
outputs [36].
While the term ‘process’ is often applied to models of annihilation, this is a
misnomer, at least from an engineering perspective, because the
mechanisms that give rise to the outputs are still unknown. The output
results are known for various inputs of particle type and energy, but the
mechanisms that transform the inputs into the outputs are hidden in a
black box. Thus an important piece of knowledge of the production
process is missing. It is like watching the assembly of a motor car from a
distance, so that the overall phases can be discerned, but not the tools,
parts, and operating procedures.
To sum up the existing body of knowledge, QCD provides a mathematical
theory and there are good mathematical models to fit the annihilation
data, but the descriptive understanding of the underlying mechanism is
lacking. It is this gap that the present paper targets, by providing a
conceptual model.
Approach
In this paper we focus on that most basic of annihilation events, that of an
electron and antielectron. Several basic principles become evident in this
simpler process, and we believe that the mechanisms are applicable to
more complex particle combinations too.
The approach we take is totally different to the conventional mathematical
modelling described above. We argue that the prevailing mathematical
311
methodology shows good quantitative outcomes, but has been unable to
create a coherent descriptive narrative of the process of annihilation. We
seek a descriptive explanation that is grounded in the physical realm, not
merely an abstract mathematical model.
We take the premise of physical realism: that the study of Physics is the
description of the physical realm, and that the mathematical
representation on its own is inadequate. Thus there should be a physical
explanation of the internal process of annihilation, if the right concept can
be found. Therefore we take a different approach, one that is totally
independent of quantum mechanics. Instead it is based on conceptual
design principles adapted from engineering. We apply this method to the
cordus conjecture [1] and thereby develop a theory for the annihilation
process. Specifically, we join the concepts from the existing model for
antimatter [15], and that for the photon [37], to create a new model for
the details of the annihilation process.
2
Cordus Background
The cordus conjecture [1] provides a novel reconceptualisation of
fundamental physics. It is radically different to quantum mechanics, and a
brief explanation is therefore necessary. We acknowledge that it is a
conjectural and untested concept. Even so, it has shown ability to provide
a coherent explanation for many of the enigmatic phenomena of
fundamental physics [1], that QM itself cannot explain. Thus it is worth
exploring antimatter from this alternative fringe perspective.90
The cordus conjecture is that all 'particles', e.g. photons and electrons,
have a specific internal structure of a cordus, comprising two reactive
ends, with a fibril joining them. The reactive ends are a small finite span
apart, and energised (typically in turn) at a frequency, at which time they
behave like a particle. When energised they emit a transient force pulse
along a line called a hyperfine fibril (hyff), and this makes up the field. We
avoid the use of the term ‘particle’ as it is too cognitively laden with the
zero-dimensional point construct of orthodox physics, which we argues is a
fundamental flaw in QM [9]. Instead we use the noun ‘cordus’ or
‘particule’ to describe this entity, or sometimes ‘particuloid’ where we
seek to emphasise that it looks like a particle at certain levels.
The main difference between matter and antimatter (M-aM), according to
cordus [15], is that the hand is inverted. However ‘hand’ has a particular
meaning in the cordus context, and is called ma [15], described as follows.
Each reactive end for a stable matter particule, e.g. the electron, has three
orthogonal hyff, in the axes [r,a,t]. The hand of these is held to be the
same for all matter particules, whether positive or negative charge, and
nominated as forma, see Figure 2. The hand is presumably created by the
sequence of energisation of the hyff. For all antimatter particules the hand
90
The title 'fringe' is peculiar to modern physics. Unlike engineering design, music, arts,
architecture, and even accounting, physics has an uneasy relationship with conceptual
innovation.
312
is inverted, and is termed hyarma. The inversion of the hand also changes
the direction of the hyff, and thus reverses the charge, but this is a
secondary effect. Thus from the cordus perspective annihilation is not a
charge effect: positive and negative charges (of like ma hand) do not
destroy each other. Annihilation is instead a hand effect.
Having established the cordus position that ma is the distinguishing
feature of matter and antimatter, we now develop a more detailed cordus
mechanics for the process of annihilation. The particular area under
examination is the annihilation of an electron (e) and antielectron (e,
positron). Note that the cordus notation uses an underscore for the
antiparticle, to show that it is conceptually different to the conventional
idea of antimatter.
Figure 2: The hand of the hyff is the differentiating factor in the cordus
model for matter and antimatter.
3
Cordus mechanics for annihilation
3.1
principle
Complementarity of ma hand is the underlying
An implication of the cordus hand lemma is that matter particules (which
have the same forma hand) cannot annihilate each other: they can only
313
balance their charges at assembly, i.e. neutralise net electrostatic force.
(But even that does not neutralise all the hyff effects, according to the
cordus gravitation model [6, 13]). Thus an electron and a proton cannot
annihilate each other, but only dance around each other’s hyff. Via the
hyff they exert forces on each other (more accurately position reenergisation constraints). This encourages them to negotiate
complementary hyff emission directions and synchronised frequency
thereof, which are the cordus SHED [7] and CoFS [5] principles. The result
is that the electron and proton are bonded together.
Thus cordus explains why the proton and electron do not annihilate: they
are the same hand, and therefore can only share space. Merging and then
collapsing their hyff is not available.
We propose the following criterion for annihilation: It occurs when all the
hyff of both particules are co-linear and in the same direction. This
requires that the hyff at the reactive end are pumping in the same
absolute direction but from opposite sides of the reactive end. In effect
this requires opposite charge and opposite hand. Thus a forma electron
and a hyarma antielectron (positron), when placed close together, can
simply merger their hyff and transform back into photon energy from
which they were made. It is the details of that process to which we now
turn.
3.2
Annihilation of matter and antimatter
The antielectron e has hyff that are in opposite in hand and direction
relative to the reactive end, compared to the electron. In cordus notation
this is shown as hyff being in the same absolute direction but on opposite
sides of the reactive end. The collapse sequence is surmised as follows,
with reference to Figure 3.
(1)
Initial engagement.
When the e and e come within proximity, their hyff start to engage - well
before the reactive ends themselves are close. This engagement aligns the
two cordi parallel and draws the reactive ends
into geometric
coincidence, see Figure 3.1. The mechanisms for this part of the process
are electrostatic and magnetic forces [6] mediated through the hyff.
314
Figure 3.1
Initial engagement of electron and antielectron is a
process of mutual alignment.
(2)
Synchronisation process.
It is one thing for the participating particules to be near each other, and
sufficiently aligned, but the next necessary step in the process, according
to this cordus model, is synchronisation. The phases of the hyff of the two
particules needs to be suitable, see Figure 3.2.
In this model we define a suitable phase as opposite, i.e. when the reactive
end of the one particule is active while that of the other particule is
dormant, i.e. 180 degree phase offset. We emphasise this is only the
current working model, and we have selected this construct as it seems to
work better than a 0o phase offset.
A suitable phase also requires that the frequency of the two particules be
sufficiently similar: the hyff need to be in complementary states for the
annihilation process to proceed. The cordus model specifically includes the
mechanisms to accomplish this: (a) the hyff and the span (hence
frequency) are interconnected within one particuloid, and (b) hyff of
neighbouring particuloids negotiate their existence (the cordus SHED
principle) and thereby transfer energy between them.91 Thus the two
particuloids can balance their energies and hence their frequencies and
spans, and get them into the correct phase. In this condition they are in a
bound state, albeit temporary. We identify this as the bonding mechanism
for positronium.
91
It is precisely because of this rapid sharing of external loads that bound
particules are stability. According to cordus, stability, including the resistance to
decay, arises because external forces (more accurately positional constraints on
the location of re-energisation of reactive ends) cannot peel off one particule
from the assembly. This applies also to the internal sub assemblies within
particules. Hence the neutron is stable when bonded with a proton, but decays
when isolated on its own.
315
So the initial engagement is a process of geometric alignment, whereas
the synchronisation is of frequency and its phase. We anticipate that the
two processes occur concurrently, so our differentiation of them into
distinct processes is for descriptive clarity rather than temporal accuracy.
Another simplification is that the diagrams show one set of hyff as active
(solid lines) and the other as inactive (dashed lines). However this should
not be interpreted as implying a step on-off change between the two sides
of the cordus. Instead it is more likely that there is a progressive transition.
For one moment there will be all the hyff at the one reactive end and none
at the other, but for the rest of the half-cycle there will be an overlap.
Figure 3.2
In parallel with geometric alignment, the electron and
antielectron also synchronise their frequencies: both the magnitude and
phase thereof. Photon emission may occur if necessary for synchronisation.
There is also an important other effect that we believe occurs at this
synchronisation stage, and that is the occasional emission of a photon. We
propose, as already stated, that the hyff of the two particules need to be
in complementary states. Sometimes this does not occur, and instead the
SHED principle drives the assembly into a metastable state whereby the
two reactive ends are energised at the same time: 0o phase offset. We
anticipate reasons for this situation:
• A natural outcome of the SHED negotiation process, i.e. the result
of the process is either 180o or 0o phase offset, nothing in
between. The two particules rotate to access whichever of these
states is geometrically closest.
• The particules do not have sufficient degrees of freedom to rotate.
Loss of freedom is in turn expected to occur for situations such as
(a) a particule being fixed by its existing bonding agreements with
316
an atom, or (b) a particule having too much momentum to be able
to make the necessary adjustment manoeuvre in the time
available.
In passing, we note that all of these reasons are ultimately geometric in
origin, and indeed the cordus conjecture suggests that 3D geometric
effects are the root causes of many fundamental effects.
Photon-emission phase-offset
Next we make the assumption, which we mark with a lemma, that
emission of a photon causes a cordus to delay the re-energisation of its
reactive end by half a frequency cycle, i.e. to change its phase by 180o.
Thus a particule-pair that is caught in the metastable 0o phase, may escape
that state by emitting a photon. In a sense the emission is a type of decay
process. A separate part of the cordus conjecture elaborates on the
emission of photons. We anticipate that either the electron or antielectron
may emit the photon, and that it will probably be whichever is more
geometrically constrained or higher energised. Emission is an energydiscard mechanism. It also discards energy from the joint system, and may
require further energy balancing subsequently.
The particules operate at the hyffon level, and so each round of force and
energy balancing requires another hyffon emission round, i.e. another
frequency cycle. Frequency cycles are time -the two are indistinguishable
[13]- and therefore the process of forging compatibility takes time.
This cordus model predicts that particules with greater disparity in energy
or less degrees of freedom, will take longer to annihilate. Also, for cases
where both particles have the same energy, higher-frequency is expected
to result in faster reactions. Possibly both of these may be testable.
We acknowledge that our proposed photon-emission phase-offset is a
convenient supposition of synthesis, i.e. we sought mechanisms to match
the observed behaviour that annihilation can cause emission of two or
sometimes three photons, and this seemed to be the most obvious and
conceptually parsimonious solution. If it seems a contrived solution, or an
artefact of the subjective synthesis method, then that is true. Nonetheless,
and to our surprise, we note that perhaps the effect has already been
observed: the somewhat obscure Sokolov–Ternov effect is that electrons
or antielectrons can invert their spin by synchrotron radiation. More work
would need to be done to confirm the convergence of these concepts, but
it would seem that cordus may explain the mechanisms underpinning the
Sokolov–Ternov effect. This also means that the cordus principle of
photon-emission phase-offset is not as preposterous as it might first seem.
(3) Docking process
Once the reactive ends are within range of each other, geometrically
aligned, at complementary frequencies, and in phase, then the docking
process is complete, see Figure 3.3. We surmise that the necessary
geometric spacing is the length of the hyffon (which in turn is the pulse
that travels on the hyff).
317
As docking progresses, so the reactive ends continue to approximate
(come closer) and the increasingly overlap of the hyffons causes a
confused CoFS state. This starts to take on some of the features of a fibril.
Thus there is a growing connection between the e1 and e1 reactive ends,
i.e. an inter-action at the expense of the intra-action. The identities of the
original participating cordi become weaker, and a temporary square
structure arises. This readies the system for the next transition.
Figure 3.3 Docking process involves the geometric alignment of the
reactive ends and a growing interaction between the e1 and e1 reactive
ends at the expense of the intra-connections.
(4) Cross-over fibril process
We assume that a fibril is formed between reactive ends when their hyff
are sufficiently co-incident, co-linear, at the same frequency, and suitable
phase. We note this as lemma Ma.3.4. In this specific case under
consideration, the e1 and e1 reactive ends thereby form a new fibril, see
Figure 3.4.
The original fibrils fade out. These had been of the pulsatile type: discrete
hyffon pulses moving in one direction. Also, the two reactive ends were
out-of-phase (180o phase offset), so that one reactive end was energised
while the complementary one was not.
318
In contrast the new fibril is the fibrillating type: two hyffon pulses moving
in the same direction, then reversing. Both the new reactive ends are
active at once (in-phase or 0o offset). This is shown in the figure for the
hyff in the [a] axis and is presumed to simultaneously incorporate the
other axes. See also lemma Ma.3.5.
Figure 3.4 Cross-over involves the formation of transverse fibrils.
We assume that the condensation of the original [r,a,t] and [r,a,t] hyff can
result in transitional structures, particularly for more energy rich input
particuloids like protons and antiprotons.
(5) Conversion to photons
The in-phase fibrillating structure is that of the photon. Thus the outcome
of this process is a photon from each pair of reactive ends, shown as y.b
and y.c in Figure 3.5. Note that in the cordus conjecture the hyff
arrangements define the particule. Thus function defines form, see
Ma.3.7. The conservation of hyff required that two photons be produced
(Ma.3.8).
The final stage of the process involves clearing up the transitional
structures: the original fibrils dry up as the hyff are withdrawn and
repurposed into the new structures. Note that according to this model of
events, the reactive ends are the most enduring structures: the pegs
around which the rest of the changing tapestry is woven.
319
Figure 3.5 Reactive ends strengthen the transverse fibril links and the
original fibrils decay, resulting in two output photons.
The two photons y.b and y.c emerge simultaneously, not sequentially, in
this particular cordus model.92 These two photons are predicted to be of
opposite polarity but identical energy. The polarity arises because the
original participating particules were of the oscillating frequency type
(180o phase). The identical energy arises because (a) the initial
synchronisation process balances the energy between the electron and
antielectron, and (b) the fibrils distribute and balance the energy between
the reactive ends. So there is a balancing of energy across all four reactive
ends involved, and this carries forward to the photons.
If there is sufficient energy then additional photons or other transitional
particules may be produced at this stage by the production of
complementary hyff pairs (Ma.3.8) and their allocation to particules
(Ma.3.7).
Details of the conversion to photons
The proposed details of the conversion are shown in Figure 4.
92
If we had taken an in-phase model at synchronisation (#2) then the photons would be sequential,
and the original fibrils would need to persist for one half-frequency cycle longer, re-energising the
other pair of reactive ends, collapsing their hyff, and creating a second photon out of the hyff.
However this is not the preferred model here, though we mention it as it the evidence for its exclusion
is not overwhelming.
320
Figure 4 Conversion details for photons. This diagram shows only one
reactive end, and the other follows a complementary process to also
produce a photon.
The very last stage, reversal from one direction to the other, is held to be a
consequence of the dynamic the coupling between hyff field and fibril
nature of the particule. The energy shuttles from one to the other. The
photon cannot release its hyffon into the wild, unlike the electron,
because it is an integrated source-sink. Consequentially the propagation of
the hyffon, i.e. the discrete field, is pushed one way (towards the right in
the figure), elastically recoils from the fabric, and reverses direction
(leftwards). The fibril allows the two hyff to be instantly coordinated, so
that what happens at one reactive end also happens at the other, (or at
least the complementary action occurs, because the hyff are in different
directions relative to the reactive end).93
93
Time does not exist within the fibril, because time is only generated at the next level up,
which is the frequency oscillations of the cordus as a whole.
321
3.3
Lemma
The following lemmas summarise the assumptions in this annihilation
model, and the principles of the basic mechanics.
Ma.3 Annihilation lemma
Ma.3.1
Cordus principle of Convergent hyff emission: Annihilation
occurs when the hyff of two separate particules are, at
their adjacent reactive ends, pumping in the same
absolute direction but from opposite sides of the reactive
end.
Ma.3.2
In this model we define a suitable complementary phase
for the annihilation of electron and antielectron as
opposite, i.e. when the reactive end of the one particule is
active while that of the other particule is dormant, i.e. 180
degree phase offset. It may take frequency cycles to
accomplish this, hence time. See also O.3.13 [38].
Ma.3.3
Cordus Principle of photon-emission phase-offset:
emission of a photon from a particule will delay the reenergisation of its reactive end by half a frequency cycle,
i.e. change its phase by 180o.
Ma.3.3.1
This is equivalent to flipping the QM 'spin'.
Ma.3.3.2
The concepts of spin, hand, chirality, and ma are
not identical, and should not be confused.
However they are expected to be related at a
deeper level.
Ma.3.4
A fibril is formed between reactive ends when their hyff
are sufficiently co-incident, co-linear, at the same
frequency, and suitable phase.
Ma.3.5
When hyff form such a fibril, they can change from the
pulsatile type (discrete pulses moving in one direction) and
180o offset (out-of-phase), to the fibrillating type (both
move in the same direction, energised at once, and then
reverse) and 0o offset (in-phase).
Ma.3.6
Cordus principle of Complementarity of bonding and
annihilation. Bonding and annihilation are complementary
processes
for
sameand
contrary-handedness
respectively.
Ma.3.6.1
Same-hand ma structures can interact to form
bonds, by sharing hyff emission directions.
Ma.3.6.1.1
When the charges are the same (++ or - -)
then the particules can co-exist, but only
providing they also take opposite phase in
their frequency cycles. Hence the Pauli
exclusion principle for electrons. If they are
in phase then electrostatic repulsion
results.
Ma.3.6.1.2
For opposite charges (+ -) the particules
form attractive interactions (bonds) when
the reactive ends are in phase with each
other (electrostatic attraction).
322
Ma.3.6.1.3
Ma.3.6.2
Ma.3.6.2.1
Ma.3.6.2.2
Ma.3.7
Ma.3.8
Ma.3.9
Annihilation is not available for same-hand
ma particules.
Hyff from contrary ma handed particules can
interact.
Particles can annihilate by merging hyff
emission directions. However they have to
align and get into complementary 180o
phase, and this make take frequency
cycles and hence time. The particles may
need to have the same form, e.g. electron
and antielectron. The principles for
annihilation of different form particles are
uncertain.
Particles can form bonded structures, at
least temporarily, when they are in phase
with each other. Hence positronium,
kaons, and other exotic mesons.
Cordus principle that Hyff Function defines Particule Form.
The hyff functional variables are identified as: the quantity
of hyff (charge), their direction (sign of charge), colour or
direction in the [r,a,t] axes (hyff emission directions,
HEDs), phase offset across the two reactive ends (pulsatile
vs. fibrillating), and ma hand (energisation sequence).
These factors determine what the particule will be, thus its
form.
Hyff are conserved in annihilation and bonding, though
complementary hyff may collapse each other. If a new hyff
is created then a complementary hyff is also created.
The annihilation process itself is fast (125E-12 s for
parapositronium), whereas the geometric pre-positioning
is relatively slower.
4
Discussion
4.1
What has been achieved?
We have developed a candidate model for the annihilation process
between an electron and antielectron (positron). This explains the process
in terms of the ma handedness of matter and antimatter, the interaction
of the two particules as they approach, the collapse of their hyff structures
and their reformation into photon hyff. This is a deeper level of
explanation than provided by conventional physics, and thus goes into
new territory.
Compared to QCD, the present work offers a conceptual theory for
annihilation as compared to the mathematical modelling of QCD. It is
possible that the two might be complementary.
Overall, cordus now provides a more logically consistent descriptive
explanation across a wider range of phenomena than any other theory,
323
QM included. Cordus has already been used to explain wave-particle
duality, optical reflection and refraction, entanglement effects,
superfluidity & superconductivity, and a variety of other effects. This work
on antimatter and annihilation extends its coherence further. That does
not necessarily make it valid of course, but it does make it more
interesting.
4.2
What are the implications?
We can use the cordus annihilation model to explain some of the other
empirical evidence regarding annihilation of electrons and positrons.
Various output photon scenarios
The annihilation of an electron and antielectron is known to produce two
photons (or less often 4, 6..) or three (less often 5). It is known to depend
on the relative spins: antiparallel or parallel spins respectively. Note that
spin refers to the quantised angular momentum of the particules, and is
not the same as chirality nor even the ma hand. Output of a single photon
is possible, but only if there is other matter nearby to absorb some of the
energy.
Applying the cordus model allows these various outcomes to be explained.
The final outcome of the annihilation of the electron and antielectron is
one of these cases:
• One photon. Single photon, nominally y.b, is emitted. Its
companion y.c is emitted and immediately absorbed by nearby
matter (e.g. other electrons) before detection.94 This effect may
also remove photons from any of the following cases.
• Two photons, y.b. and y.c are produced from each pair of reactive
ends. This occurs if the original e and e were in a suitable phase at
the outset: the cordus working model suggests this is opposite
energisation (180o phase offset).
• Three photons. The first photon, y.a is produced as an initial
adjustment to get the e and e into in a suitable initial phase. The
y.b and y.c photons are subsequent outcomes when the reactive
ends rearrange their hyff. If this is true then we would expect the
y.a photon to have a different energy to the y.b and y.c (which
should be identical in energy).
• Four or six photons. This is an extension of the two-photon model,
where transitional structures (e.g. more electron-antielectron
pairs) form at stage #4 cross-over.
• Five photons. This is an extension of the three-photon model, with
additional pair production at stage #4 cross-over.
The criteria are uncertain for transition into the multiple photon
production process at stage #4. We presume this route is determined by
94
Another possibility is that the hyff are absorbed by another particuloid, even as they are
created. Thus absorption before photon v.c is created. However this is not the preferred
current model.
324
the energy content of the original electron and antielectron, i.e. the
energy in the e1 and e1 coalescence, and perhaps the degree of external
constraint/freedom (see the cordus fabric concept [16]).
The conventional explanation for the production of two photons, rather
than one, is that this is necessary for conservation of energy and
momentum. The cordus explanation is consistent with this, and suggests a
mechanism: at initial engagement (#1) the interaction of the hyff
repositions the reactive ends of the electron and antielecton, and this
repositioning is set into the motion of the resulting photons at #5.
Positronium
It will be evident that the cordus model also explains the different
annihilation outcomes of parapositronium and orthopositronium, but
space does not permit elaboration here, and we leave this to a companion
paper.
Genesis
There is nothing stopping the annihilation process running in reverse: if
two photons come close together (stage 5) they can entangle each other’s
reactive ends to form cross-over fibrils (stage 4), and then undock those
form separate electron and antielectron particules (stage 3) which can
then be pulled out of engagement by the surrounding fabric (stage 1).
Thus we have also given a physical description of pair-creation.
Complementarity of bonding and annihilation
The cordus conjecture suggests that bonding and annihilation are similar
effects, both involving mutual coordination of hyff, and the primary
differentiating factor is the ma hand. Same-hand structures can bond
together, by sharing hyff emission directions. This providing their cordus
frequencies are sufficiently similar. This is so for electrons, especially as
they are flexible about the energies, hence frequency, they adopt. This
makes the electron an ideal bonding medium. If the frequencies are
dissimilar then the high-frequency partner has spare off-duty cycles in
which to do things, including forming liaisons elsewhere, hence instability.
Thus we interpret the instability in the non-nucleon hadrons as an
example of this cordus principle, and the relationship between the
electron and the nucleus as another example.
Thus cordus proposes that same-hand particules can bond, whereas
contrary handed particules can annihilate. In a sense bonding and
annihilation are complementary processes for ipsilateral and contralateral
handedness respectively. The common deeper mechanism is the way the
hyff behave at the reactive end.
What happens to the information at annihilation?
Before the particuloids annihilate they are sending out
electromagentogravitational (EMG) hyffons into the surrounding space,
advertising their existence [13]. The hyffons propagate distally on the hyff
325
at the speed of light. Thus a remote mass may become aware of one of the
particuloids, and an EMG force, say of gravitational attraction starts to act.
(Force is more accurately a prescribed constraint on re-energisation
position of the reactive end, i.e. an incremental displacement effect.) The
hyffons for matter particuloids are discrete structures, and their
production is pulsatile, alternating between the two reactive as they reenergise. Note that the reactive ends are separated by a span, and this
plus the conservation of hand, means that the two reactive ends are not
identical in their field behaviour. Thus a mirror image of any particule is
not identical to itself, about every mirror plane. Hence parity violation only
occurs at small scales where the span becomes evident [7].
However, what happens when the particules annihilate? According to this
cordus model, the production of new hyffons (EMG force pulses) ceases
when the reactive ends change over to the fibrillating production method
for photons. What then happens to the particule’s responsibility to the
remote mass? The answer, according to this view of events, is that the
existing hyffons that are in-transit continue to propagate outwards, and
the remote mass continues to respond to the force while those hyffons
continue to be supplied. When the flow ceases then the force also ceases.
So the remote mass continues to feel the force after the particules have
annihilated. One could say that the information about the cessation in
production also travels outward at the speed of light. All knowledge of the
existence of the two annihilated particuloids is thus progressively wiped
from the universe.
In quantum mechanics the information contained in matter, such as its
quantum numbers, cannot vanish. By comparison the cordus model
suggests that the information about the electron and antielectron does
vanish, being replaced by photons with some of the information (but not
necessarily all). However this is not really a problem because the initial
process of genesis, which manufactured photons into electrons and
antielectrons introduced variables that were only temporary anyway:
those two particuloids had lives with greater degrees of freedom, which
the annihilation subsequently collapsed. It does not matter that the
annihilating particuloids were not the same as those original created.
4.3
What are the limitations and implications for further
research?
We acknowledge that the validity of this cordus annihilation model is
untested. Furthermore, the model is built on prior cordus models, and we
acknowledge those might have flaws too. The lemmas introduced here are
logically consistent with the whole codex of prior lemmas, thus providing
coherence across the wider work, but this does not make it valid.
What we have presented here is a conceptual contribution. For validation
it will be necessary to check the model against the known empirical
evidence for other annihilation events, i.e. go beyond electronantielectron interactions. It would also be necessary to enumerate the
326
cordus mathematics, which would be a large and interesting project of its
own. At this time we cannot make a direct comparison between cordus
and QCD, since their mechanics are formulated differently. However we
expect there to be a basic compatibility.
This particular model purports to describe the process of annihilation
itself. This is way beyond the reach of all other theories of fundamental
physics, most of which are still working on how to produce a working
concept for the discretisation of the electromagnetic field. If cordus was
found to be a valid, then the consequences would be significant, as it
would open up new lines of enquiry into fundamental physics.
5
Conclusions
To what extent has the original purpose been met?
The original purpose was to tease out the mechanics of annihilation. We
have now achieved that, with the process decomposed into stages and the
proposed mechanisms identified for each. Yes, we can now explain how
matter and antimatter annihilate: they transform their field structures called hyff - into those of the photon.
We can also attempt an answer to the deeper philosophical question of
why annihilation happens at all: because matter and antimatter are
segregated forms of energy - segregated by ma hand that is - and
annihilation is simply the reversal of that process. We tend to
anthropomorphise 'annihilation', and the conventional construct and
terminology, suggests a destructive loss. Yet cordus suggests that at a
deeper level there is a conservation at work, one of hyff and reactive ends
and energy, so that the process is better thought of as 'remanufacture'.
We also show that a deeper common mechanism exists for annihilation,
pair-creation, and bonding.
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329
Cordus
process
diagrams:
Symbolic
representation of annihilation mechanics
Pons, D.J. 95
Abstract
We introduce a new system-modelling representation for the interaction of
particules with internal structures (hidden variable solutions). This is an
improvement on Feynman diagrams that only represent points and limited
information about state. The notation is able to represent key variables
describing the internal states, such as phase and the three dimensional
discrete field structures. The latter include the cordus hyff emission
directions (HEDs). With this method it is possible to model the different
stages in an interaction processes. It is applied to the cordus annihilation
mechanics, and the resulting models qualitatively distinguish between the
parapositronium and orthopositronium annihilation phenomena.
Keywords: annihilation, fundamental physics, orthopositronium,
parapositronium, alternative representation, notation, IDEF0, Feynman
diagram
Edition 1 > Date: Saturday, 11 February 2012 > Document:
Pons_Cordus_5.4_SymbolicMechanics_E1.0.26.doc
1
Introduction
This paper describes a method for representing the interaction process
between particules, and applies it to electron-antielectron (positronium)
annihilation. We have separately established a cordus model [1] for
matter (M) and antimatter (aM), that distinguishes the two species
primarily by their ma hand. We have also described the annihilation
process itself at the level of the internal structures of the two cordus
particules, and set out the lemmas for the mechanics [39].
Feynman diagrams
The best current representation of particle interaction is Feynman
diagrams. These represent the inputs and outputs of particle interactions,
especially the transformation to different particles, such as annihilation,
weak processes, impact, and decay. They represent the main phases (or
stages) in the process. For an example, see Figure 1.
95
Please address correspondence to Dr Dirk Pons, University of Canterbury, Christchurch, New
Zealand. Copyright D Pons 2011: this work is licensed under a Creative Commons AttributionNonCommercial-ShareAlike 3.0 Unported License.
330
Figure 1: Feynman diagram for electron-antielectron annihilation to two
gamma photons. The inputs are on the left and comprise an electron e and
an antielectron e (with reversed arrow). These two interact to produce two
output photons y. Conventional physics does not explain how that
interaction occurs, but cordus does.
As a graphical representation, Feynman diagrams have the disadvantage
of variable notation, particularly the meaning assigned to the direction of
arrows. Specifically, some of the notations encourage the idea that
antiparticles travel back in time, which adds mystery more than meaning.
Feynman diagrams do not represent the underlying mechanisms at the
deeper level, nor all the intermediate structures. This is not a criticism of
the diagrams, but simply a statement of the inability of conventional
physics to provide a physical explanation for the mathematical models.
The diagrams are consistent with empirical observed tracks where certain
intermediates are not detected until a transformation to another particle
occurs, i.e. there are gaps in the tracks. The diagrams encapsulate the idea
that these unobservable structures are ‘virtual’ particles. Thus we have
various virtual bosons identified as part of the deconstruction process, and
even the photon is repurposed as a virtual photon for the electromagnetic
effect.
The physics way of thinking (Kuhn’s ‘paradigm’ [14]) is to preferentially
interpret subatomic entities as ‘particles’. These particles have no internal
structure, except sometimes other more fundamental particles, and are
thus zero dimensional regarding structure. However, they have other
directional attributes of spin and momentum, and indeed several other
properties or ‘intrinsic variables’ and thus we refer to this as a onedimensional construct. This is evident in the Feynman diagrams, which
show 0-D points with direction. The paradigm is also seen in the
prevalence to interpret anything whatsoever that happens in a high energy
physics impact, observed or theorised, as a particle, hence the W and Z
bosons, gluons, Higgs, etc. From the cordus perspective this is a very
limiting paradigm, and cordus specifically refutes the point particle
construct that underpins much of it [9].
331
The cordus conjecture offers a solution where the subatomic entities have
internal structure. A specific structure, called a cordus, is proposed [8].96
This is used to produce a coherent set of explanations for a wide variety of
enigmatic effects in fundamental physics, including wave-particle duality.
Cordus identifies internal structures, and the states thereof, as being
important in the annihilation process [39]. For example, the different
outcomes for para- and ortho-positronium are shown to depend on the
relative phase difference of the input particules. Thus it is important to
have a representation, like Feynman diagrams but better, that can
represent how the internal structures affect the outcomes.
Needed, a finer-scaled representation
There is nothing fundamentally wrong with Feynman diagrams, other
than disputable treatment of antiparticles, but they just don’t have the
necessary power to represent the new processes suggested by the cordus
mechanics. At the other extreme are the cordus diagrams showing the
detail of the interaction, but these are too cumbersome for general use.
We seek something in between: a notation that represents the detail of
the cordus annihilation mechanics but retains at least some of the
simplicity of the Feynman diagrams.
2
Approach
Process diagrams are common in production engineering, because the
nature of that discipline is to manage processes. We thus apply production
engineering thinking to create a diagrammatic representation and a shorthand notation.
2.1
Process diagram
The first thing we do is simplify the Feynman diagram, for example that for
electron-antielectron annihilation, to produce Figure 2.
96
The cordus conjecture is that all 'particles', e.g. photons and electrons, have a specific
internal structure of a cordus, comprising two reactive ends, with a fibril joining them. The
reactive ends are a small finite span apart, and energised (typically in turn) at a frequency,
at which time they behave like a particle. When energised they emit a transient force pulse
along a line called a hyperfine fibril (hyff), and this makes up the field. We call this a cordus
‘particule’, and stress it is very different to the zero-dimensional point assumed by
conventional physics.
332
Figure 2: Cordus process diagram for electron-antielectron annihilation to
two gamma photons. The inputs are on the left and comprise an electron e
and an antielectron e (no reversal of arrow) as we do not accept the
Feynman concept that an antielectron travels backwards in time. The
activity of interaction is represented by the rectangle. At this point we
retain the circles (nodes) of the Feynman diagram and the interlinking bar,
but this is simply for explanatory continuity and later we omit these. The
output is two photons y.
Next, we need to diagrammatically represent the perspective that these
are not 0-D points, but rather cordus particules. First, we define some
convenient symbols, wherein the frequency state is represented, see
Figure 3.
Figure 3: Symbolic representation of charged particules. These symbols
capture the variables of phase, charge, and ma hand (matter vs.
antimatter).
At the same time we adopt a process formalism, i.e. a diagrammatic
notation. Since the choice of notation always limits what can be
represented, and perhaps even conceived, with any diagram, we need to
333
adopt a relatively powerful system modelling approach to this problem.
We elect to use what we term ‘dynamic process analysis’ as it is designed
to capture changeable effects (or multiple pathways of activity) under high
epistemic uncertainty. In turn, it is expressed graphically as a flowchart
using the integration definition zero (IDEF0) notation [40-41], see legend in
Figure 4.
Legend
Initiators that
start the
Activity
Constraints
that limit the
outputs
Feedback,
controls on
the outputs
boon, unexpected
advantage
value (benefit),
intended or perceived
Inputs and
consumed
resources
Description of Activity
(number:additional
sheet)
outputs
ommissions (nonoutputs) latent or
patent
mechanisms
supporting the activity
detriments
(side effects, unwanted
or unanticipated
outputs)
Figure 4: Notation for IDEF0. The object types are inputs, controls, outputs,
and mechanisms (ICOM), and are distinguished by placement relative to
the box, with inputs always entering on the left, controls above, outputs on
the right, and mechanisms below. The box itself describes a function (or
activity), and the arc (line arrow) describes an object.
IDEF0 is more powerful than we currently need, but we are only dealing
with the relatively simple case of electron-antielectron annihilation here,
whereas there are more complex interactions to be considered for the
future.
We also need an abbreviated notation to complement the diagrams, as
simple expressions like e + e -> 2y are inadequate when representing
internal structures. Hence the following complementary notation.
2.2
HED notation
In the cordus concept, a particule consists of two reactive ends
geometrically separated from each other, and connected instantaneously
by a fibril [8]. A core concept is that the reactive ends, at least of massy
particules, emit field structures (hyffons) in three orthogonal directions.
These are called hyff emission directions (HEDs), and implicated in the
strong interaction and indeed all bonding [7].
334
The three HEDs are named radial [r], axial [a], and tangential [t], and their
orientation is relative to the fibril and the motion or spin of the particule.
Two hands are possible for this co-ordinate system, and these are termed
forma and hyarma, and proposed as the structural difference between
matter and antimatter respectively [15].
Electric charge is identified as the direction of propagation of the hyffon
(field pulses) along the hyff emission directions. Negative charge is
nominally an outward propagating hyffon, and positive is inward (this is
merely a sign convention). Each hyffon corresponds to a fundamental
charge of 1/3. So an electron has one of these in each of three HEDs,
hence an overall charge of -1. Charges of quarks (+2/3 and -1/3) are readily
accommodated as partially filled HEDs.
The previous work on the internal processes of annihilation [39] shows
that it is the field structures, collectively the hyff, hyffons, & HEDs, that are
remanufactured when an electron meets an antielectron. Therefore we
need a diagrammatic short-hand way to represent the state of these HEDs.
We use a simple notation, which we call HED notation. Basically, for each
particule it shows the three HEDS, and how they are filled with hyffons,
see Figure 5.
Figure 5: HED Notation, showing usage of the various components. The
example is for an electron, and shows the arrangement of its field
components.
The HED notations for several common particules are given below.
Electron
e(r1 .a1 .t1)
Antielectron
e(r1 .a1 .t1)
335
Photon
y(r! .a .t) See note 1.
U Quark
u(r1 .a1 .t)
D Quark
d(r1 .a .t)
Proton
p(r1.1 .a11 .t1) See note 2.
Antiproton
p(r1.1 .a11 .t1) See note 2.
Neutron
n(r11 .a11 .t) See note 2, 3.
Antineutron
n(r11 .a11 .t) See note 2, 3.
[Note 1]
The photon is a fibrillating hyff pump in that it does not
release its hyffons, but instead immediately recalls them
[37]. By contrast all other massy particules release their
hyffons, then switch over to the opposite reactive end and
release a hyffon from there.
[Note 2]
The cordus models for the proton and neutron internalstructures & quarks have been previously identified [7].
These are assembly structures. The examples given here
show the current working model for the allocation of
hyffons to the HEDs and we acknowledge that several
other combinations are possible.
These internal
arrangements are believed to correspond to quark colour.
[Note 3]
The difference between the neutron and antineutron is
the ma hand: the charges themselves are neutral in both
cases, though the process of obtaining that neutrality is
different. The HED notation shows this difference in hand.
We now have three representations for the interaction of particules: (1)
the detailed cordus models of the 3D structures, though these are too
cumbersome for general use, (2) the process diagrams, and (3) the HED
notation. We refer to the latter two as cordus process diagrams. We can
now use these to represent the annihilation processes.
3
Positronium annihilation
Regarding annihilation, the main difference between matter and
antimatter (M-aM), according to cordus [15], is that the ma hand of the
hyff is inverted. Separately we have developed a candidate model for the
annihilation process between an electron and antielectron (positron) [39].
This explains the process in terms of the ma handedness of matter and
336
antimatter, the interaction of the two particules as they approach, the
collapse of their hyff structures and their reformation into photon hyff.
We now represent the mechanics with cordus process diagrams. The
specific focus area is positronium: the temporary bound states of electronantielectron. Two states are known: parapositronium (life of about 125E12 s), and orthopositronium (life 142E-9 s). Positronium has been relatively
well studied e.g. [42] and production channels modelled mathematically
[31, 43-44]. Positronium has the known behaviour of producing two
photons when the electron and positron have antiparallel spins
(parapositronium),
and
three
photons
for
parallel
spins
(orthopositronium). However, spin is ill-defined in quantum theory,
because QM denies that there is any internal structure. Instead QM
considers spin to be merely an intrinsic variable. Only with a hiddenvariable theory, like cordus, can a physical interpretation be gives for the
many intrinsic ‘quantum numbers’ that QM relies on but cannot explain. In
this particular case, cordus explains ‘spin’ as the frequency phase of the
particules. Once this concept is adopted, then it becomes possible to
explain the different behaviours of positronium in a natural way.
3.1
Parapositronium
It is known that in parapositronium the two particles have antiparallel
spins. The life before annihilation is the shorter of the two forms.
Annihilation is known to produce two photons, or less often 4 or 6 etc.
The cordus explanation for the annihilation process itself, including the
production of two photons, is described in the companion paper [39]. Here
we focus on representing it diagrammatically, see Figure 6.
Figure 6: Cordus process diagram for annihilation of electron and
antielectron, where they are initially out of phase with each other. This is
the parapositronium state.
337
The numbers in the figure correspond to the stages in the detailed model
[39]. According to the cordus interpretation, parapositronium already has
the electron and antielectron in the correct ‘complementary’ phase of
180o phase difference (hence opposite ‘spin’), so the synchronisation
(stage #2) is pre-arranged. The process therefore proceeds directly to
docking, cross-over fibrils, and conversion to photons (stages 3-5).
The diagram itself is an elaboration of the simple cordus process diagram
of Figure 2. Note the inclusion of additional activity boxes. Each of these
can be further decomposed, which is achieved in the detailed model [39].
Note the diagram also includes the symbolic cordus particule that
represents the ma hand state and the relative phase. These are two
variables that are important in the process, and therefore need to be
represented at this level. The output photons also have a cordus particule
structure, which is shown in the output activity (stage #6). While we retain
the wave symbol for ease of comprehension and compatibility with
Feynman diagrams, the photon is not fundamentally either a wave nor a
particle, but instead another cordus particule.
In some ways the complementary phase of parapositronium state looks
like bonding or entanglement, and cordus states that those effect do
indeed all use the same underlying mechanism of CoFS [5].
Note that in the process diagram the horizontal axis is time. More
specifically, cordus identifies that time at the deeper level corresponds to
the re-energisation frequency cycles of the particules [13]. Thus particules
need cycles to accomplish the process activities.
The short-hand representation of this in the HED notation is:
e(r1 .a1 .t1)|0 deg + e(r1 .a1 .t1)|180 deg
=> o(r11 .a11 .t11)
=> y.b(r! .a .t)|0 deg + y.c(r! .a .t)|180 deg
=> y.b + y.c
where ‘o’ represents a transitional state. In this particular case, this can be
identified as parapositronium. We note that the structure o(r11 .a11 .t11) is
capable of reforming to two photons, having previously demonstrated the
mechanics [39], and therefore note this as a core annihilation process in
lemma Ma.4.2.
In the reduced format without the HED details:
e + e => 2y
which is what the Feynman diagram states. Thus an electron and
antielectron in parapositronium annihilate to two photons.
Obviously these models do not represent the full details of the
remanufacture of the hyff into photons. For that see the detailed model
[39]. Instead all we seek to achieve here is a representation of the overall
338
process, so that we can compare different processes. The next case,
orthopositronium, starts to show the power of the method to differentiate
similar cases.
3.2
Orthopositronium
Orthopositronium is the other temporary association of an electron and
antielectron, and has the longer life before annihilation, though still short.
It is known that the two particles have parallel spins. Annihilation is
known to produce three photons, less often five.
The cordus explanation for the annihilation process, including the
production of three photons, has been described [39]. The process
diagram is shown in Figure 7.
Figure 7: Cordus process diagram for annihilation of electron and
antielectron, where they are initially in phase with each other. This is the
orthopositronium state.
This diagram is more complex than the previous one. This is because
orthopositronium has additional activities required before the main
annihilation process can get underway. Thus the particules are in-phase (0o
offset between re-energisation) (stage 2.1), and one of them needs to
emit photon y.a to change phase (stage 2.2). We also know the mechanism
for this, or at least can identify part of it as lemma Ma.3.3. Note that the
mechanism is shown under the activity block, this being the IDEF0
notation. The diagram identifies that photon y.a is emitted at stage 2.2.
339
Thereafter the assembly is effectively parapositronium, and proceeds to
conversion to an additional two photons y.b and y.c (stages 3-6).
The short-hand representation of this in the HED notation is:
e(r1 .a1 .t1)|0 deg + e(r1 .a1 .t1)| 0 deg
=> y.a(r! .a .t) + e(r1 .a1 .t1)|0 deg + e(r1 .a1 .t1)|180 deg
=> y.a + o(r11 .a11 .t11)
=> y.a + y.b(r! .a .t)|0 deg + y.c(r! .a .t)|180 deg
=> y.a + y.b + y.c
Or in the reduced format:
e + e => 3y
Thus an electron and antielectron in orthopositronium annihilate to three
photons.
3.3
Comparison: parapositronium vs. orthopositronium
Cordus predicts that the two- and three-photon production processes for
para- and ortho-positronium are very different: the third photon is not
merely one of three, but has a different causality and comes out at a
different part of the process. Both forms of positronium use the same
core annihilation process (stages 3-6) for the production of the paired
photons.
The reason orthopositronium cannot emit only two photons is
conventionally explained as a consequence of charge conjugation
invariance.97 From the cordus perspective the reason is instead that one
photon is required to change the state into the antiparallel state (as per
Ma.3.3) and the conservation of hyff required that two photons be
produced (Ma.3.8).
Cordus offers a qualitative explanation of why the lifetime for
parapositronium is so much less than orthopositronium: the latter has
further processes to undergo, and these take time. Parapositronium is a
preassembly that is already in the docked state (stage 3), and therefore
proceeds directly to stages 4-5 and hence to photons. By comparison
orthopositronium is in stage 2 and first has to emit a photon before it can
continue.
If this interpretation is correct, then we can make another inference: that
the time taken to get the particules into the correct geometric position
(Ma.3.2) is much the greater contributor to the decay time than the
annihilation process to photons. We noted this as lemma Ma.3.9 [39].
97
Charge conjugation invariance is the expectation that process, such as the emission of
photons, are the same -hence invariant- if all the particles are replaced with antiparticles.
Cordus rejects the implication that antiparticles are simply opposite charge.
340
The cordus explanations for the production of two and three photons is
thus consistent with known behaviour of positronium. Cordus also
independently derives the spin requirement, and the direction thereof.
Cordus also goes further in making the ‘spin’ tangible, which is otherwise
only an intrinsic variable to quantum mechanics. In the orthopositronium
case one of the photons may be of a different energy [45], and cordus
accommodates this too.
3.4
Scattering
The impact of moving particles does not necessarily cause deconstruction.
Particles are known to recoil elastically from the impact, and this is termed
scattering. The cordus interpretation is that the particuloids interact
through their hyff as they approach each other. The hyff have to negotiate
mutual emission directions (HEDs) and thus exert force on each other’s
particuloid before the reactive ends actually coincide. So the effect
happens at a small distance away from the reactive: see also the cordus
Principle of Wider Locality [3]. According to the cordus mechanics, the
scattering outcome ultimately depends on the frequency & phase. Thus it
depends on which reactive ends are energised at the time, what their
relative frequency states are, and which way their hyff are directed. The
latter depends on the velocities of the particuloids, since cordus identifies
that the orientation of the hyff is aligned to the direction of motion.
Furthermore the orientation of the hyff is determined by the species:
matter and antimatter differing by the ma hand of their hyff.
One form of scattering is particularly associated with electron-antielectron
interaction, and is discussed next.
Bhabha scattering
The system model of Figure 7 also includes Bhabha scattering. In this
effect an electron and antielectron recoil from impact. This is anomalous
given that matter and antimatter more generally annihilate. Cordus
explains the scattering as caused by two factors: the two particules have
phases that are too close, and therefore the SHEDs principle [7] causes
repulsion, and the momentum is such that the particules do not have
enough frequency cycles (‘time’) to get into a complementary phase state.
The latter is covered in lemma Ma.3.2 [39].
3.5
Lemma
The following lemmas summarise the additional assumptions made here.
Ma.4 HED principles
Ma.4.1
Principle of conservation of hyff. The total number of
active hyff, i.e. hyffons, owned by input particules is
conserved across the output particules, unless annihilation
occurs. See also Ma.3.8.
Ma.4.2
A core annihilation process: A fully HED-complementary
structure, i.e. o(r11 .a11 .t11), collapses to two photons
2y(r!.a.t).
341
4
Conclusion
What we have achieved is a new system-modelling representation for the
interaction of particules. The notation is able to represent the different
stages in the interaction processes.
The advantage of the HED notation is that it permits the intermediate
structures to be worked out. Thus it is able to represent different states of
particules, including their key internal structures. This is an advance on
Feynman diagrams. We have applied this method to the cordus
annihilation mechanics, and have shown how to develop models that can
distinguish between the parapositronium and orthopositronium
annihilation phenomena.
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344
345
Cordus
Conjecture
Part 6: Neutrino mediated effects
The field structure of
the
neutrino
is
predicted and used
to explain several
phenomena > weak
interaction > field
structure of W and Z
bosons
>
decay
process for neutrons
>
asymmetrical
genesis of matter
over antimatter by
the
neutrino
emission route
346
Structure of the neutrino and antineutrino
Pons, D.J. 98
Abstract
The neutrino is involved in many of the unsolved areas of fundamental
physics and cosmology, and therefore a better understanding of the causes
of its behaviour is useful. This paper develops a conceptual theory for the
internal structure of the neutrino, particularly the arrangement of its
discrete field structures. The model is created using the concept of the
cordus hyff emission directions (HEDs).
Using the known quark
composition of the neutron and proton, and the existing cordus models for
their discrete field structures, and using the beta decay processes, we
determine the discrete field structure of the neutrino by a reverseengineering process. The structure of the neutrino in HED notation is found
to be v(r1 1 .a .t11) or variants thereof, and the antineutrino to be v(r11 .a
.t11) etc. The results are consistent whether using beta - decay, beta +, or
electron capture. The results suggest that the neutrino is not its own
antiparticle. Consequently neutrinoless double beta decay is predicted to
be infeasible. The model predicts the neutrino has zero nominal mass,
though a dynamic noise-mass is expected. The reasons why the neutrino
moves at the speed of light are explained, and involve the engagement of
its field structures, which are incomplete, with the fabric (spacetime). The
gravitational bending of its trajectory is explained, even for a massless
neutrino. This explanation requires the abandonment of both locality and
the invariance of the vacuum-speed of light. The model also explains why
neutrinos are always found with left-spin-hand, and antineutrinos with
right, and suggests that the opposite structures are fundamentally
unavailable. By moving away from the 0D point assumption of orthodox
physics, cordus is able to generate a novel and radical model of the
neutrino, and ground its behaviour in physically realistic interpretations.
Edition 1 > Date: Saturday, 11 February 2012 > Document: Pons_cordus_5.6_Neutrinos_E1.0.28.doc
1
Introduction
Neutrinos are the most enigmatic of particles. They are very light, or even
massless, and do not interact much with matter, so they might be
considered inconsequential. Yet they are useful in ways both practical and
theoretical:
98
Please address correspondence to Dr Dirk Pons, University of Canterbury, Christchurch, New
Zealand. Copyright D Pons 2011.
347
•
•
•
•
•
•
They are probes for the interior of stellar objects, since they are
not appreciably blocked by the outer layers of stars, nor
interstellar dust.
A more fundamental use is probing the theoretical validity of the
standard model of particle physics. The properties of neutrinos,
particularly mass and handedness, might point to a different
physics at work.
If the behaviour of neutrinos and antineutrinos is different, then it
could help explain why CP violation occurs, and explain why there
is more matter than antimatter in the universe.
Neutrinos are an integral part of the weak interaction, and
understanding neutrinos could help better understand that effect.
They are also important in theories of cosmology, for example
some string theories propose superluminal sterile neutrinos, which
if detected could help confirm that theory.
Neutrinos may be involved in the dark matter problem.
So the neutrino is implicated as being involved in many of the unsolved
areas of fundamental physics and cosmology, and therefore a better
understanding of its behaviour would be useful. Unfortunately, the theory
of neutrinos is incomplete, and empirical measurement is challenging
because their low interaction with matter makes them difficult to detect.
This paper develops a qualitative conceptual theory for the internal
structure of the neutrino. It is worthwhile attempting this for the potential
to extract the mechanisms of causality, i.e. how internal structures cause
the observed external behaviour. The idea is based on an extension of the
cordus conjecture, which proposes a particular internal structure for
particles. By comparison, conventional physics takes the premise that
fundamental particles are zero-dimensional points. Thus the cordus
approach is unorthodox, and results in a solution that cannot be
contemplated from the conventional paradigm of quantum mechanics
(QM) and the standard model.
2
What we know about neutrinos
In the standard model the neutrino is a neutral particle (zero charge).
There are three generations in total: electron neutrino ve, muon neutrino
vu, and tau neutrino vt. For each there is known to be an antimatter
version: the relevant antineutrino. These three generations are suggested
by the lifetimes of the Z boson, and while it is satisfying to have three
generations as also seen in quarks, it is uncertain whether this is a
fundamental limit.
The neutrino does not interact much with other matter, thus does not
appear to respond to the strong force, though it does to the weak: indeed
it practically defines the weak interaction. It does appear to respond to
gravity. Whether it reacts electromagnetically is uncertain.
348
Neutrino hand
Empirical results suggest that neutrinos always have left-handed helicity
(spin relative to velocity), and antineutrinos have right-handed helicity.
Hence also chirality, which is related to helicity by the frame of reference
of the observer.
Whether right-spin-handed neutrinos even exist is uncertain. Some
theories predict they do. (Note that spin-hand/helicity is not the same as
the cordus ma hand concept [1].)
Neutrino mass
Whether or not neutrinos have mass is uncertain. In the standard model
of quantum mechanics it was initially believed that neutrinos would be
massless, because they are all left-spin-handed. No right-spin-handed
neutrinos have been detected. This absence plus the requirement for
conservation of angular momentum at formation, requires the lefthanded neutrino to travel at the speed of light, and for the neutrino to be
massless. Thus they should not respond to gravitation, i.e. not interact
with the hypothesised Higgs boson. However there is now evidence for a
small mass, see oscillation below, and this is something of a challenge for
the standard model, e.g. [2].
How the mass might arise is uncertain. Since neutrinos are always lefthanded, there does not seem to be an easy way for the Higgs boson to
provide mass, unless right-handed neutrinos (and left-handed
antineutrinos) are added to the Standard Model. However, these sterile
neutrino particles have not been observed. Another conjecture is that the
neutrino is its own antiparticle and thereby obtains mass through the
Majorana effect. However the magnitude of this is doubtful. So the
question of neutrino mass, and the mechanisms thereof, is still an open
question.
Neutrino oscillation
The neutrino may change generation (’flavour’ or state) while in transit,
and this is termed oscillation. The conventional explanation is that the
three states, which have different masses, are in coherent superposition
within any one neutrino.99 The phases of the various states are believed to
be slightly different, so that the neutrino periodically advances through a
harmonic mixture of all these states. Neutrinos are difficult to detect, and
the various generations are detectable differently. Thus oscillation explains
why neutrinos are often missing when measurement is attempted. In turn,
oscillation is generally interpreted as requiring different mass, more
specifically superposition between three different mass states, and
therefore neutrinos should not be massless.
99
This is an odd theory, for several reasons. First, quantum superposition usually
refers to two states, not three of appreciably different mass. Second, the
periodicity in the neutrino model is in contrast to the randomness that quantum
mechanics otherwise associates with superposition.
349
Neutrino creation and detection
Neutrinos are created in the decay of subatomic particles, e.g. in the sun,
nuclear reactors, and particle accelerators. They are also regularly created
by impact of cosmic rays (typically fast protons) into the atmosphere, and
travel some distance into the earth because of their low interaction with
matter.
Neutrinos interact little with matter, so detection is more difficult than
other particles. Methods include watching for secondary photons
(Cherenkov radiation) in a tank of water or volume of plastic (neutral
current interaction), or for radioactive breakdown products in substances
like chlorine or gallium.
3
Method
We start by adopting the cordus conjecture [3]. This provides a set of
general principles governing the internal structure of subatomic entities.
Cordus proposes that the particle is not a zero-dimensional point (as
orthodox physics asserts) but rather a two-ended internal structure. We
call this a cordus ‘particule’.100 This idea has been used to create a novel
model of the internal structure of the photon. It is a radical idea that goes
to the roots of fundamental physics, and is unorthodox in that it bypasses
the conceptualisation of quantum mechanics (but accepts much of its
mathematical machinery). Cordus has already been used to resolve waveparticle duality [4], explain entanglement, redefine locality [5], quantise
the field forces, and explain a unified electricity-magnetism-gravitation [6].
Cordus has also described the internal structure of quarks and nucleons
[7], electrons [8], and differentiated between matter and antimatter [1]. It
has also been used to describe a detailed internal mechanics for the
process of electron-antielectron annihilation [9], and is therefore able to
show how the mass structures of those particules transform into the
energy structures of the photon. The key to understanding annihilation
proved to be a better model of the discrete field structures for particules:
both their physical structure and their basic mechanics. The concepts here
were hyffon pulses, hyff threads, reactive ends, and fibrils. Also crucial was
a better understanding of the fundamental difference between matter and
antimatter, which was identified as a special handedness characteristic
called ma. This also explained why parity violation occurs at sufficiently
small scales (but is not evident at larger).
100
The cordus conjecture is that all particles, e.g. photons and electrons, have a specific
internal structure of a cordus, comprising two reactive ends, with a fibril joining them. The
reactive ends are a small finite span apart, and energised (typically in turn) at a frequency,
at which time they behave like a particle. When energised they emit a transient force pulse
along a line called a hyperfine fibril (hyff), and this makes up the field. We call this a cordus
‘particule’, and stress it is very different to the zero-dimensional point assumed by
conventional physics.
350
A subsequent development was to create a new system modelling method
to represent the annihilation process [10]. Specifically, Feynman diagrams
are incapable of representing the crucial internal variables, because
naturally those diagrams are also premised on the zero dimensional point
assumption. A new representation was therefore developed, one more
suitable for capturing the critical process variables. This is called HED
notation [10]. The name arises since it models the three hyff emission
directions (HEDs) that are presumed to exist at each of the two reactive
ends of a particule, and how those HEDs are filled with hyffons (discrete
field elements). The HEDs are geometric axes: [r], [a], and [t] and aligned
with the movement/spin of the particule. A summary of the HED notation
is shown in Figure 1 by application to the electron and antielectron
(positron).
Figure 1: The cordus structure comprises two reactive ends, connected by a
fibril, with hyffons (discrete field components) in three orthogonal
directions. The diagram shows the physical structures, and underneath is
the shorthand HED notation. Both the electron and antielectron are
shown, the difference being identified as primarily the hand of the HED
(forma for matter, and hyarma for antimatter), and secondarily the
direction of the hyffons relative to their base, hence charge. Thus the HED
notation differentiates charge and hand.
351
Note that we use underscore to represent antimatter. For details about
the photon hyff structure, its fibrillating nature, and how it differs from all
the matter and antimatter particules, see [8].
Our method is then to apply the HED notation to known interactions
involving neutrinos, and thereby reverse-engineer the HED structure for
the neutrino (and antineutrino). In the process we need to make some
assumptions, which we mark as lemmas e.g. Ma.6, and we collect these at
the end.
4
Neutrino structure
Our approach is to start with the known quark composition of the neutron
and proton, convert those into HED notation and substitute into the beta
decay process, assuming equifinality. We have some initial assumptions to
guide us in this task, and we make several additional assumptions that we
mark as lemmas.
4.1
Neutron structure
We know that the neutron comprises quarks: udd. We also know the
charges of those quarks are -2/3 u and +1/3 d. We have previously
identified the cause of fractional charge of quarks as selective activation of
the three orthogonal HEDs [7]. We express those quarks in HED notation
as:
u Quark u(r1
and
1
d Quark d(r
.a1 .t)
.a .t)
Colour
The allocation of the hyffons to specific HEDs [r,a,t] is nominal at this
stage. We simply allocate them in the order of the HEDS. They can
subsequently change to another vacant HED, and we believe that this
corresponds to the known phenomenon of colour-change, see Ma.6.3. In
this cordus interpretation, colour refers to the pattern of energisation of
HEDs, i.e. directional charge. The three HEDs provide three combinations,
hence the three colours. This cordus concept also explains why there are
only three colour charges, no more or less: because there are only three
geometric directions. It also explains why colour is only seen in fractional
charge situations: because there are no free HEDs in unit-charge
particules.
Confinement
We are not saying that the neutron necessarily consists of uud quarks at
the fundamental level. Those are only the convenient transient (unstable)
breakdown shapes taken: the accessible HED structures that the energy
352
can take. Just because quarks appear at the breakdown of the neutron
does not mean that the neutron originally comprised three intact quarks
glued together. Anyway, and contrary to how they are popularly
represented, quarks do not appear as discrete observable particles. They
have not been observed on their own. Instead they are only inferred as the
internal components of hadrons, and this is termed 'confinement'.
In this interpretation of the cordus principles, the neutron consists of an
assembly of hyffons, and those assembly relationships are the reality. A
high energy impact can deform those relationships so the hyffons
dynamically regroup into quark structures.
At the same time, the number of same-hand hyffons evident in the output
quarks is understood to represent the number of hyffons in the original
neutron (which is assumed to likewise consist of one hand), see Ma.6.6.
Therefore we assume that the neutron comprises the same numbers of
hyffons as evident in its production of quarks, even if it does not actually
consist of discrete quarks.
Thus the internal structure of the neutron is surmised to be:
n(r .a11 .t11)
A similar logic provides the HED structure of the proton as:
p(r1.11 .a1 .t1)
As noted above, the allocation of hyffons to particular HEDs is nominal.
Though in this case the specific n and p structures proposed above are
complementary in an assembly, in the sense of adding to where the other
is weaker.
4.2
Beta- decay and the antineutrino (v) HED structure
In β- decay, or electron emission, the free-neutron decays, after a
relatively long life, into a proton, electron, and an electron antineutrino:
n => p + e + ve
This process is known, and we assume there is no other missing
component. Β- decay occurs spontaneously in nuclei that have too many
neutrons relative to protons, i.e. the process is a consequence of a need to
enhance nuclear stability.
We now represent this with HED notation. All the HED structures are now
known, so the only unknown in the beta decay process is the antineutrino.
We start with the derived neutron HED structure:
n(r .a11 .t11)
353
Assume that the proton is the nearest accessible structure, and we know
its HED structure: p(r1.11 .a1 .t1). A free neutron is not obliged to arrange its
hyffons in a complementary way to the proton to which it was formerly
associated, so it can rearrange its hyffons (by colour change |% Ma.6.3) to
be more consistent with the proton-outcome of its upcoming
metamorphosis state:
n => n(r .a11 .t11)|% => n(r1.11 .a.. .t.1)
Add to the neutron the charge-neutral incipient hyffon-antihyffon twinpairs (↑ = x11 and ↓ = x11), see Ma.6.7. These are as required to form the
proton structure. In this case we place the unused other pairs outside the
brackets until we decide where to assign them. Then expand the internal
pairs to create a transitional assembly ‘O’ (Ma.6.8):
n => O(r1.11 .a↓.. .t.1↓)↑↑ => O(r1.11 .a11 .t11.1) ↑↑
Next, partition off the proton HEDs and place the remaining hyffons into a
secondary structure O1 (see Ma.6.6.5):
n => p(r1. 11 .a1 .t1) + O1(r.. .a.1 .t.1.1) ↑↑
Consider fragment O1 and bring the other hyffon-antihyffon pairs into the
brackets to form the next heaviest structure, which is the electron. The
target is e(r1 .a1 .t1), so simply place a ↑ wherever a hyffon is missing. Note
that in the process we also consume the previous pairs. Then expand:
n => p(r1. 11 .a1 .t1) + O1(r.↑. .a. ↑1 .t.1.1)
n => p(r1. 11 .a1 .t1) + O1(r11 .a11.1 .t.1.1)
Then partition off the electron HEDs, and place the remaining hyffons into
another secondary composite structure, O2:
n => p(r1. 11 .a1 .t1) + e(r1 .a1 .t1) + O2(r1 .a11 .t.1)
The remaining O2 structure appears to have a basic stability because it is
all the same hand. We already have the proton and electron from the
expression, so we identify the O2 as the antineutrino:
n => p(r1. 11 .a1 .t1) + e(r1 .a1 .t1) + v(r1 .a11 .t.1)
Dynamic neutrino structures
The allocation of hyffons to specific HEDs is not known with certainty. If
we assume a different layout of the neutron e.g. n(r11 .a11 .t), and proton
e.g. p(r1. 1 .a11 .t1), then the predicted layout of the antineutrino also
changes.
However this is not a problem, because the structure is assumed to be
dynamic anyway, i.e. the hyffons can relocate to other HEDs (colour
change, Ma.6.3). The main variants are of the following types: v = v(r1.1 1.1
.a .t) = v(r1 .a1 .t11) = v(r .a11 .t11) = v(r! .a11 .t11)
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Since the antineutrino is a free particule, it can (and must) rearrange its
hyffons to suit its needs (constraints). The stability lemmas [work in
progress] suggest its closest stability is to concentrate its hyffons on the [r]
and [t] HEDs, and then move on the fabric. Therefore the HED structure of
the antineutrino is inferred to be:
Antineutrino: v = v(r11 .a .t11)
This is shown in Figure 2.
Figure 2: The cordus structure for the antineutrino, specifically the v(r11 .a
.t11) variant. The diagram shows the HED notation and the proposed
physical field structures.
Other variants are possible.
By the matter-antimatter cordus lemmas [1], the neutrino is the
corresponding mirrored HED structure:
Neutrino v = v(r1 1 .a .t11)
This is shown in Figure 3.
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Figure 3: The cordus structure for the neutrino, specifically the v(r1.1 1.1 .a .t)
and v(r1 1 .a .t11) variants. The diagram shows the HED notation and the
proposed physical field structures.
Thus we have inferred the discrete field structures of the neutrino and
antineutrino. Next we check the neutrino structure by analysing the β+
process.
4.3
Beta+ decay and the neutrino (v) structure
Derivation of neutrino structure
β+ decay, also called positron emission, occurs in proton rich nuclei and
involves the conversion of an energetic proton into a neutron, antielectron
(positron) and neutrino:
p + energy => n + e + ve
We represent this in HED notation to derive the structure of the neutrino.
First, we note that the addition of energy, in the form of a photon, does
not change the HED structure but simply puts more energy into the
system, hence higher frequency:
p(r1. 11 .a1 .t1) + y(r!.a.t) => p(r1. 11 .a1 .t1)|+
where |+ denotes an energetic state and y is a photon. Then we add
incipient hyffon pairs to accommodate the known requirements for the
neutron. We are unsure at this stage whether to add a full set of hyff, or a
single twin, hence the optional designation (↑↑or↓) (Ma.6.7.6). We also
include a colour change |%:
p(r1.11 .a1 .t1)|+% => O(r1.1..a11.t1↑)(↑↑or↓)
=> O(r1.1..a11.t1.11) (↑↑or↓)
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Extract the neutron:
P => n(r .a11 .t11)
+ O1(r1.1 .a. .t.1.)(↑↑or↓)
Add incipient hyffon pairs in preparation for the antielectron. Note that we
have added a full set of pairs now, i.e. we decided to use (↑↑ rather than
↓:
p => n + O1(r1.1↑ .a↑ .t.1.) => n + O1(r1.1.11 .a11 .t.1.)
Extract the antielectron, and place the remaining hyffons into a secondary
composite structure, O2:
p => n(r .a11 .t11) + e(r1 .a1 .t1) + O2(r1.11 .a1 .t)
Identify the O2 as the neutrino:
p => n(r .a11 .t11) + e(r1
.a1 .t1) + v(r1.11 .a1 .t)
Rearrange the hyffons for the free neutrino:
Neutrino v = v(r1.1 1.1 .a .t)
This is consistent with the outcome from the β- analysis.
Explanation for the input energy
An interesting feature of this model is that it gives another explanation of
why the β+ process involves extra energy at the outset. If we aggregate all
the incipient hyffon pairs into a superstructure then we obtain:
p|y% => O(r1.1↑..a1↑1.t1↑) => n + e + v
The interesting part is the substructure with the hyffon pairs:
O3(r↑..a↑.t↑) => O3(r11.a11.t11)
We recognise this O3(r11.a11.t11) structure from the annihilation model for
positronium: it is equivalent to two photons, see Ma.4.2 [10]. It has
vertical separation of the hyffons by hand, and thus the potential to create
an independent electron and antielectron, which can exist enduringly
(hence require energy).
This confirms that input energy is required for the β+ process. Thus we can
explain why additional energy is required. Moreover, we now have an
explanation for exactly how that energy feeds into the process: it creates
new hyffon field structures.
Comparison with β- decay
By comparison the β- process has an aggregated superstructure of:
n => O(r1.1↑1 .a↓↑. .t1↓) => p + e + v
The substructure with only the hyffon pairs is:
O3(r↑ .a↓↑ .t↓) => O3(r11.a1.11.1.t11)
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This does not correspond to photons, but is instead a set of balanced pairs
of hyffons. There is no vertical separation of the hyffons by hand, so the
structure cannot form stable particules, and consequently it needs no
permanent energy allocation.
4.4
Electron capture
In electron capture a proton absorbs an electron and converts to a
neutron, emitting a neutrino. This occurs in nuclei that have more protons
than required for a stable state. Representing this in HED notation:
p + e => n + v
p(r1.11 .a1 .t1) + e(r1 .a1 .t1) => O(r1.11.1.a11.t11)
=> n(r .a11 .t11) + O1(r1.11.1.a...t..)
=> n(r .a11 .t11) + v(r1.11.1.a...t..)
So the neutrino emerges as before. The method correctly identifies that it
is the neutrino rather than antineutrino that is involved.
Electron capture may involve one of the atom's own inner electrons, in
which case there may be a cascade of consequences as the other electrons
adjust, and this may result in a photon being emitted or an electron (Auger
electron).
Electron capture is known to occur when there is insufficient energy for
decay via positron emission. We have already explained why β+ decay
requires more energy - it needs a net increase in field structures to form
the antielectron. The bigger open question is then: Why does the decay
not always prefer the electron capture route?
The answer may be that the electron capture conserves the total mass of
the atom, whereas β+ decay is a way of achieving all those some outcomes
and also getting rid of unwanted energy in the process. We have
encountered a similar idea elsewhere in the cordus conjecture: that a
structure that cannot contain the energy it is given is in trouble if it cannot
find a way to get rid of it, hence also photon emission.
4.5
Alpha decay
Alpha decay involves a cluster of two protons and two neutrons (i.e.
helium nucleus) being ejected from a larger nucleus. It does not involve
neutrinos, and it is easy to see why: it does not involve any internal
reassembly of the protons or neutrons. It is primarily a decay caused by
instability of the bonds within the nucleus. In terms of the cordus
explanation both the strong interaction (or residual strong force) that
binds the nucleons, and the weak interaction (W and Z bosons) are
different manifestations of the a single HED mechanics.
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5
Discussion
5.1
What has been achieved?
We have used the beta decay outcomes to determine the HED field
structure of the antineutrino:
Antineutrino: v = v(r11 .a .t11) etc
And the neutrino:
Neutrino v = v(r1 1 .a .t11) etc
We propose the structure is dynamic, and that several variants may exist.
All of these variants have the same number of hyffons: two negative and
two positive, of 1/3 charge each. The cordus structure of the neutrino is
therefore neutral regarding charge. We can now use this information to
explain other behaviours of the neutrino.
HED notation for common particles
The HED notations for several common particules are given below.
Matter (forma)
Electron e(r1 .a1 .t1)
Antimatter (hyarma)
Antielectron e(r1 .a1 .t1)
Proton p(r1.11 .a1 .t1)
Antiproton p(r1.1 .a11 .t1)
Neutron n(r .a11 .t11)
Antineutron n(r .a11 .t11)
U Quark u(r1 .a1 .t)
Charge +2/3
D Quark d(r1 .a .t)
Charge -1/3
Neutrino
v(r1 1 .a .t11)
AntiU Quark u(r1 .a1 .t)
Charge -2/3
AntiD Quark d(r1 .a .t)
Charge +1/3
Antineutrino
v(r11 .a .t11)
Photon y(r! .a .t) or y(¦r¦ .a .t)
The photon has no hand
We provide, in the HED concept, a physical and geometric interpretation
for the QCD concept of ‘colour’. Existing quantum theory depends on the
0D point-construct and denies the existence of internal structures to
particles. Hence it cannot conceive of a physical interpretation to an
internal variable such as ‘colour’, so it remains only an abstract
mathematical concept. Cordus manages to ground the concept back into
the physical domain.
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5.2
Implications
Neutrino not its own antiparticle
The first implication is the neutrino is not its own antiparticle. The reason
is that it cannot be converted to an antineutrino solely by the addition of
↑or ↓ hyffon-antihyffon pairs.
Thus the neutrino is not a Majorana fermion. By implication neutrinoless
double-beta decay will not occur by annihilation. The idea behind
neutrinoless double-beta decay is that two neutrons decay
simultaneously, producing two antineutrinos. If one antineutrino was able
to spontaneously convert into a neutrino, then perhaps the two might
annihilate, hence neutrinoless decay. This is currently an area of active
research for physics, partly because it may allow the mass of the neutrino
to be determined. Cordus suggests that the mutual annihilation pathway is
verboten, though this does not preclude other ways of disposing of the
antineutrinos.
Neutrino speed
We can anticipate why the neutrino travels at the speed of light. A
neutrino structure of v(r1.1 1.1 .a .t) or v(r1 1 .a .t11) does not have hyff in all
HEDs, and therefore does not meet all the stability criteria. Its only option
is to move on the fabric [11]. This is the same basic model for how the
photon moves [8]. We suggest that the neutrino fills its [a] axis by
interacting with the hyffons of the fabrics, thereby obtaining a dynamic
stability. A comparison of the photon and neutrino HED structures is
shown in Figure 4.
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Figure 4: The cordus HED structures for the photon and neutrino. In both
cases there are unfulfilled HEDs, and it is proposed that this feature drives
the movement of these particules, though we acknowledge that the
specific mechanisms are still sketchy.
This also implies that the speed of the neutrino will be dependent on the
density of the fabric. In particular, it should slow down in locations where
gravitation is stronger or matter is denser. Hence the neutrino appears to
show refraction-like behaviour in matter. The Mikheyev–Smirnov–
Wolfenstein effect, whereby the oscillation of neutrinos between
generations is different in matter and the vacuum [12], may have a related
causality.
Spin-hand
The neutrino is only left-spin-handed. This is strange, because it is the only
fermion with this property. All neutrinos are left-spin-handed, and all
antineutrinos are right-spin-handed, or at least that is what empirical
results suggest. In a QM context left-hand means that the spin of the
particle (by the right-hand grip rule) is in the opposite direction to the
motion. We use the term ‘left-spin-hand’ to show that the concept is
related to spin, not the ma-hand [1].
Plain ‘spin’ is an overloaded concept that should not be used without
clarification. To explain the neutrino spin-hand, we first need to
reconceptualise 'spin'. In this particular case we interpret the neutrino
'spin' as angular momentum, SPIN-M. This suggests that the neutrino
always and only has angular momentum in one direction, and the
antineutrino in the other. With the cordus model we can start to see why.
Quantum mechanics recognises that particles have intrinsic angular
momentum, even when stationary. Cordus provides a physical
interpretation of the particule spinning on the spot. Furthermore, that
spinning is driven by the energisation sequence, which in turn is linked to
the ma-hand.
Unlike the photon which has no ma-hand, the neutrino has a ma-hand, i.e.
it has an energisation sequence for its hyff. Nominally the sequence is [r],
[a], [t], and these axes are arranged in the forma hand, with the
antineutrino taking the hyarma hand. The peculiar spin arrangements of
the neutrino and antineutrino arise because of the combination of three
factors: the need for the particule to spin, its need to move in the [a]
direction, and the handedness of the energisation sequence of the HEDs,
see Figure 5.
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Figure 5: The cordus spin model for the neutrino and antineutrino. In both
cases the particule needs to move (for stability) and therefore its spin is
limited to the [r,t] plane. The ma-hand, which distinguishes between
matter and antimatter, controls the energisation sequence of the HEDs,
and hence the direction of spin. Thus, unlike other particules that are stable
when stationary, the neutrino species have their spin direction determined
by their ma-hand.
Thus it is proposed that the spin of the neutrino works like this: the
energisation of the HEDs creates a spin (SPIN-M). However the stability
requirement forces the neutrino to move: we nominally reserve the axial
[a] axis for that. Therefore the spin is constrained to the [r,t] plane. The
forma hand constrains that spin to be clockwise (i.e. left-spin hand).
The antineutrino spins in the opposite direction, anticlockwise or rightspin-hand for the same reasons. It is the change in hand, from forma to
hyarma, that creates this difference.
Cordus predicts that we would see a similar spin effect in other particules,
except that none move at the speed of light and therefore are not
constrained to arrange their spin relative to their motion, or keep the [a]
axis free for motion. The only other particule that moves at c is the
photon, and it does not have any hand and therefore the effect does not
arise there at all.
The explanation and the diagram were given in terms of the v(r1 1 .a .t11)
HED variant. What happens with other variants such as v(r1.1 1.1 .a .t)? We
cannot be entirely sure, but there does not seem to be any reason why the
explanation would not still hold. We acknowledge that we have not
detailed the yet deeper mechanisms for how spin arises, but it is clear
enough that spin does arise.
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This cordus model therefore predicts that neutrinos are all left-spinhanded, and that there are no right-spin-handed neutrinos or left-spinhanded antineutrinos. If this is true, then it would have serious
consequences for those theories that depend on such particles.
Neutrino mass
The cordus model for gravitation is that the sequential energisation of the
HEDs creates a torsional pulse that is transmitted outwards, and this
creates gravitational attraction [6]. Activation of the three HEDs seems
necessary for an enduring mass or gravitational effect. The neutrino does
not have the necessary complete HEDs to offer its own gravitation: a
similar situation to that of the photon.
Therefore the gravitation part of the cordus model predicts that the
neutrino has no nominal mass, based on its lack of the necessary
structures. The stability part of the cordus model also predicts a massless
neutrino, based on its speed being that of light.
However, ‘mass’ may not be everything that it seems to us. In particular,
both the photon and neutrino make up for their incompletely energised
HEDs by moving in the fabric. Thus they temporarily do have full HEDs,
albeit only instantaneously. Therefore it is possible that they also do have
an instantaneous mass and gravitation. While it may register as mass, it
would however not be an enduring mass. We conceptualise it rather as
noise-mass, i.e. an artefact of the propagation process. So it is possible to
conceive of the neutrino having zero nominal mass, though a small
dynamic localised noise-mass.
This may sound weird, but the MSW effect [12] predicts something similar:
it models the situation as the neutrino obtaining an ‘effective mass’ (by a
‘forward scattering’ process) when propagating through matter.
Cordus is more radical still, in suggesting that 'mass', 'gravitation' and
'gravitational trajectory-bending' could be subtly independent effects [8].
Specifically, with the cordus conjecture it is possible to envisage
gravitational bending of the neutrino locus occurring without the particule
needing to have mass of any kind. The gravitational bending might instead
be explained as the gradient in the fabric density near a large mass,
the same explanation as previously given for the photon [8]. The fabric is
slightly denser on the side of the neutrino nearest the mass, so a
frequency cycle on that side accomplishes a slightly lesser displacement,
i.e. the speed of light is slightly slower, thus bending the trajectory.
Furthermore, neutrinos are thought to exhibit refraction-like behaviour in
their passage through matter. This cordus model readily accommodates
this refraction, i.e. neutrinos should slow down in denser materials.101
101
Superluminal neutrinos are not naturally predicted by cordus, but it could nonetheless
accommodate them. One possible cordus explanation is tunnelling at generation change
(i.e. skipping interactions when there is no activity in the particule). Another might be an
initial transient non-orthogonality between the [r][t] plane and the direction of
propagation. These might be transients caused by the creation mechanism, i.e. the
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Trajectory-bending reconceptualised as a non-mass effect
Thus mass may not be required for trajectory-bending effects. Indeed,
optical refraction is a trajectory-bending effect that does not require the
photon particule to have mass, though it is dependent on the density
(including gravitational field) of the fabric medium.
Reconceptualising the trajectory-bending of neutrinos as a fabric effect
rather than gravitation is unconventional. This has the profoundly radical
implication that the vacuum-speed of light is variable, i.e. that the speed
of light is not only dependent on the amount of matter that it passes
through, the absence of which is conventionally the 'vacuum', but on the
gravitational fields from neighbouring areas. Thus cordus also upsets the
orthodox idea of 'locality' [5]. By comparison, physics currently
conceptualises the speed of light as only determined by the local density
of matter, and hence invariant in the vacuum. Cordus suggests the
vacuum-speed of light is not invariant, but dependent on the density of
the fabric. The fabric is the irregular mesh of background hyffons of
(potentially) all the other particules in the universe [11]. This also gives a
better model for time, and is consistent with the observation that time
runs slower (dilation) for bodies that are accelerating or in higher
gravity.102
Why are neutrinos so unreactive?
The cordus explanation for why neutrinos react little with matter is that
their frequency is too low. That plus their motion. Reactivity between
particules requires that their reactive ends be in the same place and
phase at a moment in time. The fast motion of the neutrino, and the
presumed relatively large span of its cordus (span is inversely related to
frequency or mass [13]) makes co-location difficult. In a similar way longwavelength radio waves have greater penetration (less engagement with
matter) than visible light.
What happens in neutrino detectors?
The neutrino detectors are, according to the cordus interpretation,
operating by an occasional impact of a neutrino (or antineutrino) into a
proton or neutron. The injection of its hyffons into the target creates a
temporary assembly structure which subsequently decays. It is those
decay products that are detected.
neutrino settles down later. Or it may simply be that the neutrinos are released late in the
process. There could be other explanations, since moving away from the 0D point premise
opens up a lot of other alternatives. However it is too early to be definitive as the empirical
evidence is limited.
102
Cordus explains this as the reactive ends of the particules in the body encounter the
fabric at a greater rate (acceleration) or density (higher gravity). For a moving particule like
the neutrino in a gravitational field, this means that it progresses a smaller displacement
along its trajectory at each frequency cycle. For a stationary particule in higher gravitation,
the increased fabric density compromises the hyff emission process and slows the reenergisation of the reactive ends, which then slows the frequency of the cordus.
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Differentiation between neutrino and neutron
The neutrino and neutron have nominally similar HED structures:
Neutrino v(r1 1 .a .t11)
Neutron n(r .a11 .t11)
Both have two hyffons of each charge. Furthermore, we have already
anticipated that hyffons may change to free HEDs. So what is the
fundamental difference between these two particules?
One difference is obviously the mass. Our current working model is that
the neutron is a complex assembly that includes hidden internal hyff that
we do not see overtly externalised, but which nonetheless contribute to
the propagation of external EMG hyffons (Ma.6.9). This explains why the
neutron has a higher frequency and mass than the neutrino despite the
same nominal HED structure.
The neutrino is, by comparison, a minimalist particule: it has the cordus
structure and a functional ma-hand system, but not a lot of energy. It is
possible, though not our currently preferred working model, that adding
energy to the neutrino might convert it into a neutron. Instead we suspect
that the neutrino is making a complete disclosure of all its hyffons, and no
amount of additional energy would make it into a neutron.
From the cordus perspective, a fundamental particule is one that overtly
displays all its hyffons. Examples would then be the photon, electron, and
neutrino, for the matter (forma) hand. Assembly particules can cloak their
balanced hyffons and thus appear to have greater frequency and mass
than their external HED structure suggests. Examples would be the quarks,
proton, neutron, and all higher assemblies thereof. So in the cordus
interpretation the quark is probably not a fundamental particule, but can
be expected to have a deeper sub-structure.
Do neutrinos decay?
Neutrinos do not decay in the standard model, but they are predicted to
do so in the extended model: the hypothetical right-handed neutrinos
decay to electrons. This provides an asymmetric leptogenesis model, and
then another hypothetical particle called the ‘sphaleron’ converts the
leptons to bayons, and hence the asymmetry predominance of matter
over antimatter. However these mechanisms are highly speculative.
Nonetheless the interest in neutrinos is high because of the potential to
answer the bigger questions about the asymmetry of baryogenesis.
We do not support the concept of neutrino decay in the current cordus
working model, though we acknowledge that it is not precluded either. In
particular, the present cordus model explains the speed of the neutrino as
a consequence of its incomplete stability: it is a compromise for an
incomplete deck of HEDs. By implication, an arrested neutrino would no
longer have that compromise mechanism available, and would decay.
However 'decay' is perhaps not the right word, because the process of
fully arresting the neutrino (as opposed to merely slowing it down in a
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strong field) would require that it be captured by another particule. In
which case the neutrino would inject its hyff into that new assembly, and
new daughter products would form. Hence the detection methods.
However we doubt that the free neutrino would ever decay (unlike the
neutron).
Neutrino oscillation
Our current working model for neutrino oscillation is that it is a phasechange in the way the discrete field structures are energised, and the
frequency (hence mass) required to sustain the HEDs. If so, the structures
of the generations are:
ve(r1 1 .a .t11); vμ(r1.1 1.1 .a .t); vτ(r1.1 .a .t1.1)
Similarly for antineutrino. Note that the [a] axis is reserved for
propagation, so it is only the [r] and [t] axes that have hyffons. Across
these two axes there are indeed only three possible arrangements. The
oscillation could conceivable be due to dynamic transient effects at
formation of particule, or subsequent interaction with energetic fabric
medium.
Implications for fundamental physics
It has long been thought, even in the orthodox paradigm of physics, that
better understanding of the neutrino might test the theoretical validity of
the standard model of particle physics, and perhaps even lead to a
different physics. Indeed, if the cordus conjecture is correct, the
implications are that neutrinos do indeed point to a deeper physics, but it
appears not to be an extension of quantum mechanics or of the standard
model, but rather a turn in an unexpected direction.
With this cordus model we can now suggest answers to some of the
neutrino riddles raised at the beginning of this paper.
Why do neutrinos exist?
They remove excess field structures from assemblies of particules
so that they can convert into other types of particules, e.g. the beta
decays convert between neutrons and protons.
Do neutrinos have mass?
They do not have the necessary structures to create a gravitational
field, and hence do not have mass either. However they may have
a small dynamic mass (noise-mass).
Why are neutrino trajectories bent by gravity?
The bending occurs due to the gradient in the density of the fabric,
not the mass of the particule. Controversially, this explanation
requires that the speed of light in the vacuum is not constant, but
determined by the fabric-density.
Why are neutrinos so difficult to measure?
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Their frequency is so low, and their speed so high, that they seldom
have opportunities to meet other matter particules. (Macroscopic
objects are not continuously solid). Interaction requires that the
HED field structures of the two particules be in the same space and
time, and of compatible frequencies. The neutrino is more likely to
use any HEDs it encounters for its propulsion rather than stop and
interact.
Why do neutrinos travel at the speed of light?
They have incomplete field structures and have to compensate by
moving on the fabric of spacetime, the relativistic speed of which is
c.
Why are neutrinos left handed?
They have to both move and spin, and this leaves only one
direction in which they can spin. This spin direction is fixed by the
matter-antimatter chirality called ma-hand.
Could right-handed neutrinos exist?
Probably not. It is not obvious how these could exist in the cordus
model.
Is the neutrino its own antiparticle?
No, this is verboten in the cordus model.
What is behind CP violation?
It is a consequence of every particule having a span, and its two
reactive ends being energised in turn. Therefore what happens at
one reactive end is not a mirror image of the other. However this
only becomes apparent at small scales: at the coarser scale of
quantum mechanics the particules do look like points.
Future work
The cordus concept of hyff emission directions (HEDs) also provides a
discrete field theory,103 which is coherent across small-scale effects like
annihilation and wider effects including gravitation. By comparison,
quantum field theory and quantum chromodynamics are more advanced
in their mathematical formalisms, but lacking in physically realistic
interpretations, and more narrowly focussed. The quantum theory
undoubtedly works, whereas the cordus solution is simply conjectural. If
cordus really does point to a deeper mechanics and a new physics, then it
would be expected to subsume much of the quantitative machinery of
quantum mechanics, and checking this could be a line of future work.
Further work that we have already undertaken is to identify the internal
structures of the W and Z bosons, and hence better understand the weak
interaction [work in progress].
103
We use the term ‘discrete’, and avoid ‘quantum’, because the hyffons are not required
to be in quantum increments.
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There is further work to be done in exploring the mechanisms at the next
deeper level of physics, e.g. spin, and the reactive ends. Furthermore we
have not fully explained the difference between the neutron and neutrino,
but only given a general suggestion that the neutron has cloaked field
structures that we are not seeing. Clearly this requires more work.
6
HED lemmas
We made several assumptions for how the hyffons behave in the HEDs,
and these are summarised below as a set of lemmas.
Ma.6
HED (hyff emission direction) dynamics
Ma.6.1
Ma.6.1.1
Ma.6.1.2
Ma.6.1.3
Ma.6.1.4
Ma.6.2
Ma.6.2.1
Ma.6.2.2
Ma.6.2.3
Ma.6.2.4
Ma.6.3
Ma.6.3.1
A particule’s HED structure determines its functionality.
For example the electron is uniquely different to the
antiproton in HED notation.
The HED structure refers to the (a) hand of the
hyff emission directions, (b) the number of active
hyffon pulses in each HED, and (c) the direction
(charge) of those hyffons.
The cordus particule concept applies to what are
conventionally considered ‘fundamental particles’
as well as assemblies thereof, providing the latter
are in coherence i.e. have synchronised
frequencies. The proton is considered such an
assembly.
Particules may have oppositely charged hyff that
neutralise each other internally, and therefore are
not expressed externally as charge. These are
nonetheless expected to contribute to mass. See
also Ma.6.7.
The quantum chromodynamic (QCD) concept of
‘colour’ corresponds to the selective energisation
of the [r], [a], and [t] HEDs, where the HEDs are
not all full.
Any HED may have multiple hyffons, at least temporarily.
These multiple hyffons may be opposite charge.
These multiple hyffons may even have opposite
ma-hand.
A hyffon and an antihyffon (opposite hand and
opposite charge) in the same HED, e.g. r11, do not
generally reduce to zero.
An exception is that O(r11. a11. t11) reduces to two
photons, or an electron and antielectron, see also
Ma.4.2.) See also Ma.6.7.3 for another exception.
Hyffons may move: Colour migration
A hyffon (active field structure) can migrate to
another vacant HED, e.g. o(r1 .a1 .t) => o(r1 .a .t1).
368
Ma.6.3.2
Ma.6.3.3
Ma.6.3.4
Ma.6.4
Ma.6.4.1
Ma.6.4.2
Ma.6.4.3
Ma.6.5
Ma.6.5.1
Ma.6.5.2
Ma.6.5.3
Ma.6.5.4
Ma.6.5.5
Ma.6.5.6
Ma.6.6
Ma.6.6.1
It can do this dynamically.
This corresponds to colour change.
Pairs of hyffons may likewise move.
Principle of HED negotiation: reactive ends, whether single
or when bonded between particules, negotiate hyff
emission directions dynamically.
‘Negotiation’ means that change to a HED at one
reactive
end or particule
requires
a
complementary change in the other HEDs in that
space.
We suggest the mechanisms is first-come-firstserved, i.e. the HED that energises first tends to
get the choice, and in turn that choice is
influenced by the spaces left by the HEDs that are
de-energising.
The QCD equivalent idea is the gluons, being the
mediators of colour change among quarks.
However we do not accept the point-particle
interpretation that QCD gives to gluons.
Bonding as a shared HED effect
The HEDs and hyffons of one particule can feed
into those of another particule, and this is
bonding.
The shared interlocking of HEDs is what creates
the force that holds the assembly together. This
force is strong.
However this force is also short-ranged, since
there are many other hyffons that will be
attracted into the union if the original
participating particules are pulled apart.
This force is better described as a constraint on
the positional re-energisation of the reactive ends.
They are forced to re-energise, i.e. emit HEDs, in a
location that is consistent with the generally
negotiated HED environment.
This mechanism underpins the strong interaction
(force), Pauli exclusion principle, and bonding
generally.
The particules may negotiate common frequencies
(the same frequency or a harmonic), to create
coherence. Alternatively they may dynamically
form fluid bonds with a changing dance of other
particules.
Principle of conservation of hyff in assembly and
disassembly.
Two particules may assemble into one, by merging
their HED structures. Disassembly occurs as the
369
Ma.6.6.2
Ma.6.6.3
Ma.6.7
Ma.6.7.1
Ma.6.7.2
Ma.6.7.3
Ma.6.7.4
Ma.6.7.5
Ma.6.7.6
Ma.6.7.7
reverse process. Assembly and disassembly are
therefore primarily HED processes.
The total number of active hyff, i.e. hyffons,
owned by input particules is conserved across the
output particules, unless annihilation occurs. See
also Ma.3.8 [10].
Charge is preserved in assembly and disassembly.
In HED notation, this means that the hyffon sums
above and below the line must also be preserved.
(Conservation of charge is a common assumption
in physics).
Charge-neutral and hand-neutral twin-pairs of hyffons
may be added to, or removed from HED assemblies.
A hyffon-antihyffon twin-pair, x↑↓ = x11 + x11 =
x1.11.1 may be created in any single HED position,
[r], [a], or [t], or split across multiple.
These pairs are charge neutral, and do not change
the net number of hyffons (hence not violating the
conservation principle), though do change the
gross number and thus permit access to other
output states. They are a type of fibrillating pump
like the photon [8], but offset across the span of
the cordus. They are also hand-neutral.
The twin-pair x1.11.1 may be removed from an
assembly.
The twin-pairs are created or destroyed at the
same time. However for convenience we
sometimes show them as being applied at slightly
different times during an assembly process.
The difference in orientation (x↑ = x11 or x↓ = x11)
is interpreted as corresponding to one form of
spin: SPIN-H, the orientation of hyffon pairs within
a particular HED. The neutral-hand requirement
thus infers that SPIN-H must be zero for the added
hyffons, i.e. ↑ must numerically balance ↓.
A notable exception is that a whole increment of
three pairs all in the same direction, i.e. r↑ a↑ t↑
corresponds to two photons, or an electron and
antielectron. Thus these HED structures may be
created or destroyed.
These ↑ or ↓ pairs are spontaneously formed
during the HED negotiation processes. The
addition of hyffon-antihyffon pairs is presumed to
be initiated either by the difference in energy
between the assembled and dissembled states
(i.e. the native tendency to decay), or the fabric
pressure (this latter effect may have some
similarity with vacuum fluctuations). 104
104
This is consistent with conventional physics. For example: 'After a high energy collision, a quark or
gluon starts to move away from the rest of the formerly color-neutral object that contained it. A region
370
Ma.6.8
Ma.6.8.1
Ma.6.8.2
Ma.6.8.3
Ma.6.8.4
Ma.6.8.5
Ma.6.9
Ma.6.9.1
Ma.6.9.2
Ma.6.9.3
Ma.6.9.4
Ma.6.10
Ma.6.10.1
Ma.6.10.2
Assemblies, which we denote as O particules, may be
created by the merging of particules, the breakdown or
subdivision of parent particules, or the addition of hyffonantihyffon twin-pairs.
These assemblies may be transitional intermediate
structures as part of a process of
assembly/disassembly, or stable structures.
An Intermediate (O) structure may be overloaded
with hyffons.
Also, it can accept hyffons of both hands, though
this tends to make it unstable.
These transitional assemblies may subsequently
separate to different hyffon arrangements, hence
different particules.
These transitional assemblies have the ability to
create further hyffon-antihyffon twin-pairs and
partition off another structures.
Cloaking and disclosure of hyffons.
Assemblies of particules may include hidden
internal hyff that we do not see overtly
externalised in the HED notation. These
nonetheless contribute to the propagation of
external EMG hyffons, and therefore to higher
frequency and mass. Examples are the quarks,
proton, neutron, and all higher assemblies
thereof.
A fundamental particule is one that overtly
displays all its hyffons. Examples are the photon,
electron, and neutrino, for the matter (forma)
hand.
Assembly particules can cloak their balanced
hyffons and thus appear to have greater frequency
and mass than their external HED structure
suggests.
All discrete field structures of a particle, whether
a fundamental particule or an assembly, and
whether those are externalised or internally
cloaked hyffons, contribute to the fabric. These
hyffons all need servicing and hence a frequency
requirement arises, hence mass.
Neutrino HED structure
Neutrino v(r1 1 .a .t11)
Antineutrino v(r11 .a .t11)
of color force-field is produced between the two parts. The energy density in this color force fields is
sufficient to produce additional quarks and antiquarks. The forces between the color-charged particles
quickly cause the collection of quarks and antiquarks to be rearranged into color-neutral combinations.
What emerges, far enough from the collision point to be detected, is always a collection or jet of colorneutral hadrons, never the initial high-energy quark or gluon alone.'
http://www2.slac.stanford.edu/vvc/theory/colorchrg.html#Confinement
371
Ma.6.10.3
Ma.6.10.4
Ma.6.10.5
Ma.6.10.6
7
The [a] axis is reserved for propagation, so it is
only the [r] and [t] axes that have hyffons.
The neutrino has zero nominal mass, but a small
dynamic localised noise-mass through its
engagement with the fabric.
Generational change (neutrino oscillation) is a
phase-change in the way the discrete field
structures are energised. Some layouts require a
higher frequency (hence mass) to sustain the
more complex HEDs. If so, the structures of the
generations are:
The generations of the neutrino are assumed to
be: ve(r1 1 .a .t11); vμ(r1.1 1.1 .a .t); vτ(r1.1 .a .t1.1), and
similarly for the antineutrino. Note that the [a]
axis is reserved for propagation, so it is only the [r]
and [t] axes that have hyffons. Across these two
axes there are indeed only three possible
arrangements.
Conclusions
The cordus mechanics, particularly the HED notation, have been used to
infer the discrete field structures of the neutrino and antineutrino. The
structure of the neutrino in HED notation is found to be v(r1 1 .a .t11) or
variants thereof, and the antineutrino to be v(r11 .a .t11) etc. The results are
consistent whether using beta - decay, beta +, or electron capture. A
tentative explanation is given for the three generations of neutrinos. The
neutrino structure is nominally identical to that of the neutron. A partial
explanation is given for where the deeper differences may lie.
The results suggest that the neutrino is not its own antiparticle, and has
zero nominal mass, though a dynamic noise-mass is possible. The reasons
why the neutrino moves at the speed of light are explained in terms of
how its field structures, which are incomplete, engage with the fabric
(spacetime). The gravitational bending of its trajectory is explained, even
for a massless neutrino, by abandoning both locality and the invariance of
the vacuum speed of light. The model also explains why neutrinos are
always found with left-spin-hand, and antineutrinos with right, and
suggests that the opposite structures are fundamentally unavailable.
References
1.
Pons, D.J.: Mirror images: Cordus reconceptualisation of Matter and
Antimatter. viXra, 2011, v. 1109.0009, 1-15 DOI:
http://vixra.org/abs/1109.0009. Available from:
http://vixra.org/pdf/1109.0009v1.pdf.
2.
Murayama, H.: Origin of Neutrino mass. Physics World, 2002, May: p. 3539. http://hitoshi.berkeley.edu/neutrino/PhysicsWorld.pdf.
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3.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Cordus
Conjecture: Overview. viXra, 2011, v. 1104.0015, 1-17 DOI:
http://vixra.org/abs/1104.0015. Available from:
http://vixra.org/pdf/1104.0015v1.pdf.
4.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: WaveParticle Duality: a Proposed Resolution. viXra, 2011, v. 1106.0027, 1-18
DOI: http://vixra.org/abs/1106.0027. Available from:
http://vixra.org/pdf/1106.0027v1.pdf.
5.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Wider
Locality. Cordus matter: Part 3.1 viXra, 2011, v. 1104.0022, 1-7 DOI:
http://vixra.org/abs/1104.0022. Available from:
http://vixra.org/pdf/1104.0022v1.pdf.
6.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Gravitation,
Mass and Time. Cordus in extremis: Part 4.3 viXra, 2011, v. 1104.0029, 114 DOI: http://vixra.org/abs/1104.0029. Available from:
http://vixra.org/pdf/1104.0029v1.pdf.
7.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Quarks.
Cordus in extremis: Part 4.4 viXra, 2011, v. 1104.0030, 1-15 DOI:
http://vixra.org/abs/1104.0030. Available from:
http://vixra.org/pdf/1104.0030v1.pdf.
8.
Pons, D.J.: Contrasting internal structures: Photon and electron. viXra,
2011, v. 1109.0045, 1-9 DOI: http://vixra.org/abs/1109.0045. Available
from: http://vixra.org/pdf/1109.0045v1.pdf.
9.
Pons, D.J.: Annihilation mechanisms: Intermediate processes in the
conversion of electron and antielectron into photons viXra, 2011, v.
1109.0047, 1-21 DOI: http://vixra.org/abs/1109.0047. Available from:
http://vixra.org/pdf/1109.0047v1.pdf.
10.
Pons, D.J.: Cordus process diagrams: Symbolic representation of
annihilation mechanics. viXra, 2011, v. 1109.0068, 1-14 DOI:
http://vixra.org/abs/1109.0068. Available from:
http://vixra.org/pdf/1109.0068v1.pdf.
11.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Fabric of the
universe. Cordus in extremis: Part 4.2 viXra, 2011, v. 1104.0028, 1-8 DOI:
http://vixra.org/abs/1104.0028. Available from:
http://vixra.org/pdf/1104.0028v1.pdf.
12.
Wolfenstein, L.: Neutrino oscillations in matter. Physical Review D, 1978,
17(9): p. 2369-2374. http://link.aps.org/doi/10.1103/PhysRevD.17.2369.
13.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Matter
particuloids. Cordus matter: Part 3.2 viXra, 2011, v. 1104.0023, 1-12 DOI:
http://vixra.org/abs/1104.0023. Available from:
http://vixra.org/pdf/1104.0023v1.pdf.
373
Weak interaction: Reassembly of particules
Pons, D.J. 105
Abstract
The Standard Model interprets the weak interaction, e.g. neutron beta
decay, to be a short-range field carried by the W and Z bosons. In that
interpretation the short range arises because of the heavy mass of the W
and Z bosons. This paper reconceptualises the weak interaction and the
bosons. The cordus HED notation was used to work out the field structures
of the bosons, giving W-(r.1.1 .a.11.1 .t11) and W+( r1.1. .a1 .t). The theory
suggests that there is no single Z boson, but several varieties. Cordus
suggests that the W and Z bosons do not exist in the form of 0D point
particles with static characteristics, but instead are complex structures
undergoing dynamic assembly and disassembly processes. The
conventional concept that the bosons change the flavour of the quark is
questioned. Instead the model shows that the bosons not the cause or the
mechanism for the change, but merely the by-products and waste process
stream from the conversion process. The neutrino-antineutrino annihilation
process is modelled and predicted to result in either an electron-positron
pair and two photons, or four photons.
Edition 1 > Date: Saturday, 11 February 2012 > Document: Pons_cordus_5.7_WeakInteraction_E1.0.20.doc
1
Introduction
A companion paper has identified the structure of the neutrino and
antineutrino [14], particularly the discrete field structures. This was
achieved by analysing the beta decay processes.
This paper extends the concepts to the broader set of reactions in which
the neutrinos are involved. The structure of the W and Z bosons is
identified, and a conceptual model started for decay processes in general.
These explanations are given in terms of the cordus conjecture [13].
2
Background
Weak interaction
The weak interaction is fundamentally one of neutrinos involved in the
process of decay of particles. The Standard Model proposes that the weak
interaction is carried by W and Z bosons: W+, W− and Z (neutral).
The emission or absorption of a W+ or W− boson changes the electric
charge and spin, and changes the quark flavour type. The Z boson does not
change the charge, hence ‘neutral current interaction’, but can change
105
Please address correspondence to Dr Dirk Pons, University of Canterbury, Christchurch, New
Zealand. Copyright D Pons 2011.
374
spin. The bosons, which have been inferred from experimental
observation, are heavy: they have mass much greater than the proton. The
Z boson decays into various different particle-antiparticle pairs, such as the
neutrino and the complementary antineutrino. Higher energy Z bosons
may decay into higher generation neutrino-antineutrinos, and have
shorter lives.
Cordus model for the neutrino
The cordus conjecture [3] proposes that the particle is not a zerodimensional point as orthodox physics assumes, but rather a two-ended
internal structure, which we call a ‘particule’.106
A particule has a field structure at each of its two reactive ends. This
consists of three hyff threads, one in each of three orthogonal axes [r], [a],
[t]. These threads extend out into space from the reactive end. When
energised, a hyffon pulse is transmitted along the thread, and hence the
field is discrete. Positive and negative charge correspond to the direction
of propagation of these pulses. The reactive ends are energised in turn at
the frequency of the particule. Extensions of this idea accommodate the
electric field, magnetism, and gravitation [6]. The hyff emission directions
(HED) have a hand, called ma to differentiate it from other hand-like
concepts in quantum mechanics, and this determines the matter and
antimatter species [1].
A new modelling method, called HED notation, was created to represent
these discrete field structures [10]. This was used to work out the
structures of the neutrino and antineutrino [14]:
Antineutrino: v = v(r11 .a .t11) etc
Neutrino v = v(r1 1 .a .t11) etc
In this notation x1 represents a -1/3 charge in the x axis in the matter hand,
x1 is +1/3 charge in matter hand, x1 is -1/3 charge in antimatter hand, and
x1 is +1/3 charge in antimatter. See Figure 1 for the equivalent physical
representation.
106
The cordus conjecture is that all particles, e.g. photons and electrons, have a specific
internal structure of a cordus, comprising two reactive ends, with a fibril joining them. The
reactive ends are a small finite span apart, and energised (typically in turn) at a frequency,
at which time they behave like a particle. When energised they emit a transient force pulse
along a line called a hyperfine fibril (hyff), and this makes up the field. We call this a cordus
‘particule’, and stress it is very different to the zero-dimensional point assumed by
conventional physics.
375
Figure 1: The cordus structure for the neutrino and antineutrino. The
diagrams show the spatial arrangement of the discrete field structures
(hyffons) in the three hyff emission directions (HEDS). The v(r1 1 .a .t11)
variants are shown, and other arrangements are considered possible via
colour-change. The diagram also shows how the unique spin directions
arise for these two particules. Note that the primary difference between
matter and antimatter is the ma-hand, which is the energisation sequence
of the HEDs.
We now extend the work to determine the field structures for the W and Z
bosons.
3
W and Z bosons reconceptualised
The standard model of QM explains all the beta decay effects as the
emission of a particle of one sort or another: the W-, W+, and Z bosons.
Bosons are also produced in proton-proton collisions. In these cases the
disassembly process has additional kinetic energy to consume, so higher
generation outputs become possible, and hence more complex output
combinations (channels). Now that we have a structure for the neutrino,
we can also model the boson behaviour.
3.1
W- boson
In the conventional description, β- decay causes a d quark in the neutron
to emit a W- boson and thereby convert into a u quark, to make a proton.
The W- boson then decays into an electron and an antineutrino. Thus
d=>u+W- followed by W- => e + v. We can readily model this in HED
notation [14] to work out the structure of the W- boson.
First, express the d quark in HED notation, and then by inspection add
charge-neutral incipient hyffon-antihyffon twin-pairs (x↑ = x11 and x↓ =
x11), see [14]. These pairs may be created in any HED position, [r], [a], or
[t]. They are applied where required to form the u quark structure. Then
expand these pairs to create a transitional assembly O:
d(r1 .a .t) => O(r↓1 .a↓↑ .t↑)
=> O(r11.1 .a1.11.1 .t11)
376
Next, partition out the hyffons for the known output, which is the u quark,
and relegate the residual hyffons into a secondary structure O1:
=> u(r1 .a1 .t) + O1(r.1.1 .a.11.1 .t11)
Then partition off the hyffons for the next most energetic output, which is
the electron. The residual hyffons are placed into another secondary
structure O2, which we recognise as the antineutrino:
=> u + e(r1 .a1 .t1) + O2(r.1 .a.11 .t1)
=> u + e + v(r.1 .a.11 .t1)
This model gives the W- boson as the O1 structure, i.e.:
W- = W-(r.1.1 .a.11.1 .t11)
This structure does indeed have a unit negative charge overall, but it
achieves that with a mix of hyffons of different hand (1 and 1), i.e. matter
and antimatter components. This amalgam structure would be highly
unstable, and this qualitatively describes why it decays so fast.
In the above model for the W- boson, we applied all the incipient hyffon
twin-pairs at the outset. However another possibility is that they are
applied in stages as required. In that case, there would not be a single
structure for the boson but rather an evolving structure. Either way we do
not favour the concept of a W- boson as a particle, but rather see it as a
dynamic process of hyffon re-arrangement.
2.2
W+ boson
A similar rationale gives the W+ boson as follows:
p => n + e + v
The equivalent quark structure is:
uud => udd + e + v
Now, consider only the one quark that changes:
+
u => d + W
Then add the charge-neutral incipient hyffon-antihyffon twin-pairs (↑ and
↓) required to form the d quark structure. Then expand these pairs to
create a transitional assembly ‘O’:
u(r1 .a1 .t) => O(r1↑. .a1 .t↓) => O(r1.11 .a1 .t11)
Extract the d quark and place the remaining hyffons in a secondary
structure O1:
=> d(r1 .a .t) + O1(r1.1. .a1 .t11)
This model gives the W- boson as the O1 structure, i.e.:
W+ = W+( r1.1. .a1 .t11)
This also has unit positive charge, but is also made of contrary handed
hyff. Similar comments apply as for the W- boson regarding poor stability.
377
3.3
Z boson
The Z boson is known to decay into various outcomes: electron-positron,
neutrino-antineutrino, or quark-antiquark. In HED notation these are as
follow.
Electron-positron
e(r1 .a1 .t1) + e(r1 .a1 .t1) => Z1(r11 .a11 .t11) => 2y
So that process is simply the positronium annihilation [9-10], and the Z
boson is identified as Z1(r11 .a11 .t11). This is indeed neutral.
Neutrino-antineutrino
The neutrino-antineutrino pair has the following structure:
v(r1.1 1.1 .a .t) + v(r1.1 1.1 .a .t) => Z2(r1.1 1.11.1 1.1 .a.t)
In this case the Z boson is identified as Z2(r1.1 1.11.1 1.1 .a.t). This is neutral
regarding charge, but is not the same as the Z1 boson.
U Quark-antiquark
The boson is determined as Z3:
u(r1 .a1 .t) + u(r1 .a1 .t) => Z3(r11 .a11 .t)
In this case the Z boson is identified as Z3(r11 .a11 .t), which is not the same
as the other Z bosons.
D Quark-antiquark
The boson is determined as Z4:
d(r1 .a .t) + d(r1 .a .t) => Z4(r11 .a.t)
Once again the Z boson, Z4(r11 .a.t), is not the same as the other Z bosons.
However, we expect that the quark is cloaking some balanced hyffons
internally [14].
From this we infer that there is not a single Z boson, but many specific
varieties.
3.4
The cordus interpretation of the W and Z bosons
Note that the W and Z bosons have not been directly observed: they are
only hypothetical particles. All that is observed is the debris trail, from
which the boson is inferred as the origin. But that inference requires a
theory, which is the standard model of quantum mechanics, and therefore
the bosons are primarily theoretical constructs. This is important to note,
because the W and Z bosons are commonly misrepresented as actually
existing. They only exist within the theoretical framework of the standard
model: they are artefacts of the theory, rather than observed particles.
From the cordus perspective the bosons are simply overloaded or
mismatched-hand dynamic structures. Either way, they are unstable. They
still have a cordus structure, so the standard model's interpretation of
them as 'particles' is legitimate, even if somewhat limiting. They are not so
378
much particles with distinct static identity that cause change in quarks, as
dynamically changing waste streams.
Why are the bosons so heavy?
From the cordus perspective the reason they have high mass is that their
fibrils need a very high frequency to service the overloaded hyffons. That
implied extra energy is perhaps momentarily extracted from the fabric.
Either that or the presence of so many hyffons creates a greater
gravitational effect for the same fundamental energy, i.e. energy and mass
are decoupled. We tentatively prefer the first explanation as a working
model, but acknowledge that it is an open question.
Higher energy bosons are known to decay faster. Cordus explains this as
higher energy particules having higher frequency, hence faster refresh
rates of their reactive-ends. In turn, the decay process needs cycles of
activity, not time per se. Thus higher energy particules can accomplish the
necessary disassembly process steps in less time. In short, time is
fundamentally the local frequency oscillations of particules, not an
absolute variable [6].
3.5
Neutrino-antineutrino annihilation
The neutrino-antineutrino pair is sometimes apparent in the Z boson
interactions. The previous section identified its structure:
v(r1.1 1.1 .a .t) + v(r1.1 1.1 .a .t) => Z2(r1.1 1.11.1 1.1 .a.t)
We are interested in what this might subsequently decay to. We add
hyffon-antihyffon twin-pairs:
v + v => O2(r1.1 1.1 .a↓11.t↑11)
=> O2(r1.1 1.1 .a1.11.1.t1.11.1)
=> O2a(r1 1 .a11.t11) + O2b(r1 1 .a11 .t11)
The O2a structure is recognised as the positronium annihilation assembly
[9-10], which can go to an electron-antielectron, or two photons. Thus:
v + v => [(e + e) or 2y] + O2b(r1 1 .a11 .t11)
However there is a problem with reducing the O2b(r1 1 .a11 .t11) structure,
which we term notPositronium. No addition of hyffon-antihyffon pairs (↑
or ↓) will transform it. Superficially it might seem appropriate to partition
it into structures O(r1 .a1 .t1) and O(r1 .a1 .t1). But the problem is these
structures are not physically seen: they correspond to what we call the
antinotElectron !e(r1 .a1 .t1) and the notElectron !e(r1 .a1 .t1). Apparently
these structures are forbidden in the matter (forma) universe that we
inhabit, presumably a consequence of the asymmetry at genesis. Either
that, or the notPositronium is an artefact of the cordus HED method.
However, there does not appear to be any constraint on the O2b(r1 1 .a11
.t11) structure converting to two photons through annihilation. Thus:
379
v + v => [(e + e) or 2y] + 2y
=> [(e + e) + 2y] or [4y]
Thus annihilation of energetic neutrino and antineutrino annihilation is
predicted to result in either an electron-positron pair and two photons, or
four photons, but not two electron-positron pairs. Less energetic
particules may not annihilate at all, but instead revert to a neutrino and
antineutrino. So this cordus model predicts an unusual and non-intuitive
set of process streams (decay channels) and this may be testable.
We make the assumption that the neutrino can absorb photons and
thereby attain an energetic state. This is contrary to the prevailing ideas
about neutrinos, which is that they do not respond electromagnetically.
However we see nothing in the HED model for the neutrino to suggest it is
incapable of interacting with photons, either by absorption or emission.
4
Boson lemmas
We made several assumptions above, and these are summarised below as
a set of lemmas.
Ma.7
Boson behaviour
Ma.7.1
Boson HED structures
W- = W-(r.1.1 .a.11.1 .t11)
W+ = W+( r1.1. .a1 .t)
Z: no single Z boson, but several varieties.
Ma.7.2
W boson mass. Possible mechanisms include one or both
of the following
Their fibrils need a very high frequency to service
the overloaded hyffons (preferred model).
The presence of so many hyffons creates a greater
gravitational effect for the same fundamental
energy, i.e. energy and mass are decoupled.
Ma.7.2.1
Ma.7.2.2
Ma.7.3
Ma.7.3.1
Ma.7.3.2
Ma.7.3.3
Ma.7.3.4
NotPositronium
The structure of NotPositronium is O(r1 1 .a11 .t11).
It is
predicted in the neutrino-antineutrino
analysis, but is believed either to be verboten in a
matter dominated universe, or an erroneous
artefact of the HED method.
Its components are an antinotElectron !e(r1 .a1 .t1)
and notElectron !e(r1 .a1 .t1), both of which are
likewise verboten.
NotPositronium can annihilate, even as it forms,
to two photons through annihilation.
380
Ma.7.4
5
The neutrino can absorb photons and thereby attain an
energetic state.
Discussion
What has been achieved?
We have used the beta decay outcomes to determine the HED field
structure of the W bosons:
W- = W-(r.1.1 .a.11.1 .t11)
W+ = W+( r1.1. .a1 .t)
We infer that there is not a single Z boson, but many specific varieties.
We have also modelled the neutrino-antineutrino annihilation process.
The results suggest that an annihilation of an energetic neutrino and
antineutrino annihilation produces either an electron-positron pair and
two photons, or four photons, but not two electron-positron pairs. Less
energetic particules may not annihilate at all, but instead revert to a
neutrino and antineutrino.
Answers to common questions
The cordus model permits answers to be fielded to some puzzles about
the weak interaction.
Why is the weak interaction the only known process for changing
the flavour of quarks between u and d?
This is because the flavour-change absolutely requires a neutrino
or antineutrino, and these particules are an integral part of the
weak interaction.
Why do the W and Z bosons have such large mass?
A high frequency is required to service the large number of hyffons
in these temporary structures.
Implications
Conventional physics interprets the weak interaction to be a short-range
field, mediated by the bosons. In that interpretation the short range arises
because of the heavy mass of the W and Z bosons.
The cordus explanation is radically different, and refutes this
interpretation. First, cordus suggests that the W and Z bosons do not
exist in the form of 0D point particles with static characteristics, but
instead are cordi undergoing dynamic assembly and disassembly
processes. 'Particle' is entirely the wrong concept to be using.
Second, there is no single Z boson.
Third, the conventional concept that the bosons change the flavour of the
quark is inappropriate, according to the cordus model. The bosons are not
the cause or the mechanism for the change, but merely the by-products
and waste process stream from the conversion process.
381
Fourth, the weak interaction is a different category of fundamental force
to electrostatic, magnetic, and gravitational forces. The weak interaction
is a negotiation of the particule's right to emit HED active field structures
in specific direction. These rights are complemented by other particules,
hence a bonding force that keeps the particules together.
6
Conclusions
The cordus principle and its HED notation have been used to infer the
discrete field structures of the W bosons as follow:
W- = W-(r.1.1 .a.11.1 .t11)
W+ = W+( r1.1. .a1 .t)
Also, there appears not to be a single Z boson, but rather several varieties.
References
1.
Pons, D.J.: Structure of the neutrino and antineutrino. viXra, 2011, v. in
submission. Available from: http://vixra.org/.
2.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Matter
particuloids. Cordus matter: Part 3.2 viXra, 2011, v. 1104.0023, 1-12 DOI:
http://vixra.org/abs/1104.0023.
Available
from:
http://vixra.org/pdf/1104.0023v1.pdf.
3.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Cordus
Conjecture: Overview. viXra, 2011, v. 1104.0015, 1-17 DOI:
http://vixra.org/abs/1104.0015.
Available
from:
http://vixra.org/pdf/1104.0015v1.pdf.
4.
Pons, D.J., Pons, Arion. D., Pons, Ariel. M., & Pons, Aiden. J.: Gravitation,
Mass and Time. Cordus in extremis: Part 4.3 viXra, 2011, v. 1104.0029, 114
DOI:
http://vixra.org/abs/1104.0029.
Available
from:
http://vixra.org/pdf/1104.0029v1.pdf.
5.
Pons, D.J.: Mirror images: Cordus reconceptualisation of Matter and
Antimatter.
viXra,
2011,
v.
1109.0009,
1-15
DOI:
http://vixra.org/abs/1109.0009.
Available
from:
http://vixra.org/pdf/1109.0009v1.pdf.
6.
Pons, D.J.: Cordus process diagrams: Symbolic representation of
annihilation mechanics. viXra, 2011, v. 1109.0068, 1-14 DOI:
http://vixra.org/abs/1109.0068.
Available
from:
http://vixra.org/pdf/1109.0068v1.pdf.
7.
Pons, D.J.: Annihilation mechanisms: Intermediate processes in the
conversion of electron and antielectron into photons viXra, 2011, v.
1109.0047, 1-21 DOI: http://vixra.org/abs/1109.0047. Available from:
http://vixra.org/pdf/1109.0047v1.pdf.
382
Stability and decay: Mechanisms for stability
and initiators of decay in the neutron
Pons, D.J. 107
Abstract
Why is the neutron stable in the nucleus? Why is the free neutron unstable
outside the atom? This paper applies the cordus conjecture to address
these questions. The proposed explanation is that in the nucleus the
discrete field structures (cordus HED) of the proton and neutron fulfil each
other, thereby providing a joint stability. When the neutron is removed
from the nucleus, its stability becomes compromised. By comparison the
single proton on its own does not need the neutron, so it remains stable.
The free neutron is able to maintain a dynamic stability by moving its field
structures around. It can do this indefinitely. However it is in a
compromised state, and vulnerable to perturbation by external fields. Two
initiators are anticipated for decay. One is randomly occurring field
fluctuations from the external fabric, and these are proposed for the
conventional decay route. The second is impact by another particule. In
both cases it is the external fields that cause the decay, by constraining the
neutron so that it cannot dynamically adjust. Hence it is trapped in a state
that leads to decay at its next frequency cycle. The second path could
involve any particule with sufficient energy to disturb the neutron. Also, the
impact of a neutrino is specifically identified as a potential initiator of
decay. The implications if this is correct, are that the neutron has two
separate decay paths, which are mixed together in what we perceive as the
beta minus process. The first is determined by the local density of the
(spacetime) fabric, and the second by the number of energetic particules
and neutrinos encountered. The significance of the two decay paths is that
neutron decay rates are predicted to be variable rather than constant. A
general set of assumptions are extracted for stability and decay of
particules in general.
Edition 1 > Date: Saturday, 11 February 2012 > Document: Pons_cordus_5.8_NeutronDecay_E1.0.26.doc
1
Introduction
The standard concept in physics is that fundamental particles (electron,
photon, etc.) are zero dimensional (0D) points without internal structure.
In contrast the cordus conjecture [13] suggests that it is more helpful, in
terms of explanatory power, to conceive of a two-ended internal
structure.
This cordus particule model has been used to create a conceptual model of
the discrete field structures of the neutrino and antineutrino [14]. An
107
Please address correspondence to Dr Dirk Pons, University of Canterbury, Christchurch, New
Zealand. Copyright D Pons 2011.
383
extension of the concept identified internal structures for the W bosons in
the weak interaction [15].
This paper extends the conceptual model further, by exploring the criteria
of stability for a particle, and the initiators of decay, with specific
application to the neutron.
2
Background
Cordus particules
The cordus conjecture [3] proposes that the particle is not a zerodimensional point as orthodox physics assumes, but rather a two-ended
internal structure, called a cordus ‘particule’.
Specifically, this model proposes an internal structure of a cordus,
comprising two reactive ends, with a fibril joining them. The reactive ends
are a small finite span apart, and energised (typically in turn) at a
frequency, at which time they behave like a particle. Hence superposition
of geometric location is also explained.
When energised a reactive end emits a transient force pulse along a line
called a hyperfine fibril (hyff), which makes up the field. This consists of
three hyff threads, one in each of three orthogonal axes [r], [a], [t]. These
threads extend out into space from the reactive end. When energised, a
hyffon pulse is transmitted along the thread, and hence the field is
discrete. Positive and negative charge correspond to the direction of
propagation of these pulses. The reactive ends are energised in turn at the
frequency of the particule. Extensions of this idea accommodate the
electric field, magnetism, and gravitation [6]. All the particules in the
universe emit hyff, and these make up the fabric of the vacuum [11]. The
hyff emission directions (HED) have a hand, called ma to differentiate it
from other hand-like concepts in quantum mechanics, and this determines
the matter and antimatter species [1]. A modelling method, called HED
notation, is used to represent these discrete field structures [10].
Cordus model for the neutrino
The structures of the neutrino and antineutrino in HED notation [14] are:
Antineutrino: v = v(r11 .a .t11)
Neutrino v = v(r1 1 .a .t11)
In this notation x1 represents a -1/3 charge in the x axis in the matter hand,
x1 is +1/3 charge in matter hand, x1 is -1/3 charge in antimatter hand, and
x1 is +1/3 charge in antimatter. See Figure 1 for the equivalent physical
representation.
384
Figure 1: The cordus structure for the neutrino and antineutrino. The
diagrams show the spatial arrangement of the discrete field structures
(hyffons) in the three hyff emission directions (HEDS). The v(r1 1 .a .t11)
variants are shown, and other arrangements are considered possible via
colour-change. The diagram also shows how the unique spin directions
arise for these two particules. Note that the primary difference between
matter and antimatter is the ma-hand, which is the energisation sequence
of the HEDs.
Purpose of this paper
We now extend the work to determine why the neutron is unstable when
isolated from the nucleus. Previously we have looked at what outcomes
are produced in decay, and how those arise. Here we explore why
instability arises in the first place, with a focus on the neutron. We develop
candidate principles for stability and decay.
3
Neutron beta- decay
In β- decay, or electron emission, the free-neutron decays, after a
relatively long life, into a proton, electron, and an electron antineutrino:
n => p + e + ve
We take beta decay for granted, but why does the neutron need to decay
in the first place? Given that it is stable in the nucleus of the atom, why
does it decay outside?
The conventional answer is in terms of energy. The deuteron (one proton
and a neutron) has a total mass slightly less than that of its individual
constituents of a proton and the decay products of the neutron.
Specifically, the binding energy of the np deuteron is 2.2 MeV, whereas
the energy yield in decay of the neutron is the lesser amount of 0.78 MeV,
hence decay is not preferred.
We do not disagree with that energy interpretation, and cordus explains
qualitatively why the masses of assemblies are different to those of the
385
constituents [7]. However the energy explanation on its own is obviously
not the entire story, as conventional physics is unable to explain how the
energy effect works. Indeed, it is difficult to see how there could be any
explanation if one stays with the conventional 0-D point paradigm.
The cordus HED concept provides another way to answer the why
question, and the results complement the energy perspective.
3.1
Stable in, unstable out
Why is the deuteron stable?
First, we can use cordus to explain why the neutron is stable in the atom:
because it forms a complementary frequency synchronisation (CoFS) state
[16] with the proton. They effective bond together:
n(r .a11 .t11) + p(r1.11 .a1 .t1) => O(r1.11 .a1.11 .t1.11)
So the O assembly is the deuteron and from this we can derive some
implied requirements for stability (see Lemma Ma.8 below). Specifically, it
has full HED structures and therefore unitary charge structures. Also, the
structures are all the same hand (forma). This stability is temporally
enduring (hence ‘strong’) because it does not have to dynamically share
this relationship with other partners.
Why is the neutron unstable?
With cordus we can see why the neutron on its own is going to have
problems. We note that the HED structure of the neutron n(r .a11 .t11) is
unbalanced, in that there is no hyffon in the [r] axis. Thus it fails the
stability criterion for completeness (Ma.8.1.3).
To fix this it may be able to shift some of the hyffons to different HEDS,
e.g. n(r1 .a1 .t11), and we assume it can do this dynamically too, at the next
frequency cycle of energisation. However that action then means that
some of the HEDs carry only a single hyffon, which is inappropriate for an
uncharged particule. Thus this evasive behaviour unbalances the charge
neutralisation (Ma.8.1.6), making the neutron unstable in this
configuration too. Dynamically changing between these various HED
layouts n(r .a11 .t11) <=> n(r1 .a1 .t11) prevents instability.
So in this cordus model, the neutron is vulnerable to two different forms
of instability, depending on its structure, and it can stave off demise by
rapidly changing between these structures before the decay processes can
start.
386
3.2
Decay initiators
Perturbation/constraint mechanism of decay
However, this dynamic stability only exists while the external environment
permits (Ma.8.2). Sooner or later something occurs to compromise that
dynamic adjustment. We anticipate that might be:
(a)
An external perturbation, i.e. injection of hyffons into the HEDs,
e.g. from particule impact (Ma.8.2.1).
(b)
Externally imposed constraints on the hyffons of the neutron.
These external fields pin hyffons in certain HED directions and
prevent their dynamic movement to other HEDs. These constraints
may arise in bonding situations, from external fields, or the fabric
(Ma.8.2.2).
We call this the perturbation/constraint mechanism of decay. The two
methods are corollaries of each other, and both involve hyff constraints
from outside the particule.
Applying this to the neutron, either way the neutron lingers one
frequency cycle too long in the state of n(r .a11 .t11) or n(r1 .a1 .t11), and the
degradation process (beta decay) initiates. However it is relevant to note
that the neutron itself is not unstable: it does not have any internal
mechanism favouring decay. It has no internal timer counting backwards
to zero. Quite the opposite, it has a perfectly adequate coping mechanism,
of dynamically adjusting its structure to stay stable. However it is a
compensated system, and is not a strong stability. Sometimes the external
environment overwhelms it. When the neutron is locked into a bond with
the proton, its vacant HEDs are filled with those of the proton, and
therefore the instability does not generally arise.
The frequency of the neutron is very high, so it must survive very many
frequency cycles for the life to be as high as it is. This and the nature of
the proposed decay mechanisms means that cordus predicts that the
degradation process is a random variable. The initiator is a chance external
encounter with external hyffons. Being of external origin, these
encounters are totally independent to the internal workings of the
neutron. There is no reason to think that the rate of perturbations
generated by the external environment is anything but an unstructured
random variable. Therefore a logical consequence of the cordus model is
that the decay initiators will be a uniform random variable with time, at
least for natural decay (excludes high energy physics). At first this might
seem at odds with the known exponential decay distribution of the free
neutron, but this is not so, as explained below.
Why the Exponential distribution? Hazard rate perspective
Talking about the life of the neutron as an exponential density distribution
with mean of 15 min (or half-life 10 min), which is how it is commonly
represented, implies a determinism and central tendency that does not
exist. We need to disentangle our concepts of the 'mean'. It is true that for
a normal distribution the mean represents a 'true' estimate of the central
387
tendency, with noise superimposed.108 However, that is not a helpful
concept to apply to the exponential distribution. The mean and its
variance can be computed, but should not be considered as a 'true' value
with noise.
From a reliability-engineering perspective, the exponential distribution has
the unusual and unique property that the hazard rate is constant. This is
the probability that the system will fail in the next time interval, given that
it has survived up to the beginning of that time interval.
Applying this to the neutron: its exponential decay rate means that there
is equal chance of failure at any time: whether a free-neutron has been in
service for a long or a short time it still has the same chance of failing. Thus
inspection of the empirically-derived exponential distribution shows that
the mechanism, whatever it is, that drives the failure of the neutron
cannot be time-dependent.
For any one neutron the chance of failure is a uniform distribution over
time. Thus the individual neutron is not trying to decay in the mean
lifetime: instead it will decay with equal probability anywhere between
zero and infinite time. The 'mean' value only becomes apparent when the
outcomes of many individual neutrons are aggregated.
There is no mechanism in the exponential distribution for central tendency
towards a mean. Thus instead of talking about the mean lifetime of the
neutron, we should be asking the more fundamental question: why is it
that the neutron sometimes decays almost instantly, and at other times
takes a relatively vast amount of time (cycles)? More importantly, why is
time not a variable?
The cordus perturbation/constraint mechanism of decay fits this model: it
is not time-based. The cordus mechanism provides for an equal chance of
failure at any time which is consistent with the unique features of the
observed lifetime characteristics of the free-neutron.
What determines the decay rate?
If time is not a variable, what determines the decay rate of the free
neutron? We anticipate that the natural decay rate is dependent on the
density of the fabric at that locality.
3.3
Implications of the two decay routes
Fabric induced decay
The fabric is the irregular mesh of background hyffons of (potentially) all
the other particules in the universe [11]. All discrete field structures of a
108
By comparison the underlying reason for the normal distribution is easy to understand:
take a large number of variables, allow them each to vary randomly according to different
density distributions, and the sum of those variables will tend towards a normal
distribution, regardless of the density distributions of the individual variables.
388
particle, whether a fundamental particule or an assembly, and whether
those are externalised or internally cloaked hyffons [14], contribute to the
fabric. These hyffons all need servicing by their originating particules and
hence a frequency requirement arises, hence mass.
Every particule contributes to the creation and replenishment of the
fabric, and is actively embedded in it. Therefore particules have to engage
with the fabric. This also means that the fabric can affect the particule. A
free particule, such as the neutron outside the nucleus, no longer has its
HED vulnerabilities shielded by its assembly bonds with the proton, and is
therefore more exposed to external constraints on its HEDs from the fabric
hyffons (Ma.8.2.2).
The implications are that decay should proceed quicker in situations of
higher gravitation or acceleration, relative to other locations. This is
because the actual or apparent fabric density increases in such situations,
so the neutron encounters more fabric, and hence more opportunity to be
constrained. This may be testable. Alternatively such an effect could also
be explained as conventional time-dilation, so there may not be a big point
of difference. The fabric density would also have been greater in the early
universe, but this is not expected to change decay rates as time also
flowed faster in the cordus interpretation [6] and there is no other
contemporary location from which to observe.
Perturbative decay
We anticipate that the other mechanism for neutron decay is active
perturbation, i.e. the injection of hyffons into the HEDs, e.g. from particule
impact (Ma.8.2.1). Obviously one candidate for this is high-energy-physics
(HEP), where nucleon particules are smashed into each other at high
speed. From the cordus perspective, these situations are expected to also
accelerate the decay process, though this might be difficult to distinguish
from all the other decay activities going on.
Neutrino induced decay of neutron
Cordus also suggests that certain types of impacts could be more likely to
accelerate β decay. This suggestion arises from inspection of the field
structures. In particular the cordus HED notation suggests that the impact
of a neutrino into a neutron could cause decay as follows:
n + v = n(r .a11 .t11) + v(r11 .a .t11)
=> O(r11 .a11 .t1.11.1) => |% => O(r1.11.1 .a11 .t11)
=> p(r1.11 .a1 .t1) + O1(r1 .a1 .t1)
=> p(r1.11 .a1 .t1) + e(r1 .a1 .t1)
=> p + e
Thus adding the neutrino at the outset provides some economy, and it
may be that this encourages the decay reaction. So in principle cordus
predicts that a neutron plus a neutrino could decay to a proton and an
electron. Substituting an antineutrino does not have the same effect.
Likewise it may be shown that neither β+ decay of the proton¸ nor electron
389
capture (EC), have any economy from having the neutrino or antineutrino
pre-supplied, see Appendix A. It is specifically β- that appears to be
amenable to this effect. This is an unexpected result, but may be testable.
Conventional physics assumes that decay rates are strictly constant. The
above work suggests the otherwise. Thus cordus predicts that beta decay
rates could vary depending on the fabric density (not easy to change
experimentally), acceleration, gravitation, HEP impacts, and neutrino
loading. Most of these are probably not easy to experiment with, but the
neutrino loading idea should be testable. Indeed, it might already have
been observed, as the next section explores.
Odd neutrino effects
There has been ongoing discussion in the community about the possible
interaction of neutrinos with the decay process. Controversially, it has
been suggested that neutrinos may initiate 'transmutation' in a cold-fusion
reaction [17]. Also controversial is the idea that solar neutrinos may affect
decay rates. A meta-analysis of decay rates led to a suggestion that the
variability in decay rates (36Cl and 32Si via β-) is correlated with the
seasonal variability in distance to the Sun [18]. The decay rates reduced
when the distance to the sun increased. The Sun is thought to produce
neutrinos rather than antineutrinos. A correlation with the rotation rate of
the sun's core has also been suggested. A correlation has also been found
between reduced decay by electron capture in 54Mn during a solar flare
[18]. Those authors proposed that one explanation could be that solar
neutrinos exchange energy with the decaying nucleus.
However other studies would seem to refute the idea. No significant
deviations in decay rates were observed for Earth–Sun distance on the
Cassini spacecraft [19]. That experiment used 238Pu, which decays by alpha
emission (not β-, which is significant in the present context). Likewise [20]
found 'no evidence for correlations between the rates for the decays of
22
Na [β+ and electron capture EC], 44Ti [EC], 108Ag [EC], 121Sn [β-], 133Ba [EC],
and 241Am [α] and the Earth–Sun distance.' However they were only
checking for correlation between the data and one other hypothesis: the
Jenkins seasonal curve. Therefore there remains the possibility that some
other curve might fit the data. Indeed, there was noticeable periodic
variability in the data, especially for electron capture, though the
significance of that was not tested against alternative hypotheses.
Detection of neutrinos and antineutrinos
There is some evidence to suggest that muon neutrinos and muon
antineutrinos are detected or disappear (oscillate) differently [21-22].
Those MINOS results were reported in terms of different disappearance
rates for the two particles. The work inferred that the oscillation rates
(rate of change between the generations) were different. Possible
explanations provided, other than experimental error, were violation of
CPT symmetry, or that the interactions with matter could be different for
neutrinos and antineutrinos [21].
390
If a cordus explanation is sought, it would tend to be the latter: that the
interaction of neutrinos and antineutrinos with matter is asymmetrical.
The MINOS data were collected by measuring the muon and antimuon byproducts of collision with matter (steel). The raw results show lower
production of antimuons than muons [21][Fig 2]. Such an empirical
method and results are consistent with the cordus concept of perturbative
decay which suggests that neutrinos and antineutrinos have different
reactivity with neutrons, and hence with matter generally. That there were
some antimuons produced at all, may be a consequence of the energy of
the antineutrinos rather than antineutrinos per se.
Many of these effects mentioned: cold-fusion, non-constant decay rates,
and the MINOS results, are tentative and lack universal acceptance. It is
difficult at this time to know whether they are real effects or spurious
artefacts. If real, then new explanations will be required, since the effects
are well outside of the standard models. Confirming or refuting one of
these effects would neither validate nor falsify the cordus conjecture.
However until these effects are convincingly refuted, there is value in
keeping alive a discussion of alternative conceptual explanations.
Regarding decay rates in particular, cordus suggests that we might expect
to see decay rates for β- increase with neutrino loading, but not for β+.
The empirical evidence in support of this is slim at worst and mixed at
best, and we leave it as an open question. But the main point is that it
seems prudent to take a more thoughtfully open-minded position of
scepticism about the possibility that neutrinos might interfere selectively
with decay rates, rather than automatically assume it is impossible simply
because it is not accommodated in the standard model of QM.
Twin decay paths for neutron
The implications are that the neutron has two separate decay paths, which
are mixed together in what we perceive as the β- process. The first is
determined by the local density of the fabric, and the second by the
number of neutrinos encountered.
1: Fabric constraint induced neutron decay:
n => p + e + ve
This is the β- process, as conventionally represented.
2: Perturbative neutron decay, with neutrinos as the perturbers:
n + v => p + e
We propose this also contributes to the β- process.
Taken together, if these are true, then we expect to see the neutron decay
faster in high gravitation or high acceleration situations, or under higher
neutrino loading.
391
4
Stability and disassembly lemmas
We made several assumptions for how stability is gained and lost, and
these are summarised below as a set of lemmas.
Ma.8
Stability and disassembly of particules
Ma.8.1
Ma.8.1.1
Ma.8.1.2
Ma.8.1.3
Ma.8.1.4
Ma.8.1.5
Ma.8.1.6
Ma.8.1.7
Ma.8.1.8
Ma.8.1.9
Ma.8.2
Ma.8.2.1
Ma.8.2.2
The criteria for stability of a cordus particule or assembly
structure are assumed to be:
The hyffons must all be of the same hand (1 or 1
but not a mixture.
The structure must have an overall unit charge of
zero or +3/3 or -3/3. This means at least three
hyffons of the same hand in either the negative or
positive directions. Countering hyffons are
possible.
For positional stability, the structure must have a
hyffon in each of the HEDs, e.g. (r1 a1 t1).
It may make this allocation dynamically, while the
external environment permits.
If the structure does not have a hyffon in each of
the HEDs, then it may be stable if it can move on
the fabric.
For stability the particule must have its opposite
charged hyffons (if any exist) located on the same
HED. For example (r11 a t) not (r1 a1 t). (It needs a
balanced firing order to maintain charge
neutralisation. This lemma is tentative)
Energy is related to frequency of the cordus, i.e.
the refresh-rate for the reactive ends. Lowerfrequency configurations tend to be more stable,
all else being equal.
For any one particule there may be multiple
alternative assemblies or configurations, i.e.
combinations of hyffon arrangements. These may
not all be dynamically stable.
The relative energy attractiveness of these
configurations corresponds to the generations
(tentative). In which case the number of
generations is determined by the number of
configurations available.
Perturbation/constraint mechanism of decay. Dynamic
stability only exists while the external environment
permits (Ma.6.7.3). Events that compromise that dynamic
adjustment include:
An external perturbation, i.e. injection of hyffons
into the HEDs, from particule impact.
Externally imposed constraints on the hyffons of
the neutron. These external fields pin hyffons in
certain HED directions and prevent their dynamic
392
movement to other HEDs. These constraints may
arise in bonding situations, from external fields,
or the fabric.
Ma.8.3
Ma.8.3.1
Ma.8.3.2
Ma.8.3.3
Ma.8.3.4
Ma.8.4
Ma.8.4.1
Ma.8.4.2
5
If a structure does not meet the stability criteria, then it
decays to the nearest accessible structure.
This is one that is (a) permitted as per Ma.8.1, and
(b) one for which sufficient energy exists.
The nearest accessible structure is a HED stable
structure, and the HED negotiation process thus
naturally selects this structure. One could
figuratively say that the composite intermediate
structure is pulled into the accessible structure. It
may manifest as injection of ↑ and ↓ hyffon pairs
into the HEDs.
The left-over energy and hyffons are pushed into
a residual composite structure, O. That has the
ability to create further hyffon-antihyffon pairs
and partition off another accessible structure.
There needs to be enough energy (related to
cordus frequency) in the first place. Thus decay to
higher energy (higher frequency) daughter
products cannot commence until the input
particule has sufficient energy. This energy may be
native to the particule, i.e. embedded in its
frequency, or added via photons or field transfer.
When a particule breaks down or decays, the apparent
output products do not necessarily represent the actual
original internal structures. Nonetheless the conservation
of hyff applies.
Decay is more accurately a disassembly process,
due to the conservation of hyff, except where
annihilation occurs.
The O(r1 1 .a11 .t11) structure comprises the
assembly of the notelectron !e(r1.a1.t1) and
antinotelectron !e(r1.a1.t1) both of which are
forbidden structures in a forma cosmos. However
the assembly may convert to two photons through
annihilation (tentative).
Discussion
What has been achieved?
The main conceptual contributions of this work are:
• An explanation is given for the stability of the neutron inside the
atom, and its instability outside, using the cordus concept. This is
in terms of its field structures.
• The criteria for stability of a particule are identified, in terms of the
HED field structures.
393
•
•
•
The initiators of decay for the neutron are identified as
disturbances in the external environment, which could be the
vacuum fabric, or the local bonding arrangements, or the HED
fields of an impacting particule.
An explanation is provided for the constant hazard-rate decay of
the free neutron, i.e. why the decay lifetime has an exponential
density distribution rather than any other shape.
It is predicted that the neutrino and antineutrino may interact
preferentially with different types of matter, and thus influence
decay rates.
Answers to common questions
The cordus model permits answers to be fielded to some puzzles about
the weak interaction.
Why is the neutron stable in the nucleus?
The neutron’s stability is due to its field structures being a good
match to those of the proton. This results in a strong bond, and
thereby resistance to the forces of decay.
Why is the free neutron instable outside the atom?
Once free of the atom, the neutron has the problem that the
arrangement of its field structures is statically unstable. It can
avoid the instability by dynamically changing those structures.
However that dynamic stability can be interfered with by external
fields, resulting in decay of the neutron.
What causes the decay?
There is no clock that counts down to decay. There is nothing in the
neutron that has a finite life. The free neutron is stable, providing it
is left alone. The forces that interfere with it and precipitate decay
are field forces that arise in the external environment. Those
include the natural variability in the fabric of spacetime, and the
effect of incoming particules. These forces, represented as cordus
hyffons, upset the dynamic stability of the neutron, and thereafter
its own energies remanufacture it into more stable components, as
in beta minus decay.
Why does the beta minus weak interaction decay follow the
exponential distribution?
This is because the decay process for the neutron is fundamentally
not dependent on time. Statistically, it is a constant hazard-rate
system. This automatically produces the exponential distribution.
Could the decay rates be variable?
Yes, in principle. In this model the decay rate is not dependent on
time. Instead the underlying initiators of decay are the
disturbances in the external fabric, and the effect of the fields of
impacting particules.
394
Implications
Conventional physics interprets the decay processes to be independent of
the external environment. In other words, the half-lives are assumed to be
constant. The cordus conjecture suggests that picture is too simple, and
the constancy is only approximate. This is quite a large departure from
orthodox theory, and will require further research to confirm or deny. It is
probably going to be difficult at present to falsify the cordus explanation
for the stability/instability of the neutron inside/outside the atom, for lack
of competing explanations. However it should be possible to test the
proposed perturbation/constraint mechanisms of decay. It may also be
possible to test the idea that neutrinos interfere with some decay rates
but not others.
Clearly, and as the name cordus conjecture implies, this work is conceptual
and conjectural in nature. There is no guarantee that the above ideas are
valid, and instead they should be considered part of an extended thought
experiment, hence conceptual model. Much further work would be
required for validation, the more so as the model is unorthodox and
contrary to QM. Several lines of empirical research are suggested as being
potentially interesting, particularly the possibility of neutrinos selectively
affecting decay rates.
6
Conclusions
This is the third paper of a bracket on the beta decay processes. In the first
we used beta minus decay to work out a cordus structure for the neutrino
and antineutrino. In the second we determined structures of the W and Z
bosons. The purpose of this third paper was to explain why the neutron is
unstable at all. The related question is why the neutron is stable in the
deuteron nucleus.
The answer to those questions, from the cordus perspective, is that in the
nucleus the HED discrete field structures of the proton and neutron fulfil
each other, thereby providing a joint stability. When the neutron is
removed from the nucleus, its stability becomes compromised. By
comparison the single proton on its own does not need the neutron, so it
remains stable. The neutron is able to maintain a dynamic stability by
moving its HED structures around. It can do this indefinitely. However it is
in a compromised state, and vulnerable to perturbation by external HED
fields.
Two initiators are anticipated for how that perturbation may arise and
cause decay. One is randomly occurring field fluctuations from the
external fabric, and these are proposed for the conventional decay route.
The second is impact by another particule. In both cases it is the external
HED fields that cause the decay, by constraining the neutron so that it
cannot dynamically adjust its own HED fields. Hence it is trapped in a state
that leads to decay at its next frequency cycle. The second path could
involve any particule with sufficient energy to disturb the neutron. We also
specifically identify the neutrino as a possible initiator of decay. The
395
significance of the two decay paths is that neutron decay rates are
predicted to be variable rather than constant. If this is true, then the
implication is that neutrino loading becomes a variable in empirical tests
of decay, and will need to be controlled for.
Although most of the work specifically addresses the neutron, we also
extract a set of assumptions for stability. Since these are of a general
nature and do not require the specific structure of the neutron, we expect
that these will apply to decay in particules in general.
A
Appendix: Other beta decays
The possible effect of neutrinos and antineutrinos on several forms of
decay are documented below. These are detailed for completeness,
though most of the interactions do not show usefully different outcomes.
This is not an exhaustive analysis and it is still possible that other effects
may exist: neutrinos may have other catalytic roles not represented by
HED notation; additional impacts with secondary particules could create
different outcomes from these processes.
The analysis is done with HED notation, and relies on several lemmas, so
the results are only as strong as that logical structure might be valid.
A.1
Beta minus decay n => p + e + v
Beta minus decay is assisted by an input neutrino
The body of the document derives the HED process for the proposed
neutrino-induced decay of the neutron:
n + v => p + e
Beta minus decay may be diverted by an input antineutrino
n + v = n(r .a11 .t11) + v(r11 .a .t11)
=> O(r11 .a11 .t1.11.1) => +↑↓ => O1(r11↑ .a11↓.t1.11.1)
=> O1(r1111 .a1111 .t1.11.1)
=> |% => O1(r1111 .a111 1.t1.11.1)
=> e(r1 .a1 .t1) + e(r1 .a1.t1) + O2(r11 .a11 .t11)
=> e + e + O2(r↓ .a↓ .t↓)
=> e + e + 2y
This nominally produces an electron-antielectron pair, and the O2
structure which is tentatively thought to collapse to two photons
(Ma.8.4.2). A further assumption is that the HED structures of the neutron
and neutrino are indeed the same, which is still uncertain. The result is a
type of annihilation, not any of the known α, β or γ decay processes, so it
appears that the antineutrino does not affect the β- decay process, other
than possibly reducing it by re-direction.
396
A.2
Beta plus decay p => n + e + v
Beta plus decay is not assisted by an input neutrino
p + v = p(r1.11 .a1 .t1) + v(r11 .a .t11) +(↑↑↑)
=> O(r 1.11 11↑.a1↑ .t111↑) => O(r 1.11 1111.a111 .t11111)
=> e(r1 .a1.t1) + O1(r 1.11 111.a11 .t1111)
=> e + n(r .a11 .t11) + O2(r 1.11 111.a .t11)
=> e + n + 2v
This outcome does not appear to have any advantage: the input neutrino
simply comes out at the end again. If it precipitates the decay, we cannot
tell with HED notation.
Beta plus decay is not assisted by an input antineutrino
p + v = p(r1.11 .a1 .t1) + v(r11 .a .t11) +(↑↑↑)
=> O(r 1.11 11↑.a1↑ .t111↑) => O(r 1.11 1111.a111 .t11111)
=> e(r1 .a1.t1) + O1(r 1.11 11.1.a11 .t1.11.1)
=> e + n(r .a11 .t11) + O2(r 1.11 11.1.a .t11) => |%
=> e + n + v(r11 .a .t11) + O3(r 11.a .t11)
=> e + n + v + v
This outcome does not appear to have any advantage: the input
antineutrino simply comes out at the end again.
A.3
Electron capture p + e => n + v
Electron capture is not assisted by an input neutrino
p+e+v
=> p(r1.11 .a1 .t1) + e(r1 .a1 .t1) + v(r11 .a .t11)
=> O(r1.11111 .a11 .t1111)
=> n(r .a11 .t11) + O1(r1.11111 .a .t11) => |%
=> n + v(r11 .a .t11) + v(r11 .a .t11)
=> n + 2v
This outcome does not appear to have any advantage: the input neutrino
simply comes out at the end again.
Electron capture is not assisted by an input antineutrino
p+e+v
=> p(r1.11 .a1 .t1) + e(r1 .a1 .t1) + v(r11 .a .t11)
=> O(r1.11111 .a11 .t1111)
397
=> n(r .a11 .t11) + O1(r1.11111 .a .t11) => |%
=> n + v(r11 .a .t11) + v(r11 .a .t11)
=> n + v + v
This outcome does not appear to have any advantage: the input
antineutrino simply comes out at the end again.
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399
The preponderance of matter: Asymmetrical
genesis via the antineutrino route
Pons D.109, Pons A.D., Pons A.J.
Abstract
The existence of the universe is an enigma because the energy at genesis
should have created equal amounts of matter and antimatter, which
should have subsequently annihilated. What happened in the baryogenesis
process to cause matter to predominate in the cosmos? A candidate
conceptual solution is presented based on the cordus conjecture, and
featuring the antineutrino in a prominent role. A detailed model is
produced for the production of an electron-antielectron pair from photons.
The novel contribution is showing how the discrete field structures of the
photon dynamically transform into those of the two massy particules. A
new production process is detailed whereby an energetic antielectron is
remanufactured into a proton and two antineutrinos. The production
process could equally have converted electrons to antiprotons, and a
tentative explanation is given for why this might not have happened.
Therefore it is suggested that the apparent asymmetry of baryogenesis is
because the antimatter is hiding in plain sight, having been
remanufactured into the matter baryons themselves. In this model four
photons are transformed into an electron and proton, i.e. a hydrogen
atom, and two antineutrinos. The antimatter field structure of the
antielectron is carried away by the antineutrinos as a waste stream. This
paper therefore provides an alternative conceptual solution to the
baryogenesis asymmetry in the universe, and it also explains the
leptogenesis asymmetry. As a corollary, the conditions are identified under
which the proton may decay.
Edition 1 > Date: Saturday, 11 February 2012 > Document: Pons_Cordus_5.9_AsymmetricalGenesis_E1.0.08.doc
1
Introduction
The conversion of energy, i.e. a photon, into a matter-antimatter pair is
well known. Indeed, while energy and matter are interchangeable as per
E = mc2, the transaction always involves both matter and antimatter. We
never see energy transfer directly to only matter. Current technology is
able to replicate these processes. However there is a deeper question
when it comes to applying these principles to the formation of the
109
Please address correspondence to Dr Dirk Pons, Department of Mechanical
Engineering, University of Canterbury, Private Bag 4800, Christchurch 8020, New
Zealand, Email: dirk.pons@canterbury.ac.nz. Copyright D Pons 2011.
400
universe, and this is the asymmetrical abundance of matter and
antimatter.
Asymmetry of baryogenesis
The universe, at least our part of it, is made of matter. The energy at
genesis should have created equal amounts of antimatter, which should
have subsequently annihilated. It is an enigma as to why a matter-based
universe should even exist. Given that photons can convert to matter and
antimatter, what happened in the baryogenesis process at the formation
of the universe to cause matter to predominate?
While it is not impossible that there might be parts of the universe that
consist of antimatter, and thereby balance the matter, neither is there any
evidence that this is the case [23]. Therefore it is generally accepted that
the observed matter universe is probably a result of an asymmetrical
production of matter in the first place. What biased the genesis process to
form matter?
Some unknown process caused baryogenesis, the asymmetrical
production of baryons, i.e. the heavy particles like quarks, protons and
neutrons. Another process, also unknown, is required for asymmetrical
leptogenesis, i.e. production of matter electrons. This is a requirement of
charge conservation, which applies everywhere else in physics and is
generally thought to apply to the universe as a whole. Thus we need two
processes: one to create a predominance of protons over antiprotons, and
another to make electrons rather than positrons (antielectrons).
Existing theories include:
The initial conditions imposed on the universe favoured matter. In
other words the constraint came from outside the universe. This
explanation is generally dismissed as unnatural [23].
The Sakharov criteria for the imbalance of matter-antimatter
require, inter alia, that charge-parity (CP symmetry) violation
must occur [24]. However the mechanism for CP violation is
unknown. Leptogenesis via gravity waves have been suggested
[25].
Electroweak baryogenesis in the Standard Model [26-27].
Modifications to the Standard Model. One pathway is that righthanded neutrinos might decay into leptons, and those in turn
converted by sphalerons into bosons. The sphalerons are assumed
to have existed at the high temperatures at the formation of the
universe, and not thereafter. However right-handed neutrinos
are controversial as they have not yet been observed, and even
the existence of mass for standard neutrinos is uncertain.
Leptogenesis using a hypothesised singlet neutrino that
subsequently decays preferentially into antineutrinos, which are
in turn converted to matter. Alternatively, that neutrinos and
antineutrinos have slightly different native properties [28]. Sterile
neutrinos are also a contender [29].
A variety of supersymmetry theories including grand unification
theories (GUT), the Affleck–Dine mechanism [30], and heavy
401
Majorana neutrinos [31]. However the evidence for
supersymmetry is not compelling, and the simpler versions are
not evident in the LHC data from CERN [32] as might be expected.
This is not a complete list, but rather indicative of the theoretical
approaches. There are many hybrids between these approaches, and
some also address dark matter, e.g. [33]. The predominant method is
mathematical analysis and modelling, almost without fail, and within the
bounds of such a method there is evidence of much creativity and
innovation. However there is no obvious way to judge the validity of the
many solutions, except by building large colliders to check the existence of
the new particles they predict.
At present neither the Standard Model of quantum mechanics (QM), nor
current extensions thereof, nor supersymmetry, can explain baryogenesis
[34]. More complex models of those theories may yet be successful, or it
may be that a different physics is required.
The purpose of this paper is to apply the cordus conjecture [3], which reconceptualises the internal structure of particules, to explore the
asymmetrical genesis of matter-antimatter. Cordus proposes that the
particle is not a zero-dimensional point, but has two reactive ends and
discrete field structures, see Figure 1 for some examples of the
structure.110 The idea has been used to explain several effects including
wave-particle duality [4], entanglement [5], electricity-magnetismgravitation [6], matter and antimatter [1], annihilation [9], neutrino
structure [14], and the weak interaction [15].
Our previous cordus work on the field structure of the neutrino [14],
suggested that the neutrino was not a Majorana particle, and also
precluded the existence of the right-handed neutrino. If true, this would
invalidate many of the above theories, so it is clear from the outset that
the cordus approach is not going to be orthodox.
110
The cordus conjecture is that all particles, e.g. photons and electrons, have a specific
internal structure of a cordus, comprising two reactive ends, with a fibril joining them. The
reactive ends are a small finite span apart, and energised (typically in turn) at a frequency,
at which time they behave like a particle. When energised they emit a transient force pulse
along a line called a hyperfine fibril (hyff), and this makes up the field. We call this a cordus
‘particule’, and stress it is very different to the zero-dimensional point assumed by
conventional physics.
402
Figure 1: Cordus models for the electron, antielectron, and photon. The
basic cordus structure is shown, including reactive ends, fibril and hyff. Also
shows are the different characteristics of their hyff pumps: oscillating and
fibrillating. Underneath is the shorthand representation of the field
structures using cordus HED notation. For HED notation see [10].
Fundamentally what we need to do is show how photons could be
converted to massy particles including electrons and protons, with a lesser
number of antiparticles.
Pair production and Two-photon physics
Where two photons are involved, conventional physics assumes that
photons do not couple directly with each other, but instead one of the
photons fluctuates into a particle-antiparticle pair, and the other photon is
absorbed into (couples to) one of those particles, hence two-photon
physics. The particle-antiparticle pair is thought to comprise leptons or
quarks, and their antiparticle, e.g. pion or kaon pairs. The fluctuation is
held to be a random event driven by the Heisenberg uncertainty principle.
403
Unfortunately the mechanism for converting a photon into a matterantimatter pair is unknown. This is an obstacle to the understanding of
baryogenesis: if we do not understand the first stage of conversion into
particle-antiparticle pairs, then it is going to be difficult to find where the
asymmetry creeps in. So we probably have to understand the pair
production process first.
Cordus has already shown why the problem is difficult: the nature and
number of field structure (hyff) for the photon (one at each reactive end,
fibrillating) is very different to those of the massy particules like the
electron (one or more, pulsating) [8]. So the conceptual leap from the one
to the other is large: they are not simply similar states that can randomly
jump from one to the other in some Markov-like process. Instead there are
substantial structural changes that are required to convert a photon into a
quark or electron.
Fortunately cordus also suggests some solution paths that could be
explored, and some to be avoided. There is no value in approaching it from
the uncertainty principle, for two reasons. First, that principle is devoid of
deeper mechanisms: it is merely a statistical summary. Second, cordus
refutes the conventional uncertainty principle as it is usually formulated,
though supports a modified form [5]. Instead a more useful approach
would seem to be via the discrete field structures of particules. QM does
not have a robust theory in this area, but cordus does and has already
used it to explain the annihilation process [9-10], infer the structure of the
neutrino [14] and the W bosons [15]. So the idea is to draw on this theory
to work out how photons are converted to electron-antielectron pairs, and
then examine how the antielectron can be remanufactured.
2
Method
Our previous work on neutrino structure [14] provided an interesting clue
for the genesis question, since it suggested that the purpose of the
neutrino was to remove unwanted HEDs, including those of the unwanted
hand, from assemblies.
‘Unwanted hand’ is exactly the genesis asymmetry problem. This is
because the difference between matter and antimatter is ma-hand, at
least in the cordus explanation [1]. So the germ of the concept is this: Is it
possible that the neutrino (or antineutrino) might have removed the
unwanted hand from antimatter? Starting from photons, is it possible to
conceptualise a genesis process where the antimatter is consumed within
the process, so that the asymmetry never arises?
We now explore that idea by working out the field structures for a genesis
scenario. The method used is HED notation [10] and the HED mechanics
for the manipulation of these field structures in re-assembly situations
[14]. HED notation models the three hyff emission directions (HEDs) at
each of the two reactive ends of a particule, and how those HEDs are filled
with hyffons (discrete field elements).
404
3
Genesis via discarded neutrinos
There are three stages in this genesis model, and they are all important.
We first provide a cordus model for the production of an electronantielectron pair from photons. We then show how the involvement of the
antineutrino can remanufacture the antielectron into a proton. Thereafter
we explain why the process consumed antielectrons rather than electrons.
3.1
Production of an electron-antielectron pair
Cordus model for annihilation
We have already shown how the process of electron-antielectron
annihilation occurs [9]. We produced a 3D model of how the discrete field
structures (hyffons) of those two particules reassemble and form photons.
We can also represent the process symbolically in the HED notation [10]:
e(r1 .a1 .t1)|0 deg + e(r1 .a1 .t1)|180 deg
=> O(r11 .a11 .t11)
=> yb(r! .a .t)|0 deg + yc(r! .a .t)|180 deg
=> yb + yc
=> 2y
Thus an electron-antielectron pair annihilates to two photons.
The inverse process is known to occur, whereby a photon transforms into
an electron and antielectron, hence pair production. It is commonly
represented as involving a single input photon.
Cordus production of an electron-antielectron pair
The cordus model for production of an electron-antielectron pair is simply
a reverse of the annihilation process:
2y => yb(r! .a .t)|0 deg + yc(r! .a .t)|180 deg
=> O(r11 .a11 .t11)
=> e(r1 .a1 .t1) + e(r1 .a1 .t1)
However we need to check that process further, and work out the details.
Note that cordus suggests that two photons are required (not one) for the
production of an electron-antielectron pair, and that they need to be in
complementary (opposite) phases. So there is a small discrepancy
between cordus and conventional physics regarding the number of
photons involved, and the way they couple. Possibly this may be testable.
Of course, if a single photon is able to split into two sub-photons of
opposite phase – which cordus does not forbid – then there may be no
discrepancy at all. Either way, we do not think it is a big obstacle, as the
405
larger point is that production of an electron-antielectron pair is possible:
both cordus and quantum mechanics agree on that.
The 3D field-model for cordus electron-antielectron pair production is
shown in Figure 2.
The Reader is referred to the diagram for a detailed explanation. In
essence, the incoming photons are unable to negotiate shared use of the
field emission directions (HEDS) (1.3), nor evade each other, so are forced
to convert to the oscillating type of reactive end instead (2.1). This type
has one reactive end active and the other dormant, thereby satisfying the
constraints. The process also creates a new fibril to coordinate the new
pairs of reactive ends (2.2). This type also requires three hyff, so a 3D field
structure is set up (3.1) according to the ma hand system (4.1).
406
Figure 2: The cordus production process for converting two photons into an
electron-antielectron pair.
407
Curious features and future work
We acknowledge that we have not explained all the deeper mechanics of
how the reactive ends transform, nor even identified the composition of
the fibrils and hyffons. At this point we simply propose their existence as
part of the cordus lemmas, and leave their elucidation for future work.
However there are two effects that are curious and need commenting.
The first is that we need to assume that the outward hyffons take the
forma hand, not hyarma (4.2). We do this to avoid the formation of the
positive notElectron !e(r1 .a1 .t1) and negative antinotElectron !e(r1 .a1 .t1)
at step 5.2. We came across these structures previously in the model for
the neutrino-antineutrino annihilation process [15](lemma Ma.7.3). We do
not see these structures in our universe. As we identified there, we are
uncertain whether these structures are an artefact of the cordus HED
method, or really are forbidden. If the latter, we suspect that the
verboten-constraint arises with the ma hand: the primary charge in the
forma hand is negative, as indeed the definition of the hand shows. In
other words, there are only two hands in a 3D world, and for these to be
unique regardless of rotation, the direction of the arrows (direction of
propagation of hyffons) must also be built into the hand.111
To put it another way, a notElectron cannot form alone, but would be
accompanied by an antinotElectron. There is a precursor assembly
structure, and it has no incentive to go down this particular path. Also,
where notPositronuim assemblies might occur, they can reverse back out
into photons instead [15].
The second issue is that the output electron and antielectron particules
could bond to form parapositronium and then annihilate back to photons
(5.3), see [9-10]. To avoid this, they must be parted before they form such
bonds. We have not worked out the parting mechanism in detail. Our
current concept is that an elastic recoil and separation of the two
particules occurs, due to the way the span varies dynamically with
frequency cycle (5.4).
Therefore, these other matters outstanding, we have provided a
conceptual model for how the field structures of the photons are
reassembled into an electron and antielectron.
The next concept shows how to get rid of the antielectron.
111
So there are two basic configurations of the twin-hand-system, and therefore the
deeper question is why the pre-universe physics chose forma to be negative charge not
positive (and hyarma positive not negative). However we can dismiss this, on the grounds
that the universe had to go with one configuration or the other, and the outcome would
have been the same to any observer inside the universe.
408
3.2
Remanufacture of the antielectron
We now show how the antielectron (positron) may have its hand changed
to convert it into matter.112 In summary, the waste antimatter hand is
discarded in the antineutrino. We illustrate this process with the HED
notation.
HED model of leptogenesis and baryogeneis
Given the electron-antielectron pair production:
2y => e(r1 .a1 .t1) + e(r1 .a1 .t1)
Now add the energy equivalent of an additional two photons in the form
of a triple bolus (↓↓↓ = r11 .a.11 .t11), and a twin-pair (↑↓ = x1111). These
arrows represent balanced pairs of hyffon-antihyffon, and their mechanics
were identified in the work on neutrinos [14]. Essentially, these
structures are balanced regarding both charge and hand (matterantimatter). Thus a single hyffon pair, ↑ or ↓ may not be added, only a
twin set or a triple bolus. The hyffon pairs are added by inspection, with a
particular target in mind. In this case the target is a proton, the HED
structure of which has also been previously inferred [14]. Thus the
production process is:
2y + 2y => e + e(r1.a1 .t1)( ↓↓↓)(↑↓)
Now bring all the hyffon-antihyffon pairs (arrows) into the antielectron113
and expand them to create a transitional structure O:
=> e + e(r1↑↓↓ .a1↓ .t1 ↓)
=> e + O(r1.111111 .a1.11 .t1 .11)
Intermediate structures like this are unstable since they have hyffons of
mixed hand (matter-antimatter) and they are overloaded with hyffons.
Other examples of these assemblies are the W and Z bosons [15]. They
have a tendency to reorganise into simpler and more stable structures.
Extract a proton p(r111.a1.t1) and put the remaining hyffons into another
transitional structure O1:
=> e + p(r111.a1.t1) + O1(r1.11.1 .a11 .t1 1)
Extract an antineutrino v(r11 .a .t11 ) and put the remaining hyffons into a
transitional structure O2:
=> e + p + v(r11 .a .t11 ) + O2(r1 1 .a11 .t)
Move the hyffons about in O2 (colour change) and identify it as another
antineutrino:
112
We generally use the term ‘reassembly’ for the movement (colour change) of hyffons in
the processes of particule transformation. However we use ‘remanufacture’ in this
particular transformation since it is the change in hand (L: manus) that is the focus.
113
Note the assumption that it is the antielectron that transforms, not the electron. We
explain why later.
409
=> e + p + v+ v (r1 1 .a .t1 1)
Therefore the reaction as a whole is
2y + 2y => e + p + 2v
To sum up, the cordus model for genesis shows that four photons are
remanufactured into an electron, a proton, and two antineutrinos.
This prediction may be testable and falsifiable.
3.3
Dominance of the matter-production stream
Why did the forma matter hand prevail?
This model starts with the production of an electron-antielectron pair,
after which the antielectron is remanufactured. By why the antielectron?
Why were electrons not remanufactured to antiprotons? Why not 2y + 2y
=> e + p + 2v instead?
In other words, while we may have solved the problem of where the
antimatter has gone to, there is a deeper asymmetry. What switched the
production process to the matter route?
Our current conceptual answer is that there may have been a species war
in the beginning, where both production processes were at work. We
imagine an initial extraordinarily energetic photon-pair colliding114 and
producing an electron and antielectron. With both streams of the
remanufacturing process active, electrons and protons would have been
created, alongside antielectrons and antiprotons. Any mixing across the
species would have further annihilated back to photons. Those photons in
turn would have been available to feed back into the production
processes again, providing they were energetic enough.
At this point we invoke the cordus field model for electrostaticmagnetism-gravitation and the fabric [6, 11, 35]. Once some matter and
antimatter particules had formed they would produce handed hyff and
propagate those out, producing a proto-fabric (spacetime). That fabric
would carry a matter forma hand, or an antimatter hyarma hand [1]. In
turn that fabric would
predispose the production processes it
encountered to switch into the same hand. The massy particules would
have extraordinary energy, hence high frequency. In turn that frequency
would create an enormously high mass and strong fields.
Domains of matter and antimatter may have formed, being multiple
separate volumes of space where one of the hands dominated. Generally
we would expect that these domains would be geometrically symmetrical
with respect to each other.
114
Readers who prefer a faith interpretation could call this the ‘Handclap of God’.
410
There could have been a stage of domain warfare as the domains
aggregated, broke up, and forcibly converted opposing domains. We
assume that somewhere in there the geometric symmetry broke down, so
that the matter and antimatter domains were not the exact mirror images
of each other. We can see several possibilities for how the geometric
asymmetry might first have arisen: external perturbation from outside the
universe; a random event in an increasingly large and disorderly system,
i.e. a consequence of growing complexity; a natural oscillating dominance
between the two species that was frozen in as the system expanded and
cooled, i.e. the proto-universe was flipping between matter and
antimatter dominated states when suddenly the fuel was cut off and the
state at the time dominated. This last idea is our currently preferred
model.
Cosmological start-up process
Whatever the cause of the switch, the forma fabric obtained the edge in
dominance, and grew that to dominate the cosmos. This forma fabric then
controlled which branch the remanufacturing process took, and thus
antielectrons were converted to protons, rather than electrons to
antiprotons. With time115 the proto-universe became dominated by
matter.
The production process would have caused the particules to move
outwards (Ma.9.1.5). Also, the initially high-energy protons and electron
would blow off their extra energy as photons. This and the cascade of
formation-annihilation would have produced a cloud of photons, the
energy of which would have decreased as the process consolidated
energy into massy particules and the products expanded. Also, the
photons themselves would move and escape, and therefore become
unavailable for reuse. Eventually the genesis photon cloud would be too
cool and lacking in density, and the formation of matter would abruptly
cease.
Why do we not see this process today?
The photon density and energy in the current universe are insufficient for
the remanufacture process to convert antielectrons into protons. Also,
the fabric density in the current epoch is too low to predispose the
remanufacture process exclusively into the matter branch. So
antielectrons are allowed to exist at this stage, whereas they would have
been mangled to protons in the early universe.
To sum up, the remanufacture process initially had two balanced
workstreams, converting antielectrons into protons, and electrons into
antiprotons. However the process was biased into the former. The
tentative explanation is that the two process streams oscillated in their
dominance and this was frozen-in as the system cooled.
115
Time in the cordus context refers to the frequency cycles of the particules involved,
rather than any absolute time. So time would have passed in the early universe, but since
the particules had high energy and therefore high frequency, time would have flowed very
fast.
411
3.4
Other implications
Looking at the equation 2y + 2y => e + p + 2v and noting that in general all
these equations can be reversed, suggests that that the proton may not be
absolutely stable. Hitting it with two antineutrinos should remanufacture
as follows:
p + 2v => p(r111.a1.t1) + v1(r 11.a.t1 1) + v2(r11.a.t1 1)
=> O(r1111.11.1.a1.t1. 1111) => |% + O(r1111.11.1.a1.11.t1.11)
=> e(r1.a1 .t1) + O1(r11111.1.a11.t11)
=> e + O2(r11.a11.t11) + |% + O3(r1111.a.t)
=> e + O2( ↓↓↓) + O3(r1111.a.t)
=> e + 2y + O3(r↑↓.a.t)
=> e + 2y
Where:
(r11.a11.t11) = (↓↓↓) = 2y
r1111 = ↑↓ = nil
|% = movement of hyffon to different HED (colour change)
This conceptually confirms the reverse direction. What this means is that
the proton could unravel back into a positron and two photons, with the
right kind of forcing by antineutrinos. However, given the low reactivity of
antineutrinos, and their high speed, this would be a rare event.
4
Discussion
4.1
What has been achieved?
The main conceptual contributions of this work are:
• A detailed model has been produced for the production of an
electron-antielectron pair from photons. The novel contribution is
showing how the discrete field structures of the photon
dynamically transform into those of the two massy particules. This
model is conceptual in nature.
• A production process has been envisaged whereby an energetic
antielectron is remanufactured into a proton and two
antineutrinos. This idea appears not to have been considered
before, and therefore may be novel in itself. In addition, the
possible production process itself is detailed, and the inputs and
outputs are predicted.
• The production process could equally have converted electrons to
antiprotons, and a tentative explanation is given for why this
might not have happened.
412
•
The conditions are identified under which the proton may decay.
Qualitative description of genesis
This genesis process is therefore conceptually very simple: two initial
photons get converted into an electron, and an antielectron. The
antielectron receives another two photons, the field structures of which
are used to form a larger structure that re-assembles into a proton and
two antineutrinos. The original electron and proton combine to form a
simple hydrogen atom. Fortunately for us in this universe, the
antineutrinos have almost no reactivity with matter, so they simply escape
the scene. The antineutrinos produced at the original genesis of the
universe will now mostly be at the outer edge of the universe, having got
into motion before the massy particules.
Purpose of the neutrino
Effectively the antielectron (positron) is reassembled, with some input
energy, into a proton. The antimatter hand of the antielectron is carried
away by the antineutrinos as a waste stream. Thus the purpose of the
neutrino and antineutrino in the grand scheme of the particules is to
remove unwanted HEDs, and in doing so it has the ability to also remove
unwanted hand.
Dissolving the asymmetry
The significance is that we do not need to worry about the asymmetry of
baryogenesis. Where has all the antimatter gone? The antimatter is hiding
in plain sight, having been remanufactured into the matter baryons
themselves. Well, almost all, since a small amount of the original
antimatter energy has been discarded into the waste stream of
antineutrinos.
Curiously, this cordus explanation suggests that it could be true, in a way,
to say that the antimatter has been pushed to another part of the
universe. However it is not antimatter in the form of antiatoms, antisuns,
and antigalaxies, but a plain desert of relatively inert antineutrinos spread
through the matter universe and at its edge.
4.2
What are the implications?
Parity violation
It may not be explicit, but the cordus genesis solution also implies a new
concept for parity. Quantum mechanics struggles with parity. Historically
there was an expectation that a particle and its oppositely-changed
antiparticle should behave with the same physics (C-symmetry). This has
been observed to be the case for effects like electromagnetism. However,
it does not hold for quark-level interactions, so the next step was to add
parity-symmetry, which is mirroring the co-ordinate system. Thus parity
refers to symmetry of behaviour between a particle and its mirror
structure (spatial inversion). Combining this with charge symmetry results
in CP-symmetry, in which it is expected that behaviour should be the same
413
for a particle and its spatially inverted antiparticle, i.e. that charge and
parity were always inverted together so that the combination was still
preserved. However that too has been observed to be violated in kaons
(particles comprising two quarks).
QM cannot explain why parity is violated, nor use the information in its
baryogenesis models. This is a consequence of the QM insistence that
particles are 0D points. A point has insufficient dimensions to support
many variables, so it is reasonably obvious that particles cannot really be
points at all, if we wish to have physical realism. Cordus provides an
internal structure for particules, and therefore many more variables to
explain effects like polarisation, spin and parity. The reason for CP
violation becomes clear with cordus: the particule has a finite span, being
the geometric distance between the two reactive ends. Nor are the two
reactive ends energised simultaneously (except for the photon). Thus a
particule is not symmetrical: a mirror image of the handed HED field
structures of one reactive end is not identical to the other end.
Furthermore, the mirror image of one whole particule is not identical to
itself, and this is a key feature in the cordus model for antimatter [1].
Parity/handedness proved to be one of the keys in the cordus method for
unlocking the problem of asymmetrical genesis. (That and the neutrino
structure). The concepts of parity and handedness are core components in
the cordus explanations of matter-antimatter, annihilation, and pair
production. In turn those ideas were all used in the cordus genesis model.
It is difficult to see how any genesis model could be created without some
prior concepts for parity/handedness. The problem with quantum
mechanics is that it assumes that matter is a zero-dimensional point [36]
and therefore cannot construct a handed co-ordinate system.
Limitations
Cordus is a conjecture and there is no certainty that its mechanics are
valid. It is based on a large set of assumptions or lemmas, any number of
which could be wrong. We prefer to consider it a thought-experiment, or
candidate solution, and a contribution to the ongoing epistemic journey of
fundamental physics. The cordus conjecture does not have to be totally
correct to achieve that. If the cordus conjecture were to be substantively
true, then the implications for fundamental physics would be profound,
because it refutes the 0D point construct of orthodox physics, and the
edifice built on that conceptual foundation.
The whole of the cordus conjecture could readily be falsified by showing
empirically that there is no possible way that data support an
interpretation of a particle having two ends.
Implications for future work
There are several streams of potential future work. First, that the cordus
conjecture needs testing for validity. Second, and if it passes that test, it
will be necessary to quantify it, i.e. build a mathematical model around
the concepts. If cordus is correct, then we would still expect it to be able
414
to accommodate much of the QM machinery [37], which obviously works
for most things.
5
Genesis lemmas
We made several assumptions in the genesis model, and these are
summarised below as a set of lemmas. Each of these papers in the cordus
series has identified its assumptions in this way, and together they form a
qualitative statement of the cordus mechanics.
Ma.9 Asymmetrical genesis
Ma.9.1
Production of an electron-antielectron pair from photons.
Ma.9.1.1
Two photons are required (not one) for the
production of an electron-antielectron pair.
Ma.9.1.2
These need to be in reinforcing phases, incident
on each other, and the same frequency.
Ma.9.1.3
Where hyffons from fibrillating reactive ends
(photons) are unable to negotiate shared use of
the field emission directions (HEDS), nor evade
each other, the issuing reactive ends may be
forced to convert to the oscillating type of reactive
end instead. The process also creates a new fibril
to coordinate the new pairs of reactive ends, and
requires the setup of a 3D field structure according
to the ma hand system.
Ma.9.1.4
Outward hyffons must take the forma hand, not
hyarma. Hence the formation of the positive
notElectron !e(r1 .a1 .t1) is verboten. This is because
the primary charge in the forma hand is negative.
Ma.9.1.5
An elastic recoil and separation of the resulting
electron and antielectron occurs, rather than
immediate annihilation, due to the way the span
varies dynamically with frequency cycle.
Ma.9.2
Ma.9.2.1
Ma.9.2.2
Ma.9.2.3
Ma.9.2.4
Cordus model for genesis
Four photons are remanufactured into an
electron, a proton, and two antineutrinos:
2y + 2y => e + p + 2v
The antimatter hand of the antielectron is carried
away by the antineutrinos as a waste stream.
The predominance of the forma (matter) hand at
the start-up of the cosmos was due to warfare
between the matter and antimatter domains. The
currently preferred model, though there are other
candidates, is that a natural oscillating dominance
between the two species was frozen in as the
system expanded and cooled.
The apparent asymmetry of baryogenesis is
because the antimatter is hiding in plain sight,
415
having been remanufactured into the matter
baryons themselves.
Ma.9.3
Ma.9.3.1
6
Proton stability
The proton could unravel back into a positron and
two photons, when struck by two antineutrinos.
Conclusions
What has been achieved here is a novel alternative conceptual model for
the asymmetry of matter over antimatter in the universe. We started with
the basic cordus idea that particles are not 0D points but have a distinct
internal structure with two ends, and accept previous conceptual models
for matter and antimatter and the annihilation process.
We then created a descriptive model for electron-antielectron pairproduction, showing how the structures of the photon are reassembled
into an electron and antielectron. That is a novel accomplishment in itself,
though of course its validity depends on that of the underlying cordus
conjecture itself.
Thereafter we showed that it was conceptually feasible that the
antielectron could be eliminated using antineutrinos. In this cordus model
for genesis it is proposed that four photons are remanufactured into an
electron, a proton, and two antineutrinos. The original electron and
proton combine to form a simple hydrogen atom. The antineutrinos have
little reactivity, so they escape. The antimatter field structure of the
antielectron is carried away by the antineutrinos as a waste stream.
We also gave some explanations for why the matter hand prevailed, not
antimatter, during the cosmological start-up process. Therefore the
apparent asymmetry of baryogenesis is because the antimatter is hiding in
plain sight, having been remanufactured into the matter baryons
themselves.
To answer the question identified at the outset:
Why is there more matter than antimatter in the Universe?
The initial process converted energy into equal quantities of
matter and antimatter, in the form of electrons and antielectrons
(positrons). We propose that a second process converted the
antielectrons into a matter form, namely the protons, and the
waste antimatter component was carried off by antineutrinos.
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418
Cordus
Conjecture
Part 7: Philosophy and physics
Cordus
conjecture
used to predict the
limits of coherence,
and implications for
philosophy
are
explored > explains
why there is no
coherence in living
creatures
>
explanation of where
time
and
irreversibility arise >
mechanisms
that
create the arrow of
time
41
Limits of coherence: Where and why is the
transition to discoherence?
D. Pons116
Abstract
This paper provides a conceptual solution to the questions of what causes
discoherence and where the limits of coherence might be. Coherence is
reinterpreted from the cordus perspective, as being a state when all the
particules have synchronised frequencies and phases thereof, i.e. a form of
complementary frequency state synchronisation (CoFS). Alternatively
coherence can be perceived as a special state of assembly where the
particules provide for mutual preservation of the de-energised locations of
each other. Cordus anticipates three mechanisms for discoherence. First, a
coherent material cannot accept internal shear velocity. Second, higher
temperatures lead to decoherence because phonons (internal thermal
vibrations) disturb the stability. Third, more complex assemblies of matter
are harder to put into coherence, and the complicating factors are
expected to be the number of components in the assembly, and the variety
of species (simplicity and purity). Accordingly,
the upper limit for
coherence could be a simple crystal, or perhaps even a virus, with a limited
number of species (different molecules or elements), at low temperature.
However this is thought to be an optimistic prediction. This model predicts
that coherence is already unachievable at the assembly level of the
smallest metal grains, mineral crystals, and cell organelles, at ambient
temperature. Thus warm macroscopic objects and living creatures cannot
be put into coherence or superposition. However there is no problem with
having coherent domains within a discoherent body, e.g. molecules that
are internally coherent. Single particules, such as electrons, are selfcoherent under any conditions.
Edition 1 > Date: Saturday, 11 February 2012 > Document: Pons_Cordus_6.0_CoherenceLimits_E1.0.9.doc
1
Introduction
Surprisingly, quantum mechanics (QM) does not apply to reality at our
macroscopic level of existence, nor to the universe at large. To be sure,
there are some contrary perspectives: e.g. the many-worlds theory, or
observer-dilemmas (such as a literal interpretation of the Schrodinger’s
cat thought-experiment). Nonetheless the physical evidence is that QM
does not apply macroscopically. The strangeness it that does apply so well
to the particle level.
116
Please address correspondence to Dr Dirk Pons, Department of Mechanical
Engineering, University of Canterbury, Private Bag 4800, Christchurch 8020, New
Zealand, Email: dirk.pons@canterbury.ac.nz. Copyright D Pons 2012.
420
Quantum behaviour, specifically superposition of location, is only evident
in particles and some microscopic objects cooled to close to absolute zero
temperature [1-2]. QM suggests should it should be attainable in larger
and warmer objects [3], but this has proved difficult to achieve. Clearly
there is a discontinuity in the physics between the small and large scales
of nature. It is not clear where the boundary is between the quantum
world of particles and the macroscopic world, and quantum mechanics
itself cannot identify why there should be a boundary, nor where it would
be.
Purpose of this paper
The purpose of this paper is to apply the cordus conjecture [4] to
determine where in the scale of things the transition occurs between
coherence and discoherence, and why the limits are where they are.
The point of comparison is the cordus conjecture, with its predicted
internal geometry for particules. This paper builds on earlier work which
explains why quantum mechanics does not scale up [5].
What is the cordus conjecture?
The cordus conjecture is a novel alternative theory of fundamental
physics, constructed on a different concept for ‘particles’. It is currently
primarily a qualitative conceptual method [4].
The conjecture states that all 'particles', e.g. photons of light, electrons,
and the protons in the nucleus of the atom, are not zero-dimensional
points, but have a specific internal structure called a 'cordus'. The term
‘particule’ is used to differentiate this important conceptual difference
from the QM construct. The cordus consists of two ‘reactive ends’, which
are a small finite distance apart (‘span’), and each behave like a particle in
their interaction with the external environment. A ‘fibril’ joins the reactive
ends, and is a persistent and dynamic structure, but does not interact with
matter [6]. The reactive ends are energised (typically in turn) at a
frequency [7]. The reactive ends emit one or more force lines called
‘hyperfine fibrils’ (hyff) into space, and when the reactive end is energised
it sends a transient force pulse (‘hyffon’) outwards along the hyff curve [8].
This makes up the field, which is thus also discretised in 3D space. Various
features of the hyff and hyffon carry the electrostatic field, magnetism,
and gravitation simultaneously. Thus a unification of these forces is
provided [9].
In this model the photon has a single radial hyff which it periodically
extends and withdraws [6]. By comparison all massy particules have
permanent hyff (including neutral particules like the neutron)[8], see
Figure 1. Electric charge is carried at 1/3 charge per hyff, so stable
particules like the electron are surmised to have three hyff, arranged
orthogonally [10]. The hyff from multiple massy particules compete for the
three hyff emission directions (HEDs), and may synchronise their emissions
to access those spaces. Thus there is an element of mutual negotiation,
421
based on shared 3D geometric timing constraints, and this explains the
strong force [10].
Figure 1: Models for the photon and electron, showing the different
characteristics of their discrete field structures. The photon has a
fibrillating pump that only shuttles energy outwards and then immediately
afterwards brings it back inwards, whereas the electron consistently
pushes hyffon (force fragments) outwards in a pulsating manner. Both
cordi therefore have a frequency, but the difference is what they do with it.
All other matter and antimatter behaves like the electron, though the hand
of the hyff is inverted for antimatter, and the direction of pumping is
reversed for positive charge.
In terms of its conceptual design, cordus has high fitness because it is able
to explain many effects within one logically consistent framework [4].
However, cordus is a conjecture and the validity thereof is uncertain.
Therefore derivatives of the idea, as here, should be considered
speculative. They are also exploratory and subject to possible future
revision.
2
Reconceptualising coherence
Reinterpreting coherence
We need to clarify what we mean by coherence, because doing so helps
understand where it breaks down and why. As usual, the cordus concept
that emerges is radically different to the orthodox interpretation, and
these two should not be confused. Cordus refutes the QM concepts of
particle and causal (temporal) superposition, though accepts positional
variability [5]. The following explanation is summarised from [11] and [5].
From the QM perspective coherence is the ability for particles to interfere.
This includes constructive and destructive interference of photons or
422
waves (hence fringes), and dependencies (‘correlation’) between two
different particles. The dependency may exist to a greater or lesser
extent, i.e. involving more variables between the particles. There is also
the matter of how strongly the dependency is preserved over time. The
concept of coherence also includes the idea that only one wave or particle
is involved: that its properties at one instant of time can be linked those at
a different location or time (‘self-coherence’). Examples of QM coherence
at the large-scale include the laser, electrical superconductivity, and
superfluidity. Nonetheless, even within QM there are differences of
opinion about the interpretation of coherent states [12]. Quantum
mechanics does not obviously apply to large bodies, living creatures, or the
universe as a whole.
From the cordus perspective, superposition is simply that the cordus
particule is actually physically oscillating between two positions: the
locations of the reactive ends at the end of their span. The cordus particle
(e.g. photon cordus) collapses to one of these ends when it is grounded
[11].
Mechanisms for coherence
Coherence, from the cordus perspective, is when all the particules, which
may be photons, electrons, protons, and possibly atoms & molecules, etc.,
have synchronised frequencies and phases thereof, i.e. a form of
complementary frequency state synchronisation (CoFS) [11]. The bonds
between any cordus particles are hyff and carry forces that synchronise
the cordus frequency and phase of particules, providing the frequencies
are compatible. We term this ‘body coherence’. For photons in light
beams, where the bonds are weak if they exist at all, the coherence may
be mainly temporal and coincidental.
Coherence is a special state of assembly where the particules provide for
mutual preservation of the twin locations of each other: when any one
particule is energised at its one reactive end, the position of its other
dormant reactive end is filled by the active end of another particule.
Coherence is, according to cordus, best understood as an ordered
complementary relationship (COFS) between two or more particules [11].
Thus in a coherent body, e.g. Bose-Einstein condensate or superfluid, the
positions of all the reactive ends are locked together in a complementary
sharing relationship. The positions of the reactive ends would otherwise
change in response to external fields, perturbations from the fabric, and
the impositions of impinging particules [13].
Particules in coherence with each other develop a negotiated state of
sharing the 3D hyff emission directions (HEDs). (Much like planes shuttling
between two nearby airports and sharing landing slots). External fields,
which are also hyff whether from the fabric or nearby matter of the fields
created by remote particules, can upset that negotiation. The coherent
state has some protection from the close timing of the participating hyff
(providing the material is pure): we see the same mechanism at work in
the strong force. However with larger assemblies the HEDs are negotiated
423
at longer ranges, and are therefore weaker, hence more vulnerable to
disruption by external hyffons. Implicit in this cordus explanation is an idea
that the external environment, even of the vacuum, consists of a fabric of
hyffons [14].
Mechanisms for discoherence
All macroscopic objects in our world are discoherent as a whole. They
cannot be coherent, and cordus gives three reasons why.
First, in the specific case of living creatures, there is a requirement for
internal flows of matter, which is incompatible with the lock-step nature of
a coherent material. To put this requirement another way, a coherent
material cannot accept internal shear velocity (dynamic relative motion of
the particules), though it can tolerate some shear strain (static relative
deformation). This behaviour is also evident in superfluidity.
Second, hot bodies tend towards discoherence, because the resulting
phonons (internal thermal vibrations) disturb the coherence. Quantum
coherence is known to be a delicate state that is easily disturbed, as
evident in the limited success with high-temperature super-states. Cordus
is not a quantitative model and so cannot predict the temperatures
involved.117
Third, more complex assemblies of matter are harder to put into
coherence, and cordus suggests that the factors are simplicity and purity.
For a simple and pure assembly, consider two electrons sharing an orbital:
a simple structure (only two particules) between pure components
(homogeneous states of frequency, energy, etc.). (See Figure 2, level 3).
This pair of electrons are coherent, hence the Pauli Exclusion principle. So
the electron-pairs in a living creature are coherent even if the creature
itself is not.
Atoms are more complex assemblies of particules with different masses,
hence frequencies [7]. Cordus suggests that stability of these assemblies
requires consonance of the frequencies of the individual components
(hence the energy quanta of electron orbitals). Atoms manage this and are
therefore internally coherent. (See Figure 2, level 4). Probably molecules
too (level 5).
As with any coherent structure, the effect of an externally imposed change
is communicated to neighbouring internal components at the next
frequency cycle. For assemblies with high purity, this may be fast indeed,
hence second sound in superfluids, and rapid electron transmission across
117
Cordus suggests that materials with stronger internal bonds should be capable of coherence at
higher temperatures. This is because coherence is effectively the strong force writ large, i.e. a
synchronised HED effect > it is already known that the strength of the strong force drops steeply with
range > so the geometric nature of the assembly should determine the range of the required bonds,
and thus the bonding strength within the assembly > some assemblies will have long-range hence
weak bonds, and therefore be fragile to disruption by thermal phonons > the relationship between
temperature and severity of phonon will need to be established.
424
biological molecules.118 Hence also the successes in putting molecules into
geometric superposition. Thus communication within atoms and
molecules is rapid, being able to take advantage of the internal frequency
network.
Many atoms of a pure material may be brought into coherence, though it
apparently needs a low temperature (level 6) to reduce the phonons to a
level that the bonds can withstand. Hence superfluids, and the success
with the likes of pure iron objects showing geometric superposition at
cryogenic temperatures.
However, as temperature rises, or the variety of components increases
(purity decreases), or more particules are assembled, so coherence
becomes difficult.
Thus, according to this model, coherence is already unachievable at the
assembly level of the smallest metal grains, mineral crystals, and cell
organelles. However, note that the atoms within those are always
internally coherent.119
Macroscopic diamond crystals appear to have shown entanglement [1516], however the implications are debateable. That experiment sent a
coherent photon into each of two diamonds at room temperature, using
an interferometer, and observed that the resulting phonons were
correlated for a short time (~7ps). Sending another photon pulse into the
diamonds caused a coherent photon to be emitted. They interpreted that
as entanglement of the phonons, i.e. that there arose ‘a single phonon
excitation distributed across the two crystals’ (p1254). The cordus
interpretation is the correlation between the phonons was simply a
temporary artefact caused by a photon with two reactive ends.120 From
the cordus perspective, the reason the phonons were correlated at all was
because (a) the beam splitter separated the reactive ends of the photon
into two paths, and (b) the purity of the diamond material and its
consistency between the two samples, so that the two phonons were
initially sufficiently similar. Thus the subsequent measurement-photon,
which followed soon after, was affected in the reverse way, and picked up
the energy in the phonons. In this interpretation the phonons are merely a
precarious short-term vibratory storage device for entanglement, rather
than themselves being entangled. If the diamonds were replaced with
118
For a descriptive overview of quantum biology, and applications to odour reception, electron
transfer in ATP, & photosynthesis, see Brooks, M., The weirdness inside us. New Scientist, 2011.
2832(1 October 2011): p. 34-37.
119
Atoms have to be internally coherent, at least while they exist as atoms. This is because the
interactions of the hyff emission directions create both the strong force holding the atom together,
and the coherent behaviour.
120
The competing explanation provided by the cordus conjecture: photons have two reactive ends
separated by a fibril > the beam splitter of an interferometer sends the reactive ends down different
legs > in this case for the input photon, one reactive end went into each diamond > each reactive end
created a phonon in its diamond > those phonons naturally had inverse-symmetry, due to the
communicative effect of the fibril joining the reactive ends > those phonons therefore initially showed
correlation between each other, but this decays with time > a subsequent probe photon likewise sent
one reactive end into each diamond > the reactive ends of the probe photon picked up the energy of
the local phonon and assimilated it into the photon> the probe photon emerged with higher energy
and was picked up at the detector.
425
variable and less pure materials, we would still expect to see phonons
produced, but for their correlation to be lost sooner. It does not appear
that they were able (in the absence of any mediating photon) to change
one phonon and see the other likewise change. For this reason alone the
claim is doubtful. This particular experiment is therefore evidence of
geometric correlation of phonons, as induced by a photon that went
down two paths after a beam splitter. It does not prove that the two
diamonds were coherent, nor does it prove superposition of a single roomtemperature diamond (not that those authors claimed the latter).
The cordus conjecture does not disagree with the QM idea that a photon
or particule can be in two geometric places, but only accepts this one type
of superposition, and argues that QM’s concept of superposition
inappropriately confounds two different effects: positional and causal
variability [5].
As the variety of components increases, i.e. the purity decreases, and the
assembly becomes more complex, then it becomes harder to find ways to
arrange the cordus hyff, and thus coherence becomes harder to
form/easier to lose, or simply inaccessible. Cordus suggests this boundary
could be quite early in the overall scheme of assembly complexity, perhaps
as early as the interaction of two dissimilar molecules (note interaction not
joining). Once coherence is unavailable, the components within the
assembly are unable to interact at their intrinsic frequency, but must
instead act in response en-masse to the fields that each generates. This is
a much slower form of interaction, and thus chemical reactions are slower.
Assembly level model
The three factors are therefore proposed as shear velocity, temperature
phonons, and complexity of assembly. We summarise the assembly
constraints in Figure 2.
426
Figure 2: Assembly level diagram ranging from simple structures (level 1)
through to complex (level 13). The different types of coherence are shown.
The diagram summarises the previous discussion, and introduces classes of
coherence.
•
Class A1 is for intrinsic internal coherence for individual particules
ranging from the most fundamental through to molecules. This
class should display superposition of location, though see [5] for
fringe limitations.
427
•
Class B is coherence that has been created by special situations,
e.g. artificially, and is not stable at our ambient conditions. The
low temperature superfluids are in this category.
•
Coherence is a special type of stability, or bond, one based on the
sharing of HEDs in the strong force. The discoherent state arises
when either the coherent state becomes unstable, or cannot form
in the first place. Therefore we include Class A2 with some
examples of internal instability such as the W bosons and
positronium. Cordus predicts that these materials will not support
lasting coherence.
•
Finally, we provide Class C for the complex matter assemblies.
These are naturally discoherent for the reasons given above.
Where is the upper assembly boundary for coherence?
According to this cordus model, the upper limit for coherence could be as
high as Level 7: External interaction of dissimilar particules (limited
number of species) at low temperature. For example a simple crystal or
perhaps even a virus, at low temperature. This is the optimistic prediction.
To our knowledge it has not yet been achieved: only pure materials have
shown the behaviour so far. Therefore a pessimistic prediction is that the
limit has already been reached, at Level 6: External interaction of pure
particules at low temperature.
We expect that discoherence is unavoidable at Level 9, where a body
consists of numerous species of matter, at ambient temperature. We also
predict that a many-species body (level 8) will be discoherent even at the
lowest temperatures.
So we can, using cordus, estimate that the transition occurs at the end of
level 7 (limited number of dissimilar species, cold), though we
acknowledge there is some uncertainty.
Coherence in biological systems
There is no doubt in this model about the discoherence of macroscopic
objects and living creatures: Cordus predicts it will be impossible to
achieve coherence for macroscopic objects at ambient conditions (level
11), or put them into superposition. This does not preclude coherence
effects, e.g. rapid electron transport, from occurring in the molecules
within biological systems. However it does exclude superposition (of either
kind), double-slit behaviour, and fringes.
3
Discussion
From the cordus perspective, coherence is interpreted as all particules in
an assembly having synchronised frequencies and phases thereof. In the
cordus explanation this is a form of complementary frequency state
synchronisation (CoFS) [11]. This also involves the sharing of hyff emission
directions (HEDs).
428
Thus there is a common mechanism for the strong nuclear force, Pauli
Exclusion principle, bonding within molecules, and coherence.
Consequently coherence can be perceived as a type of bonding and
stability arrangement. Alternatively it is a special state of assembly where
the particules provide for mutual preservation of the de-energised
locations of each other. Thus positions of all the reactive ends are locked
together in a complementary sharing relationship.
Cordus anticipates three mechanisms for discoherence. First, a coherent
material cannot accept internal shear velocity. Second, higher
temperatures lead to decoherence because phonons (internal thermal
vibrations) disturb the stability. Third, more complex assemblies of matter
are harder to put into coherence, and the complicating factors are the
number of components in the assembly, and the variety of species
(simplicity and purity). We represented this as an ‘Assembly level model’.
Comparison to the QM explanations
The conventional QM explanation is that decoherence arises because the
object has many particles, hence too many degrees of freedom (DoF). This
DoF idea finds support in this cordus model.
QM also proposes that the atoms are strongly coupled to the external
environment. However QM is unclear about how that coupling mechanism
works, or why it should be so much stronger than the atomic bonds, or the
bonds for coherence. In the cordus interpretation the way the coupling
with the external environment operates is through disturbance of the
negotiated HEDs.
Both cordus and QM recognise that temperature and the resulting atomic
vibrations (phonons) can destroy coherence. However QM is does not
explain how that happens (how is a 0-D point affected by phonons?). In
contrast, cordus readily explains it as phonons causing displacement of the
reactive ends, and thus interrupting the existing HED arrangements with
other particules.
Upper limit for coherence
According to this cordus model, the upper limit for coherence could be a
simple crystal, or perhaps even a virus, with a limited number of species
(different molecules or elements), at low temperature. However this is
thought to be an optimistic prediction.
Thus, according to this model, coherence will be unachievable at the
assembly level of the smallest metal grains, mineral crystals, and cell
organelles, at ambient temperature. Macroscopic objects and living
creatures are therefore well beyond being put into coherence or
superposition. However there is no problem with having coherent
domains within a discoherent body, e.g. molecules that are internally
429
coherent. Single particules, such as electrons, are self-coherent under any
conditions.
The interaction of biological organisms or discoherent macroscopic bodies
with other bodies or particules, whether or not coherent, is always
discoherent. This implies that Observers of a quantum experiment are not
themselves in a quantum state of superposition.
The theory of QM has created an expectation that coherence is the norm
and therefore should be found in macroscopic bodies. Cordus suggests
that we should instead view discoherence as the normal state, and
coherence as a special state of extended application of the strong force
into bonding. There has also been much philosophical speculation about
the role of measurement, including human observation, on the future of
behaviour of particles and coherent bodies. Cordus likewise refutes those
ideas, and instead suggests that in those rare cases where coherence of
macroscopic objects is attainable, this does not mean that the object has
two futures, only that it can have two locations.
Conclusions
This paper has applied the cordus conjecture to determine where in the
scale of things the transition occurs between coherence and
discoherence, and why the limits are where they are. The reasons for
discoherence are proposed to be internal shear velocity of the body,
temperature phonons, and complexity of assembly (particularly purity of
composition). The upper limit for coherence is expected to be at currently
achieved levels of material complexity, or slightly beyond. However
cordus rules out coherence for warm macroscopic objects and living
creatures.
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431
Time: Frequency, irreversibility,
connectedness of matter
and
Pons D.J.121
Abstract
A novel conceptual model is described for time, one that is independent of
existing theories. The cordus conjecture suggests that time consists of
frequency oscillations of matter. The arrow is applied to time where
irreversibility arises. The interconnectedness of matter, via its fields,
creates a patchwork of temporal cause-and-effect. At its most basic level
time originates with the frequency cycles of the particules of matter and
photons. The rate of time is thus determined by the mass of the particule,
in turn how it is assembled, from what subcomponents, and the external
environment (hence also time-dilation). Thus time is locally generated, and
cordus rejects the idea of an absolute clock. The forward arrow is only
applied to the ticks of time when irreversibility arises. The paper explains
how the irreversibility arises, in terms of the interaction between two
volumes of matter and the statistically impossibility of returning all
particules in the system to their original positions and states. Thus
decoherence, irreversibility, entropy, cause-and-effect, and the arrow of
time all arise at the same discontinuity in physics. There is a
connectedness between volumes of matter that are at different geometric
locations. A phenomena that occurs in one volume is communicated via
photons, or massy particules, or fields, to other matter around it. This
communication applies cause positional constraints on the recipient. The
combination of connectedness, frequency, and irreversibility, results in
temporal cause-and-effect. Thus human perceptions of time are a
construct, with all the potential for illusion that implies, founded on a real
physical principle of temporal causality. Time is a series of delayed
irreversible interactions (temporal ratchets) between matter, not a
dimension that can be traversed in both directions. Cordus provides a
more basic concept of time from which quantum mechanics and general
relativity emerge as different approximations. The resulting conceptual
model provides a novel integration of quantum mechanics, general
relativity, and the human-perception models of time.
Edition 1 > Date: Saturday, 11 February 2012 > Document: Pons_Cordus_6.2_Time_E1.0.07
1
Introduction
Though intuitively familiar, time is a mystery. Time is a variable
throughout physics: classical mechanics, quantum mechanics (QM), and
121
Please address correspondence to Dr Dirk Pons, University of Canterbury,
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New
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Email:
dirk.pons@canterbury.ac.nz. Copyright D Pons 2012. This work is made available
under the Creative Commons Attribution-Non-Commercial-ShareAlike 3.0 license.
43
2
general relativity (GR) all include it. Yet the constructs in each are very
different. Nor are those constructs always coherent with humans’
personal cognitive perception of time. For example, the idea that time
runs differently depending on location, or that time may have had a
beginning, is deeply puzzling to the mental model of most people. It is
natural that various philosophical questions also arise.
All these approaches, physics, psychology, philosophy, have developed
models for time. Yet they are poorly integrated, indeed sometimes in
conflict (e.g. QM and GR). Time is still a mystery, and there is no basic
model that is acceptable to all the disciplines.
The existing theories of time are well-developed, having enjoyed much
attention. Yet no universal-theory of time has emerged from any of the
extant approaches, despite the effort. It suggests the possibility that
existing theories may be conceptually inadequate. Thus there are two
lines of enquiry: to continue to refine existing theories of time, or seek a
conceptual breakthrough. The latter approach involves striking out in a
totally new direction: coming up with a new foundational concept.
This is the approach we take here. The purpose of this paper is to explore
the concept of time through the lens of the cordus conjecture. The
foundational idea is a reconceptualisation of the structure of the
‘particle’. This is a radical concept without precursors, and therefore
detached from the orthodox literature.
The cordus conjecture is a novel alternative theory of fundamental
physics, constructed on a different concept for ‘particles’. It is currently
primarily a qualitative conceptual method [4]. Cordus was originally
conceived as a conceptual solution for the problem of wave-particle
duality [17]. It turns out to be useful, as a reconceptualising tool, for other
problematic areas of fundamental physics. It should be considered a
conceptual solution or extended thought-experiment rather than a
validated theory, hence ‘conjecture’. It is intended to be thoughtprovoking, and this means it is sometimes unorthodox. In this specific
area it provides, as will be shown, a novel concept for time, and offers
solutions to the problem of what time is and how its arrow arises.
2
Background
It turns out with cordus that the key to understanding time is to
reconceptualise matter, especially ‘particle’. Doing so accesses new
concepts for entropy [18], coherence [19], special condensed and superstates of matter [11], and offers an explanation of why quantum
mechanics does not scale up to macroscopic scales [5]. All of those
concepts have some connection to the explanation for time, developed
below.
433
What is the cordus conjecture?
The conjecture states that all 'particles', e.g. photons of light, electrons,
and the protons in the nucleus of the atom, are not zero-dimensional
points, but have a specific internal structure called a 'cordus'. The term
‘particule’ is used to differentiate this important conceptual difference
from the QM construct. The cordus consists of two ‘reactive ends’, which
are a small finite distance apart (‘span’), and each behave like a particle in
their interaction with the external environment. A ‘fibril’ joins the reactive
ends, and is a persistent and dynamic structure, but does not interact with
matter [6]. The reactive ends are energised (typically in turn) at a
frequency [7]. The reactive ends emit one or more force lines called
‘hyperfine fibrils’ (hyff) into space, and when the reactive end is energised
it sends a transient force pulse (‘hyffon’) outwards along the hyff curve [8].
This makes up the field, which is thus also discretised in 3D space. Various
features of the hyff and hyffon carry the electrostatic field, magnetism,
and gravitation simultaneously. Thus a unification of these forces is
provided [9].
In this model the photon has a single radial hyff which it periodically
extends and withdraws [6]. By comparison all massy particules have
permanent hyff (including neutral particules like the neutron)[8], see
Figure 1. Electric charge is carried at 1/3 charge per hyff, so stable
particules like the electron are surmised to have three hyff, arranged
orthogonally [10]. The hyff from multiple massy particules compete for the
three hyff emission directions (HEDs), and may synchronise their emissions
to access those spaces. Thus there is an element of mutual negotiation,
based on shared 3D geometric timing constraints, and this explains the
strong force [10].
Figure 1: Models for the photon and electron, showing the different
characteristics of their discrete field structures. The photon has a
fibrillating pump that only shuttles energy outwards and then immediately
afterwards brings it back inwards, whereas the electron consistently
434
pushes hyffon (force fragments) outwards in a pulsating manner. Both
cordi therefore have a frequency, but the difference is what they do with it.
All other matter and antimatter behaves like the electron, though the hand
of the hyff is inverted for antimatter, and the direction of pumping is
reversed for positive charge.
In terms of its conceptual design, cordus has high fitness122 because it is
able to explain many effects within one logically consistent framework [4].
However, cordus is a conjecture and the validity thereof is uncertain.
Therefore derivatives of the idea, as here, should be considered
speculative.
What is coherence?
Cordus permits a more specific definition of coherence and superposition
than is possible from within the 0D point construct of QM [17]. From the
cordus perspective, superposition is simply that the cordus particule is
actually physically oscillating between two positions: the locations of the
reactive ends at the end of their span. The cordus particle (e.g. photon
cordus) collapses to one of these ends when it is grounded [11]. Likewise
coherence, from the cordus perspective, is when all the particules, which
may be photons, electrons, protons, and possibly atoms & molecules, etc.,
have synchronised frequencies and phases thereof. This also involves the
sharing of hyff emission directions (HEDs).
Thus coherence is a special state of assembly where the particules provide
for mutual preservation of the twin locations of each others’ reactive end:
when any one particule is energised at its one reactive end, the position of
its other dormant reactive end is filled by the active end of another
particule. Coherence is, according to cordus, best understood as an
ordered complementary frequency state synchronisation (CoFS) between
two or more particules [11].
For materials with a coherent structure, the effect of an externally
imposed change is communicated to neighbouring internal components at
the next frequency cycle. For assemblies with high purity, this may be fast
indeed, hence second sound in superfluids, and rapid electron
transmission across biological molecules.123 Hence also the successes in
putting molecules into geometric superposition. Thus communication
within atoms and molecules is rapid, being able to take advantage of the
internal frequency network.
122
Fitness in conceptual-design sense of providing explanations that are consistent with numerous
empirically observed phenomena.
123
For a descriptive overview of quantum biology, and applications to odour reception, electron
transfer in ATP, & photosynthesis, see Brooks, M., The weirdness inside us. New Scientist, 2011.
2832(1 October 2011): p. 34-37.
435
Cordus anticipates three mechanisms for discoherence [19]. First, a
coherent material cannot accept internal shear velocity. Second, higher
temperatures lead to decoherence because phonons (internal thermal
vibrations) disturb the stability. Third, more complex assemblies of matter
are harder to put into coherence, and the complicating factors are the
number of components in the assembly, and the variety of species
(simplicity and purity).
What is entropy?
Cordus explains entropy as a spatial and temporal dilution of energy [18].
Thus an atom that has surplus energy can dispense it in five main forms:
electron orbital change (including bonding), electron ejection, photon
ejection, electron flow (plasmons), and phonon propagation. If phonons,
then another atom some distance away receive some of the energy and
will likewise use what it can and dispense with the rest. That remote atom
might emit a photon for example. Even if that photon was sent straight
back to the original atom (which is not generally the case), there would
still be less energy in the feedback loop because of the phonon dilution in
the bulk, and the time required for the photon flight. Thus the individual
mechanisms are all reversible (elastic), but the system as a whole is not,
and we suggest this is what creates entropy.
Both photons and phonons tend to be dispersed out into the surrounding
space or material (respectively), and this dilution of the original energy is
the primary mechanism for thermodynamic irreversibility and entropy.
The geometric and micro-structural complexity of the matter accessible to
the photons and phonons introduces so many dilution paths that it is
extremely unlikely that the energy fragments will spontaneously
recombine. Geometric separation is another contributory factor: when
the matter separates or radiates photons across space, then the dilution is
further increased and the number of paths reduced by which the energy
can come back together. The enormous radiative loss of photons from
stars contributes to entropy, because that energy cannot realistically all be
recovered after it has travelled billions of years and stopped in our eye,
and even if it were reflected back it would be more billions of years to
travel back. In the meantime space expands, which adds to the delay. Thus
the expansion of space in the universe further contributes to entropy.
Geometric separation of matter causes the photon travelling between
them to arrive late, the more so if it involves transmission through denser
material. Thus the energy is not delivered at the time it might have been,
but is instead postponed into the future. If that postponement is
indefinite, it takes energy out of the system. This is another barrier to
recombining the original energy, and thus another contribution to
entropy.
Not only is the energy delayed, but so too is any information carried by the
photon. Furthermore, the cordus model for transmission of discrete field
force-elements (hyffons) [8-9, 14] suggests that these too travel at the
speed of light. Thus information about the strength and direction of the
fields of the remote particule only arrives at the basal particule after some
436
time. The basal particule cannot respond to external fields until it receives
them. This contributes a delay to the exchange of information between
decoherent objects.
3
Time at the assembly level
Cordus offers a construct of time that depends on the number of
particules and the nature of their relationship, i.e. the ‘level of assembly’
of matter [19]. This is an unusual approach, since time is conventionally
associated with a dimension of the cosmos. Nonetheless it has the
potential to better-explain certain features of time, as will become
apparent.
3.1
Time at the particule level: frequency (level 1)
Time, at the level of the individual particule (e.g. electron), refers to the
frequency of the re-energisation cycles of its two reactive ends. This is
because the particule is only available to interact with other particules
when it is energised. Particules with greater masses have higher
frequencies, and therefore tick faster. Cordus provides a specific internal
structure for particules, hence a physical explanation for frequency [7].
When a reactive end is energised it issues a discrete field force (hyffon).
These are propagated outwards at local fabric speed c, the speed of light.
The hyffon carries the electro-magnetic-gravitational field, which
therefore is also discrete. These fields inform neighbouring particules,
even remote ones, about the state of the basal particule. In turn, the basal
particule responds to hyffons from the external environment when its
reactive ends energise. Thus the periodic re-energisation of the reactive
ends is a mechanism whereby the particule communicates with other
particules and responds to their forces. ‘Force’ is not quite the right word
to use, since the cordus concept suggests that the mechanism is
prescribed positional relocation of reactive ends, i.e. displacement. Thus
the external hyffons force the reactive end to energise in a slightly
different position to that which it might have preferred. The mechanism is
held to negotiation between the particules for momentary rights to the
three-dimensional hyff emission directions (HEDs). Separately we have
shown that HEDs explains the strong force [10], annihilation [20], and
coherence [19].
3.2
Time at the level of molecular assembly (level 2)
The above applied to a single particule, e.g. a lone electron or proton.
Such a particule can keep its own time. However it is more common for
matter to be assembled together, i.e. bonded. That assembly may be
coherent, discoherent, or a mix of the two. We take the simpler case of
coherent matter first.
437
Time at the level of coherent matter (level 2.1)
Each coherent domain of matter has its own time: the common frequency
cycle of its re-energisation. The whole of the coherent body has the same
frequency, this being necessary for coherence according to the cordus
definition thereof. The phase of the particules must also be
complementary. Thus there is a ‘global’ time, but only within the
assembly of matter that makes up the coherent body.
Time at the level of discoherent matter (level 2.2)
Macroscopic objects at our level are discoherent as a whole, since they
lack the homogeneity of composition and are too warm to be coherent
[19].
There is an assembly tree to any macroscopic object, where the subcomponents may be a mixture of individually coherent and discoherent
domains. Indeed at suitably small scales all matter becomes individually
coherent, and cordus predicts this boundary is at or below the molecular
level [19]. Thus electrons, protons, and atoms are always internally
coherent, that being a necessity for their stability.124 However as the
assembly grows in size and diversity of composition, so a synchronous
HED arrangement becomes impossible to negotiate by the protagonist
particules, and thus discoherence arises. Thus at some intermediate level
of assembly an object consists of coherent and discoherent domains. For
example, even if individual molecules are indeed coherent (this is
presumed but uncertain) then an aggregation of different molecules will
be discoherent as a whole.
Single particules are automatically coherent. These, and any coherent
domains (assemblies of multiple particules) manifest their properties at
their own internal frequency. These properties are their fields (of which
there are three (electrical, magnetism, and gravitation[8-9]), the
orientation thereof, and the position of the reactive ends (of which there
are two). The fields themselves are discrete pulses (hyffons), and the
frequency of production is very high.
However other neighbouring domains of matter of different composition,
even if independently coherent, do not perceive the individual hyffons of
the first domain in their discrete form.125 Instead they perceive each other
(experience each other’s forces) as a continuous rain of field forces. Hence
classical mechanics and discoherence arise at the same point in the
assembly tree of matter. The perception of time arises at the same point.
As does entropy.
124
Bonding stability, strong-force, and coherence are simply different manifestations of the deeper
synchronous HED mechanism, according to the cordus perspective.
125
The two domains would need to have the same frequency (hence mass characteristics) for the
individual hyffons to be apparent, in which case they could move into a bonded state of assembly, i.e.
become one coherent body. Thus there is no problem with independent coherent domains merging to
form larger domains, but it requires homogeneity of composition (to satisfy the mass and frequency
requirements).
438
The arrow is applied to time where irreversibility arises
Decoherence causes a time delay to be inserted into the functional
interaction of two or more domains – whether or not those domains are
individually coherent. This because the frequencies differ, so the faster
oscillating domain will have to mark more ticks before the slower
responds. If there is geometric separation then the finite speed of field
propagation (c, speed of light) further adds a time delay. Consequently
the one domain generally has done something different before the
second has fully responded. Therefore getting domains back into their
initial positions becomes unlikely and statistically impossible as the
number of participating domains increases. Note that even in the simplest
situation of two interacting domains, there is still the perturbation of the
fabric that they both feel, i.e. the rest of the particules in all the accessible
universe affect the two domains. So what happens stays happened, and
does not naturally self-repair.
3.3
Time at the level of organic life: chemistry (level 3)
Within our own physical bodies, which are decoherent at any level which
our unaided senses can perceive, the different coherent domains run at
their own times. These volumes of matter are smaller than a cell, and
smaller even than organelles. We anticipate that the only coherent
domains with physical bodies are at the molecular level and smaller.
Time, at the level of an individual cell, consists of the fuzzy aggregation of
the frequencies of the many individual coherent particules (electrons,
atoms, molecules) and decoherent sub-components (clumps of molecules,
organelles). ‘Fuzzy’ because the discrete field hyffons are not individually
distinct. Chemical transport within the cell occurs as and when the subcomponents are able to interact. Thus the cell takes much longer to
achieve anything (more frequency ticks) than a simple sum of the times
required by the coherent subcomponents. The actions of the cell are not
superluminal, as is possible within a coherent domain, i.e. entanglement is
only possible within coherent systems.
The process of human thought takes time. The photosensitive chemicals
in the retina need frequency cycles to react to incoming photons,
frequency cycles of the electrons to transit down the nerve fibre into the
cortex, more frequency cycles of the neurotransmitter molecules to
interact with cells, and thus time for the brain to assign a meaning to
what is seen. Thus at the level of organic life, time is based in chemistry.
3.4
Time at the cognitive level: phenomenal (level 4)
Our human perception of time is the next level up, and is a construct of
the cognition. The brain does not have a global atomic/molecular clock,
but instead has a subjective counter of events and infers ‘time’ from
439
that.126 Our cognitive quantification of time is very rough, and varies with
the situation. Nonetheless we perceive time as flowing. This is because it
does indeed take chemical time for us to accomplish anything, even
thought, and especially motion. But the perception of time for us is a
cognitive construct that we overlay on chemical time, and that in turn on
the frequency of matter.
We might perceive our thoughts to be effortless and instantaneous, and
the resulting movement of our body to be immediate. We can perceive,
and respond within, tenths of a second. But the deeper clocks of the
particules of matter beat so fast as to be beyond our sensation.
We also perceive that time flows in one direction: forward. There is an
obvious arrow of time, whereby cause precedes effect. This too arises
from the non-linearity of the transition from particle time to chemical
time.
We also perceive that time is universal: that what happens to me is also
how you see things happening. So when we meet and I extend my hand
and voice a greeting, I believe that you too hear those words, and the
touch of the hands is real. Clearly this is the case, because when meeting
we do indeed see the smile and confirmatory signs that we expect.
3.5
The connectedness of time
There is a connectedness of phenomena that are at different geometric
locations. It seems that spacetime is continuous, because it seems that it
is possible to coordinate the two phenomena in time. But that does not
mean there is a master clock. The two phenomena are linked, because
they share the same fabric.
Any communication between the two objects is a result of photons, or
massy particules, or fields, and these cause positional constraints on the
other, i.e. the geometric location of the reactive end is affected by the
communication. Thus all force is ultimately prescribed displacement of
position of the target particule.
A phenomena that occurs in one volume of matter, be that combustion,
noise, motion, etc, thereby communicates that to other matter around it.
Consider one volume to be my body: my speaking communicates forces to
the volume of air immediately around me, which in turn propagates the
dynamic displacement throughout its volume, so that the membrane in
your ear is displaced, and you hear the sound.
126
Exactly what ‘events’ the brain counts to infer passage of time is a wider mystery, and cordus does
not specifically address this cognitive question. Nor does it explain what the biological mechanism
might be for accumulating the sense of elapsed time. If ‘events’ include external stimuli and internal
markers (perhaps physiological depletion) then there is no particular difficulty explaining why
perception of time is so flexible. However, a cognitive model is beyond the present scope.
440
In general the phenomenon is that one volume of matter causes an effect
in the second. The interactions at the most basic level all require
frequency cycles, so this causes temporal causality. This is a physical
reality, and is also the basis for cognitive perceptions of time.
It is not a master clock that accomplishes this, nor does it require
continuity of spacetime. The piece-wise communication between volumes
of matter (whether coherent or not) achieves the effect of time.
4
Discussion
4.1
Outcomes
What we have achieved here is a description of how time arises, within
the cordus framework. As we noted at the outset, that conceptual model
is conjectural and the results here are likewise speculative.
According to the cordus model, entropy, classical mechanics, and our
perception of time all arise at the boundary between coherence and
discoherence.
Thus time starts out as a frequency property of particules, and by
extension of the strong force (explained via synchronous HEDs) to
coherent domains too. At this level, time is the re-energisation sequence –
the oscillating firing of the reactive ends. Thus it is appropriate to measure
time in terms of the frequency-dependent activities of individual atoms
(e.g. atomic clocks). The frequencies of the various types of particules do
differ, based on their mass, but the relative difference is constant. So the
ticks of one particule may be used to count those of a different type.
Time-dilation
The existence of time as a frequency effect also explains why time-dilation
occurs. Acceleration, or the presence of higher gravitational fields
(hyffons) slows time.
Cordus explains this as the particule’s hyffons having to interact with the
fabric of the vacuum, which in these cases has increased pressure density.
The interaction changes the re-energisation behaviour and slows the
frequency of the particule. This fabric comprises all the hyffons of all the
other particules in the accessible universe, and the overall effect is
somewhat like a relativistic aether [14]. For the particule, local time is the
ticks of its frequency, so time really does change when the frequency
does. Therefore all the process of interaction that depend on frequency,
e.g. chemical reaction with a second particule, or transport of a
messenger electron/atom/molecule, or emission of a photon, or nuclear
decay, will be happen faster/slower relative to an external observing
particule.
441
So there is absolute time at the particule level (or coherent domain) but it
only applies locally. There is no universal time. The cosmos is filled not
with one time, but a patchwork of many times.
Cause-and-effect
Thus there is both a cause-and-effect in the interaction of two or more
volumes of matter, and a small time delay at each interaction. It is the
sum of these delays that we perceive as time. Not only perceived in a
cognitive sense, but also measured in an objective sense by atomic clocks
and other instruments.
4.2
Arrow of time
That there is an arrow of time is a consequence of the irreversibility of
most interactions between volumes of matter. It maybe helpful to think of
these volumes as molecules, though the precise boundary between
coherent and discoherent bodies is not known with complete confidence.
Entropy, decoherence, and time emerge together at the boundary.
However we anticipate that there are several levels of arrow. One is at the
subatomic level, where the arrow can perhaps be reversed. This might be
possible in simple systems of only a few coherent subatomic entities, in
prescribed states, and a stable external environment. If the particules can
only be in a few states, then their behaviour is effectively reversible.
There is still interaction at frequency cycles, i.e. time, but it no longer has
an arrow pointing away from past states. So time, and the arrow-of-time
are not synonymous at all levels. The self-stability of the proton may be an
example. However it is impossible to fully control the external
environment of the fabric and its perturbations. The decay of the free
neutron is held to be an example of a stable case slipping into
decoherence [13].
While reversibility seems feasible at simple levels, we never see this for
macroscopic bodies. This is because such bodies are discoherent.
Therefore they interact inelastically with their environment: they do not
return to precisely their initial states. Inability for one body to return
thereby means that all the other bodies in the accessible universe cannot
either, because the fabric of background field hyffons has been changed.
The cordus concept of the fabric is therefore important in explaining how
irreversibility arises.
At this second level the irreversibility of cause-and-effect creates a
physical arrow of time. This is not merely a cognitive perception, but a
real physical flow.
In some ways there is a third level at which the one-wayness of time
becomes apparent, and this is the cognitive meaning that the brain
constructs for it. Proprioception, and the underlying neural systems that
support it, creates a personal arrow of time. We think, then our limbs
442
move, then our peripheral nerves confirm the new position, likewise the
eyes confirm and calibrate the proprioception. To the cognitive system,
the arrow of time is the immediate and predictable sequence of causeand-effect in the neuro-muscular-skeletal system and the immediate
surrounding environment.
Cognitively we struggle to interpret events when the sensory signals
conflict, like sea-sickness, echoes in a large room, or time-delay in a longdistance call. The fact that the cognition struggles in such cases is
circumstantial evidence of a cognitive model for the arrow of time.
Worse, if one person was existing at a faster (or slower) pace of time, as in
time-dilation, then the cognitive model fails and we perceive the situation
as bizarre. That our feet age slightly differently to our head is only strange
because we expect, cognitively, that time be continuous and universal.
4.3
Implications: Addressing common questions about time
What about time travel? Can bodies travel faster than the speed of light
and could this result in time flowing backward? Could spacetime be folded
back on itself in a loop?
Probably no to the first. The speed of light is the local speed at which
hyffons (discrete force field elements) are propagated. It is not certain
that a body would be able to withstand the self-inflicted onslaught of the
fabric pressure were it to travel faster than c, but even if this were
possible its interactions with other matter would still require frequency
cycles, hence time, for both participants. Even when the interactions are
reversible (which is expected to only apply to the simplest levels and even
then conditionally, see above), all this means is that there is no arrow of
time. In every macroscopic situation there is irreversibility, hence a
forward arrow of time.
Regarding the second, the folding of spacetime is not possible, according
to the cordus perspective. This is because there is no spacetime: Time, in
the cordus model is not a dimension at all, but a patchwork of temporal
ratchets at the most fundamental level of matter. Time is a series of
delayed interactions between matter, not a linear scale that can be
traversed in both directions. It is not sensible, in this model, to talk of
folding time back on itself. We acknowledge that superfluids do show
quantum vortices, which cordus explains as a coherent material folded
back on itself [11], but in that case it is possible to have a void in the
middle of the vortex, whereas the patchwork of time is perfused with the
fabric which cannot be voided. It is not possible to connect two regions
where time flows differently, because the fabric flows through both. The
fabric cannot be bent, nor can time. This means that cordus also refutes
the QM idea that tiny wormholes make shortcuts through spacetime.
Entanglement and the superluminal transport of information is not time
travel, and is readily explainable with cordus [21]. Nor is there any need in
the cordus model for chronology protection (the old paradox of a timetraveller killing his grandfather), because time only flows in one direction.
443
Is time a real fundamental property of the universe?
Yes, it is a physical effect at the particule level, the mechanism being the
frequency of the particule. Yes it is fundamental in that the existence of
matter, specifically the energisation of the reactive ends, is linked to time.
No, there is no master clock or universal parameter. No, in that time does
not exist on its own. It is not a dimension linked to space but rather to
matter.
Is time the framework in which events take place?
No, not at least in the sense of a continuous spacetime. Yes, in that
individual particules negotiate their timing (frequency, energisation) with
other neighbouring particules and the fabric at large. The assembly of
matter, specifically its fields, and the patchwork of negotiated interaction
is the framework of time. All events occur in that framework, because all
events involve interactions between particules.
Can time pass at different rates for observers in different situations?
Yes, time is locally determined. But the different locations are linked
together by negotiated HEDs at their boundaries. Realistically those
domains are very small, and large coherent volumes, e.g. vats of
superfluid, are uncommon. (Where these exist the whole volume reacts as
one.)
Is time an illusion?
Yes, at least in that our cognitive construct of it emerges from deeper
effects, and is fuzzy, being stitched together in the mind as an apparently
smooth and continuous dimension. No, in the sense that time
corresponds to the frequency oscillations of matter, and these exist while
matter exists.
Are there alternative realities?
If there are many worlds or parallel universes, there is every reason to
expect that –by definition- they will be inaccessible to the present one,
and therefore unknowable. Those are metaphysical ideas, like religion in
being beyond physics, and cordus cannot confirm or disprove them. Yet
cordus can say that there is no need for alternative realities. Cordus
refutes the QM concept of many futures (temporal superposition) and
provides a model for time in which there need be only one reality in which
everything that happens simply stays happened.
Is time the passage from low to high entropy?
Not quite: entropy is a related but different effect to time. The arrow of
time arises at the level where discoherence results in irreversibility in the
interaction between particules. While time is the frequency ticks of
particules, the irreversibility of interactions contributes to the arrow of
time. The same irreversibility creates entropy. But time and entropy are
not the same effect, even if they have a common root. Irreversibility is
quantified by entropy, and also drives the local ratchets for the arrow of
time.
444
Why do the laws of physics treat the past and future the same?
This is because quantum mechanics does not include entropy, in turn
because it erroneously assumes that matter is always coherent (hence
reversible interactions). QM is unable to predict its own limits of
applicability, and therefore is erroneously assumed to apply to all matter
[5, 19]. Cordus explains why and where coherence breaks down. Likewise
classical mechanics is also symmetrical regarding time, if losses are
ignored. The arrow is only applied to time when irreversibility arises.
Why does the human brain not ‘remember’ the future?
Time is a one-way effect. There is no future that is simultaneous with the
present and the past. Cordus specifically refutes the idea that an object
can simultaneously be in multiple futures, i.e. temporal superposition.
Which perspective of time is correct: the absolute clock of quantum
mechanics or the spacetime of general relativity?
Neither, but in some ways both are adequate for their purposes.
According to cordus, time at the fundamental level is created by the local
frequency of oscillation of the particule, and the arrow is driven by
irreversibility. Thus time is locally generated, and cordus suggests the QM
idea of an absolute clock is incorrect.127 Also, cordus suggests that time is
a patchwork at the cosmos scale, not a continuous spacetime, thereby not
accepting this feature of GR either. However both QM and GR are
approximately correct, at least at the level of detail that concerns them.
Cordus provides a more primitive mechanics for time that accommodates
the thoroughly different models of QM and GR.
Where did time come from?
To the level to which cordus can penetrate, time is a consequence of the
frequency oscillations of particules. Its rate is thus determined by the
mass of the particule, in turn how it is assembled and from what
subcomponents. In that sense even massless particules (photon, neutrino)
have frequency and therefore time. However the forward arrow of time
arises where coherence lets off and decoherence starts. This discontinuity
in the physics of time occurs at different levels of assembly depending on
temperature and homogeneity [19]. Time therefore comes from the
frequency oscillation of matter, which in turn comes from the primal
photon(s) at genesis [22]. Thus time started when the universe started.
At a still deeper level we have to ask what the mechanism might be for
frequency in the particule. Cordus currently explains it as dynamic energy
oscillation between the field structures at the two reactive ends, but
undoubtedly there is more to it than this.
Will time end, and when?
Time is part of matter, and shares the same origins and fate.
127
If the wave-functions of QM were rewritten in terms of the de Broglie frequency for the particule,
rather than probability in absolute time, then QM and cordus might be closer. A secondary effect is
that cordus also suggests that the simple presence of an observer does not collapse the wave-function
or influence the outcome of an experiment, unless that observer was bonded in a coherent way to the
experiment – which cordus suggests is practically impossible to achieve.
445
Is time a dimension?
No, it is not a dimension: it is neither smooth nor infinitely sub-divisible. It
is not a ratio variable. It only looks that way when viewed from a
sufficiently high level of assembly, hence the approximations of the
classical mechanics. The concept of spacetime is also an approximation. In
the cordus view, time is more like a patchwork of cause-and-effect
ratchets between sub-microscopic domains.
5
Conclusions
Applying the cordus conjecture yields a novel alternative
conceptualisation of time. According to this conceptual model, time
originates at several levels.
At its most basic level time originates with the frequency cycles of the
particules of matter and photons. Specifically, the ticks of time are the
frequency oscillations of particules. Cordus provides a specific internal
structure for particules, hence a physical explanation for frequency. The
rate of time is thus determined by the mass of the particule, in turn how it
is assembled and from what subcomponents. The local conditions and
external environment, specifically relativistic velocity, acceleration, and
high gravitation, affect the energisation process of the reactive ends. This
effects the frequency of the particule, and thus the local time, hence timedilation.
Thus time is locally generated, and cordus rejects the idea of an absolute
clock, or a universal one. Time therefore comes from the frequency
oscillation of matter, which in turn comes from the primal photon(s) at
genesis. Thus time started when the universe started, and will end with it
too.
However the ticks of time are not the same as the arrow of time. The
forward arrow is only applied to time when irreversibility arises. This is
where coherence lets off and decoherence starts. This discontinuity in the
physics of time occurs at different levels of assembly depending on
temperature and homogeneity, but is well before the macroscopic or
even cellular level. Cordus explains how the irreversibility arises in the
time-delay that is introduced (frequency ticks required) when two
volumes of matter interact. This explanation applies whether those
volumes are decoherent or even independently coherent. Irreversibility
arises because it is statistically impossible to return all particules in the
system to their original positions and states. The fabric, which comprises
the discrete field forces (hyffons) of all the other particules in the
accessible universe, adds complexity to the interaction of even the
simplest assembly of particules. Therefore entropy, irreversibility,
discoherence, cause-and-effect, and the arrow of time all arise at the
same point.
446
There is a connectedness of phenomena that are at different geometric
locations, and this applies between macroscopic objects and at the small
scale. A phenomena that occurs in one volume is communicated via
photons, or massy particules, or fields, to other matter around it. This
communication applies cause positional constraints on the recipient. The
combination of connectedness, frequency, and irreversibility, results in
temporal cause-and-effect.
It is not a master clock that accomplishes this, nor does it require
continuity of spacetime. The piece-wise communication between volumes
of matter (whether coherent or not) achieves the effect of time. Cordus
does not accept the temporal superposition of QM, hence also refuting
the alternative-realities idea of QM. It also refutes the GR idea of
spacetime, instead suggesting that time is a patchwork of temporal
ratchets, not a continuous dimension. Hence cordus also rejects the idea
of time-travel via folded spacetime, or the wormhole idea of QM.
Cordus offers an answer to the question of whether the absolute clock of
quantum mechanics or the spacetime of general relativity is correct.
Neither is, but both are adequate approximations for their purposes.
Cordus provides a more basic concept of time from which QM and GR
emerge as different approximations.
At the level of organic life, time is based in chemistry, specifically the
delay introduced by the irreversible interaction of molecules. It takes
chemical time for us to accomplish anything, even thought. Human
perceptions of time are a construct founded on a real physical principle of
temporal causality.
The cordus model also offers explanations for various troublesome
questions about time: is time-travel possible via folding of spacetime (no),
is time real (yes), is time an illusion (partly), are there alternative realities
(obsolete), is time the passage of entropy (not really), why are the laws of
physics symmetrical, where did time come from, will it end (yes), is it a
dimension (no)? The validity of the cordus model is uncertain, and the
work is conjectural. Nonetheless it has high fitness in that it offers a
logically consistent set of explanations for a very wide variety of physical
phenomena.
To sum up, the cordus model suggests that time consists of frequency
oscillations of matter. The arrow is applied to time where irreversibility
arises. The interconnectedness of matter, via its fields, creates a
patchwork of time and cause-and-effect. Time is a series of delayed
irreversible interactions between matter, not a dimension that can be
traversed in both directions. Cordus proves a novel concept for time that is
independent to existing models but nonetheless conceptually integrates
QM, GR, and the human perception models of time.
447
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450
Possibly testable predictions of cordus mechanics
Neither wave theory nor QM explain why the symmetry requirement should exist for the doubleslit device: with both those theories waves/particles take all available paths, and symmetry
issues should not arise as they do. Experiments on concentricity might test the cordus
principle.......................................................................................................................................115
If Wave theory is correct, coherence is not essential and it should be possible to construct an
interference pattern from two independent light sources, e.g. one into each slit of the doubleslit experiment. The light sources need not be synchronised nor even exactly the same
frequency: according to WT, interference fringes should nonetheless form, though not
necessarily static. Cordus predicts that the outcome will be two independent gap-fringes
(which is not the same as interference fringes). If interference fringes cannot be achieved then
it suggests that light is not fundamentally a wave, but only shows wave-like behaviour. ......116
Note the implication of O.3.15 is that electrons are much ‘smaller’ than a photon, and can move
around in response to the relatively large and slower-frequency photon. ..............................138
The Cordus models of reflection suggest that the photon does not reflect at a single point, but
rather at its two reactive-ends. Furthermore, the precise locus taken by a reactive end
depends on its frequency state at the time it approaches the surface, and the nature of the
surface. Thus the reflection is not a sharp instant change in direction occurring at the surface,
but rather a curved transition. Depending on the situation, that curve might occur above the
surface (cisdermis) or beneath it (transdermis).........................................................................139
Cordus suggests that Bell’s Theorem is only applicable to point particles, and is thus generally
irrelevant. ....................................................................................................................................169
Cordus predicts that the principle of locality is not viable in its present form and needs to be
widened to include hyff interactions. ........................................................................................169
Cordus goes further than de Broglie to state that matter has a frequency even at rest. .................180
Cordus suggests that the zone of influence of the particle extends well beyond its geometric modes.
The proton is likely to have hyff that create a zone of influence: this may be somewhat diffuse,
perhaps shaped, and the outer zone may be considerably larger (though weaker) than
commonly perceived...................................................................................................................182
Cordus predicts that a proton will have many ‘diameters’ depending on what interaction is being
measured, and the nature of the probe.....................................................................................182
Cordus predicts it will be impractical to achieve coherence for macroscopic bodies at ambient
conditions. It is particularly incompatible with living creatures. .............................................197
Small bodies: From the cordus perspective, sufficiently small bodies, typically atoms and
molecules, should be able to diffract, form fringes through gaps, and pass through the doubleslit experiment with the usual outcomes, providing they are in body-coherence. ..................197
Large bodies: Macroscopic bodies cooled to near zero should be able to be placed into
coherent states of internal oscillation (coherence), as a type of supersolid. Such bodies should
be able to diffract and form fringes through sufficiently large gaps (or at edges), though the
effects may be miniscule. ...........................................................................................................198
Cordus predicts that the double-slit experiment is infeasible for macroscopic bodies, even if they
are in body-coherence. ...............................................................................................................198
Cordus predicts that practically every object at ambient temperature and visible with the naked
eye is not going to form matter waves. .....................................................................................198
Cordus suggests superfluidity will become compromised at relativistic speeds...............................200
Cordus predicts that the field will be granular at the frequency of the basal charge, and not uniform
quantum increments. Also, that the frequency should depend on the level-of-assembly – for
example a free electron will have the same magnitude of field as one involved in a bond, but
different frequency. ....................................................................................................................226
Cordus predicts that hyff penetrate everything, and no field can be shielded. ................................226
According to cordus the level of apparent electromagnetic shielding achieved should be dependent
on frequency of the field, the mobility of the charge carriers in the shield material, and the
geometry of the shield. Further that shielding may be achievable for one species of charged
matter within a space, but not for much smaller charge species..............................................227
Cordus predicts that ‘virtual’ particles are fundamentally different to normal ‘particles’, and should
be massless. This includes any bosons for gravitation. .............................................................227
451
Cordus suggests that both the electrostatic and magnetic effects should be directional for a single
moving charge (the ‘base charge’), i.e. the force should be orientated in a particular direction,
and granular, at sufficiently small scales. ..................................................................................229
Cordus suggests that at a sufficient small scale neutral mass should show magnetism, because the
positive and negative basal generators are separated slightly. ................................................231
Cordus predicts that the electric and magnetic forces apply simultaneously, and with gravitation
too. ..............................................................................................................................................231
Cordus predicts a retardation of the frequency for the remote charge during the operation of
magnetism...................................................................................................................................233
Cordus predicts a tendency to mutual synchronisation of frequency for identical moving charges.
.....................................................................................................................................................234
Cordus suggests that particuloid orientation is affected by magnetism and motion. ......................235
Cordus suggests that what QM perceives as quantum vacuum fluctuations are the passage, past the
Observer, of disorderly hyffons, not real particuloids of matter. .............................................245
Remote particuloids should be able to affect each other’s spin through gravitational interaction,
though it would only be evident when both bodies were in (separate) full body-coherence. 252
At small scales gravitation should be dependent on the directional alignment of the particuloids,
similar to magnetism. .................................................................................................................253
As two bodies move closer together under gravitational attraction, so they release energy for other
purposes, and their frequency and mass should decrease slightly, according to this model. .253
Cordus predicts that knowing the mechanisms for particuloid frequency should significantly
enhance our understanding of momentum, time, and force. ...................................................263
Cordus predicts that the proton and probably the electron have three pairs of hyff, in orthogonal
directions, but the pairs are offset across a small span.............................................................269
Cordus predicts that the quarks should be arranged in a co-linear manner. ....................................270
Cordus suggests that if the localised gradients in the fabric were too high, then the proton structure
could disintegrate. ......................................................................................................................271
Cordus suggests that a particuloid becomes unstable and decays when there is no place for its
reactive end to form, i.e. the external constraints of the fabric and the hyff of the immediate
environment dominate and preclude the emergence of the particuloids’s hyff......................271
Cordus suggests that the strong interaction is simply an application of the CoFS principle to three
axes. Thus the force that bonds quarks together is the positional convenience of their
interlocked hyff, i.e. SHEDS. .......................................................................................................272
Cordus suggests the weak interaction is not a fundamental force or interaction, but rather an effect:
a transitory form in the decay of matter....................................................................................272
The level of assembly concept suggests that at smaller scales the relationship between mass and
energy is not smooth but should become granular as whole assemblies are changed. ..........273
Cordus interprets a positive binding energy as meaning that the span of the assembly should be
greater than the parts. This is somewhat counter intuitive as we tend to think of molecular
assemblies as bonds that pull the atoms closer.........................................................................273
The assembly gauge concept suggests that a coherent body will have only one frequency, not many.
.....................................................................................................................................................274
According to cordus, the mass of any particuloid should depend on the level of assembly. ...........276
This cordus model predicts that particules with greater disparity in energy or less degrees of
freedom, will take longer to annihilate. Also, for cases where both particles have the same
energy, higher-frequency is expected to result in faster reactions. Possibly both of these may
be testable...................................................................................................................................317
452
Index
↑ or ↓ .................................................371
absorption ............................127, 187, 272
acceleration ..................................236, 256
aether ...........................................242, 244
Aharonov-Bohm ...................................174
Airy pattern ..........................................110
alpha decay...........................................359
annihilation...........................286, 311, 338
antielectron ..................................286, 314
antihydrogen ........................................286
antimatter.............................................285
antineutrino..........................................412
antineutron...........................................292
antiparallel............................................316
antiphoton [not]...................................296
aperture................................................111
arrow of time................................441, 444
assembly gauge ............................275, 277
assembly level model of discoherence.428
asymmetry............................................403
Auger electron......................................359
baryogenesis.................................366, 403
BCS theory ............................................201
Beer-Lambert law .................................187
belief system of QM ...............................51
Bell's theorem...........................58, 79, 167
Berry phase...........................................201
beta - decay ..........................354, 387, 393
beta + decay .........................................357
Bhabha scattering.................................342
binding energy......................................274
biprism..................................................174
birefringence ........................................150
blocked path.....................................89, 94
body coherence......................................42
bonding.........................................326, 370
bonds ....................................................178
Bose-Einstein condensate ....................425
boson....................................177, 199, 222
boson mass...........................................381
Brewster’s angle ...................................151
Brownian motion..........................189, 202
Canals-Frau .............................................15
Casimir effect........................................179
causal variability .............................40, 428
charge conjugation invariance .............341
charge conservation .............................371
chirality ................................ 269, 287, 290
circular-polarisation............................. 177
cisdermis.............................................. 137
cloak..................................................... 366
cloaked hyffons............................ 366, 372
CoFS131, 165, 191, 246, 261, 269, 271,
274, 296, 315
cognitive dissonance.............................. 15
coherence42, 181, 196, 212, 253, 275,
423, 437
body ................................................. 197
coherence, assembly level model........ 428
coherence, biological systems............. 430
coherence, limits of ............................. 430
coherence, mechanisms for................. 425
coherent conceptual framework ......... 281
collapse .................................................. 83
collider .......................................