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Extrasensory Perception Phenomena
From consciousness to life
Janina Marciak-Kozłowska
Institute of Electron Technology, Warsaw, Poland
Mirosław Kozłowski
Józef Piłsudski University, Warsaw, Poland
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Contents
Introduction ........................................................................................................ 5
Chapter I
Schumann and brain waves. Quantum description ...................... 11
Chapter II
Heisenberg uncertainty and human brain..................................... 30
Chapter III
Heaviside quantons as the carriers of the ESP ............................. 40
Chapter IV Brain waves as the solution of the modified Schrodinger
equation ........................................................................................ 66
Chapter V
Brain vibrations and Planck mass ................................................ 84
Chapter VI Riemann Zeta(x) functions and Consciousness ........................... 92
Chapter VII Mathematical model of tumour growth and host
consciousness ............................................................................. 110
Chapter VIII Evolving consciousness.............................................................. 125
Chapter IX On the possible new brain waves ω = 100MHz and
microtubule quantum oscillations .............................................. 132
Epilogue:
Mathematics, Physics, Plants and Fibonacci Series................... 140
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4
Introduction
Modern physics might well be regarded as study of the structure of matter and of
the behavior of radiation. A criterion for success pursuit of the former study
demands that analysis of material structures into atoms and molecules, and of
these into nuclei with groups of associated electrons, must be capable of giving
rise to verifiable prediction of the bulk properties of matter, mechanical, thermal,
chemical, and electrical. Criteria for theories as to the behaviour of radiation are
that the phenomena of light, colour, radio, X-rays, heat radiation, must become
explainable by some single mechanism; the only mechanism so far successful has
been the propagation of electric and magnetic quantities with a unique and
universal speed which is accurately measurable. This speed exceeds that of the
fastest material particles, as a limit towards which the latter can only approach.
Within the scope of these two most general schemes, the structure of matter has
been a prime example of pattern since D Mendeleyev in XIX century arranged all
the then known chemical species or elements into a two- dimensional framework.
Written down in a table of horizontal rows and vertical columns, the chemical
elements were found to repeat certain properties periodically, much as the
harmonic properties of the notes on a piano keyboard repeat themselves at
intervals of octaves. To form the gross substances which we distinguish by touch,
smell, taste, etc. , the affinities for chemical combining of atomic species are
found to wax and wane with precise regularity throughout the periods of this table.
The whole assemblage of empirically periodic patterns is now understood as
manifesting the way in which successive electrons can become associated with
atomic nuclei of definite mass: these additions proceed until one after another
their possible federations into electrically and mechanically stable groups or subpatterns are.
There have been eras in which an educated man could only live up to his standard
if he were at the same time a poet and a philosopher and an experimental or
mathematical researcher. E. Schrodinger is a good example. He attended a
gymnasium, which emphasized the study of Greek and Latin classics. His book
Nature and the Greeks published in 1948 is an elegant exposition of ancient
physical theories and their relevance. Schrodinger wrote in 1925 an intensely
account of his beliefs, Seek for the Road. The book was influenced by Hinduism
and is an argument for the essential oneness of human consciousness.
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Many theories of ESP- part of consciousness phenomena can be viewed as signaling models, in the sense that they involve the transmission of information or
energy via some sort of particle or field (these concepts being linked in modern
physics). Often the field involved is already part of the current paradigm. This
includes, for example, explaining ESP in terms of electromagnetic waves or neutrinos
Models which explain precognition in terms of tachyons or advanced waves
might also be regarded as being within the current paradigm, even though they
involve rather exotic aspects of it. Even more extreme are models which adopt
the spirit of the current paradigm but invoke particles like psitrons or ESP waves
with the specific purpose of explaining ESP. All these approaches might be regarded as tinkering with the current paradigm.
Generally speaking, the experimental evidence indicates that ESP can occur at
great distances and does not decline with distance. These findings do not fit well
with most hypotheses that physical energies mediate the transmission of extrasensory information. Indeed, the information transmission model may itself be erroneous.
However, as discussed below, even if signaling models cannot work in four dimensions, they may still be viable in higher dimensions, since the viewer and the
viewed may become contiguous in the higher-dimensional space. This is a crucial
feature of my own proposal.
There are also many theories which invoke some form of biophysical field, even
though the status of such fields is questionable from a physicist's perspective.
Mesmer's early ideas on animal magnetism and vitalistic fluids might be included
in this category. Unfortunately, none of these approaches has gained general acceptance among paraphysicists and all of them have been criticized on the
grounds that they are ad hoc and unfalsifiable. On the other hand, the link with
biology is important and reflects the growing interaction between physicists and
biologists in orthodox science. It also raises the issue of whether psi is involved
in some forms of complementary medicine and in reincarnation cases, and
whether it is a feature of mind alone or life in general.
Quantum theory – which for present purposes we regard as part of the current
paradigm – provides at least some scope for an interaction of consciousness with
6
the physical world. It also completely demolishes our normal concepts of physical
reality, so it is not surprising that some physicists have seen in its weirdness some
hope for explaining psi. Indeed, E.H. Walker (1984) has argued that only quantum theory can explain ESP. The most concrete realization of the quantum approach is 'observational theory', according to which consciousness not only collapses the wave-function but also introduces a bias in how it collapses. In this
picture all psi is interpreted as a form of PK which results from the process of
observation itself (i. e. there must be some kind of feedback). For example, clairvoyance is supposed to occur because the mind collapses the wave-function of
the target to the state reported. This process can even explain retro-PK), since it
is assumed that a quantum system is not in a well-defined state until it has been
observed. Another feature of observational theory is that the brain is regarded as
being akin to an REG. Thus an ordinary act of will occurs because the mind influences its own brain, and telepathy occurs because the mind of the agent influences the brain of the percipient. Of course, there is still the question of how
consciousness collapses the wave-function (Stapp, 1993). One possibility is to
modify the Schrodinger equation in some way. (Marciak-Kozlowska, Kozlowski,
2013). Observational theory has the virtue that it can make quantitative predictions. For example, one can estimate the magnitude of PK effects on the basis that
the brain has a certain information output and the results seem comparable with
what is observed in macro-PK effects. On the other hand, observational theory
also faces serious criticisms. One can object on the grounds that psi sometimes
occurs without any feedback. For example, (Beloff 1988) has pointed out that
there are pure clairvoyance experiments in which only a computer ever knows the
target. One can also question the logical coherence of explaining psi merely on
the grounds that one observes it and there are alternative models for retro-PK
Finally, David Bohm (1986) has cautioned that the conditions in which quantum
mechanics apply (low temperatures or microscopic scales) are very different from
those relevant to the brain.
Nevertheless, many physicists back some form of quantum approach. Some proposals exploit the non-locality of quantum theory, as illustrated by the famous
EPR paradox. An atom decays into two particles, which go in opposite directions
and must have opposite (but undetermined) spins. If at some later time we measure the spin of one of the particles, the other particle is forced instantaneously into
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the opposite spin-state, even though this violates causality. This non-locality effect is described as 'entanglement' and) tried to explain this in terms of hidden
variables, which he invoked as a way of rendering quantum theory deterministic.
Experiments later confirmed the non-locality prediction (Aspect, 1982) and
thereby excluded at least some models with hidden variables (though not Bohm's).
Indeed, John Bell, who played a key role in developing these arguments (Bell,
1966) and was much influenced by Bohm's ideas, compared the non-locality property to telepathy. Einstein made the same comparison, although he intended it to
be disparaging!
Although quantum entanglement has now been experimentally verified up to the
scale of macroscopic molecules, it must be stressed that it is not supposed to allow
the transmission of informations (i. e. no signal is involved). For example, attributing remote viewing to this effect would violate orthodox quantum theory. Theorists have reacted to this in two ways. Some have tried to identify what changes
are necessary in quantum theory in order to allow non-local signalling (Valentini,
2002). For example, (Josephson and Pallikari-Viras (1991) have a model in which
entanglement can be utilized biologically. More generally, Jack Sarfatti (1998)
has argued that signal non-locality could still be allowed in some form of 'postquantum' theory which incorporates consciousness. He regards signal locality as
the micro-quantum limit of a more general non-equilibrium macro-quantum theory. The relationship between micro and macro quantum theory is then similar to
that between special and general relativity, with consciousness being intrinsically
non-local and analogous to curvature. His model involves non-linear corrections
to the Schrodinger equation and may permit retrocausal and remote viewing effects. Others accept that there is no signaling but invoke a 'generalized' quantum
theory, which exploits entanglement to explain PSI acausally. This is also a feature of the model of pragmatic information, which interprets psi effects as meaningful non-local correlations between a person and a target system. This model
may account for many of the observed features of psi, including the difficulty of
replicating psi under laboratory conditions). It may also be relevant to homeopathy (Radin, 2006) has argued that entanglement is fundamental to ESP. This is
because he regards elementary-particle entanglement, bio-entanglement (neurons), sentient-entanglement (consciousness), psycho-entanglement (psi) and socio-entanglement (global mind) as forming a continuum, even though there is an
explanatory gap (and sceptics might argue an evidential gap) after the second step.
8
If the Universe were fully entangled like this, he argues that we might occasionally feel connected to others at a distance and know things without use of the
ordinary senses. This idea goes back to (Bohm, 1980), who argued that there is a
holistic element in the Universe, with everything being interconnected in an implicate order which underlies the explicit structure of the world: - The essential
features of the implicate order are that the whole Universe is in some way enfolded in everything and that each thing is enfolded in the whole. This implicit
order is perhaps mediated by ESP. Most mainstream physicists regard such ideas
as an unwarranted extension of standard quantum theory, but one clearly needs
some sort of extension if one wants to incorporate mind into physics.
There are various other quantum-related approaches to explaining ESP. Some of
these exploit the effects of 'zero point fluctuations vacuum energy. This is a perfectly respectable physical notion, so it is not surprising that some people have
tried to relate this to the traditional metaphysical idea that there is some all-pervasive energy field which connects living beings (eg. chi, qi, prana, elan vital).
Indeed, views the zero-point-energy sea as a blank matrix upon which coherent
patterns can be written. These correspond to particles and fields at one extreme
and living structures at the other, so some connection with psi is not excluded. A
related proposal is that the radiation associated with zero-point-energy might be
identified with subtle energy fields These allegedly involve some form of unified
energy of such low intensity that it cannot be measured directly In the electromagnetic context, this idea was introduced to describe the quantum potential and
maybe relevant to Bohm's, (Bohm, 1986) implicate order.
Although these ideas might be regarded as being on the fringe of the standard
paradigm, the recent discovery that 70% of the mass of the Universe is in the form
of 'dark energy' – most naturally identified with vacuum energy – is stimulating
interest in this sort of approach. For example, (Sarfatti, (2006) has a model which
associates both consciousness and dark energy with the effects of vacuum fluctuations, although he does not explicitly identify them.
It should be cautioned that the literature in this area comes from both expert physicists and non-specialist popularizers, so it is important to discriminate between
them (Clarke & King, 2006). Although quantum theory is likely to play some role
in a physical model for psi, my own view is that a full explanation of psi will
9
require a paradigm which goes beyond standard quantum theory. Of course, nobody understands quantum theory anyway, so claiming that it explains psi is not
particularly elucidating – it just replaces one mystery with another one Also, many
of the above proposals already deviate from standard quantum theory, so this
raises the question of how radical a deviation is required in order to qualify as a
new paradigm. In my view, most of those mentioned above are insufficiently radical and one needs a new approach – perhaps of the kind envisaged by Bohm –
that can explain both psi and quantum theory. One also suspects that the new
paradigm will incorporate the idea of retrocausality discussed earlier, since proposed tests of this all involve some form of EPR effect (Cramer, 2006).
In this book we present theoretical model for the emission of the Heaviside type
wave model for the ESP phenomena. In our papers we developed the quantum
model for the emission of the brain waves.
References
Bohm, D.J., 1986, A new theory of the relationship between mind and matter,
JASPR 80, 113-136, 1.
Cramer J.G., 2006, Reverse causation and the transactional interpretation of quantum mechanics, Science 14-26Larmor J (Ed), Cambridge: Cambridge University Press, 1884.
Bell J.S., 1966, On the problem of hidden variables in quantum theory, Reviews
of Modern physics, 88, 447.
Beloff J., 1988, Parapsychology and physics: can they be reconciled? Theoretical
Parapsychology, 6, 23.
Josephson B.D., Pallikari-Viras, 1991, Biological utilization of quantum non-locality, Foundations of Physics 21, 197.
Heaviside, O., 1885, Electrical papers, vol 1, Chelsea Publishing Company, NY,
1970, p. 430.
Valentini A., 2009, Beyond the quantum, Phys. World, 22, 32-37, 2009.
10
CHAPTER I
Schumann and Brain Waves
Quantum description
Introduction
Geospace is the term that relates to the solar-terrestrial environment and the relevant space occupied by Earth and her fields. Schumann Resonances (SR), global
electromagnetic resonances, excited by lightning, is one of the natural EM fields
in our planetary environment. But resonances can be excited by any electromagnetic disturbance in the atmosphere. The fundamental SR mode roughly corresponds to a wave with a wavelength equal to the circumference of the Earth.
Transverse resonance is predominantly a local phenomenon containing information on the local height and conductivity of the lower ionosphere and on nearby
thunderstorm activity. Waves in the ULF range ULF range (i.e., below the first
Schumann Resonance), will have wavelengths much larger than the circumference of the Earth. ULF waves, at approximately 1 mHz to 1 Hz, play a major role
in propagating energy throughout the magnetospheric system. At the lowest end
of this frequency band, the wavelength of ULF waves is comparable to the entire
magnetosphere. In this frequency range, the global structure of the magnetosphere
can lead to global cavity resonances and waveguide modes. The structure of these
modes is determined by the gradients in the Alfvén and fast mode speeds in the
magnetospheric system. SR is not the internally-generated resonant frequency of
the planet Earth, which is 10 Hz as Tesla discovered. It is electromagnetic oscillations – the Earth’s global electric circuit consisting of the frequencies that play
through the ionospheric cavity (space between the ground and ionosphere) as
waves in a plasma. The ionosphere is a highly-conductive region of cosmic
plasma.
The solar-terrestrial environment is modulated by solar cycles which affect the
global climate and all organisms in the biosphere. Interference patterns are the
transducers of energy, which at its most fundamental is described as information.
Earth functions like a planet-sized electrical capacitor or condenser, storing electrical potential.
11
The space between Earth and the ionosphere is a dissipative closed cavity between
50-375 miles that can sustain quasi-standing waves at wave lengths of planetary
dimension. Electrical conductivity in the atmosphere is driven largely by cosmic
rays that generate a torsion field. Conductivity increases exponentially with altitude because the lower atmosphere buffers collision frequency. The ionosphere
begins about 50 miles out from the Earth’s surface and extends out over 180 miles.
It consists of charged particles. This highly dynamic region is constantly exposed
to harsh ultraviolet radiation from the Sun. It breaks down molecules and atoms.
Highly charged ions and free electrons therefore fill the ionospheric layers creating a “spectral power station”. Lightning radiates broadband EM fields that spread
laterally into the cavity. Global thunderstorms excite the Schumann resonances,
which can be observed around 7, 8, 14, 20, 26, 33, 39 and 45 Hz. The resonant
spectrum is a superposition of global lightning discharge. For these resonant values to change, the planet would have to change diameter.
The Schumann resonance modes, like other low-frequency modes, are able to leak
into the ionosphere, particularly at night when the plasma density is lower... Using
measurements from the Communications/Navigation Outage Forecasting System
(C/NOFS) satellite, we report, for the first time, Schumann resonance signatures
detected well beyond the upper boundary of the cavity. These results offer new
means for investigating atmospheric electricity, tropospheric-ionospheric coupling mechanisms related to lightning activity, and wave propagation in the ionosphere. The detection of Schumann resonances in the ionosphere calls for revisions to the existing models of extremely low frequency wave propagation in the
surface-ionosphere cavity. Such frequencies have wrapped earth’s life since its
inception. Normal daily variation ranges ± 0.5 Hertz. Driven by lightning, this
primal SR pulse calibrates us and enhances our physical and mental well-being.
That natural resonance helps us achieve our optimal brainwave states, but this
atmosphere to human linkage is disrupted by the electrosmog of today’s technology.
1. Schumann waves
That information is propagated as sequential series of digital signals along distinct
paths whose lengths are much longer than their widths is a primary assumption of
contemporary neuronal function. Dispersion rates are within the range of 1-100
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m/s with space constants in the order of about 1 mm. The fastest of these transients
exhibit saltatory movements between specialized conductive spaces along the
axon barrels. The ratios and scaling of the spatial and temporal relationships of
these mediators of the “language of the brain” share remarkable similarities to
lightning. Because lightning’s absolute spatial scale is so large compared to the
observer’s reference point, minute characteristics are discerned whose equivalence at the level of the axon are below contemporary resolution. Quantitative
identities between these two classes of phenomena could encourage alternative
interpretations of the electromagnetic (EM) components of action potentials and
reveal recondite relationships concerning neuronal function.
The identity between exogenous and endogenous “electricity” is not really a new
idea. The observation that atmospheric electricity, lightning, and the electrical
fields within living systems, “nerve conduction”, shared similar origins was considered as early as the 18th century by Galvani and Volta. Galvani showed contractions in frog muscles elicited from Leyden jars and electric machines was the
same as those evoked during lightning when a long metallic wire was connected
to the nerves and pointed to the sky. The similarity has been viewed historically
as more of a congruence of quality than a potential blueprint for quantitative characteristics. In the present comparison these features are demonstrated. To facilitate understanding the calculations and reasoning for the similarities between action potentials and lightning will be articulated in greater detail than the usual
narrative discussion in the neurosciences.
The concept of scale-invariance or recurrent ratios within measurements of the
physical world assumes an intrinsic repeated structure within the varying increments of space (∆s) and time (∆t) as well as their relationship. For example the
proportion of matter (protons and electrons) that occupies the space (volume) occupied by an atom is about 1 part per trillion. The ratios of the volume of the sun
and planets within the space of the solar system and the stars within galactic space
are the same order of magnitude.
One temporal example is the equivalent order of magnitude of the ratio of the
electron orbital time of a hydrogen atom to its precession and the earth’s rotation
to its spin axis gyration. Comparable “scale-invariance” has been found within
the human brain and for functional EM fields within the cerebrum and over very
large spaces
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2. Classical description of the Schumann and brain waves
The brain is a massive source of ELF signals that get transmitted throughout the
body through the nervous system, which is sensitive to magnetic fields. Brainwaves and natural biorhythms can be entrained by strong external ELF signals,
such as stationary waves at Schumann resonance. Entrainment, synchronization,
and amplification leads toward coherent large-scale activity, rather than typical
flurries of transient brainwaves. Thus, resonant standing waves emerge from the
brain, which under the right conditions facilitates internal and external bioinformation transfer, via ELF electromagnetic waves. These SR waves, exhibit nonlocal character and nearly-instant communication.
The EEG (electroencephalograph) measures brainwaves of different frequencies
within the brain. Rhythmicity in the EEG is a key variable in the coordination of
cortical activity. Electrodes are placed on specific sites on the scalp to detect and
record the electrical impulses within the brain. Frequency is the number of times
a wave repeats itself within a second. It can be compared to the frequencies on a
radio. Amplitude represents the power of electrical impulses generated by the
brain. Volume or intensity of brain wave activity is measured in microvolts.
Raw EEG frequency bands include Gamma (higher than 30Hz); Beta (14-30Hz);
Alpha (7.5-13Hz); Theta (3.5-7.5Hz); and Delta (less than 4Hz). Their ranges
overlap one another along the frequency spectrum by 0.5Hz or more. These frequencies are linked to behaviors, subjective feeling states, physiological correlates, etc. Clinical improvement with EEG biofeedback is traceable to improved
neuroregulation in the basic functions by appeal to their underlying rhythmic
mechanisms.
Schumann's resonance forms a natural feedback loop with the human mind/body.
Our brains and bodies developed in the biosphere, the EM environment conditioned by this cyclic pulse. Conversely, this pulse acts as a "driver" of our brains,
and can also potentially carry information as well. Functional processes may be
altered and new patterns of behavior facilitated through the brain's web of inhibitory and excitatory feedback networks.
Like sound waves, the brain has its own set of vibrations it uses to communicate
with itself and the rest of the body; EEG equipment distinguishes these waves by
14
measuring the speed with which neurons fire in cycles per second. At their boundaries these waves can overlap somewhat, merging seamlessly into one another, so
different researchers may give slightly different readings for the range of cycles
per second. Rate of cycling determines the type of activity, kindling wave after
wave over the whole surface of the brain, by igniting more neurons.
BETA waves (14 cycles per second and above) dominate our normal waking state
of consciousness when attention is directed towards cognitive tasks and the outside world. Beta waves range between 13-40 Hz. Gamma (above 30 Hz) represents hyperarousal. The Beta wave is associated with peak concentration, heightened alertness and visual acuity. Nobel Prize winner, Sir Francis Crick and other
scientists believe that the 40Hz beta frequency may be key to the act of cognition.
ALPHA waves (7-13 cycles per second) are present during dreaming and light
meditation when the eyes are closed. As more and more neurons are requited to
this frequency, alpha waves cycle globally across the whole cortex. This induces
of deep relaxation, but not quite meditation. In Alpha, we begin to access the
wealth of creativity that lies just below our conscious awareness. It is the gateway,
the entry point that leads into deeper states of consciousness. Alpha is also the
home of the window frequency known as the Schumann Resonance, which is the
resonant frequency of the earth's electromagnetic field. SR waves propagate with
little attenuation around the planet. When we intentionally generate alpha waves
and go into resonance with that earthy frequency, we naturally feel better, refreshed, in tune, in synch. It is, in fact, environmental synchronization.
THETA waves (4-7 cycles per second) occur most often in sleep but are also
dominant in the deepest state of mediation (body asleep/mind awake). The optimum level for deep thought is this realm of Theta. In Theta, our senses are withdrawn from the external world and focused on the mindscape, internally originating signals. Theta waves are associated with mystery, an elusive and extraordinary realm we can explore. It is that twilight state which we normally only experience fleetingly as we rise from the depths of delta upon waking, or drifting off
to sleep. In theta we are in a waking dream, vivid imagery flashes before the
mind's eye and we are receptive to information beyond our normal conscious
awareness. Theta has also been identified as the gateway to learning and memory.
Theta meditation increases creativity, enhances learning, reduces stress and awakens intuition and other extrasensory perception skills.
15
DELTA waves range between 0-4 Hz. Delta is associated with deep sleep. In
deepest meditation and dreamless sleep, Delta waves are generated. Each of these
brainwave frequencies serves an important function. DELTA waves confer a suspension of external existence and provide the most profound feelings of peace. In
addition, certain frequencies in the delta range trigger the release of growth hormone beneficial for healing and regeneration. This is why sleep, deep restorative
sleep is so essential to the healing process.
There is a harmonic relationship between the earth and our mind/bodies. Earth's
low frequency isoelectric field, the magnetic field of the earth, and the electrostatic field which emerges from our bodies are closely interwoven. Our internal
rhythms interact with external rhythms, affecting our balance, REM patterns,
health, and mental focus. SR waves probably help regulate our bodies' internal
clocks, affecting sleep/dream patterns, arousal patterns, and hormonal secretion.
The rhythms and pulsations of the human brain mirror those of the resonant properties of the terrestrial cavity, which functions as a waveguide. This natural frequency pulsation is not a fixed number, but an average of global readings, much
like EEG is an average of brainwave readings. SR actually fluctuates, like brainwaves, due to geographical location, lightning, solar flares, atmospheric ionization and daily cycles.
The most important slow rhythm is the daily rhythm sensed directly as change of
light. Rhythms connected with the daily rhythm are called circadian (an example
is pineal gland melatonin secretion). Some experiments in the absence of natural
light have shown that the basic human "clock" is actually slightly longer than one
day, and closer to one lunar day (24h 50min). The lunar day has a similar period
(24h 50min).
On a slower scale, a strong influence on the Earth is its geomagnetic field, which
is influenced by the following periods: the Moon's rotation (29.5 days); the Earth's
rotation (365.25 days); Sun spots (11 and 22 years); the nutation cycle (18.6
years); the rotation of the planets (88 days to 247.7 years); and all the way out to
the galaxy's rotation cycle (250 million years).
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Very important rhythms are in the order of 1-2 hours, like hormone secretion, and
dominant nostril exchange. In the range of human EEG, we have the Sun's electromagnetic oscillation of 10Hz, while the Earth-ionosphere SR system is resonant at frequencies in the theta, alpha, beta1 and beta2 bands.
Different species often have internal generators of environmental rhythms, which
can be extremely precise, up to 10-4. The frequency of these oscillators is then
phase locked loop (PLL) synchronized with the natural rhythms. Environmental
synchronization sources are often called "zeitgebers". The mechanism of optical
synchronization can be shown. The presented rhythms should inspire a better understanding of the interaction of internal and external rhythms during specific
states of consciousness.
This bioelectrical domain is geared to thalamocortical generation of rhythmic activity. In neurofeedback, what is being trained is the degree of rhythmicity of the
thalamocortical regulatory circuitry. Rhythmicity manages the entire range of activation and arousal in the bio-electrical domain. One role advocated for rhythmic
activity is that of time binding, the need for harnessing brain electrical activity
which is spatially distributed while maintaining it as a single entity. Brainwaves
indicate the arousal dimension, and arousal mediates a number of conditions.
Changes in sympathetic and parasympathetic arousal "tunes" the nervous system.
Underarousal leads toward Unipolar or Reactive Depression, Attention Deficit
Disorder, chronic pain and insomnia. Overarousal is linked with anxiety disorders, sleep onset problems, nightmares, hypervigilance, impulsive behavior, anger/aggression, agitated depression, chronic nerve pain and spasticity. A combination of under- and overarousal causes anxiety and depression, as well as
ADHD. Instabilities in certain rhythms can be correlated with tics, obsessivecompulsive disorder, aggressive behavior, rage, bruxism, panic attacks, bipolar
disorder, migraines, narcolepsy, epilepsy, sleep apnea, vertigo, tinnitus, anorexia/bulimia, suicidal ideation and behavior, PMS, multiple chemical sensitivities, diabetes, hypoglycemia, and explosive behavior.
Delta waves are the slowest but highest in amplitude. They are abundant in deep,
dreamless sleep, non-REM sleep, trance, and unconsciousness. Theta waves mean
'slow" activity connected often with creativity, intuition, daydreaming or recalling
emotions and sensations. Focus is internal in this state between waking and sleep.
17
Under stress it may manifest as distraction, lack of focus. Alpha waves aid relaxation and overall mental coordination, calmness, alertness, inner awareness,
mind/body integration and learning.
Beta is a 'fast' activity, present when we are alert or even anxious; problem-solving, judgment, decision making, processing information, mental activity, focus.
Gamma appears to relate to simultaneously processing information from different
brain areas: memory, learning abilities, integrated thoughts, information-rich task
processing. Gamma rhythms modulate perception and consciousness, which disappears with anesthesia. Synchronous activity at about 40Hz appears involved in
binding sensory inputs into the single, unitary objects we perceive.
The brain responds to inputs at a certain frequency or frequencies. The computer
can create wave form patterns or certain frequencies that compare with the mind's
neural signals in terms of mind patterns. If people can control their mind patterns,
they can enter different states of being (mental relaxation, study, etc.) What happens when the mind is entrained with a sound or vibration that reflects the thought
patterns? When the mind responds to certain frequencies and behaves as a resonator, is there a harmonic frequency that the mind vibrates to or can attune to?
What does the study of harmonic resonance - sound or vibration have to do with
the brain's frequency waves?
Soundwaves are examples of periodicity, of rhythm. Sound is measured in cycles
per second (Hertz or Hz). Each cycle of a wave is in reality a single pulse of
sound. The average range of hearing for the human ear is somewhere between 16
hz. and 20,000 Hz. We can not hear extremely low frequencies (ELFs), but we
can perceive them as rhythmic. Action potentials are the carriers of the discrete
signals along the axon barrel. An average net potential difference for an action
potential (-70 to +50 mV) is 1.2 × 10-1 V which would exert on each unit charge
of 1.6 × 10-19 Coulomb (A·s) an energy of 1.9 × 10-20 J. If we assume ~1010 neurons occupy human cerebral cortices with an average frequency of propagation of
1 Hz, the total energy per second involved with just the effects of all action potentials within brain space would be about 10-10 J/s. The volume (~1330 cc) of an
average brain is 1.3 × 10-3 m3. This results in an energy density of about 10-7
J/s·m3. On the other hand the typical lightning stroke involves a flow of ~10 Coulomb (C) of electrons across a potential difference of 108 V resulting in 109 J.
There are about 70-100 lightning flashes/s world wide resulting in (assuming 100
18
flashes) the generation of 1011 J/s or 100 Gigawatts of power. For reference there
is 4.3 × 1012 J per kiloton (kT) of standard explosives such that the energy generated every approximately 14 min by global electrical discharges is equivalent to
about a 20 kT (Hiroshima-like) nuclear explosion.
Most of this energy from lightning discharges is within a narrow shell of about 2
km within the biosphere. The volume of this shell, assuming a radius of 6,378 km
for the earth, would be about 1 × 1018 m3. This means the energy density would
be 1011 J/s·1018 m3 or 10-7 J/s·m3 (10-7 W/m3). This energy density is remarkably
similar to that generated by action potentials within the brain. When applied
across the 3– 5 mm thickness of the cerebral cortices, the value is equivalent to
10-10 W/m2 which is within the range of power of photon emissions near the skull
when subjects engage in specific imagination and which is strongly correlated
with the power of electroencephalographic (EEG) activity
Scaled densities. About 5 C is distributed within a lightning channel with an average current of 100 A. Although the width of a leader channel is about 1 m the
current flows through a channel with a radius of about 1 cm. With this crosssectional area the density is 10 × 101 A divided by 3.14 × 10-4 m2 or 3.2 × 105
A/m2. A reasonable radius for an axon is 1 µm. However the actual locations of
the major movements of ions that affect the transmission of EM field-mediated
information along the axon are within the membrane which is about 10 nm in
width. The cross-sectional area of this small annulus around the axon would be 2
× 10-14 m2. Given the average current of 10-9 A (from the approximately 103 ion
channels each with 1 pA capacities around the ring or circumference of the axon),
this would mean that the cross-sectional current “density” would be ~105 A/m2.
Consequently even though the current is much larger in a lightning stroke because
of its absolute size by a factor of 1010, the “minuscule” axon potential current is
comparable per cross-sectional area. The range in the widths of normal axons
would affect the coefficients rather than the order of magnitude. It may also be
relevant that the actual charge and current per lightning stroke also displays a
comparable range in the coefficient of variation. Such a large relative magnitude
of potential across neuronal membranes is not a new concept. For example, the
90 mV potential difference across a 10 nm membrane is equivalent to 9 × 107
V/m. Most lightning (90%) is between clouds. The leader moves in discrete jumps
of 50 m at about 1.2 × 105 m/s to 1.5 × 105 m/s. This conspicuous conduction of
19
lightening has a ratio of [1.2 × 105 m/s]/50 m or 2.4 × 103 Hz (about 2 kHz or 0.5
ms) which is remarkably similar to the absolute refractory period of the action
potential. In comparison the action potential moves along the myelinated axon in
discrete steps of 1 mm compared to the approximately 2 µm width of the nodes
of Ranvier.
The wave shape characteristics of action potentials and lightning flashes are similar. -all lightning pulses were the same polarity; most were single peak but about
one-third were multiple-peaked. Although the mean width of the initial peak was
25 µs (SD 13 µs), the ratio of the overshoot duration to the initial peak was 5.7
(SD 2.1). This ratio is within the range of the typical relative refractory to absolute
refractory period in the average axon. More recent measurements of artificially
triggered lightening revealed comparable peak widths. Interestingly, the initialstage discharge time was about 20 ms and the time between strokes ranged from
18 to 210 ms (mean 87 ms). This interval is within the range of the global rostral–
caudal propagating, coherent waves over the cerebral cortices and the microstates
that determine a percept and consciousness. (Nikolaenko, Hayakawa, 2014)
Although the velocity of a leader exceeds the 10 m/s values exhibited by nonmyelinated axons by a factor of 1.2 – 1.5 × 104, the scaled values for the mass
mediating the movements of charges are similar. For example, the mass of Na+,
the major mediator of the action potential, is 30 Daltons or 48 × 10-27 kg while the
mass of an electron is 9.8 × 10-31 kg. The difference is in the order of 104. The
coefficients converge more closely when the range of hydration states (accompanying H2O molecules) associated with the ions are included. As the leader approaches to about 10 m above the ground it creates an electric field sufficient to
initiate discharges rising from the ground (streams). When contact is made between the upward and downward fields a heavy surge of current occurs within 1
– 5 ms. This surge produces the luminosity that progresses up the path produced
by the step leader at ~108 m/s. About 40 – 50 ms after the return stroke, another
region of luminosity, about 50 m long, moves from the cloud to the ground (dart
leader). It does not fork or branch. There is an average of three to four strokes
with a maximum around 20. The approximately 10 m interface or boundary where
the exchange of energy between the atmosphere and ground occurs is about 3 ×
10-3 the length of the pathway. For cortical axons with lengths between 1 and 5
mm, this would be equivalent to a length of between 3 and 15 µm which is within
20
the range of the length of the terminal endings or boutons within which the digital
information of the action potential is transformed to chemical equivalents.
The surge of current lasting for 1 – 5 ms is within the range of the time involved
with release of the contents of the synaptic vesicles. The energy transfer mediated
by the mass of molecules released from the vesicles into the synaptic space would
be analogous to this relatively large increment of current. The occurrences of subsequent surges from the cloud to the ground after an interval of 40 – 50 ms or
about 20 times after the first surge is comparable to the first and second surges of
vesicular releases.
The billions of action potentials and their correlates per second within the cerebral
cortices generate emergent phenomena inferred by EEG measurements that include microstates and transient coherence of activity over areas (tens of mm2 to
tens of cm2) of the human brain’s cortical surface. Between the earth’s surface
and the lower ionosphere there is a shell of optimum conduction within which the
results of focal energies in one area are generated throughout the volume. Cloudto-ground lightning discharges from global thunderstorm activity are the main
excitation sources within the earth-ionospheric cavity. These omnipresent pulses
propagate for megameters without appreciable attenuation and behave as a “cortical manifold” for distributing tissue-level energies throughout the biosphere.
The fundamental frequency (1/s = Hz) is the velocity divided by the circumference. Assuming the speed of light of 3 × 108 m/s and the circumference of the
earth as 40,000 km (4 × 107 m) the natural frequency is 7.8 Hz. Harmonics for
this values, often described as the Schumann resonances, can be obtained by taking the square root of [(n(n + 1))/2] multiplied by the base frequency (7.8 Hz),
where n is the progressive series of integers 1, 2, 3, …, etc. Those that have been
measured have peaks around 8, 14, 20, and 26 Hz.
As described by Nunez (1995) in his classic chapter on “Towards a physics of the
neocortex”, comparable solutions exist for the human brain. The probability density function for myelinated cortico-cortical propagation peaks at about 6– 9 m/s
with the half-width of the distribution is estimated to be between 3 and 4.5 m/s.
Published estimates of the neocortical surface areas range from 1,600 to 4,000
cm2. The effective cortical radius after flat-mapping is between 11 and 18 cm. As
a result the non-dispersive brain waves from mode n = 1 would be between 7 and
18 Hz. Subtle shifts in peak power in this frequency vary with head size, defined
21
by the cube root of the product of three linear measures. As the size increased
over a normal range of volunteers the peak frequency decreased from 10.6 to 9.8
Hz.
The EM signals associated with lightning are propagated through a medium. The
simplest calculation of a time constant is the product of the resistance (in Ohms)
and capacitance in Farads (F). For free space resistance is 3.70 × 102 Ohms
[(kg·m2)/(A2·s3)] and capacitance is 8.8 × 10-12 F/m [(A2·s4)/(kg·m2)]/m or 32.56
× 10-10 S/m. When multiplied by the circumference of the earth, the time constant
is 130 ms or about 7.7 Hz; this is within the natural variation of the fundamental
Schumann resonance.
Cerebral tissue is also a medium. The permeability (inductance/m) of cortical gray
matter at 1 kHz is about 10-2 Henrys, while the permittivity of gray matter is 2 ×
10-1 F/m. Application of the formula f = 1/(2π(LC)-1/2), the equation for resonance
frequency of a closed circuit, results in a value of about 7 Hz. The convergence
of a fundamental cerebral resonance with the Schumann solutions indicates that
higher order harmonics may exist within EM fields within cerebral space and be
associated with specific functions. There are often strong correlations between
fluctuations in power values measured by quantitative EEG across traditional frequency bands. That resonance could occur between fields within cerebral volumes
and the Schumann phenomena may have significant implications for the biosciences.
The classical although arbitrary division of EEG activity into delta, theta, alpha,
and beta activity with a myriad of complexes and transients have been considered
both emergent and reflective of “distant” fields of neuronal activity. As shown by
Koenig et al. (1981) all of the fundamental frequencies and patterns of EEG activity are measured within the Schumann (earth-ionospheric) cavity or as local
electric field configurations during thunderstorms. In addition, biofrequency (1–
100 Hz) pulses of about 0.5 ms whose carrier frequencies diminish from 100 kHz
to about 10 kHz at distances more than 1000 km from the source display magnitudes in the nanoTesla (nT) to picoTesla (pT) range
Within the range of 7–40 Hz the electric field components associated with the EM
fields generated through the ionospheric – earth cavity are about a mV/m, while
22
the magnetic field components are between 1 and 10 pT. For comparison the magnetic field intensities within galaxies are in the order of 10-10 T with upper limits
of 10-13 T for extragalactic fields. In a manner similar to the changing, averaged
power outputs of neuronal activity within the cerebral volume that can vary in
response to fluctuations in subtle external energy, the Schumann values also display discrete alterations.
The long-term averages for the Schumann frequency, damping, and amplitude
change as a function of solar proton events (SPE). They increase the Schumann
resonance frequency from a reference value of ~7.8 Hz by between 0.04 and 0.14
Hz depending upon the intensity of the proton flux. The amplitude of the resonance increased by several 10% from a mean value of about 1.0 pT. Electric fields
within the mV/m range and magnetic fields within the pT range also define the
operating intensities overly spatially distributed cerebral functions. The strong
correlations between variable power densities within the ionosphere-earth cavity
and power changes within quantitative EEG measures as well as the quantum-like
properties of interhemispheric interactions indicate that physical connectivity
may be pervasive. Phase modulation has been considered the most optimal means
to propagate the most information over distance. Phase shift can be obtained by
time divided by the square root of v2/c2. Because the EM fields associated with
lightening generated within the earth– ionospheric cavity are within the 10–100
kHz (“atmospherics” or “sferics”) range, the ∆c/c (c, velocity of light) is 0.05 for
this range. This means that the phase shift for every 1 s is 1/0.9897 s or 16 ms.
This magnitude of phase shift is remarkably similar to phase comparisons associated with the presence of the continuous “40 Hz-oscillations” over the entire cerebral cortical mantle. An approximately 12 ms phase shift between the rostral and
caudal pole of the brain has been reported). A search for the “missing” equivalents
between lightning and action potentials could be revealing in a manner similar to
the search for Mendeleyev’s missing elements in the Periodic Table. There is no
traditional equivalent of the “return stroke” at the synapse, although backpropagation might be considered a conceptual candidate). However, backpropagation
influences the dendrites of the neuron from which the action potential has been
propagated. Its variable effect depends upon the extent by which the neuron’s
action potential penetrates into its own distal dendrites.
When a stepped leader approaches within a few tens of meters above the ground,
it is met by a positively charged return stroke towards the cloud. Within a synaptic
23
scenario, this would be equivalent to a “return field” transiently generated from
the post-synaptic region towards the presynaptic membrane just before the arrival
of the action potential. If the quantitative scale-invariant relationships between
lightning and action potentials can be generalized in this context, then impulse
magnetic flux densities from the post-synaptic membrane must emerge and cross
the synapse into the presynaptic membrane during the few milliseconds before
the helical EM field (the action potential) reaches the synapse. In other words, a
comparison with lightning would predict that sub-threshold, electrotonic-like
shifts in voltage (approximately the Landauer principle limit: ln 2 kT, or about
10-21 J) should be apparent at the synapse in advance of the arrival of the major
action potential. It is more likely we have not measured this equivalent rather than
a frank deviation from Newton’s third law: for every force there is an equal and
opposite force. It is well known the repolarization of the (heart) atria after its depolarization (P) during electrocardiographic measurements is masked by the QRS
component of the massive depolarization of the ventricles.
As a possible historical example, the conspicuous retrograde movements in Mars
across the star canopy over successive nights was explained just as well by the
epicycles superimposed upon the concentric orbits around the earth (the “geocentric” universe) described in the Almagest by Ptolemy Claudius of ancient Alexandria as by the heretical heliocentric models proposed by Copernicus and Kepler.
Only detailed examination and finer temporal and spatial resolutions revealed the
relevancy of the more precise mechanism.
As indicated, the scale-invariant similarities between lightening and action potentials evoke the possibility of mutual interaction. In addition to comparable values
for magnetic and electric fields, the power density for Schumann resonances
within the 8 – 21 Hz range is in the order of 10-10 W/m2/Hz (. This is the same
order of magnitude as the power density of photon emissions from the human
brain during imagination and the correlated changes in power measures from
quantitative EEG. Laboratory experiments who exposed volunteers for about 1 ks
to simulated lightening-related sferics by generating 10 kHz signatures (amplitude 50 nT, pulse repetition: 7 – 20 Hz; pulse duration 0.5 ms), demonstrated that
protracted changes within the alpha band and experiences similar to those attributed to natural phenomena were reliably elicited. The similarities in quantitative characteristics between action potentials and lightening presented in this pa24
per might be expected if the intrinsic organizations of matter and energy are reflected within different spatial and temporal levels of observation Perhaps by
careful quantification and observation of the larger phenomena, such as lightning,
processes can be discerned that will point the direction of focus for what we have
not yet measured.
3. Quantum description of Schumann and brain waves
In order to put forward the classical theory of the brain and Schumann waves we
quantize the both fields. In the model (Marciak-Kozlowska, Kozlowski, 2013) we
assumed (i) the brain is the thermal source in local equilibrium with temperature
T. (ii) The spectrum of the brain waves is quantized according to formula
E = ℏω
(1)
where E is the photon energy in eV, ℏ =Planck constant, ω = 2πν ,ν -is the frequency in Hz. (iii). The energies of the photons are the maximum values of energies of waves. In this paper we extended the model for Schumann waves too For
the emission of black body brain and Schumann waves we propose the well know
formula for the black body radiation.
In thermodynamics we consider Planck type formula for probability dE for the
emission of the particle (photons as well as particles with m≠0) with energy (E,
E+dE) by the source with temperature T is equal to:
N (E)dE= AE2 e (-E/kT) dE
(2)
where A= normalization constant, E=total energy of the particle, k = Boltzmann
constant=1.3 × 10-23 J K-1. K is for Kelvin degree. However in many applications
in nuclear and elementary particles physics kT is recalculated in units of energy.
To that aim we note that for 1K, kT is equal k1K = K x 1.3 × 10-23 J x K-1= 1.3 ×
10-23 Joule or kT for 1K is equivalent to 1.3 10-23 Joule= 1.3 × 10-23 /(1.6 10-19) eV
= 0.8 × 10-4 eV. For comparison measured and calculated energy densities we
applied the formula:
dP [ Watt ] = BE 2e( − ET )
dE m 2eV
(3)
25
where
dP
denotes radiation surface energy density for waves with frequency E,
dE
E +dE
where, B is the normalization constant, T is the temperature of the wave source
in eV.
In Fig. 1-3 we present the results for brain waves and in Figs 4-6 for Schumann
waves.
As can be easily seen the agreement of calculated and measured spectra is very
good.
Fig. 1: Energy density spectrum for brain waves, measured
26
Fig. 2: Energy density spectrum for brain waves, calculated
Fig. 3: Comparison energy density spectrum of the brain waves calculated and measured
27
Fig. 4: Energy density spectrum for Schumann waves, measured (Nikolaenko A, Hayakawa
M),
Fig. 5: Energy density spectrum for Schumann waves, calculated
28
Fig. 6: Comparison theoretical to measured energy density for Schumann waves
References
Nikolaenko A., Hayakawa M., Schumann Resonance, Springer Japan, 2014
Nunez P.L., (1995). “Towards a physics of the neocortex”, in Neocortical Dynamics And the Human EEG Rhythms, ed. Nunez P.L., editor. (New York:
Oxford), 68– 131
Polk C., (1982). “Schumann resonance”, in CRC Handbook of Atmospherics, Vol.
1, ed. Volland H., editor. (Boca Raton: CRC Press), 111– 178
Marciak-Kozlowska J. and Kozlowski M., On the brain and cosmic background
photons. NeuroQuantology 2013; 11(2): 223-236.
29
CHAPTER II
Heisenberg Uncertainty and Human Brain
1. Introduction
The issue of observation in QM is central, in the sense that objective reality cannot
be disentangled from the act of observation, as the Copenhagen Interpretation (CI)
nearly states In the words of John A. Wheeler 1981, we live in an observer-participatory Universe. The vast majority of today's practicing physicists follow CI's
practical prescriptions for quantum phenomena, while still clinging to classical
beliefs in observer-independent local, external reality). There is a critical gap between practice and underlying theory. In his Nobel Prize speech of 1932, Werner
Heisenberg concluded that the atom "has no immediate and direct physical properties at all". If the universe's basic building block isn't physical, then the same
must hold true in some way for the whole. The universe was doing a vanishing
act in Heisenberg's day, and it certainly hasn't become more solid since. (R.
Schild, 2012)
This discrepancy between practice and theory must be confronted, because the
consequences for the nature of reality are far-reaching. An impressive body of
evidence has been building to suggest that reality is non-local and undivided.
Non-locality is already a basic fact of nature, first implied by the Einstein-Podolsky-Rosen thought experiment despite the original intent to refute it, and later
explicitly formulated in Bell's Theorem.
Moreover, this is a reality where the mindful acts of observation play a crucial
role at every level. Heisenberg again: "The atoms or elementary particles themselves... form a world of potentialities or possibilities rather than one of things or
facts". He was led to a radical conclusion that underlies our own view in this
paper: "What we observe is not nature itself, but nature exposed to our method of
questioning". Reality, it seems, shifts according to the observer's conscious intent.
There is no doubt that the original CI was subjective (R. Schild, 2012)
Quantum theory is not about the nature of reality, even though quantum physicists
act as if that is the case. To escape philosophical complications, the original CI
was pragmatic: it concerned itself with the epistemology of quantum world (how
30
we experience quantum phenomena), leaving aside ontological questions about
the ultimate nature of reality. The practical bent of CI should be kept in mind,
particularly as there is a tendency on the part of many good physicists to slip back
into issues that cannot be tested and therefore run counter to the basic tenets of
scientific methodology.
2. Heisenberg’s uncertainty
Quantum physics, as exemplified by the Copenhagen school (Bohr, 1934, 1958,
1963; Heisenberg, 1930, 1955, 1958), also makes assumptions about the nature
of reality as related to an observer, the "knower" who is conceptualized as a singularity. Because the physical world is relative to being known by a "knower"
(the observing consciousness), then the "knower" can influence the nature of the
reality which is being observed. In consequence, what is known versus what is
not known becomes relatively imprecise (Heisenberg, 1958).
For example, as expressed by the Heisenberg uncertainty principle (Heisenberg,
1955, 1958), the more precisely one physical property is known the more unknowable become other properties, whose measurements become correspondingly imprecise. The more precisely one property is known, the less precisely the
other can be known and this is true at the molecular and atomic levels of reality.
Therefore it is impossible to precisely determine, simultaneously, for example,
both the position and velocity of an electron.
However, we must ask: if knowing A, makes B unknowable, and if knowing B
makes A unknowable, wouldn't this imply that both A and B, are in fact unknowable? If both A and B are manifestations of the processing of "knowing", and if
observing and measuring can change the properties of A or B, then perhaps both
A and B are in fact properties of knowing, properties of the observing consciousness, and not properties of A or B.
In quantum physics, nature and reality are represented by the quantum state. The
electromagnetic field of the quantum state is the fundamental entity, the continuum that constitutes the basic oneness and unity of all things.
31
The physical nature of this state can be "known" by assigning it mathematical
properties (Bohr, 1958, 1963). Therefore, abstractions, i.e., numbers, become representational of a hypothetical physical state. Because these are abstractions, the
physical state is also an abstraction and does not possess the material consistency,
continuity, and hard, tangible, physical substance as is assumed by Classical
(Newtonian) physics. Instead, reality, the physical world, is created by the process
of observing, measuring, and knowing (Heisenberg, 1955).
Consider an elementary particle, once this positional value is assigned, knowledge
of momentum, trajectory, speed, and so on, is lost and becomes "uncertain". The
particle's momentum is left uncertain by an amount inversely proportional to the
accuracy of the position measurement which is determined by values assigned by
the observing consciousness. Therefore, the nature of reality, and the uncertainty
principle is directly affected by the observer and the process of observing and
knowing (Heisenberg, 1955, 1958).
The act of knowing creates a knot in the quantum state; described as a "collapse
of the wave function"; a knot of energy that is a kind of blemish in the continuum
of the quantum field. This quantum knot bunches up at the point of observation,
at the assigned value of measurement.
The process of knowing, makes reality, and the quantum state, discontinuous.
"The discontinuous change in the probability function takes place with the act of
registration... in the mind of the observer" (Heisenberg, 1958).
Reality, therefore, is a manifestation of alterations in the patterns of activity
within the electromagnetic field which are perceived as discontinuous. The perception of a structural unit of information is not just perceived, but is inserted into
the quantum state which causes the reduction of the wave-packet and the collapse
of the wave function.
Knowing and not knowing, are the result of interactions between the mind and
concentrations of energy that emerge and disappear back into the electromagnetic
quantum field.
However, if reality is created by the observing consciousness, and can be made
discontinuous, does this leave open the possibility of a reality behind the reality?
Might there be multiple realities? And if consciousness and the observer and the
32
quantum state is not a singularity, could each of these multiple realities also be
manifestations of a multiplicity of minds?
Heinsenberg (1958) recognized this possibility of hidden realities, and therefore
proposed that the reality that exists beyond or outside the quantum state could
better understood when considered in terms of "potential" reality and "actual" realities. Therefore, although the quantum state does not have the ontological character of an "actual" thing, it has a "potential" reality; an objective tendency to
become actual at some point in the future, or to have become actual at some it in
the past.
Therefore, it could be said that the subatomic particles which make up reality, or
quantum state, do not really exist, except as probabilities. These "subatomic" particles have probable existences and display tendencies to assume certain patterns
of activity that we perceive as shape and form. Yet, they may also begin - -play a
different pattern of activity such that being can become nonbeing and something
else altogether.
The conception of a deterministic reality is therefore subjugated to mathematical
probabilities and potentiality which is relative to the mind of a knower which
effects that reality as it unfolds, evolves, and is observed (Bohr 1958, 1963; Heisenberg 1955, 1958). That is, the mental act of perceiving a non-localized unit of
structural information, injects that mental event into the quantum state of the universe, causing "the collapse of the wave function" and creating a bunching up, a
tangle and discontinuous knot in the continuity of the quantum state.
Heisenberg (1958), cautioned, however, that the observer is not the creator of reality: "The introduction of the observer must not be misunderstood to imply that
some kind of subjective features are to be brought into the description of nature.
The observer has, rather, only the function of registering decisions, i.e., processes
in space and time, and it does not matter whether the observer is an apparatus or
a human being; but the registration, i.e., the transition from the "possible" to the
"actual", is absolutely necessary here and cannot be omitted from the interpretation of quantum theory".
Shape and form are a function of our perception of dynamic interactions within
the continuum which is the quantum state. What we perceive as mass (shape,
form, length, weight) are dynamic patterns of energy which we selectively attend
33
to and then perceive as stable and static, creating discontinuity within the continuity of the quantum state. Therefore, what we are perceiving and knowing, are
only fragments of the continuum.
However, we can only perceive what our senses can detect, and what we detect
as form and shape is really a mass of frenzied subatomic electromagnetic activity
that is amenable to detection by our senses and which may be known by a knowing mind. It is the perception of certain aspects of these oscillating patterns of
continuous evolving activity, which give rise to the impressions of shape and
form, and thus discontinuity, as experienced within the mind. This energy that
makes up the object of our perceptions, is therefore but an aspect of the electromagnetic continuum which has assumed a specific pattern during the process of
being sensed and processed by those regions of the brain and mind; best equipped
to process this information. Perceived reality, therefore, becomes a manifestation
of mind.
However, if the mind is not a singularity, and if we possessed additional senses
or an increased sensory channel capacity, we would perceive yet other patterns
and other realities which would be known by those features of the mind best attune: to them. If the mind is not a singularity but a multiplicity, this means that
both - and B, may be known simultaneously.
∆E∆t = ℏ
∆E = 0 → ∆t = ∞
2. Model
In order to put forward the classical theory of the brain waves we quantize the
brain wave field. In the model (Marciak-Kozlowska, M. Kozlowski, 2012) we
assume (i) the brain is the thermal source in local equilibrium with temperature
T. (ii) The spectrum of the brain waves is quantized according to formula
E = ℏω
(1)
where E is the photon energy in eV, ℏ =Planck constant, ω = 2πν ,ν -is the frequency in Hz. (iii). The number of photons emitted by brain is proportional to the
(amplitude)2 as for classical waves. The energies of the photons are the maximum
values of energies of waves. For the emission of black body brain waves we propose the well know formula for the black body radiation.
34
In thermodynamics we consider Planck type formula for probability P (E) dE for
the emission of the particle (photons as well as particles with m≠0) with energy
(E, E+dE) by the source with temperature T is equal to:
P(E)dE= BE2 e (-E/kT) dE
(2)
where B= normalization constant, E=total energy of the particle, k = Boltzmann
constant=1.3 × 10-23 J K-1. K is for Kelvin degree. However in many applications
in nuclear and elementary particles physics kT is recalculated in units of energy.
To that aim we note that for 1K, kT is equal k1K = K x 1.3 × 10-23 J x K-1= 1.3 ×
10-23 Joule or kT for 1K is equivalent to 1.3 × 10-23 Joule= 1.3 × 10-23 /(1.6 × 1019
) eV = 0.8 × 10-4 eV. Eventually we obtain 1K= 0.8 × 10-4 eV, and 1eV= 1.2 ×
104 K.
( − Emax )
dN
2
= BEmax e T
dE
(3)
where, B is the normalization constant, T is the temperature of the brain thermal
source in eV. The function
dN
describes the energy spectrum of the emitted brain
dE
photons
In Fig. 1 the calculated energy spectrum, formula (2) is presented. We present the
result of the comparison of the calculated and observed spectra of the brain waves.
The calculated spectra are normalized to the maximum of the measured spectra.
The calculated spectrum is for temperature of brain source T= 0.8 × 10-14 eV. The
obtained temperature is the temperature for the brain source in the thermal equilibrium. The source is thermally isolated (adiabatic well). However in very exceptional cases the spectrum is changed – by the tunneling to the quantum potential well. The temperature 1 eV ≅ 104 K then brain wave thermal spectra T=0.8 ×
10-14 eV= 0.8 × 10-10 K.
In Fig. 2 we present the calculation of the energy spectrum for the Cosmic Background Radiation. Tke formula (2) was used for the model calculation. The normalized theoretical spectrum describe very well the observed CBR. The calculated temperature T=2.53K, which is in excellent agreement with experimentally
verified values
35
It must be stressed that in a paper we abandon the idea that every physical object
is either a wave or a particle. Neither it is possible to say that particles “become”
waves in the quantum domain and conversely that waves are “transformed “into
particles. It is therefore necessary to acknowledge that we have here a different
kind of an entity, one that is specifically quantum. For this reason Levy-Leblond
and Balibar developed the name quanton, (Levy-Leblond, Balibar, 1990). Following that idea the human brain emits quantons with energies E = ℏω formula
(8). The brain quantons are the quantum objects that follows all quantum laws:
tunneling, the superposition and Heisenberg uncertainty rule. For the wave length
of the quantons is of the order of Earth radius the quantum nature of the brain will
be manifested in the Earth scale.
The formula for Heisenberg uncertainty formula can written as
∆E ∆ t = ℏ
(4)
Where E is the characteristic energy of the system and t is the characteristic time.
From formula (4) we can calculate the characteristic times for energy of the
sources. In Table 1 the result of the calculations for characteristic times, formula
(4) are presented. According to Libet theory (Libet, 2004). The characteristic time
for the nerve brain response is of the order of 1.4 s.
In history of the Universe the characteristic time for appearance of all interactions:
gravity, electromagnetic, electroweak, and strong is of the order of 10-11 s (Perkins, 2000)
36
Fig. 1: Model calculations for energy spectra of brain photons. The temperature of the source,
T= 7.8 10-11 K
Fig. 2: Model calculations for energy spectra of Cosmic Background Radiation Temperature
of the source T= 2.35 K
37
Table 1: Characteristic times for Human Brain and Universe
Source
Human Brain
Cosmic Background
Radiation
Energy [eV]
(This paper)
7.8 × 10-15
2.5 × 10-4
Characteristic time, [s]
(Heisenberg inequality)
0.45
3.1 × 10-11
Table 2: Hypothesis
Source
Brain
Universe
Energy[eV]
(This paper)
7.8 × 10-15
2.5 × 10-4
Time[s]
(This paper)
0.45
3.1 × 10-11
Comparison to :
Libet and Perkins
Libet, 1.4 s
Perkins, 10-11 s
References
Schild R., 2012. Cosmology of Consciousness, Quantum Physics & Neurosscience of Mind, Cosmology Science Publishers, Cambridge, 2012
Marciak-Kozlowska J., Kozlowski M., 2012, Neuroquantology, to be published
Bohr, N. (1934/1987), Atomic Theory and the Description of Nature, reprinted as
The Philosophical Writings of Niels Bohr, Vol. I, Woodbridge: Ox Bow
Press.
Bohr, N. (1958/1987), Essays 1932-1957 on Atomic Physics and Human
Knowledge, reprinted as The Philosophical Writings of Niels Bohr, Vol. II,
Woodbridge: Ox Bow Press.
Bohr, N. (1963/1987), Essays 1958-1962 on Atomic Physics and Human
Knowledge, reprinted as The Philosophical Writings of Niels Bohr, Vol.
Ill, Woodbridge: Ox Bow Press.
Einstein, A. (1905a). Does the Inertia of a Body Depend upon its Energy Content?
Annalen der Physik 18, 639-641.
Einstein, A. (1905b). Concerning an Heuristic Point of View Toward the Emission and Transformation of Light. Annalen der Physik 17, 132-148.
Einstein, A. (1905c). On the Electrodynamics of Moving Bodies. Annalen der
Physik 17, 891-921.
38
Einstein, A. (1926). Letter to Max Born. The Born-Einstein Letters (translated by
Irene Born) Walker and Company, New York.
Heisenberg. W. (1930), Physikalische Prinzipien der Quantentheorie (Leipzig:
Hirzel). English translation The Physical Principles of Quantum Theory,
University of Chicago Press.
Heisenberg, W. (1955). The Development of the Interpretation of the Quantum
Theory, in W. Pauli (ed), Niels Bohr and the Development of Physics, 35,
London: Pergamon pp. 12-29.
Heisenberg, W. (1958), Physics and Philosophy: The Revolution in Modern Science, London: Goerge Allen & Unwin.
Schild R 2012. Cosmology of Consciousness, Quantum Physics & Neuroscience
of Mind, Cosmology Science Publishers, Cambridge, 2012
Marciak-Kozlowska J., Kozlowski M., 2012, Neuroquantology, vol. 10 No. 3
Perkins D H, 2000, Introduction to high energy physics, Cambridge University
Press
39
CHAPTER III
Heaviside Quantons as the Carriers of Extrasensory Perception Phenomena
The spark of ESP is glowing brighter than ever before, but enlightenment is fleeting and fragile. It's risky exploring unnamed realms. But
what's life worth living for? Pushing the horizons of science invariably
involves risk and controversy, but the potential of real discovery always
makes those risks worthwhile. Be bold. Cultivate that spark of curiosity.
Courage!
Dean Radin, Entangled Minds
Introduction
In this paper we investigate the EPS phenomena with the help of the contemporary
elementary particle physics. We assume that ESP phenomena are rooted in subnuclear physics. First of all supported by the results of the Oliver Heaviside we
conclude that special relativity is not in opposition to the existence of the particles
with finite mass and velocities greater than light velocity. The spark of ESP phenomenon in “source” subject is created by the emission of the new particle- antiparticle Heaviside quantons, which consists of Heaviside particles with mass of
the order of 10-15 eV, which propagate with velocity greater than the light velocity.
The recombination of the Heaviside pair generates the additional Hydrogen atom
in the brain medium of the receiving subject
1. ESP data
The type of data which can be acquired in ESP phenomena can be summarized
as:
1) The overall ambience of the scene is accurately perceived.
2) Certain details are accurately identified; others are misconstrued or totally ignored.
40
3) A feature which is impressive to the agent is not necessarily so to the percipient, and vice versa.
4) The composition of the scene may be distorted by errors in scale, relative positions of key objects, or total right- left inversions.
5) The aesthetic aspects, such as colors, general shapes, degree of activity, noise
level, climate, and other ambient features tend to be more accurately perceived
than more analytical details such as number, size, or relative positions.
6) The perception is not necessarily centered on the defined target, and may even
provide accurate information on adjacent areas external to the target, unnoticed by the agent.
7) The fidelity of the perception seems to be independent of the remoteness of
the target, up to distances of several thousand miles.
8) The time of the perception effort need not coincide with the time the agent is
at the target. Perceptions obtained several hours, or even days, prior to the
agent's visit to the target, or even prior to selection of the target, display at least
as high a yield as those performed in real time.
The philosophical and practical implications of items 7 and 8 are clearly substantial. If the data are valid, the most parsimonious explications would require access
of the percipient's consciousness to other portions of the space-time grid than that
in which it is currently immersed, or that it can reach by normal processes of
communication or memory. These same items also seriously delimit the potential
physical mechanisms for such access.
In this paper we develop the new model for ESP phenomena based on pre- Einseinian relativity theory. The model we developed takes into account that relativity theory not precludes existence of the particles with finite mass and velocity
greater than light velocity in vacuum. Oliver Heaviside formulated the theory of
superluminal particles in XIX century. (Heaviside, 1885). Following the Heaviside`s theory we postulate the new charged particle with mass m= 10-15 eV, Heaviside particle which is responsible for the ESP phenomena. The pilot Heaviside
particle emits Heaviside electric field (velocity=c) in very narrow angle θ ,
41
Tan(θ ) =
1
u2
−1
c2
In a sense the subject (emitter) “sees “the subject (receiver)
2. Physics of the ESP
Action at distance First of all we will discuss the basis for ESP given by physics.
Let`s start with action at distance (points 7 and 8) Ampere was, indeed, a man of
genius, but even after his work on interacting electrical currents there were still
great, puzzles to be addressed. The major difficulty was that of the nature of the
interaction between currents (or electrically charged bodies). This interaction involved, obviously, forces bodies, but these forces were not produced by anything
obviously pushing or pulling on bodies. It was action-at-a-distance. Action-at-adistance was nothing new in physics Ampere's time, as Newton himself had been
faced with the same concern in his theory of masses interacting gravitationally
and instantaneously across the empty vastness of spaces. Newton was not happy
about action-at-a-distance, and indeed his gravitational theory attacked by many
who claimed it was a reversion to "explaining" Nature by invoking powers. Unable to suggest anything else in place of it he contented himself with his famous
passage (Newton, 1693):
That Gravity should be innate, inherent and essential to Matter, so that one body
may act upon another at a Distance thro' a Vacuum, without the Mediation of
anything else, by and through which their Action and Force may be conveyed
from one to another, is to me so great an Absurdity, that I believe no Man who
has in philosophical Matters a competent Faculty of thinking, can ever fall into it.
Gravity must be caused by an Agent acting constantly according to certain Laws;
but whether this Agent be material or immaterial?
The aether the nature of all forces known to Newton and his contemporaries by
direct t~ experience seemed always to be that of contact, i.e., a push or a pull by
the intimate interaction of one thing (via a rope, or a stick, or one's hand, etc.)
with another. Gravitation action-at-a-distance (whether instantaneous or not) is
most mysterious if acting in a meets way through a vacuum which is truly empty.
But suppose that even a vacuum is filled i substance that can transmit forces, a
42
substance something like air but ever so much thin: penetrating, a substance that
can slip through all of ponderable matter and fill every noo cranny of the universe.
Suppose the universe is embedded in an ocean of this mist called (or aether) –
then what? Interacting bodies, even though apparently separated by the empty
gulf of a vacuum. Then be imagined as actually still in mechanical communion
via stresses and strains ii the ether. So attractive is this idea, in fact, that the ether
concept can be traced to ancient at least as far back as Aristotle. The price paid
for this imaginative idea, however, was one – for every sort of apparent action-ata-distance phenomenon it was necessary to corresponding ether until, as Maxwell
complained (Niven, 1890), 'Aethers were invented for the swim in, to constitute
electric atmosphere and magnetic effluvin, and so on, to sensations from one part
of our bodies to another, and so on, till all space had been filled or four times over
with aethers".
This aether was thought able to transmit wave motion (from the interference experiment Thomas Young it was generally known by 1801 that light is a wave
phenomenon), muci gas conducts sound waves. Sound waves, however, are longitudinal waves, with the "waving" back-and-forth along the direction of wave
propagation. The initially puzzling fact that light can be polarized was, however,
incompatible with longitudinal or "back-and-forth" compression waves. Then
Young and Augustin Fresnel, in 1817-18, showed how polarization can be explained by transversal waves, with the medium "waving" in a direction perpendicular to the direction of the wave propagation. This, in turn, made a gaseous
ether unthinkable, as it would be unable to support the shear stresses required by
a transversal wave. The aether could not, in fact, be a gas at all, but instead must
be an elastic, jellylike solid, a bit of imagery due to William Thomson's old friend,
G. G. Stokes. The required mechanical properties of such an aether are fantastic,
to say the least.
This jelly had to be both thin enough for "the planets to swim in" without any
observable retardation or deviation from Newton's laws of motion and rigid
enough to propagate waves (light) at a speed of 300, 000 per second. To imagine
such a substance is not easy, yet in 1854 William Thomson wrote, (Thomson,
1884):
That there must be a medium forming a continuous material communication
throughout space to the remotest visible body is a fundamental assumption in the
43
undulatory Theory of Light. Whether or not this medium is (as appears to me most
probable) a continuation of our own atmosphere, its existence is a fact that cannot
be questioned....
The XIX/XX position in respect to aether was perhaps put best by Heaviside when
he wrote (Heaviside 1893):
As regards the ether, it is useless to sneer at it at this time of day. What
substitute for it are we to have? Its principal fault is that it is mysterious.
That is because we know so little about it. Then we should find out
more. That cannot be done by ignoring it. The properties of air, so far
as they are known, had to be found out before they became known.
This passage shows an increase in either Heaviside's optimism or desperation, as
earlier in 1885 (Heaviside, 1885) he had written,
Ether is a very wonderful thing. It may exist only in the imaginations
of the wise, being invented and endowed with properties to suit their
hypotheses; but we cannot do without it... But admitting the ether to
propagate gravity instantaneously, it must have wonderful properties,
unlike anything we know.
and then a few months later
The actual constitution of the ether is unknown. It never can be known.
3. Beyond special relativity.
The original version of relativity, the so-called special theory, is actually a law and a rather
simple one at that, being not an equation of motion at all but a property of that equation,
a symmetry. The most mature form of relativity is a speculative post-Newtonian theory
of gravity motivated by this law. Einstein, who discovered early in his career that the
public was more interested in the mystical aspects of relativity than the physical ones,
encouraged the growth of his image as a seer even though he was not a seer at all but a
professional with a razor-sharp mind. However, Einstein's writing is characteristically
well-reasoned, direct, and open. He was capable of being wrong, just like the rest of us,
but he rarely hid his mistakes in abstruse mathematics. Symmetry is an important, if often
abused, idea in physics. An example of symmetry is roundness. Billiard balls are round,
44
and this allows one to make some predictions about them without knowing exactly what
they are made of, for example, that they will roll in straight-line paths across the table
when struck with a cue. But roundness does not cause them to move. The underlying
laws of motion do that. Roundness is just a special property that sets billiard balls apart
from arbitrary rigid bodies and is revealed by the unusual simplicity and regularity of their
motion. Symmetry is especially helpful in situations where one does not know the underlying equations of motion and is trying to piece them together from incomplete experimental facts. If, for example, you knew that all billiard balls were round and were trying
to guess their equations of motion, you could eliminate certain guesses on the grounds
that round things could not possibly do this. Situations of this kind are the rule rather than
the exception in subnuclear physics. For this reason there is a tradition in physics of ascribing to symmetries an overriding importance even though they are actually a consequence, or property, of the equations of motion.
The symmetry of relativity involves motion. Einstein and other early twentieth-century
figures came upon this symmetry through thinking about electricity and magnetism,
whose equations had just been worked out by James Maxwell and were rapidly leading
to the invention of radio. Rotational symmetry requires the behavior of billiard balls on a
round table to appear qualitatively the same regardless of where one stands on the perimeter. Relativistic symmetry requires their behavior to appear the same regardless of how
one is moving. That being the case, the equations of electricity and magnetism would
have to appear the same on the two trains, and thus the speed of light must also be the
same. One then encounters a logical contradiction unless some common ideas about simultaneity and measurement on the two trains are wrong. All of these musings and their
fascinating logical implications, including the weight gain acquired by objects moving at
high speeds and the equivalence of mass and energy, are now routinely verified in laboratories all over the world, and have passed into history as self-evident truth.
The story of Einstein's triumph is so romantic it is easy to forget that relativity was a discovery and not an invention. It was subtly implicit in certain early experimental observations about electricity, and it took bold thinking to synthesize these observations into a
coherent whole. But no such boldness would be required today. An unsuspecting experimentalist armed with a modern accelerator would stumble upon the effects of relativity
the first day and would probably figure the whole thing out empirically in a month. Relativity is actually not shocking at all. The ostensibly self-evident worldview it supplanted
was simply based on incomplete and inaccurate observations. Had all the facts been
known, there would have been no controversy and thus nothing for Einstein to prove. The
45
popular view of relativity as a creation of the human mind is wonderfully ennobling but
in the end incorrect We believe in relativity today not because it ought to be true, but
because it is measured to be true.
Einstein's theory of gravity, in contrast, was an invention, something not on the verge of
being discovered accidentally in the laboratory. It is still controversial and largely beyond
the reach of experiment. 5 Its most important prediction is that space itself is dynamic. The
equations Einstein proposed to describe gravity are similar to those of an elastic medium,
such as a sheet of rubber. Conventional gravitational effects result when this medium is
distorted statically by a large mass, such as a star. When the source oscillates rapidly,
however, such as when two stars revolve around each other in tight orbit, there is a new
effect: outwardly propagating ripples of gravity. Conventional gravity is thus like the dimples under the feet of a water skimmer, and gravitational radiation is like the disturbances
generated by the skimmer when it scampers away. There is much indirect evidence that
the prediction of gravitational radiation is correct, the strongest being the steadily diminishing orbital period of the famous binary pulsar discovered by Joseph Taylor and Russell
Hulse in 1975. There is as yet no direct evidence. Detecting gravitational radiation directly
is one of the key goals of modern experimental physics, 7 but most physicists are already
persuaded by other evidence that Einstein's theory of gravity is probably correct.
It is ironic that Einstein's most creative work, the general theory of relativity, should boil
down to conceptualizing space as a medium when his original premise was that no such
medium existed. The idea that space might be a kind of material substance is actually very
ancient, going back to Greek Stoics and termed by them aether. Ether was firmly in
Maxwell's mind when he invented the description of electromagnet-ism we use today. He
imagined electric and magnetic fields to be displacements and flows of ether, and borrowed mathematics from the theory of fluids to describe them. Einstein, in contrast, utterly rejected the idea of ether and inferred from its nonexistence that the equations of
electromagnetism had to be relative. But this same thought process led in the end to the
very ether he had first rejected, albeit one with some special properties that ordinary elastic
matter does not have.
The word aether has extremely negative connotations in theoretical physics because of its
past association with opposition to relativity. This is unfortunate because, stripped of these
connotations, it rather nicely captures the way most physicists actually think about the
vacuum. In the early days of relativity the conviction that light must be waves of something ran so strong that Einstein was widely dismissed. Even when Michelson and Morley
46
demonstrated that the earth's orbital motion through the ether could not be detected, opponents argued that the earth must be dragging an envelope of ether along with it because
relativity was lunacy and could not possibly be right. The virulence of this opposition
eventually had the scandalous consequence of denying relativity a Nobel Prize. (Einstein
got one anyway, but for other work). Relativity actually says nothing about the existence
or nonexistence of matter pervading the universe, only that any such matter must have
relativistic symmetry.
It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic
structure similar to that of ordinary quantum solids and fluids. Subsequent studies with
large particle accelerators have now led us to understand that space is more like a piece
of window glass than ideal Newtonian emptiness. It is filled with "stuff" that is normally
transparent but can be made visible by hitting it sufficiently hard to knock out a part. The
modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic aether. But we do not call it this because it is taboo.
How Einstein came to conclude that space was a medium is a fascinating story. His starting point was the principle of equivalence, the observation that all objects fall under the
pull of gravity at the same rate regardless of their mass. This is the effect that causes astronauts in near earth orbit to experience weightlessness. The pull of gravity is not significantly smaller in low orbit than on earth, but the effect of this gravity is simply to make
them and their spacecraft fall together around the earth. Einstein inferred from this effect
(more precisely from versions of it he imagined in 1905 when there were no astronauts)
that the force of gravity was inherently fictitious, since it could always be turned off by
allowing the observer and his immediate surroundings to fall freely. The important effect
of a nearby massive body such as the earth was not to create gravitational forces but to
make free-fall paths converge. Astronauts falling straight down onto the earth (an unfortunate experiment) might at first think they were in deep space, but after a while would
notice that objects traveling with them were slowly getting closer. This is because all the
nearby free-fall paths are directed toward the center of the earth and eventually meet there.
Einstein was struck by the similarity between this effect and the convergence of lines of
longitude at the north and south poles. In that case, the tendency of some straight-line
paths to converge is a consequence of the curvature of the earth – a medium made out of
conventional matter. Then, in a flash of insight that leaves us breathless even today, he
guessed that free-fall paths actually are lines of longitude on a higher-dimensional surface, and that gravity occurs because large masses stretch this surface and cause it to
47
curve. He then made a second, masterful guess about the specific relation between mass
and curvature known to us today as the Einstein field equations. These respect relativity
and thus contain the same paradoxes of simultaneity found in the original version of relativity. For this reason they are more accurately described as a relation between stressenergy and the curvature of four-dimensional space-time. Their prediction that space can
ripple in addition to stretching is a consequence of its obeying relativity, a symmetry of
motion. It is consistent with our physical intuition, however, since it is basically the same
thing as a propagating seismic wave on the surface of the earth generated by an earthquake.
The clash between the philosophy of general relativity and what the theory actually says
has never been reconciled by physicists. On the one hand, we have the view, founded in
the success of relativity, that space is something fundamentally different from the matter
moving in it and thus not understandable through analogy with ordinary things. On the
other, we have the obvious similarities between Einsteinian gravity and the dynamic
warping of real surfaces, leading us to describe space-time as a fabric. Their curiosity is,
however, neither naive nor inappropriate. The closet of general relativity contains a horrible skeleton known as the cosmological constant. This is a correction to the Einstein
field equations compatible with relativity and having the physical meaning of a uniform
mass density of relativistic ether. Einstein originally set this constant to zero on the
grounds that no such effect seemed to exist. The vacuum, as far as anyone knew, was
really empty. He then gave it a small nonzero value in response to cosmological observations that seemed to indicate the opposite, and then later removed it again as the observations improved. A nonzero value is again in fashion due to the development of a new
technique for measuring astrophysical distances using supernovae. However, none of this
adjustment addresses the deeper problem. Given what we know about radioactivity and
cosmic radiation, there is no reason anyone can think of why the cosmological constant
should not be stupendously large – many orders of magnitude larger than the density of
ordinary matter. The fact that it is so small tells us that gravity and the relativistic matter
pervading the universe are fundamentally related in some mysterious way that is not yet
understood, since the alternative would require a stupendous miracle.
The view of space-time as a non-substance with substance-like properties is neither logical nor consistent with the facts. It is instead an ideology that grew out of
old battles over the validity of relativity. At its core is the belief that the symmetry
of relativity is different from all other symmetries in being absolute. It cannot be
violated for any reason at any length scale, no matter how small, even in regimes
48
where the underlying equations have never been determined. This belief may be
correct, but it is an enormous speculative leap. One can imagine moon people
applying similar reasoning and chastising their brightest students for asking what
the earth was made of on the ground that its roundness made the question moot.
This would clearly be an injustice, since the earth is not absolutely round but only
approximately so. On length scales smaller than the naked eye can easily discern
from the moon, there are troublesome little details such as the Mount Everest.
Advances in observation technology would eventually vindicate the students, at
least the ones who remained defiant. It would be discovered that the earth is not
perfectly round, and moreover is approximately round for the reason that the rocks
from which it is made become plastic at the high pressures found underground,
so that large objects on the surface slowly sink.
Despite its having become embedded in the discipline, the idea of absolute symmetry makes no sense. Symmetries are caused by things, not the cause of things.
If relativity is always true, then there has to be an underlying reason. Attempts to
evade this problem inevitably result in contradictions. Thus if we try to write
down relativistic equations describing the spectroscopy of the vacuum, we discover that the equations are mathematical nonsense unless either relativity or
gauge invariance, an equally important symmetry, is postulated to fail at extremely short distances. No workable fix to this problem has ever been discovered.
Thus the innocent observation that the vacuum of space is empty is not innocent
at all, but is instead compelling evidence that light and gravity are linked and
probably both collective in nature. Real light, like real quantum-mechanical
sound, differs from its idealized Newtonian counterpart in containing energy even
when it is stone cold. According to the principle of relativity, this energy should
have generated mass, and this, in turn, should have generated gravity. We have no
idea why it does not, so we deal with the problem the way a government might,
namely by simply declaring empty space not to gravitate. It also demonstrates the
severity of the problem, for one does not resort to such desperate measures when
there are reasonable alternatives. The desire to explain away the gravity paradox
microscopically is also the motivation for the invention of supersymmetry, a
mathematical construction that assigns a special complementary partner to every
known elementary particle.2 Were a superpartner ever discovered in nature, the
49
hope for a reductionist explanation for the emptiness of space might be rekindled,
but this has not happened, at least not yet.
The belief of Lorentz and Poincare day was aether, or more precisely the naive
version of aether that preceded relativity. The unsubstantiated belief of our day is
relativity itself. It would be perfectly in character to reexamine the facts, toss them
over in his mind, and conclude that beloved principle of relativity was not fundamental at all but emergent – a collective property of the matter constituting spacetime that becomes increasingly exact at long length scales but fails at short ones.
This is a different idea from Lorentz, Poincare, Heaviside original one but something fully compatible with it logically, and even more exciting and potentially
important. It would mean that the fabric of space-time was not simply the stage
on which life played out but an organizational phenomenon, and that there might
be something beyond.
John Bell suggestion (Bell, 1964) is like going back to relativity as it was before
Einstein, when people like Lorentz and Poincare thought that there was an aether
- a preferred frame of reference - but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether
Now, in that way we can imagine that there is a preferred frame of reference, and
in this preferred frame of reference things do go faster than light. But then in other
frames of reference when they seem to go not only faster than light but backwards
in time, that is an optical illusion. Behind the apparent Lorentz invariance of the
phenomena, there is a deeper level which is not Lorentz invariant. This is not
sufficiently emphasized in textbooks, that the pre-Einstein position of Lorentz and
Poincare, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent
with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not
detect motion through the aether - that is a perfectly coherent point of view. I
think that the idea of the aether should be taught to students as a pedagogical
device, because I find that there are lots of problems which are solved more easily
by imagining the existence of an aether. The reason me must to go back to the
idea of an aether here is because in these EPR experiments there is the suggestion
that behind the scenes something is going faster than light. Now, if all Lorentz
frames are equivalent, that also means that things can go backward in time. That
is the big problem. And so it's precisely to avoid these that I want to say there is
a real causal sequence which is defined in the aether. Now the mystery is, as with
50
Lorentz and Poincare, that this aether does not show up at the observational level.
It is as if there is some kind of conspiracy, that something is going on behind the
scenes which is not allowed to appear on the scenes. That's extremely uncomfortable. The aether in 21th century physics is a continuum theory, generally nonclassical, which interprets fundamental activity in terms of space time geometry or
action in medium, (Duffy, 2006)
4. Model of the ESP phenomena
Signaling models In producing a physical theory of psi, we need to decide whether
we are demanding a new paradigm of physics or merely tinkering with the current
one. It is natural to start off by trying the second (less radical) approach, and there
are many reviews of 'tinkering' models. However, the danger is that one will end
up grafting so many extra bits onto the old paradigm (like adding epicycles to the
Ptolemaic model of the Solar System) that it becomes hopelessly complicated.
There is also the problem of testability: there are actually many models for psi
and, by adding enough bits to the standard paradigm, one can doubtless explain
anything. However, a crucial requirement of a scientific theory is that it should be
falsifiable and, as emphasized by many theories are inadequate in this respect. .
Nevertheless, it will be useful to start off by reviewing less radical approaches,
since some aspects of these may still feature in the new paradigm. The discussion
below, groups theories of psi into three general categories: field or signalling
models, quantum models and higher-dimensional models.
Many theories of ESP can be viewed as signalling models, in the sense that they
involve the transmission of information or energy via some sort of particle or field
(these concepts being linked in modern physics). Often the field involved is already part of the current paradigm. This includes, for example, explaining ESP in
terms of electromagnetic waves or neutrinos It also includes explaining PK in
terms of electrostatic forces.
Models which explain precognition in terms of tachyons or advanced waves
might also be regarded as being within the current paradigm, even though they
involve rather exotic aspects of it. Even more extreme are models which adopt
the spirit of the current paradigm but invoke particles like psitrons or ESP waves
with the specific purpose of explaining ESP. All these approaches might be regarded as tinkering with the current paradigm.
51
Generally speaking, the experimental evidence indicates that ESP can occur at
great distances and does not decline with distance. These findings do not fit well
with most hypotheses that physical energies mediate the transmission of extrasensory information. Indeed, the information transmission model may itself be erroneous.
However, as discussed below, even if signalling models cannot work in four dimensions, they may still be viable in higher dimensions, since the viewer and the
viewed may become contiguous in the higher-dimensional space. This is a crucial
feature of my own proposal.
There are also many theories which invoke some form of biophysical field, even
though the status of such fields is questionable from a physicist's perspective.
Mesmer's early ideas on animal magnetism and vitalistic fluids might be included
in this category. Unfortunately, none of these approaches has gained general acceptance among paraphysicists and all of them have been criticized on the
grounds that they are ad hoc and unfalsifiable. On the other hand, the link with
biology is important and reflects the growing interaction between physicists and
biologists in orthodox science. It also raises the issue of whether psi is involved
in some forms of complementary medicine and in reincarnation cases, and
whether it is a feature of mind alone or life in general.
Quantum theory – which for present purposes we regard as part of the current
paradigm – provides at least some scope for an interaction of consciousness with
the physical world. It also completely demolishes our normal concepts of physical
reality, so it is not surprising that some physicists have seen in its weirdness some
hope for explaining psi. Indeed, E.H. Walker (1984) has argued that only quantum theory can explain ESP. The most concrete realization of the quantum approach is 'observational theory', according to which consciousness not only collapses the wave-function but also introduces a bias in how it collapses. In this
picture all psi is interpreted as a form of PK which results from the process of
observation itself (i. e. there must be some kind of feedback). For example, clairvoyance is supposed to occur because the mind collapses the wave-function of
the target to the state reported. This process can even explain retro-PK), since it
is assumed that a quantum system is not in a well-defined state until it has been
observed. Another feature of observational theory is that the brain is regarded as
52
being akin to an REG. Thus an ordinary act of will occurs because the mind influences its own brain, and telepathy occurs because the mind of the agent influences the brain of the percipient. Of course, there is still the question of how
consciousness collapses the wave-function (Stapp, 1993). One possibility is to
modify the Schrodinger equation in some way. (Marciak-Kozlowska, Kozlowski,
2013). Observational theory has the virtue that it can make quantitative predictions. For example, one can estimate the magnitude of PK effects on the basis that
the brain has a certain information output and the results seem comparable with
what is observed in macro-PK effects. On the other hand, observational theory
also faces serious criticisms. One can object on the grounds that psi sometimes
occurs without any feedback. For example, (Beloff 1988) has pointed out that
there are pure clairvoyance experiments in which only a computer ever knows the
target. One can also question the logical coherence of explaining psi merely on
the grounds that one observes it and there are alternative models for retro-PK
Finally, David Bohm (1986) has cautioned that the conditions in which quantum
mechanics apply (low temperatures or microscopic scales) are very different from
those relevant to the brain.
Nevertheless, many physicists back some form of quantum approach. Some proposals exploit the non-locality of quantum theory, as illustrated by the famous
EPR paradox. An atom decays into two particles, which go in opposite directions
and must have opposite (but undetermined) spins. If at some later time we measure the spin of one of the particles, the other particle is forced instantaneously into
the opposite spin-state, even though this violates causality. This non-locality effect is described as 'entanglement' and) tried to explain this in terms of hidden
variables, which he invoked as a way of rendering quantum theory deterministic.
Experiments later confirmed the non-locality prediction (Aspect, 1982) and
thereby excluded at least some models with hidden variables (though not Bohm's).
Indeed, John Bell, who played a key role in developing these arguments (Bell,
1966) and was much influenced by Bohm's ideas, compared the non-locality property to telepathy. Einstein made the same comparison, although he intended it to
be disparaging!
Although quantum entanglement has now been experimentally verified up to the
scale of macroscopic molecules, it must be stressed that it is not supposed to allow
the transmission of information (i. e. no signal is involved). For example, attrib53
uting remote viewing to this effect would violate orthodox quantum theory. Theorists have reacted to this in two ways. Some have tried to identify what changes
are necessary in quantum theory in order to allow non-local signalling (Valentini,
2002). For example, (Josephson and Pallikari-Viras (1991) have a model in which
entanglement can be utilized biologically. More generally, Jack Sarfatti (1998)
has argued that signal non-locality could still be allowed in some form of 'postquantum' theory which incorporates consciousness. He regards signal locality as
the micro-quantum limit of a more general non-equilibrium macro-quantum theory. The relationship between micro and macro quantum theory is then similar to
that between special and general relativity, with consciousness being intrinsically
non-local and analogous to curvature. His model involves non-linear corrections
to the Schrodinger equation and may permit retrocausal and remote viewing effects. Others accept that there is no signalling but invoke a 'generalized' quantum
theory. Which exploits entanglement to explain PSI acausally. This is also a feature of the model of pragmatic information, which interprets psi effects as meaningful non-local correlations between a person and a target system. This model
may account for many of the observed features of psi, including the difficulty of
replicating psi under laboratory conditions). It may also be relevant to homeopathy (Radin, 2006) has argued that entanglement is fundamental to ESP. This is
because he regards elementary-particle entanglement, bio-entanglement (neurons), sentient-entanglement (consciousness), psycho-entanglement (psi) and socio-entanglement (global mind) as forming a continuum, even though there is an
explanatory gap (and sceptics might argue an evidential gap) after the second step.
If the Universe were fully entangled like this, he argues that we might occasionally feel connected to others at a distance and know things without use of the
ordinary senses. This idea goes back to (Bohm, 1980), who argued that there is a
holistic element in the Universe, with everything being interconnected in an implicate order which underlies the explicit structure of the world:-The essential
features of the implicate order are that the whole Universe is in some way enfolded in everything and that each thing is enfolded in the whole. This implicit
order is perhaps mediated by ESP. Most mainstream physicists regard such ideas
as an unwarranted extension of standard quantum theory, but one clearly needs
some sort of extension if one wants to incorporate mind into physics.
54
There are various other quantum-related approaches to explaining ESP. Some of
these exploit the effects of 'zero point fluctuations vacuum energy. This is a perfectly respectable physical notion, so it is not surprising that some people have
tried to relate this to the traditional metaphysical idea that there is some all-pervasive energy field which connects living beings (eg. chi, qi, prana, elan vital).
Indeed, (Puthoff, 2007) views the zero-point-energy sea as a blank matrix upon
which coherent patterns can be written. These correspond to particles and fields
at one extreme and living structures at the other, so some connection with psi is
not excluded. A related proposal is that the radiation associated with zero-pointenergy might be identified with subtle energy fields These allegedly involve some
form of unified energy of such low intensity that it cannot be measured directly
In the electromagnetic context, this idea was introduced to describe the quantum
potential and maybe relevant to Bohm's, (Bohm, 1986) implicate order.
Although these ideas might be regarded as being on the fringe of the standard
paradigm, the recent discovery that 70% of the mass of the Universe is in the form
of 'dark energy' – most naturally identified with vacuum energy – is stimulating
interest in this sort of approach. For example, (Sarfatti, (2006) has a model which
associates both consciousness and dark energy with the effects of vacuum fluctuations, although he does not explicitly identify them.
It should be cautioned that the literature in this area comes from both expert physicists and non-specialist popularizers, so it is important to discriminate between
them (Clarke & King, 2006). Although quantum theory is likely to play some role
in a physical model for psi, my own view is that a full explanation of psi will
require a paradigm which goes beyond standard quantum theory. Of course, nobody understands quantum theory anyway, so claiming that it explains psi is not
particularly elucidating – it just replaces one mystery with another one Also, many
of the above proposals already deviate from standard quantum theory, so this
raises the question of how radical a deviation is required in order to qualify as a
new paradigm. In my view, most of those mentioned above are insufficiently radical and one needs a new approach – perhaps of the kind envisaged by Bohm –
that can explain both psi and quantum theory. One also suspects that the new
paradigm will incorporate the idea of retrocausality discussed earlier, since proposed tests of this all involve some form of EPR effect (Cramer, 2006).
55
In this paper we present theoretical model for the emission of the Heaviside type
wave model for the remote viewing phenomena. In our ealier papers we developed the quantum model for the emission of the brain waves. In order to put forward the classical theory of the brain waves we quantize the brain wave field. In
the model (Marciak-Kozlowska, M. Kozlowski, 2013) we assume (i) the brain is
the thermal source in local equilibrium with temperature T. The spectrum of the
brain waves is quantized according to formula
E = ℏω
(1)
where E is the photon energy in eV, ℏ =Planck constant, ω = 2πν ,ν -is the frequency in Hz. (iii). The number of photons emitted by brain is proportional to the
(amplitude)2 as for classical waves. The energies of the photons are the maximum
values of energies of waves For the emission of black body brain waves we propose the well know formula for the black body radiation.
In thermodynamics we consider Planck type formula for probability P (E) dE for
the emission of the particle (photons as well as particles with m≠0) with energy
(E, E+dE)by the source with temperature T is equal to :
P(E)dE= BE2 e (-E/kT) dE
(2)
where B = normalization constant, E = total energy of the particle, k = Boltzmann
constant =1.3 × 10-23 J K-1. K is for Kelvin degree. However in many applications
in nuclear and elementary particles physics kT is recalculated in units of energy.
To that aim we note that for 1K, kT is equal k1K = K x 1.3 × 10-23 J x K-1= 1.3 ×
10-23 Joule or kT for 1K is equivalent to 1.3 × 10-23 Joule=1.3 × 10-23/(1.6 × 1019
) eV = 0.8 × 10-4 eV. Eventually we obtain 1K = 0.8 × 10-4 eV, and 1eV = 1.2
× 104 K
( − Emax )
dN
2
= BEmax e T
dE
(3)
where, B is the normalization constant, T is the temperature of the brain thermal
source in eV. The function
dN
describes the energy spectrum of the emitted
dE
brain photons
56
For the ESP phenomena we argue the emission of ESP signal by the source with
temperature T=10-15 eV the charged particle with charge = electron charge and
mass < 10-15 eV which propagates in aether with velocities greater than the light
velocity and emits the Heaviside type waves.
O. Heaviside (Heaviside, 1895) claimed never to have been seduced by increasing
mass with velocity:
I will not go so far as to say, that the view which is popular now, that
"mass" is due to electromagnetic inertia, is a mere Will o' the Wisp. I
will however say that the light it gives is somewhat feeble and uncertain, and that it eludes or evades distinct localisation. The mere idea,
that electromagnetic inertia might account for "mass", occurred to me
in my earliest work on moving charges, but it seemed so vague and
unsupported by evidence, that I set it on one side. It explains too much,
and it does not explain enough.
One curious feature of the predicted mass variation with speed is the infinity that
results at the speed of light. This is a result we interpret today to mean that nothing
with mass can travel fast as light (in a vacuum). Light can travel (obviously) as
fast as light because photons are massless. Heaviside writes
The argument... seems to be that since the calculated energy of a
charged body is infinite... at the speed of light, and since this energy
must be derived from an external source, an infinite amount of work
must be done, that is, an infinite resistance will be experienced. There
is a fallacy here. One easy way of disproving the argument... is to use
not one, but two bodies, one positively and the other negatively charged
to the same degree. Then the infinity disappears, and there you are, with
finite energy when moving at the speed of light.
and
When mathematicians come to an infinity they are nonplused, and
hedge around it... We must not be afraid of infinity.
It must be admitted that O. Heaviside was well aware of the Einstein relativity.
57
Oliver Heaviside in a hand written letter to Prof. Bjerknes, discussed Einstein`s
compulsory shift to position from claiming that the aether was superfluous to stating directly that the aether was fundamental to Einstein`s theory: “I don`t find
Einstein`s Relatibvity agrees with me It is the most unnatural and difficult to understand way of representing facts that could be thought of”.
Heaviside was absolutely right about his claims for hyperlight motion the medium
is something other than a vacuum, such as water. Then the speed of light is less
than it is in a vacuum, charged particles can exceed the speed of light, and, in fact,
Heaviside's conical, electromagnetic shock wave is observed today we call it Cherenkov radiation after the Russian physicist P.A. Czerenkow who exhaustively
studied it experimentally in the 1930s, although Madame Skłodowska Curie apparently the first to notice, in 1910, this radiation effect in radium solutions (but
she did not appreciate its true origin).
Oliver Heaviside (Heaviside, 1902), showed that a point charge q in steady rectilinear motion along the axis of z, at a speed u, less than c, was associated with the
potential
q
V=
1
4πε  z 2 + γ −2 ( x 2 + y 2 ) 
(4)
.2
where γ −2 is a fraction ranging from 1 to 0, as u increases from 0 to c. Here it is
to be understood that V is the potential at the point x, y, z when the origin is at
the charge, so that V accompanies q in its motion. It is further to be understood
that the electric force E is derived from the potential in the manner specified by
E = −∇V
(5)
The question now to be considered is what occurs when u is greater than c. Are
the formulae still valid? We can see immediately that some reservations are necessary, even though no change of formula may be required. For γ −2 is now negative; and V, and also E and H are made imaginary when
2
u
z < (  − 1) x 2 + y 2 = Cot 2θ ( x 2 + y 2 )
c
2
(
)
58
(6)
This means that V is real inside the two cones to right and left of the moving
charge whose angles are 2 θ , equation (6), but unreal in the intermediate region
outside the cones.
But next, seeing that disturbances are propagated only at speed c, whilst the
charge q moves at the greater speed u, the locus of the spherical waves sent out
by the charge as it moves along forms the left conical surface only. So we must
reject the right cone altogether, if we are considering a charge brought from rest
up to speed u.
So far is rejection without change. But closer consideration will make it probable,
if not certain, that a change in the formula is wanted as well. For, assuming that
equation (1) is correct when γ 2 is negative, provided we keep to real values, it still
belongs to both cones. Now it was standardised so to make the total displacement
leaving the charge be q. This was with u<v, when the displacement emanated in
all directions. As we employ now the same formula, the same property should
hold good, keeping to the real values, however. But V is symmetrical. At corresponding points in the two cones V is the same. So the displacement leaving q for
the right cone can be only and similarly for the left cone. The practical meaning
is that if we reject the right cone, and still have the charge at the apex of the left
cone represented by q, we must double the right side of equation (1). Similarly,
the right members of the formula for E and H, true when u<c, must be doubled
when u>c
At any point P inside the cone, we have
qTan (θ )
V =
1
2 2
(7)
2πε [ z Tan (θ ) − ( x + y ]
2
2
2
So V is a minimum on the axis, and increases to infinity on the cone. Outside the
cone V is zero. Deriving the electric force by equation (7), it will be found that E
is radial, and is directed towards the charge. This is inside the cone. Its size is
E=
qrTan(θ )
2πε l 2
(8)
at distance r from the apex, where l is the geometrical mean of the distances of
the point P from the surfaces of the cone. The conical surface is the seat of a sheet
59
of displacement away from the apex. This follows because V suddenly drops to
zero outside the cone.
In recent years, (Boyd, 2009), (Gehring, 2006), (Wang, 2000) the physics community has come to realize that studies of the properties of light can be used to
address deep questions that lie at the foundations of physics. Under certain circumstances, light pulses are observed to propagate with velocities that exceed the
velocity of light in vacuum c. We then review theoretical arguments showing that
the principle of causality limits the maximum velocity with which signals can be
transmitted to the velocity of light in vacuum. This apparent contradiction is resolved by arguing that the velocity at which the peak of a pulse moves through a
material (known as the group velocity) is not the same as the velocity at which
information is transmitted through a material. Finally, we speculate on what it
would mean to live in a universe in which the principle of causality could be violated. One broad conclusion to be drawn from work of this sort is that studies of
the properties of light can shed insight on questions of a fundamental and philosophical nature.
As was mentioned above, recent research has shown that it is possible to find
situations in which pulses of light can propagate with velocities greater than the
velocity of light in vacuum c or even with negative group velocities. Such behavior is certainly counterintuitive. But from a more formal point of view, these results are disturbing in that at first glance they seem to be at odds with some wellestablished features of the special theory of relativity. In particular, a direct consequence of the special theory of relativity is that the transmission of information
at a speed greater than the velocity of light in vacuum would allow one to violate
the principle of causality. But is not the case.
The probability of the emission of particle with mass m by the source with temm
perature T is governed by Boltzmann factor, P  
T 
~ P  m  ≈ Exp[ − m ]
T
T 
(9)
From formula (9) we conclude that the source with temperature T emits the particles of mass m of the order of T (temperature and mass in energy units). The
theoretical spectra are presented in Fig 1. The emitted particle with velocity u
60
propagate through the aether and emits the electric field E (6). The electric field,
Heaviside quanton interacts with subject brain and create the ESP phenomena,
The comparison of the Heaviside wave, E, with experimental data of ESP.
1. In accordance with points 7 and 8 the Heaviside particle with mass m
reaches the subject brain at once (velocity u >>c) and generates electric
field E in brain cells
2. The field E is concentrated in very narrow angle θ . In a sense the subject
(source) sees the receiver subject
3. The field E does not depend on the distance of the subjects
4. Hypothesis, Elusive Heaviside Particles H + , H −
In our paper we argue that the new particle called Heaviside (H) particles are the
carriers of ESP phenomena. The Heaviside particle are proposed in the frame of
the new law electroweak baryogenesis
The word baryogenesis refers to the generation of baryons (particles such as protons and neutrons) and leptons (particles such as electrons and neutrinos) out of
energy states. But in physics, a process can be reversed. Tippler (Tipler, 2007)
assumed that the process worked in reverse- baryons and leptons (p+ e) annihilate.
and produced the pair (ν + ν ). Recently baryogenesis is in front of the elementary
particle physics (Shu Jing, 2011). In arXiv portal exists over 103 preprints with
word baryogenesis
In our hypothesis of EPS phenomena instead of the neutrinos the new particles
(antiparticles), for the moment nonobservable are produced in the reaction, formula (10)
e− + p → H + + H − + B
(10)
In formula (10) B is the hydrogen binding energy, the masses of, H + ,− are equal
mH = 10 −15 eV , the charge of Heaviside particle q+ ,− = charge of electron. If the
+ ,−
weak baryogenesis exists the quantons H + ,− with very high energy will cause the
subjects brain atoms to recoil and so the recoiling atoms would leave the tracks
The tracks can be observed in brain matter with transmission electron microscope
61
(TEM) The ESP phenomena are rooted in subnuclear physics. First of all supported by the results of the Oliver Heaviside (1850-1925) we conclude that special
relativity is not in opposition to the existence of the particles with finite mass and
velocities greater than light velocity. The spark of ESP phenomenon in “source”
subject is created by the emission of the new particle- antiparticle Heaviside quantons, which consists of Heaviside particles with mass of the order of 10-15 eV,
which propagate with velocity greater than the light velocity. The recombination
of the Heaviside pair generate an additional hydrogen atom in the brain medium
of the receiving subject. It is worth to mention that recently the search for new
minicharged particles was undertaken (Dobrich, 2012).
Fig. 1: The cross section of the cone of the Heaviside electric field E. The charge q is located
in point with coordinates x=y =z =0
62
 m
Fig. 2: The probability emission P  −  of the quanton with mass m by the source with
 T
temperature T
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65
CHAPTER IV
Brain Waves as the Solution of Modified Schrodinger
Equation
Introduction
Schrodinger equation is not the wave equation from the mathematical point of
view. It is the first order (in time) parabolic equation, whereas the wave equation
is the hyperbolic partial equation with the wavy motion solution. In this paper we
obtain the Schrodinger second order (in time) wave equation. With this equation
we will study the brain wave problems. In our earlier papers (Marciak-Kozłowska, Kozlowski, 2013) we showed that the spectrum of the brain photons can be
analyzed with the help of the Planck formula for equilibrium thermal radiation we
calculated the temperature of the brain waves and compared it to the temperature
of the Cosmic Microwave Background radiation. In this paper we solve the second order Schrodinger equation for brain waves and calculate the brain wave frequencies. The model for brain waves presented in this paper opens the new horizon for the study of the human consciousness.
1. Quantum mechanics and consciousness
A majority of contemporary Western scientists specializing in consciousness research, such as neuroscientists, psychologists, psychiatrists, and philosophers, espouse a materialist and reductionist explanation for consciousness. The wellknown philosopher Daniel Dennett, for example, adheres to monistic materialism.
Dennett, like many others, is of the opinion that consciousness is nothing but matter and that our subjective experience of consciousness as something purely personal and distinct from other people's consciousness is merely an illusion. According to Dennett, consciousness is produced by the matter that comprises our
brain. This materialist hypothesis is supported by scientific patterns of thought
and paradigms that he and many other scientists and philosophers deem absolutely
unassailable and are therefore reluctant to challenge. Scientists often struggle to
free themselves from prevailing paradigms. And such dogmatic convictions seem
66
to beget prejudice. It prompted Albert Einstein to say, "It is harder to crack a
prejudice than an atom". (Schild, 2012)
If the materialist standpoint were correct, everything we experience in our consciousness would be nothing but the expression of a machine controlled by classical physics and chemistry. In Dennett's view, our behavior is the inevitable result of neuronal activity in our brains. The idea that all thoughts and feelings are
no more than a consequence of brain activity obviously means that free will is an
illusion. In response to this materialist position John C. Eccles said:
I maintain that the human mystery is incredibly demeaned by scientific
reductionism, with its claim in promissory materialism to account eventually for all o f the spiritual world in terms o f patterns o f neuronal
activity. This belief must be classed as a superstition... We have to recognize that we are spiritual beings with souls existing in a spiritual
world as well as material beings with bodies and brains existing in a
material world.
The materialist approach, which is based on the premise that consciousness is a
product or effect of brain function, is taught at many medical schools in the Western world. The approach is generally not made explicit and simply taken for
granted without any kind of debate. Not surprisingly then, nearly all Western doctors believe that consciousness is the result of brain function
What have we read about the relationship between consciousness and the brain in
the contemporary literature? Many serious and trustworthy people have reported
that, to their great surprise, they were able to experience an enhanced consciousness, independently of their body.
• On the basis of a few scientifically sound studies of NDE among cardiac
arrest survivors, researchers have come to the conclusion that current scientific knowledge cannot offer an adequate explanation for the cause and
content of a near-death experience.
• Some prospective, empirical studies provide conclusive evidence that it is
possible to experience an enhanced and lucid consciousness during a cardiac arrest.
67
• We appear to have scientific proof that the cerebral cortex and brain stem
are devoid of measurable activity during a cardiac arrest arid that the clinical picture also reflects a loss of all brain function.
• Brain studies have shown that under" normal circumstances a functioning,
collaborative network of brain centers is a prerequisite for the experience
of waking consciousness. This is absent during a cardiac arrest.
• Oxygen deficiency in itself provides no explanation because NDEs can be
reported under circumstances that are not life-threatening, such as mortal
fear or a serious depression.
• Our mind is capable of altering the anatomy and function of the brain (neuroplasticity).
• In many respects, both consciousness and brain function remain a huge
mystery.
Some prospective and many retrospective studies of near-death experience have
shown that various aspects of an NDE correspond with or are analogous to some
of the basic principles from quantum mechanics, such as nonlocality, entanglement or interconnectedness, and instantaneous information exchange in a timeless
and placeless dimension. Past, present, and future are everywhere at once (nonlocally). We can say that the quantum physics idea that consciousness determines
if and how we experience our reality is particularly important for the further theoretical underpinning of this relationship. However, this radical interpretation of
quantum physics is not yet commonly accepted. Science challenges us to devise,
test, and discuss new ideas that might explain the reported connection between
one's own consciousness and that of other living persons or deceased relatives.
The same applies to nonlocal phenomena such as the life review and preview, in
which past, present, and future can be experienced simultaneously and which
elude our conventional embodied conception of time and space. For me the biggest challenge is to find an explanation for the fact that an enhanced consciousness
can be experienced independently of the body during the temporary loss of all
cortical and brain-stem function.
68
A final theoretical possibility, one that has not been mentioned so far, is the theory
of transcendence, or rather the continuity hypothesis. It views the NDE as an altered state of consciousness in which memories, self-identity, lucid thought, and
emotions can be experienced independently of the unconscious body and in which
(extrasensory) perception outside the body remains a possibility. The empirical
studies have shown that NDErs can experience an enhanced consciousness independently of their normal, embodied waking consciousness. I am reluctant to use
the word transcendence because it suggests something transcending or rising
above the body. Transcendence is usually associated with the supernatural or with
the concept of; transcendental meditation; hence my preference for the term continuity hypothesis. Besides, because consciousness is continuous and nonlocal, if!
do not believe that consciousness rises above the body. It is always present outside
and often inside the body. As mentioned, current medical and scientific
knowledge cannot account for all aspects of the subjective experiences reported
by cardiac arrest survivors with an NDE. However, science means asking questions with an open mind. And science is also about searching for possible explanations for new, initially perplexing problems instead of clinging to old facts and
concepts. The problem lies less in accepting the content of new ideas than in rejecting old and familiar conceptions. The history of science tells us that sooner or
later – and sometimes very soon – new empirical findings will force us to abandon
our acquired knowledge. Quantum physicist David Bohm, (Bohm, 1987) believed
that "fixed ideas which underlie scientific hypotheses are not aids but obstructions
to clarity, and that a methodology which combines discipline with openness
would be better equipped to keep pace with the truth that is revealed as scientific
investigation progresses and deepens.
According to one concept, our brain can be compared to a television set that receives information from electromagnetic fields and decodes it into sound and vision. Our brain can also be compared to a television camera, which converts sound
and vision into electromagnetic waves, or encodes it. These electromagnetic
waves contain the essence of all information for a TV program but are available
to our senses only through a television camera and set. In this view, brain function
can be seen as a transceiver; the brain does not produce but rather facilitates consciousness. And DMT or dimethyltryptamine, which is produced in the pineal
gland, could play an important role in disturbing this process. Consciousness contains the seeds of all the information that is stored as wave functions in nonlocal
69
space. It transmits information to the brain and via the brain receives information
from the body and the senses. That consciousness affects both form and function
of the brain and the body has been described in the discussion of neuroplasticity
("The mind can change the brain"). This view corresponds with what David Bohm
has written: "Consciousness informs and in-forms”.
The wave functions in nonlocal space ψ , which possess both personal and universal information, is nonlocal consciousness However nonlocal space is more
than a mathematical description; it is a metaphysical space in which consciousness can exert influence because nonlocal space possesses subjective properties
of consciousness. In this view consciousness is nonlocal and functions as the
origin or basis of everything, including the material world.
Aspects of consciousness must resonate in different parts of the brain in order to
be experienced as waking consciousness. Resonance involves oscillation with the
same frequency. As we saw earlier, neurological imaging techniques such as
fMRI and PET show that different states of consciousness activate various brain
centers. Depression, joy, fear, pain, meditation, decision making, cognitive functions, mindfulness, sleeping, or perception all activate different centers of the
brain. But while the imaging techniques can establish the neurological correlations, they do so without accounting for the content of the different aspects of
consciousness. They merely point out the place of resonance of the different aspects of consciousness. Our waking consciousness has a biological basis because
our body functions as an interface. But there is no logical basis for endless or
enhanced consciousness, which is located in a multidimensional nonlocal space.
So enhanced consciousness is not limited to our brain because it is nonlocal, and
under normal circumstances our brain only allows us to experience waking consciousness. Like the particle and wave aspects of light, this perspective on the
relationship between nonlocal and waking consciousness constitutes a complementary theory. Conscious subjective experiences and their corresponding objective and visible brain activities, the physical effects of waking consciousness,
which can be established with the help of an fMRI or EEG, are two different
manifestations of one and the same underlying reality; they cannot be reduced to
one another. Experiments appear to provide scientific proof of the nonlocal entanglement or connectedness of consciousness. Pairs of people were placed in two
separate Faraday cages, which are rooms shielded from electromagnetic radiation
to block out any electromagnetic information transfer. If these two people were
70
strongly connected to each other, such as parent and child or two people who
practiced many years of joint meditation, simultaneous changes in their EEG
could be registered. In one isolated Faraday chamber, sensory stimulation through
random computer-generated flashes of light caused visual evoked potentials in
the EEG registration of the stimulated person, and this activity was instantaneously received by the other, unstimulated person in the second Faraday cage. As
a result, the registered patterns in the EEG of the unstimulated person changed
the moment the lights flashed in the other Faraday cage. This transferred electrical
activity, the so-called transferred potentials, the coherence or correlation between
the two EEGs, can be ascribed only to nonlocal influence. Because the experiment
design excluded electromagnetic information transfer, this correlation cannot be
explained with classic scientific models,
Physicist Fred H. Thaheld has outlined a potential scientific basis for this macroscopic and biological nonlocal entanglement. The first studies of this nonlocal
entanglement of consciousness were carried out at the University of Mexico by
the neurophysiologist Jacobo Grinberg-Zylberbaum. The research initially met
with criticism because of its poor design, but scientists at three different laboratories later replicated identical EEG correlations. Two fMRI studies found evidence of nonlocal entanglement between the brains of two isolated individuals
while nonlocal influence has also been identified in subjects whose fMRI registration changed significantly when a healer at some distance focused attention on
these subjects. And a recent study using laser stimulation and local EEG registration has shown nonlocal biological and macroscopic entanglement between two
cultivated specimens of fully isolated human neural networks. All of these carefully executed and replicated empirical studies confirm the nonlocal properties of
consciousness and point to a nonlocal entanglement in biological and macroscopic systems such as the brain. Neither the classical physics model of science
nor contemporary biological theories can account for this correlation of biological
systems. The human brain is an extremely complex and in many respects mysterious organ with physiological, chemical, and biological properties. But because
consciousness is not physiological, chemical, or biological, the brain is much
harder to analyze. Mathematician and physicist Roger Penrose has argued that on
theoretical grounds consciousness cannot be produced by the brain. He has also
demonstrated that computers will never be able to fully replicate or produce consciousness.
71
Consciousness is nonlocal, that is, everywhere in nonlocal space and intrinsically
entangled with all potential information stored in wave functions. Consciousness
triggers collapse of the wave function and is thus the source of embodied waking
consciousness. There is a theoretical possibility that consciousness in nonlocal
space is linked to – or serves as the basis for – the electromagnetic field connected
to the nervous system and the brain. In that case consciousness would be hitchhiking, as it were, on the electromagnetic field that probably originates, like consciousness, in nonlocal space
The process shows a certain analogy with the double-slit experiment, in which as
soon as the intensity of the light dwindles from a massive bombardment to the
transmission of individual photons there is a shift from an electromagnetic wave
to a probability wave. In the case of a single photon, no electromagnetic wave can
be measured, but the (immeasurable) probability wave is used to statistically predict where the photon will hit the photographic plate. Perhaps we could apply this
to the brain, with brain activity measured through the registration of the electromagnetic field (EEG). In the event of a cardiac arrest this electromagnetic activity
will slow to individual pulses with extremely low electromagnetic energy so that
these minimal energy packets (pulses) come to resemble individual photons.
These minimal energy packets must then be described with the probability waves
from quantum physics instead of the electromagnetic waves from classical physics. When the electromagnetic activity can no longer be measured, it does not
mean that there are no more probability waves. In fact, this is where the probability wave becomes a useful descriptor. In theory, the complete loss of brain function is still accompanied by (immeasurable) probability waves. Any potential influence on the minimal processes occurring in the brain at that moment cannot be
ruled out (the neurons' pilot-light state). NDE studies suggest that during the loss
of all measurable brain function people continue to experience nonlocal consciousness; this nonlocal consciousness is theoretically based on probability
waves.
Photons (waves or particles) are intrinsic quantum objects and natural long-distance carriers of information both in classical communication via radio, TV, mobile phones, and wireless Internet and in quantum communication. In Science and
Nature recently the results were published of research carried out under laboratory
conditions that proved information transfer between matter and light through elec72
tron spin and nuclear spin resonance on the basis of nonlocal quantum entanglement. This form of information transfer between light and matter is comparable
to reciprocal information transfer between nonlocal consciousness and the brain
via the model of nuclear spin correlation or nuclear spin coherence. DNA may
play an important role in this form of information transfer, and this will be discussed at length in the next chapter.
Recent studies among volunteers have found strong indications of a nonlocal therapeutic effect of certain drugs such as morphine, when the substance was placed
between a pulsating magnetic source and the brain. The subjective therapeutic
effect in these volunteers was identical to the effect of receiving this drug directly
into the body. And the same subjective therapeutic effect was achieved when the
subjects drank water that had been exposed to a pulsating magnetic source, to
laser light, microwaves, or even to a flashlight, with the drug placed i between the
photon source and the water. The authors ascribe this empirically proven positive
effect to quantum entanglement between nuclear spin and/or electron spin in the
water and nuclear spin and/or electron spin in the brain. The nonlocal information
transfer is made possible by, respectively, the magnetic, laser, or flashlight source
or the microwaves.
In conclusion, these three possible models of an interface between nonlocal consciousness and the brain will have to be elaborated though future research because
the questions continue to outnumber the answers. As mentioned, nonlocal and
reciprocal information exchange between consciousness and the brain will never
be fully knowable or verifiable, rendering any theories on the subject by definition
difficult ;-p prove or disprove. Perhaps a combination of data from empirical nd
theoretical scientific research could contribute to more definitive answers. As I
said, I personally prefer the model of nuclear spin or quantum spin resonance.
On the strength of the prospective studies of near-death experience and recent
data from neurophysiological research and concepts from quantum theory, I
strongly believe that consciousness cannot be localized in any particular place –
not even in the brain. It is nonlocal (that is, everywhere) in the form of probability
waves. For this reason it cannot be demonstrated or measured in the physical
world. There is, independent of the body, a continuity of consciousness that is
intrinsically connected to or entangled in nonlocal space, though not identical to
this space. The different aspects of consciousness are all nonlocal and accessible,
73
although there is probably some kind of hierarchy. The essence or foundation of
consciousness (protoconsciousness) probably lies in the vacuum or plenum of the
universe, from where it has a nonlocal connection with consciousness in nonlocal
space (pariproto-psychism). In this view, the vacuum is the source both of the
physical world and of consciousness. Perhaps nonlocal space could be called the
absolute or true vacuum because the vacuum and nonlocal space are either identical or nonlocally connected and therefore indistinguishable. Everything is a form
of space. Consciousness encompasses nonlocal space, and both my consciousness
and yours encompass all space. In fact, each part of our consciousness encompasses all space because each part of infinite is infinite itself. This is exactly what
the concept of nonlocality means.
Nonlocal consciousness is the source of our waking consciousness. The two are
complementary aspects of consciousness. Under normal, everyday circumstances
people experience waking consciousness (the "particle" aspect), which is just one
small part of overall and endless nonlocal consciousness (the "wave function"
aspect). During life people perceive with the senses while the brain functions as
interface. Under abnormal circumstances, people can experience the endless aspect of nonlocal consciousness independent of the body, which is called the continuity of consciousness, and perceive directly via consciousness in space. This is
known as a near-death experience. DMT from the pineal gland, of which the release seems to be triggered or stimulated by events in our consciousness, could
play a key role in establishing and disrupting the interface between the brain and
nonlocal consciousness. As mentioned, this interface may be based on quantum
spin coherence (nuclear spin resonance).
Nonlocal consciousness is endless, just as each part of consciousness is endless.
But our body is not endless. Every day, fifty billion cells are broken down and
regenerated in our body. And yet we experience our body as continuous. Where
does the continuity of the constantly changing body come from? How can we
explain long-term memory if the molecular composition of the neurons' cell membrane is completely renewed every two weeks? And how can we have a long-term
memory if the millions of synapses in the brain undergo a process of constant
adaptation (neuroplasticity)
74
2. Modified Schrodinger equation
When M. Planck made the first quantum discovery he noted an interesting fact.
The speed of light, Newton’s gravity constant and Planck’s constant clearly
reflect fundamental properties of the world. From them it is possible to derive
the characteristic mass MP, length LP and time TP with approximate values
LP = 10-35 m
TP = 10-43 s
MP = 10-5 g.
The constants LP, TP and MP, describe Planck Epoch. The enormous efforts of
the physicists, mathematicians and philosophers investigate the Planck Epoch.
In the subsequent we argue that the source of the “hard “consciousness phenomena are routed in Planck Epoch
To start with we derive modified Schrodinger equation from the study of the
thermal phenomena. The thermal history of the system (brain, Universe) can
be described by the generalized Fourier equation
t
q (t ) = − ∫ K (t − t ' ) ∇T (t ' )dt '.
−∞ thermal history
(1)
diffusion
In Eq. (1) q(t) is the density of the energy flux, T is the temperature of the
system and K(t – t') is the thermal memory of the system
K (t − t ' ) =
K
 (t − t ' ) 
exp−
,
τ
τ 

(2)
where K is constant, and τ denotes the relaxation time.
As was shown in [Marciak-Kozlowska, Kozlowski, 2013]

 Kδ (t − t ' )

K (t − t ' ) =  K = constant
K
(t − t ' ) 
 exp −

 τ
τ 

diffusion
wave
damped wave or hyperbolic diffusion.
75
The damped wave or hyperbolic diffusion equation can be written as:
∂ 2T 1 ∂T DT 2
+
=
∇ T.
τ
∂t 2 τ ∂t
(3)
For τ → 0 , Eq. (3. 3) is the Fourier thermal equation
∂T
= DT ∇ 2T
∂t
(4)
and DT is the thermal diffusion coefficient. The systems with very short relaxation time have very short memory. On the other hand for τ → ∞ Eq. (3) has
the form of the thermal wave (undamped) equation, or ballistic thermal equation. In the solid state physics the ballistic phonons or electrons are those for
which τ → ∞ . The experiments with ballistic phonons or electrons demonstrate
the existence of the wave motion on the lattice scale or on the electron gas
scale.
∂ 2T DT 2
=
∇ T.
∂t 2
τ
(5)
For the systems with very long memory Eq. (3) is time symmetric equation
with no arrow of time, for the Eq. (5) does not change the shape when t → −t .
In Eq. (3) we define:
D 
υ =  T ,
 τ 
(6)
velocity of thermal wave propagation and
λ = υτ,
(7)
where λ is the mean free path of the heat carriers. With formula (3. 6) equation
(3. 3) can be written as
1 ∂ 2T
1 ∂T
+ 2
= ∇ 2T .
2
2
υ ∂t
τυ ∂t
(8)
76
From the mathematical point of view equation:
1 ∂ 2T 1 ∂T
+
= ∇ 2T
2
2
υ ∂t
D ∂t
is the hyperbolic partial differential equation (PDE). On the other hand Fourier
equation
1 ∂T
= ∇ 2T
D ∂t
(9)
and Schrödinger equation
iℏ
∂Ψ
ℏ2 2
=−
∇Ψ
∂t
2m
(10)
are the parabolic equations. Formally with substitutions
t ↔ it , Ψ ↔ T
(11)
Fourier equation (9) can be written as
iℏ
∂Ψ
= − Dℏ∇ 2 Ψ
∂t
(12)
and by comparison with Schrödinger equation one obtains
ℏ2
2m
(13)
ℏ
.
2m
(14)
DT ℏ =
and
DT =
Considering that DT = τυ 2 (6) we obtain from (14)
τ=
ℏ
.
2mυh2
(15)
Formula (15) describes the relaxation time for quantum thermal processes.
Starting with Schrödinger equation for particle with mass m in potential V:
77
iℏ
∂Ψ
ℏ2 2
=−
∇ Ψ + VΨ
∂t
2m
(16)
and performing the substitution (11) one obtains
∂T ℏ 2 2
=
∇ T − VT
∂t 2m
(17)
∂T
ℏ 2
V
=
∇ T − T.
∂t 2m
ℏ
(18)
ℏ
Equation (18) is Fourier equation (parabolic PDE) for τ = 0. For τ ≠ 0 we obtain
∂ 2T ∂T V
ℏ 2
τ 2 +
+ T=
∇ T,
∂t
∂t ℏ
2m
τ=
(19)
ℏ
2mυ 2
Where the relaxation time τ is the real constant. Considering (19) we obtain.
1 ∂ 2T 2m ∂T 2Vm
+
+ 2 T = ∇ 2T .
2
2
υ ∂t
ℏ ∂t
ℏ
(20)
With the substitution (11) equation (19) can be written as
iℏ
∂Ψ
ℏ2 2
∂2Ψ
= VΨ −
∇ Ψ − τℏ 2 .
∂t
2m
∂t
(21)
The new term, relaxation term
τℏ
∂ 2Ψ
∂t 2
(22)
describes the interaction of the particle with mass m with space-time. The relaxation time τ can be calculated as:
−1
τ −1 = (τ e−−1p + ... + τ Planck
),
(23)
where, for example τe-p denotes the scattering of the particle m on the electronpositron pair ( τ e − p ~ 10 −17 s) and the shortest relaxation time τPlanck is the Planck
time ( τ Planck ~ 10−43 s).
78
From equation (23) we conclude that τ ≈ τ Planck and equation (21) can be written
as
iℏ
ℏ2 2
∂Ψ
∂ 2Ψ
= VΨ −
∇ Ψ − τ Planck ℏ 2 ,
∂t
2m
∂t
(24)
where
1
τ Planck
ℏ
1  ℏG  2
=  5  =
.
2 c 
2M p c 2
(25)
In formula (25) Mp is the mass Planck. Considering Eq. (25), Eq. (24) can be
written as
∂Ψ
ℏ2 2
ℏ2
ℏ2
ℏ2 ∂2Ψ
2
2
iℏ
=−
∇ Ψ + VΨ −
∇ Ψ+
∇ Ψ−
.
∂t
2m
2M p
2M p
2M p c 2 ∂t 2
(26)
The last two terms in Eq. (26) can be defined as the Bohmian pilot wave
ℏ2
ℏ2 ∂2Ψ
∇2Ψ −
= 0,
2M p
2M p c 2 ∂t 2
(27)
i.e.
∇ 2Ψ −
1 ∂ 2Ψ
= 0.
c 2 ∂t 2
(28)
It is interesting to observe that pilot wave Ψ does not depend on the mass of
the particle. With postulate (28) we obtain from equation (26)
∂Ψ
ℏ2 2
ℏ2
iℏ
=−
∇ Ψ + VΨ −
∇2Ψ
∂t
2m
2M p
(29)
and simultaneously
ℏ2
ℏ2 ∂2Ψ
∇2Ψ −
= 0.
2M p
2M p c 2 ∂t 2
(30)
In the operator form Eq. (21) can be written as
pˆ 2
1
Eˆ =
+
Eˆ 2 ,
2
2m 2 M p c
(31)
79
where Ê and p̂ denote the operators for energy and momentum of the particle
with mass m. Equation (31) is the new dispersion relation for quantum particle
with mass m. From Eq. (21) one can concludes that Schrödinger quantum mechanics is valid for particles with mass m « MP. But pilot wave exists independent of the mass of the particles.
For particles with mass m « MP = neuron mass Eq. (29) has the form
iℏ
∂Ψ
ℏ2 2
=−
∇ Ψ + VΨ.
2m
∂t
(32)
In the case when m ≈ M p Eq. (29) can be written as
∂Ψ
ℏ2
iℏ
=−
∇ 2 Ψ + VΨ,
∂t
2M p
(33)
but considering Eq. (30) one obtains
∂Ψ
ℏ 2 ∂ 2Ψ
=−
+ VΨ
2 M p c 2 ∂t 2
∂t
(34)
ℏ 2 ∂ 2Ψ
∂Ψ
+ iℏ
− VΨ = 0.
2
2
2M p c ∂t
∂t
(35)
iℏ
or
We argue that Equations (35) and (30) are the master equation for the brain
waves, Ψ
We look for the solution of Eq. (35) in the form
Ψ ( x, t ) = e − iω u ( x ).
(36)
After substitution formula (36) to Eq. (35) we obtain
ℏ2
ω 2 − ωℏ + V ( x ) = 0
2
2 M pc
(37)
80
with the solution
M p c2 + M pc2 1 −
ω1 = −
ℏ
M pc − M pc
2
ω2 =
for
M pc2
2
2
> V and
ω1 =
ω2 =
2
2V
−1
M pc2
ℏ
M p c 2 − iM p c 2
M pc2
(38)
2V
1−
M p c2
ℏ
M p c 2 + iM p c 2
for
2V
M pc2
(39)
2V
−1
M pc2
ℏ
< V.
Both formulae (38) and (39) describe the “string” oscillation, formula (38)
damped oscillation and formula (39) over damped “string” oscillation. From
elementary particles physics we know that the internal energy MP c2 is the maximum energy per particle in the Universe for elementary particles (Fig. 1). In
that case we argue that the first solution (38) is the valid solution.
For
M pc2
2
≫ V we obtain
2 M Pc2
ℏ
V
ω2 =
ℏ
ω1 =
(40)
The angular frequency ω1 represents the Planck frequency ω1 = τ P −1 and ω2 is the
frequency of the brain waves. Fig. 2 presents the ω2 as the function of V. As can
be seen from Fig. 2, for the potential energy V ≈ 10−15 eV angular frequency of the
brain waves is of the order of 10Hz in agreement with the measured frequencies.
81
It is very interesting to observe that the same equation describes the two modes
of the wave motion: the vibration of the space-time, Planck vibration, for primordial Universe and the brain vibration. Moreover from formulae (38-40) we conclude that the first order Schrodinger equation, i.e., equation with M P = 0 can not
describe the brain vibration.
Fig. 1: The elementary particle masses
82
Angularfrequency 1 s
2.0
1.5
1.0
0.5
0.0
0
2. 10 15
4. 10 15
6. 10 15
8. 10 15
1. 10 14
Energy eV
Fig. 2: presents the ω2 as the function of V.
References
Bohm D, Science, order and creativity, Bantam Books, 1987.
Marciak-Kozlowska J. Kozlowski M. On the brain and cosmic background photons, NeuroQuantology, 2013; 11(2) p. 223-236.
Pim van Lommel Consciousness beyond life, Harper One, 2010.
Schild R. Cosmology and and consciousness, quantum physics & neuroscience of
mind, Cosmology Science Publishers, 2012.
83
CHAPTER V
Brain Vibrations and Planck Mass
Introduction
Review and update of a 120-year-old theory of consciousness published in Physics of Life Reviews claims that consciousness derives from deeper level, finer
scale activities inside brain neurons. The recent discovery of quantum vibrations
in "microtubules" inside brain neurons corroborates this theory, according to review authors Stuart Hameroff and Sir Roger Penrose. They suggest that EEG
rhythms (brain waves) also derive from deeper level microtubule vibrations, and
that from a practical standpoint, treating brain microtubule vibrations could benefit a host of mental, neurological, and cognitive conditions.
The theory, called "orchestrated objective reduction" ('Orch OR'), was first put
forward in the mid-1990s by eminent mathematical physicist Sir Roger Penrose,
FRS, Mathematical Institute and Wadham College, University of Oxford, and
prominent anesthesiologist Stuart Hameroff, MD, Anesthesiology, Psychology
and Center for Consciousness Studies, The University of Arizona, Tucson. They
suggested that quantum vibrational computations in microtubules were "orchestrated" ("Orch") by synaptic inputs and memory stored in microtubules, and terminated by Penrose "objective reduction" ('OR'), hence "Orch OR". Microtubules
are major components of the cell structural skeleton.
Orch OR was criticized from its inception, as the brain was considered too "warm,
wet, and noisy" for seemingly delicate quantum processes. . However, evidence
has now shown warm quantum coherence in plant photosynthesis, bird brain navigation, our sense of smell, and brain microtubules. The recent discovery of warm
temperature quantum vibrations in microtubules inside brain neurons by the research group led by Anirban Bandyopadhyay, PhD, at the National Institute of
Material Sciences in Tsukuba, Japan (and now at MIT), corroborates the pair's
theory and suggests that EEG rhythms also derive from deeper level microtubule
vibrations. In addition, work from the laboratory of Roderick G. Eckenhoff, MD,
at the University of Pennsylvania, suggests that anesthesia, which selectively
erases consciousness while sparing non-conscious brain activities, acts via microtubules in brain neurons.
84
"The origin of consciousness reflects our place in the universe, the nature of our
existence. Did consciousness evolve from complex computations among brain
neurons, as most scientists assert? Or has consciousness, in some sense, been here
all along, as spiritual approaches maintain?" ask Hameroff and Penrose in the
current review. "This opens a potential Pandora's Box, but our theory accommodates both these views, suggesting consciousness derives from quantum vibrations in microtubules, protein polymers inside brain neurons, which both govern
neuronal and synaptic function, and connect brain processes to self-organizing
processes in the fine scale, 'proto-conscious' quantum structure of reality. "
After 20 years, "the evidence now clearly supports Orch OR", continue Hameroff
and Penrose. "Our new paper updates the evidence, clarifies Orch OR quantum
bits, or "qubits", as helical pathways in microtubule lattices, rebuts critics, and
reviews 20 testable predictions of Orch OR published in 1998 -- of these, six are
confirmed and none refuted".
An important new facet of the theory is introduced. Microtubule quantum vibrations (e.g. in megahertz) appear to interfere and produce much slower EEG "beat
frequencies". Despite a century of clinical use, the underlying origins of EEG
rhythms have remained a mystery. Clinical trials of brief brain stimulation aimed
at microtubule resonances with megahertz mechanical vibrations using transcranial ultrasound have shown reported improvements in mood, and may prove useful against Alzheimer's disease and brain injury in the future.
Lead author Stuart Hameroff concludes, "Orch OR is the most rigorous, comprehensive and successfully-tested theory of consciousness ever put forth. From a
practical standpoint, treating brain microtubule vibrations could benefit a host of
mental, neurological, and cognitive conditions".
"Consciousness depends on nonharmonic vibrations of microtubules inside neurons, similar to certain kinds of Indian music, but unlike Western music which is
harmonic", Hameroff explains.
2. Consciousness and Quantum Theory
The issue of observation in QM is central, in the sense that objective reality cannot
be disentangled from the act of observation, as the Copenhagen Interpretation (CI)
85
nearly states in the words of John A. Wheeler 1981, we live in an observer-participatory Universe. The vast majority of today's practicing physicists follow CI's
practical prescriptions for quantum phenomena, while still clinging to classical
beliefs in observer-independent local, external reality). There is a critical gap between practice and underlying theory. In his Nobel Prize speech of 1932, Werner
Heisenberg concluded that the atom "has no immediate and direct physical properties at all". If the universe's basic building block isn't physical, then the same
must hold true in some way for the whole. The universe was doing a vanishing
act in Heisenberg's day, and it certainly hasn't become more solid since. (R.
Schild, 2012)
This discrepancy between practice and theory must be confronted, because the
consequences for the nature of reality are far-reaching. An impressive body of
evidence has been building to suggest that reality is non-local and undivided.
Non-locality is already a basic fact of nature, first implied by the Einstein-Podolsky-Rosen thought experiment despite the original intent to refute it, and later
explicitly formulated in Bell's Theorem
Moreover, this is a reality where the mindful acts of observation play a crucial
role at every level. Heisenberg again: "The atoms or elementary particles themselves...form a world of potentialities or possibilities rather than one of things or
facts. "He was led to a radical conclusion that underlies our own view in this
paper: "What we observe is not nature itself, but nature exposed to our method of
questioning". Reality, it seems, shifts according to the observer's conscious intent.
There is no doubt that the original CI was subjective (R. Schild, 2012)
Quantum theory is not about the nature of reality, even though quantum physicists
act as if that is the case. To escape philosophical complications, the original CI
was pragmatic: it concerned itself with the epistemology of quantum world (how
we experience quantum phenomena), leaving aside ontological questions about
the ultimate nature of reality. The practical bent of CI should be kept in mind,
particularly as there is a tendency on the part of many good physicists to slip back
into issues that cannot be tested and therefore run counter to the basic tenets of
scientific methodology.
86
3. Model
In order to put forward the classical theory of the brain waves we quantize the
brain wave field. In the model (Marciak-Kozlowska, Kozlowski, 2013) we assume (i) the brain is the thermal source in local equilibrium with temperature T.
(ii) The spectrum of the brain waves is quantized according to formula
E = ℏω
(1)
where E is the photon energy in eV, ℏ =Planck constant, ω = 2πν ,ν -is the frequency in Hz. (iii). The number of photons emitted by brain is proportional to the
(amplitude)2 as for classical waves. The energies of the photons are the maximum
values of energies of waves. For the emission of black body brain waves we propose the well know formula for the black body radiation.
In thermodynamics we consider Planck type formula for probability P (E) dE for
the emission of the particle (photons as well as particles with m≠0) with energy
(E, E+dE) by the source with temperature T is equal to :
P(E)dE= BE2 e (-E/kT) dE
(2)
where B= normalization constant, E=total energy of the particle, k = Boltzmann
constant=1.3 × 10-23 J K-1. K is for Kelvin degree. However in many applications
in nuclear and elementary particles physics kT is recalculated in units of energy.
To that aim we note that for 1K, kT is equal k1K = K x 1.3 10-23 J x K-1= 1.3 ×
10-23 Joule or kT for 1K is equivalent to 1.3 × 10-23 Joule=1.3 × 10-23/(1.6 × 1019
) eV = 0.8 × 10-4 eV. Eventually we obtain 1K= 0.8 × 10-4 eV, and 1eV= 1.2 ×
104 K
( − Emax )
dN
2
= BEmax
e T
dE
(2)
where, B is the normalization constant, T is the temperature of the brain thermal
source in eV. The function
dN
describes the energy spectrum of the emitted
dE
brain photons.
Until 2014 no one has find the experimental evidence of the cold source of the
brain photons. But recently the new sort of neutrino with the mass of the order 7
87
keV was experimentally evidenced. The neutrino ν decays according to the
scheme:
ν → 2γ
(3)
where γ denotes x ray photons with energy 3.5 keV. In the paper (Marciak-Kozlowska, Kozlowski, 2013) the comparison of the photon spectra of CBM and the
spectra of brain electromagnetic emission was performed. It occurs that both spectra can be described with formula (2), but with different temperatures. The ratio
of the temperatures is
Tbrain
= 10−10
TCBM
(4)
Following formula (4) we argue that in brain spectra the photons with energy of
the order of
10−10 i3.7103 eV = 3.710−7 eV = 3.710−3 K
(5)
can be observed
In Fig. 1, we present the result of the comparison of the calculated, formula (2),
temperatuta T= 0.8 × 10-14 eV= 0.810−10 K , and observed spectra of the brain waves.
The calculated spectra are normalized to the maximum of the measured spectra.
The obtained temperature is the temperature for the brain source in the thermal
equilibrium. The source is thermally isolated (adiabatic well). It must be stressed
that in the paper we abandon the idea that every physical object is either a wave
or a particle. Neither it is possible to say that particles “become” waves in the
quantum domain and conversely that waves are “transformed “into particles. It is
therefore necessary to acknowledge that we have here a different kind of an entity,
one that is specifically quantum. For this reason Levy-Leblond and Balibar developed the name quanton, (Levy-Leblond, Balibar, 1990). Following that idea
the human brain emits quantons with energies E = ℏω . The brain quantons are the
quantum objects that follows all quantum laws: tunneling, the superposition and
Heisenberg uncertainty rule.
In Fig. 2 we present the theoretical spectrum of the brain waves with for temperature T = 10−3 K we will call them ψ waves.
88
Fig. 1: Comparison of experimental and theoretical results for brain vibration
Fig. 2: The model calculation of the ψ wave energy spectrum
Beginning in 2009, Anirban Bandyopadhyay and colleagues at the National
Institute of Material Sciences in Tsukuba, Japan, were able to use nanotechnology to address electronic and optical properties of individual micro tubules
[Anirban Bandyopadhyay, 2013]. The group has made a series of remarkable discoveries suggesting that quantum effects do occur in microtubules at biological
temperatures. First, they found that electronic conductance along microtubules,
89
normally extremely good insulators, becomes exceedingly high, approaching
quantum conductance, at certain specific reso- nance frequencies of applied alternating current (AC) stimulation. These resonances occur in gigahertz, megahertz and kilohertz ranges, and are particularly prominent in low megahertz (e.g.
8.9 MHz). Conductances induced by specific (e.g. megahertz) AC frequencies appear to follow several types of pathways through the microtubule – helical, linear
along the microtubule axis, and ‘blanket-like’ along/around the entire microtubule
surface. Second, using various techniques, the Bandyopadhyay group also determined AC conductance through 25-nm-wide microtubules is greater than through
single 4-nm-wide tubulins, indicating cooperative, possibly quantum coherent effects throughout the microtubule, and that the electronic properties of microtubules are programmed within each tubulin. Their results also showed that conductance increased with microtubule length, indicative of quantum mechanisms.
The resonance conductance (‘Bandyopadhyay coherence’ – ‘BC’) through tubulins and microtubules is consistent with the intra-tubulin aromatic ring pathways)
which can support Orch OR quantum dipoles, and in which anesthetics bind, apparently to selectively erase consciousness. Bandyopadhyay’s experiments do
seem to provide clear evidence for coherent microtubule quantum states at brain
temperature.
In our model the new ψ wane have the frequency ω =100 MHz in rather good
agreement with Bandyopadhyay measurement. In light of the above it seems reasonable to argue that the ψ vibration postulated in this paper is the candidate for
the resonances observed in Bandyopadhyay’s experiments
In Table 1 the calculated energy, and wave length according to formulae
E[eV ] = 10 −15 ω[ Hz ] λ [m ] =
10−7
E [ eV ]
90
(6)
TABLE 1: The full spectrum of the brain vibrations with new ψ wave included
WAVE
δ
θ
α
β
ψ
MAXIMUM
FREQUENCY
[Hz]
3.9
7.9
13.9
30
ENERGY [ ×1015
eV]
Wave length [m]
∼ 3.9
∼ 108
7.9
∼ 13.9
∼ 30
∼ 108
108
8
∼ 10
∼
∼ 108
∼ 108
∼1
References
Kevork N. Abazaijan, 2014 Resonantly produced 7 keV sterile nutrino dark matter and the properties of Milky Way Satelites, Phys. Rev. Lett. 112, 161303,
2014.
Stuart Hameroff and Roger Penrose, 2013. Consciousness in the universe: A review of the ‘Orch OR’ theory. Physics of Life Reviews, 2013.
Schild R 2012. Cosmology of Consciousness, Quantum Physics & Neuroscience
of Mind, Cosmology Science Publishers, Cambridge, 2012.
Sahu S., Ghosh S., Hirata K., Fujita D., Bandyopadhyay, 2013. A Multi-level
memory-switching properties of a single brain microtubule. Appl Phys Lett
2013; 102:123701.
Marciak-Kozlowska J., Kozlowski M., 2013. On the Brain and Cosmic Background Photons, Neuroquantology vol. 11, 223, 2013.
91
CHAPTER VI
Riemann`s Zeta(x) Function and Human Consciousness
1. Introduction
What is consciousness? Some philosophers have contended that "qualia", or an
experiential medium from which consciousness is derived, exists as a fundamental component of reality. Whitehead, for example, described the universe as being
comprised of "occasions of experience". To examine this possibility scientifically,
the very nature of physical reality must be re-examined. We must come to terms
with the physics of space-time – as is described by Einstein's general theory of
relativity – and its relation to the fundamental theory of matter – as described by
quantum theory. This leads to employ a new physics of objective reduction: "OR"
which appeals to a form of quantum gravity to provide a useful description of
fundamental processes at the quantum/classical borderline (Penrose, 2013).
Within the OR scheme, Hameroff and Penrose consider that consciousness occurs
if an appropriately organized system is able to develop and maintain quantum
coherent superposition until a specific "objective" criterion (a threshold related to
quantum gravity) is reached; the coherent system then self-reduces (objective reduction: OR). They argued that this type of objective self-collapse introduces noncomputability, an essential feature of consciousness. OR is taken as an instantaneous event – the climax of a self-organizing process in fundamental space-time
– and a candidate for a conscious Whitehead "occasion" of experience.
Let us discuss the relation between consciousness and Universe. The meaning of
the 'anthropic principle', according to which it is sometimes argued that the particular dimensionless constants of Nature that we happen to find in our universe
are 'fortuitously' favorable to human existence is extremely important. (A dimensionless physical constant is a pure number, like the ratio of the electric to the
gravitational force between the electron and the proton in a hydrogen atom, which
in this case is a number of the general order of 1040). The key point is not so much
to do with human existence, but the existence of sentient beings of any kind. Is
there anything coincidental about the dimensionless physical constants being of
such a nature that conscious life is possible at all? For example, if the mass of the
neutron had been slightly less than that of the proton, rather than slightly larger,
92
then neutrons rather than protons would have been stable, and this would be to
the detriment of the whole subject of chemistry. These issues are frequently argued about (see Barrow and Tipler 1986), but the Penrose-Hamaroff theory proposal provides a little more substance to these arguments, since a proposal for the
possibility of sentient life is, in principle, provided.
The Penrose-Hameroff theory places the phenomenon of consciousness at a very
central place in the physical nature of our universe, whether or not this 'universe'
includes aeons other than just our own. It is our belief that, quite apart from detailed aspects of the physical mechanisms that are involved in the production of
consciousness in human brains, quantum mechanics is an incomplete theory. If
such a scheme as this is indeed respected by Nature, then there is a fundamental
additional ingredient to our presently understood laws of Nature which plays an
important role at the Planck-scale level of space-time structure. The PenroseHameroff proposal takes advantage of this, suggesting that conscious experience
itself plays such a role in the operation of the laws of the universe.
Such speculations also raise the issue of the 'anthropic principle', according to
which it is sometimes argued that the particular dimensionless constants of Nature
that we happen to find in our universe are 'fortuitously' favorable to human existence. (A dimensionless physical constant is a pure number, like the ratio of the
electric to the gravitational force between the electron and the proton in a hydrogen atom, which in this case is a number of the general order of 1040). The key
point is not so much to do with human existence, but the existence of sentient
beings of any kind. Is there anything coincidental about the dimensionless physical constants being of such a nature that conscious life is possible at all? For example, if the mass of the neutron had been slightly less than that of the proton,
rather than slightly larger, then neutrons rather than protons would have been stable, and this would be to the detriment of the whole subject of chemistry. These
issues are frequently argued about (see Barrow and Tipler 1986).
In 1859. B. Riemann published paper in which he defined Riemann function (Edwards, 1974)
93
∞
∏ ( s) = ∫ e− s x s dx, ( s > −1)
0
ζ ( x) = ∏
( − s)
2π i
∞
( x ) s dx
∫ ex − 1 x
−∞
The epoch-making 8-pages paper “On the Number of Primes Less Than a Given
Magnitude” inaugurated the revolution in number theory and recently in theoretical physics: quantum mechanics and cosmology. In the paper we for the time
consider the application of Zeta function to the study of the human consciousness
and especially, time recognition. We argue that time life of the Universe and the
consciousness can be described as the product of Zeta function and Planck time.
The possible scenario for the creation of consciousness is discussed.
2. Mathematical introduction
Dirichlet was especially interested in Gauss's clock calculator. In particular, he
was intrigued by a conjecture that went back to a pattern spotted by Fermat. If
you took a clock calculator with N hours on it and you fed in the primes, then,
Fermat conjectured, infinitely often the clock would hit one o'clock. So, for example, if you take a clock with 4 hours there are infinitely many primes which
Fermat predicted would leave remainder 1 on division by 4. The list begins 5, 13,
17, 29, ...
In 1838, at the age of thirty-three, Dirichlet had made his mark in the theory of
numbers by proving that Fermat's hunch was indeed correct. He did this by mixing ideas from several areas of mathematics that didn't look as if they had anything to do with one another. Instead of an elementary argument like Euclid's
cunning proof that there are infinitely many primes, Dirichlet used a sophisticated
function that had first appeared on the mathematical circuit in Euler's day. It was
called the z e t a f u n c t i o n , and was denoted by the Greek letter ζ . The following equation provided Dirichlet with the rule for calculating the value of the zeta
function when fed with a number x :
ζ ( x) =
1 1 1
1
+ x + x + ....... x + .....
x
1 2 3
n
94
To calculate the output at x , Dirichlet needed to carry out three mathematical
steps. First, calculate the exponential numbers 1x, 2x, 3x, nx, . . . Then take the
reciprocals of all the numbers produced in the first step. (The reciprocal of 2 x is
1/2x) Finally, add together all the answers from the second step.
It is a complicated recipe. The fact that each number 1, 2, 3, ... makes a contribution to the definition of the zeta function hints at its usefulness to the number
theorist. The downside comes in having to deal with an infinite sum of numbers.
Few mathematicians could have predicted what a powerful tool this function
would become as the best way to study the primes. It was almost stumbled upon
by accident.
The origins of mathematicians' interest in this infinite sum came from music and
went back to a discovery made by the Greeks. Pythagoras was the first to discover
the fundamental connection between mathematics and music. He filled an urn
with water and banged it with a hammer to produce a note. If he removed half the
water and banged the urn again, the note had gone up an octave. Each time he
removed more water to leave the urn one-third full, then one-quarter full, the notes
produced would sound to his ear in harmony with the first note he'd played. Any
other notes which were created by removing some other amount of water sounded
in dissonance with that original note. There was some audible beauty associated
with these fractions. The harmony that Pythagoras had discovered in the numbers
1, 1/21/3, 1/4, ... made him believe that the whole universe was controlled by
music, which is why he coined the expression “the music of the spheres”.
Ever since Pythagoras' discovery of an arithmetic connection between mathematics and music, people have compared both the aesthetic and the physical traits
shared by the two disciplines. The French Baroque composer Jean-Philippe Rameau wrote in 1722 that “Not withstanding all the experience I may have acquired
in music from being associated with it for so long, I must confess that only with
the aid of mathematics did my ideas become clear”. Euler sought to make music
theory “part of mathematics and deduce in an orderly manner, from correct principles, everything which can make a fitting together and mingling of tones pleasing”. Euler believed that it was the primes that lay behind the beauty of certain
combinations of notes.
95
Many mathematicians have a natural affinity with music. Euler would relax after
a hard day's calculating by playing his clavier. Mathematics departments invariably have little trouble assembling an orchestra from the ranks of their members.
There is an obvious numerical connection between the two given that counting
underpins both. As Leibniz described it, “Music is the pleasure the human mind
experiences from counting without being aware that it is counting”' But the resonance between the subjects goes much deeper than this.
Mathematics is an aesthetic discipline where talk of beautiful proofs and elegant
solutions is commonplace. Only those with a special aesthetic sensibility are
equipped to make mathematical discoveries. The flash of illumination that mathematicians crave often feels like bashing notes on a piano until suddenly a combination is found which contains an inner harmony marking it out as different.
G.H. Hardy wrote that he was 'interested in mathematics only as a creative art'.
Even for the French mathematicians in Napoleon's academies, the buzz of doing
mathematics came not from its practical application but from its inner beauty.
The aesthetic experiences of doing mathematics or listening to music have much
in common. Just as you might listen to a piece of music over and over and find
new resonances previously missed, mathematicians often take pleasure in rereading proofs in which the subtle nuances that make it hang together so effortlessly gradually reveal themselves. Hardy believed that the true test of a good
mathematical proof was that 'the ideas must fit together in a harmonious way.
Beauty is the first test: there is no permanent place in the world for ugly mathematics. For Hardy, A mathematical proof should resemble a simple and clear-cut
constellation, not a scattered Milky Way.
Both mathematics and music have a technical language of symbols which allow
us to articulate the patterns we are creating or discovering. Music is much more
than just the minims and crochets which dance across the musical stave. Similarly, mathematical symbols come alive only when the mathematics is played
with in the mind.
As Pythagoras discovered, it is not just in the aesthetic realm that mathematics
and music overlap. The very physics of music has at its root the basics of mathematics. If you blow across the top of a bottle you hear a note. By blowing harder,
and with a little skill, you can start to hear higher notes - the extra harmonics, the
96
overtones. When a musician plays a note on an instrument they are producing an
infinity of additional harmonics, just as you do when you blow across the top of
the bottle. These additional harmonics help to give each instrument its own distinctive sound. The physical characteristics of each instrument mean that we hear
different combinations of harmonics. In addition to the fundamental note, the
clarinet plays only those harmonics produced by odd fractions: 1/3, 1/5, 1/7, ...
The string of a violin, on the other hand, vibrates to create all the harmonics that
Pythagoras produced with his urn - those corresponding to the fractions1/2, 1/3,
1/4 ….
Since the sound of a vibrating violin string is the infinite sum of the fundamental
note and all the possible harmonics, mathematicians became intrigued by the
mathematical analogue. The infinite sum 1 + 1/2 +1/3+1/4+... became known as
the h a r mo n i c s e r i e s . This infinite sum is also the answer Euler got when he
fed the zeta function with the number x = . Although this sum grew only very
slowly as he added more terms, mathematicians had known since the fourteenth
century that eventually it must spiral off to infinity.
So the zeta function must output the answer infinity when fed the number x = .
If, however, instead of taking x = 1, Euler fed the zeta function with a number
bigger than 1, the answer no longer spiralled off to infinity. For example, taking
x = 2 means adding together all the squares in the harmonic series:
1+
1 1 1
+ + + .......
22 32 42
This is a smaller number as it does not include all possible fractions found when
x = . We are now adding only some of the fractions, and Euler knew that this
time the smaller sum wouldn't spiral off to infinity but would home in on some
particular number. It had become quite a challenge by Euler's day to identify a
precise value for this infinite sum when x = 2. The best estimate was somewhere
around 8/5. In 1735, Euler wrote that 'So much work has been done on the series
that it seems hardly likely that anything new about them may still turn up... I,
too, in spite of repeated effort, could achieve nothing more than approximate values for their sums'.
Nevertheless, Euler, emboldened by his previous discoveries, began to play
around with this infinite sum. Twisting it this way and that like the sides of a
97
Rubik's cube, he suddenly found the series transformed. Like the colours on the
cube, these numbers slowly came together to form a completely different pattern
from the one he had started with. As he went on to describe, 'Now, however, quite
unexpectedly, I have found an elegant formula depending upon the quadrature of
the circle' - in modern parlance, a formula depending on the number π = 3.1415...
By some pretty reckless analysis, Euler had discovered that this infinite sum was
homing in on the square of π divided by 6:
1+
1 1 1
π2
+ + + ...... =
4 9 16
6
The decimal expansion of
π2
6
like that of π , is completely chaotic and unpredict-
able. To this day, Euler's discovery of this order lurking in the number
π2
6
ranks
as one of the most intriguing calculations in all of mathematics, and it took the
scientific community of Euler's time by storm. No one had predicted a link between the innocent sum 1+1/4+1/9+1/16 + ... and the chaotic number π . This
success inspired Euler to investigate the power of the zeta function further. He
knew that if he fed the zeta function with any number bigger than 1, the result
would be some finite number. After a few years of solitary study he managed to
identify the output of the zeta function for every even number. But there was
something rather unsatisfactory about the zeta function. Whenever Euler fed the
formula for the zeta function with any number less than 1, it would always output
infinity. For example, for x = - 1 it yields the infinite sum 1 + 2 + 3 + 4 + ... The
function behaved well only for numbers bigger than 1.
Euler's discovery of his expression for
π2
6
in terms of simple fractions was the
first sign that the zeta function might reveal unexpected links between seemingly
disparate parts of the mathematical canon. The second strange connection that
Euler discovered was with an even more unpredictable sequence of numbers.
S. Ramanujan notebooks and the power of the Brahmin network had secured Ramanujan a job as an accountant with the Port Authority in Madras. He had begun
to publish some of his ideas in the Journal of the Indian Mathematical Society,
and by now his name had come to the attention of the British authorities. C.L.T.
98
Griffith, who worked at the College of Engineering in Madras, recognised that
Ramanujan's work was that of a 'remarkable mathematician' but he felt unable to
follow or criticise it. So he decided to get the opinion of one of the professors
who had taught him as a student in London.
Without formal training, Ramanujan had evolved a very personal mathematical
style. It is perhaps not surprising, then, that when Professor Hill of University
College, London received Ramanujan's papers claiming to have proved that
1 +2+3+4+ …. . =-1/12
he dismissed most of them as meaningless. Even to the untrained eye, this formula looks ridiculous. To add up all the whole numbers and get a negative fraction is clearly the work of a madman! 'Mr Ramanujan has fallen into the pitfalls
of the very difficult subject of Divergent Series', he wrote back to Griffith.
Ramanujan had recently been given a copy of Hardy's Orders of Infinity by Ganapathy Iyer, a Professor of Mathematics in Madras with whom he regularly discussed mathematics on the beach in the evenings. As he read Hardy, Ramanujan
must have recognised that here at last was someone who might appreciate his
ideas, but later he admitted that he had feared his infinite sums would prompt
Hardy 'to point out to me the lunatic asylum as my goal'. Ramanujan was particularly excited by Hardy's statement that 'no definite expression has been found
as yet for the number of prime numbers less than any given number'. Ramanujan
had discovered an expression which he believed very nearly captured this number. He was very keen to find out what Hardy thought of his formula.
Hardy's first impression on finding in the morning post Ramanujan's envelope
covered in Indian stamps was not immediately favourable. It contained a manuscript filled with wild, fantastic theorems about counting primes, alongside wellknown results presented as if they were original discoveries. In the covering letter Ramanujan declared that he had 'found a function which exactly represents
the number of prime numbers'. Hard) knew that this was a stunning claim, but
no formula had been supplied. Worst of all - no proofs of anything! For Hardy,
proof was everything. He once told Bertrand Russell across the high table at
Trinity, 'If I could prove by logic that you would die in five minutes, I should be
sorry you were going to die, but my sorrow would be very much mitigated by
pleasure in the proof. '
99
According to C.P. Snow, Hardy, having quickly looked over Ramanujan's work,
'was not only bored, but irritated. It seemed like a curious kind of fraud'. But by
the evening the wild theorems were beginning to work their magic, and Hardy
summoned Littlewood for after-dinner discussions. By midnight they had
cracked it. Hardy and Littlewood, equipped with the knowledge to decode Ramanujan's unorthodox language, could now see that these were not the outpourings
of a crank but the works of a genius - untrained, but brilliant.
They both recognised that Ramanujan's crazy infinite sum was none other than
the rediscovery of how to define the missing part of Riemann's zeta landscape.
The clue to decoding Ramanujan's formula is to rewrite the number 2 as 1/(2-1)
(2-1 is another way of writing). Applying the same trick to each number in the
infinite sum. Hardy and Littlewood rewrote Ramanujan's formula as
1+2+3+4+ …. =1 +1/2-1+ 3-1+4-1+ …=-1/12
Staring them in the face was Riemann's answer to how to calculate the zeta function when fed with the number -1. With no formal training, Ramanujan had run
the whole race on his own and reconstructed Riemann's discovery of the zeta
landscape.
3. Atomicity of Time
It is well known that idea of discrete structure of time can be applied to the ''flow''
of time. The idea that time has ''atomic'' structure or is not infinitely divisible, has
only recently come to the fore as a daring and sophisticated hypothetical
concomitant of recent investigations in the physics elementary particles and
astrophysics. Greek philosophers in the sixth and fifth centuries b. c. identified
dual aspects of time – being (the Parmenidean continuity aspect) and becoming
(the Heraclitean transience aspect) – that to this day remain unreconciled. Time
extends continuously from the past to the future (the being aspect), and things
change in time (the becoming aspect). Augustine's paradox of time is that things
in time change in time. Do things actually change in time, or do they appear to
change because we move in time? If we move in time, then we change in time.
Evidently, temporal location does not exhaust the properties of time.
100
In theoretical physics, time is fully spatial-ized and time and space have no
distinction in four-dimensional space-time. Events of the physical world are
displayed in space-time; they are fixed and never change, and space-time decomposes into the different spaces and times of observers in relative motion. The
becoming or transience aspect of time (the part that cannot be spatialized), which
consists of an awareness of change in the sensible world, is banished from the
physical world as a psychological or metaphysical characteristic of the observer.
The problem for the physicist and the philosopher, in Whitrow's words, is "How
do we get the illusion of time's transience without presupposing transient time as
its origin?"
Zeno’s paradox and the birth of atomic time. Zeno the Eleatic, by devising
paradoxes of motion, tried to prove that all apparent change in the sensible world
is illusory. In one of Zeno's paradoxes, Achilles and a tortoise hold a race in which
the tortoise starts with a lead of 100 units of distance. While Achilles runs the 100
units of distance the tortoise travels one unit, and while Achilles runs this further
unit the tortoise travels 1/100 of a unit, and so on, without limit. Hence, said Zeno,
because of the infinity of subdivisions of distance, Achilles never overtakes the
tortoise, thus demonstrating the illusory nature of change in the sensible world.
Although readers armed with infinitesimal calculus might find this argument
unconvincing, philosophers still debate the significance of Zeno's paradoxes; at
issue is the assumed mathematical continuity of time. Xenocrates, a student of
Plato and his successor as head of the academy in Athens, developed the concept
of atomic time, which has since occasionally figured in solutions of Zeno's
paradox. If time consists of indivisible moments, often referred to as chronons,
motion consists of imperceptible jerks that can, it is said, explain how Achilles
overtakes the tortoise. Also, transition from time atom to time atom might explain
our awareness of transience.
The world is created not once but repeatedly. The twelfth-century The Guide for
the Perplexed by Moses Maimonides, a Jewish scholar, serves as a primary source
of information on the kalam theory of atomic time. Maimonides wrote, "An hour
is divided into sixty minutes, the minute into sixty seconds, the second into sixty
parts, and so on; at last, after ten or more successive divisions by sixty, timeelements are obtained, which are not subjected to division, and in fact are
indivisible".
101
But continual recreation poses a problem. The countless creations are isolated in
atoms of time and have no connection with one another. How then can human
beings arrange them in an orderly sequence? The kalam solution anticipated the
theory of occasionalism). In each atom of time, the sole agent creates not only a
material world, but also a corresponding mental world of remembered events
linking together the time atoms.
Whether physics will ever adopt the characteristics of atomic time, thus making
the observer and transient time an integral part of the physical world, is a matter
for speculation. (Whitrow, 1980)
4. The Model of the time atomicity
In the recent years the growing interest for the source of Universe expansion is
observed. After the work of Supernova detecting groups the consensus for the
acceleration of the moving of the space time is established. expansion of the Universe We will study the influence of the repulsive gravity (G < 0) on the temperature field in the universe and cosmological constant Λ. To that aim we will apply
the quantum equations formulated in (Marciak-Kozlowska, Kozlowski, 2014) In
the monograph it was shown that the quantum diffusion equation for Planck Era
has the form (T= temperature field)
τP
∂ 2T ∂T
ℏ 2
+
=
∇ T.
2
∂t
∂t M p
(1)
In equation (1) τ P = ( ℏcG ) is the relaxation time, M p = ( ℏcG )
1/2
1/ 2
5
is the mass of the
Planck particle, ħ, c are the Planck constant and light velocity respectively and G
is the gravitational constant. Now we will describe the influence of the repulsion
gravity on the quantum thermal processes in the universe. To that aim we put in
equation (1) G → -G. In that case the new equation is obtained, viz.
1/2
3
∂T  ℏ G 
iℏ
= 5 
∂t  c 
1/2
3
∂ 2T  ℏ G 
2
−

 ∇ T.
∂t 2  c 
102
(2)
For the investigation of the structure of equation (2) we put:
1/ 2
3
ℏ2  ℏ G 
=

2m  c 
(3)
and obtains
m=
1
Mp
2
with new form of the equation (2)
1/ 2
3
∂T  ℏ G 
= 5 
iℏ
∂t  c 
∂ 2T ℏ 2 2
−
∇ T.
∂t 2 2 m
(3)
Equation (3) is the quantum Heaviside equation. To clarify the physical nature of
the solution of equation (3) we will discuss the diffusion approximation, i. e. we
omit the second time derivative in equation (3) and obtain
iℏ
∂T
ℏ2 2
=−
∇ T.
2m
∂t
(4)
Equation (4) is the Schrödinger type equation for the temperature field in a universes with G < 0.
Both equation (4) and diffusion equation:
∂T ℏ 2 2
=
∇T
∂t 2 m
(5)
are parabolic and require the same boundary and initial conditions in order to be
“well posed”.
The diffusion equation (4) has the propagator
(
)
TD R, Θ =
1
( 4π DΘ )
3/ 2
 R2 
exp  −
,
 2π ℏΘ 
where
R = r − r ', Θ = t − t '.
103
(6)
For equation (4) the propagator is:
 Mp 
TS R, Θ = 

 2π ℏΘ 
(
)
3/ 2
 iM p R 2 
 3π i 
exp  −
exp 

 4 
 2π ℏΘ 
(7)
with initial condition TS(R, 0) = δ(R)
The anthropic argument In equation (7) TS((R), Θ) is the complex function of R
and Θ. For anthropic observers only the real part of T is detectable, so in our
description of universe we put:
(
)
Im T R, Θ = 0.
(8)
The condition (8) can be written as (bearing in mind formula (7):
 3π  R 2 1 
 = 0,
sin  −
+ 
ɶ
 4  L p  4Θ


(9)
where LP=τPc and Θɶ = Θ / τ p . Formula (9) describes the discretization of R
RN = ( 4 N π + 3π ) L p 
N = 0,1, 2,3...
1/2
( tc )
1/2
,
(10)
In fact from formula (38) the Hubble law can be derived
Rɺ N
1
=H = ,
2τ
RN
(11)
independent of N. In the subsequent we will consider R (10), as the space-time
radius of the N − universe with “atomic unit” of space LP. It is well known that
idea of discrete structure of time can be applied to the “flow” of time. The idea
that time has “atomic” structure or is not infinitely divisible, has only recently
come to the fore as a daring and sophisticated hypothetical concomitant of recent
investigations in the physics elementary particles and astrophysics. We define
time T as
T= M τp, M = 0, 1, 2, …
(12)
104
Considering formulae (9) and (12) the space-time radius can be written as
1/2
R( M , N ) = π M
1/2
1/2
3

N + 
4

L p , M , N = 0,1, 2, 3,....
(13)
Formula (13) describes the discrete structure of space-time. As the R(M, N) is
time dependent, we can calculate the velocity, υ = dR / dt , i.e. the velocity of the
expansion of space-time
 π   N + 34 
υ =  
 c,
4  M 
1/ 2
1/ 2
(14)
where c is the light velocity. We define the acceleration of the expansion of the
space-time
dυ
1  π   N + 34  c
a=
=−   
.
dt
2  4   M 3  τ p
1/ 2
1/ 2
(15)
Considering formula (15), it is quite natural to define Planck acceleration:
1/ 2
 c7 
Ap =
=

τ p  ℏG 
c
= 1051 ms-2
(16)
and formula (43) can be written as
1/ 2
1  π   N + 34   c 7 
a=−   

 .
2  4   M 3   ℏG 
1/ 2
1/2
(17)
It is quite interesting that for N, M→∞ the expansion velocity υ < c in complete
accord with relativistic description. Moreover for N, M >> 1 the υ is relatively
constant υ =0.88 c. From formulae (38) and (42) the Hubble parameter H, and the
age of our Universe can be calculated
υ = HR,
H=
1
= 5 ⋅10−18 s−1 ,
2Mτ p
(18)
T = 2 M τ p = 2 ⋅10 s ~ 10 years,
17
10
which is in quite good agreement with recent measurement. As is well known in
de Sitter universe the cosmological constant Λ is the function of R, radius of the
Universe,
105
Λ=
3
.
R2
(19)
Substituting formula (38) to formula (47) we obtain
Λ=
3
, N = 0,1, 2....
π N 2 L2p
(20)
The result of the calculation of the radius of the Universe, R, the acceleration of
the spacetime, a, and the cosmological constant, Λ are presented in Figs. 1, 2, 3,
4 for different values of number N. As can be easily seen the values of a and R
are in very good agreement with observational data for present Epoch. As far as
it is concerned cosmological constant Λ for the first time we obtain, the history
of cosmological constant from the Beginning to the present Epoch.
5. Riemann`s Zeta (x) function and human consciousness
Riemann`s Zeta function is described by formula
∞
∏ ( s) = ∫
e − s x s dx, ( s > −1)
0
( − s)
ζ ( x) = ∏
2π i
∞
( x ) s dx
∫ ex − 1 x
−∞
In Figs. 1 and 2 we present the shape of the Zeta (x) for different ranges of x
For x=-1 we have the formula
ζ ( −1) = 1 + 2 + 3 + 4 + 5 + .... = −
1
12
According to formula (12) the Universe life time can be written as
T = ζ ( −1)τ P = − 1 τ P
12
(21)
where τ P is Planck time.
106
ZETA RIEMANNA
4
3
Zeta Riemanna
2
1
0
1
2
3
3
2
1
0
1
2
3
4
x
−3 ≤ x ≤ 4
Fig. 1: Riemann`s Zeta(x), for
ZETA RIEMANNA
0.00
Zeta Riemanna
0.05
0.10
0.15
0.20
0.25
5
4
3
2
x
Fig. 2: Riemann`s Zeta(x), for −5 ≤ x ≤ 0
107
1
0
Consequently we obtain for the Radius of the Universe
R = ζ ( −1) LP = − 1 LP
12
(22)
Where LP is Planck radius. From formulae (5) and (6) we conclude that in the Big
End Universe returns to “negative” Planck Epoch.
For T = τ P the Universe was born. According to Hameroff and Penrose
(Hameroff, Penrose, 2013) theory of consciousness at the same time consciousness was born also. From formulae (21) and (22) we conclude that Universe ended
with negative time
T (→ ∞) = −
1
τP
12
At that time in New Universe the “negative consciousness” exists. As it is well
known in e our “positive” Universe the characteristic energy is equal to Planck
Energy= 1019 GeV . What is energy characteristic for “ negative Universe?. From
the above we conclude that for “negative Universe” M p − c 2 = −1019 GeV . Considering Dirac hypothesis for negative energy states :
EDirac = ( pc)2 + ( M Pc2 )2
p = 0, EDirac = ± M Pc2
we argue that “negative Universe consists of negative Planck particles, with negative energies. The “positive” and “negative” Universes are separated by energy
gap= 2 M P c2. Moreover, the negative consciousness is connected to “neurons”
with negative mass = − M P c 2 . (Planck Mass equals the human neuron mass)
The transitions
− M P c 2 → + M P ,c 2Creation, BigBang
happened, we exist.
108
References
Whitrow, G.J. The Natural Philosophy of Time. 2nd ed. Oxford: Clarendon
Press, 1980.
Edwards H. M. Riemann`s Zeta Function, Academic Press New York, USA, 1974
Hameroff, S; Penrose, R. "Consciousness in the universe: A review of the ‘Orch
OR’ theory". Physics of Life Reviews (Elsevier) 11 (1): 39– 78. 2013.
Barrow J., Tipler F., The anthropic cosmological principle, Oxford University
press, 1986.
Marciak-Kozlowska J., Kozlowski M., From infinity to infinity and beyond, Nova
Science Publishers, 2014.
109
CHAPTER VII
Mathematical Model of Tumor Growth and Host
Consciousness
1. Introduction
Since 2002, cancer has become the leading cause of death for Americans between
the ages of 40 and 74 (Jemal, 2005). But the overall effectiveness of cancer therapeutic treatments is only 50%. Understanding the tumor biology and developing
a prognostic tool could therefore have immediate impact on the lives of millions
of people diagnosed with cancer. There is growing recognition that achieving an
integrative understanding of molecules, cells, tissues and organs is the next major
frontier of biomedical science. Because of the inherent complexity of real biological systems, the development and analysis of computational models based directly on experimental data is necessary to achieve this understanding.
Tumor development is very complex and dynamic. Primary malignant tumors
arise from small nodes of cells that have lost, or ceased to respond to, normal
growth regulatory mechanisms, through mutations and/or altered gene expression
(Sutherland, 1988). This genetic instability causes continued malignant alterations, resulting in a biologically complex tumor. However, all tumors start from a
relatively simpler, avascular stage of growth, with nutrient supply by diffusion
from the surrounding tissue. The restricted supply of critical nutrients, such as
oxygen and glucose, results in marked gradients within the cell mass. The tumor
cells respond both through induced alterations in physiology and metabolism, and
through altered gene and protein expression (Marusic, 1994) leading to the secretion of a wide variety of angiogenic factors.
Angiogenesis, formation of new blood vessels from existing blood vessels, is necessary for subsequent tumor expansion. Angiogenic growth factors generated by
tumor cells diffuse into the nearby tissue and bind to specific receptors on the
endothelial cells of nearby pre-existing blood vessels. The endothelial cells become activated; they proliferate and migrate towards the tumor, generating blood
vessel tubes that connect to form blood vessel loops that can circulate blood. With
the new supply system, the tumor will renew growth at a much faster rate. Cells
110
can invade the surrounding tissue and use their new blood supply as highways to
travel to other parts of the body. Members of the vascular endothelial growth factor (VEGF) family are known to have a predominant role in angiogenesis.
Physicists have long been at the forefront of cancer diagnosis and treatment, having pioneered the use of X rays and radiation therapy. In the contemporary initiative, the US National Cancer Institute the conviction that physicists bring unique
conceptual insights that could augment the more traditional approaches to cancer
research is very appealing.
In this paper we present the first attempt to consider the tumor cancer as the physical medium with some sort of memory.
2. Conscious of the cancer cells
Cancer is pervasive among all organisms in which adult cells proliferate. There
is Darwinian explanation of cancer insidiousness which is based on the fact that
all life on Earth was originally single-celled. Each cell had a basic imperative:
replicate, replicate, replicate. However, the emergence of multicellular organisms
about 550 millions years ago required individual cells to co-operate by subordinating their own selfish genetic agenda to that of the organism as a whole. So
when an embryo develops, identical stern cells progressively differentiate into
specialized cells that differ from organ to organ.
If a cell does not respond properly to the regulatory signals of the organism it may
go reproducing in an uncontrolled way, forming a tumor specific to the organ in
which it arises. A key hallmark of cancer is that it can also grow in an organ where
it does not belong: for example a prostate cancer cell may grow in a lymph mode.
This spreading and invasion processes is called “metastasis”. Metastatic cells may
lie dormant for many years in foreign organs evading the body’s immune system
while retaining their potency. Healthy cells, in contrast, soon die if they are transported beyond their rightful organ.
In some respect, the self centered nature of cancer cells is a reversion to an ancient
pre-multicellular lifestyle. Nevertheless cancer cells do co-operate to a certain extent. For example tumors create their own new bloody supply, a phenomenon
called “angiogenesis” by co-opting the body’s normal wound healing functions.
111
Cancer cells are therefore neither rogue “selfish cells”, nor do they display the
collective discipline of organism with fully differentiated organs. They fall somewhere in between perhaps resembling an early form of loosely organized cell colonies. In other words the cancer tumor remember the early state of existence, it
has a memory which have been erased in healthy cells.
The proliferation of the tumor cells is described by the diffusion processes (Jamal,
2005). The standard diffusion equation is based on the Fourier law in which as
we know all memory of the initial state is erased. Simply speaking diffusion equation has not time reversal symmetry, i. e. if the function f(x, t) is the solution of
Fourier equation, f(x, -t) is not.
Let us consider the one-dimensional transport “particles”, e.g. cancer cells.
These cells however may move only to the right or to the left on the rod. Moving cells may interact with the fixed host body cells the probabilities of such
collisions and their expected results being specified. All particles will be of the
same kind, with the same energy and other physical specifications distinguishable only by their direction. In the Appendix the details of the mathematical
model for the tumor growth is presented.
Let us define:
u(z, t) = expected density of cells at z and at time t moving to the right,
v(z, t) = expected density of cells at z and at time t moving to the left.
Furthermore, let
δ (z ) = probability of collision occurring between a fixed scattering cen-
trum and a cell moving between z and z + ∆.
Suppose that a collision might result in the disappearance of the moving cell
without new particle appearing. Such a phenomenon is called absorption. Or
the moving particle may be reversed in direction or back-scattered. We shall
agreeing that in each collision at z an expected total of F(z) cells arises moving
in the direction of the original cell, B(z) arise going in the opposite direction.
112
In the stationary state transport phenomena dF ( z , t ) / dt = dB ( z , t )dt = 0 and
dδ( z , t ) / dt = 0. In that case we denote F ( z , t ) = F ( z ) = B ( z , t ) = B ( z ) = k ( z ) and master
equation for tumor evolution can be written as can be written as
du
= δ ( z )(k − 1)u ( z ) + δ ( z )kv( z ),
dz
dv
−
= δ ( z )k ( z )u ( z ) + δ ( z )(k ( z ) − 1)v( z )
dz
(1)
Formula (1) describes the evolution of the cell aggregation- tumor. The development of the tumor strongly depends on the coefficient k. In the following we
will call k-the growth coefficient. The solutions of the model equation for the
density of cancer cell has the form:
u( z) =
[ f ( 0 )− f ( a ) ]
2qe
1 + βe 2 [ f ( 0 ) − f ( a ) ]
1


(1 − 2k ) 2

 cosh[ f ( x) − f (a )]
1


 (1 − 2k ) 2 − (k − 1) 
k −1
+
sinh[ f ( x) − f (a )],
1
2
(1 − 2k ) − (k − 1)
1


2qe ( f ( 0 )− f ( a ))  (1 − 2k ) 2 + (k − 1)
u(z) =
sinh[ f ( x) − f (a )],
2[ f ( 0 ) − f ( a ) ] 

k
1 + βe


and
ρ( z , t ) = u ( z , t ) + v( z , t )
1
ρ( z ) =
2qe
− (1− 2 k ) 2 aδ
1
1 + βe
− (1− 2 k ) 2 aδ
(2)
1

1
δ


(1 − 2k ) 2

2
cosh
(
2
k
−
1
)
( x − a)

1



 (1 − 2k ) 2 − (k − 1)

1


1
2
−
sinh (2k − 1) ( x − a)δ  .
1



(1 − 2k ) 2 − (k − 1)

(3)
Is the density of the tumor cells. The results of the calculations are presented
in Figs 1, 2.
For k<0.5 the density of the cell oscillate, Fig. 1a, 2a. On the other hand for
k>0.5 the cell density grows exponentially, Fig. 2a, 2b.
113
For k<0.5 the cell aggregation emits the wave with length λ= δ-1= size of the
tumor. For k=0.5 the cancer development has singularity ρ→∞.
The first stage k<0.5 we will call the “hesitation’ period in which tumor send
the “information” waves to the host body. The response of the host depends on
the willing to cooperate with cancer. For k<0.5 the response of the host is negative and tumor is stable. For k>0.5 the angiogenesis starts – the host cooperates with tumor and tumor grows abruptly
It seems that the first “hesitation’ stage is the exchange the information tumor→
host→tumor and vice versa. Next, through the singularity point k=0.5 the cancer obtain the information, go and metastasis process starts.
From the therapeutic point of view the most important result of the paper is the
description of the “information-conscious” waves in the host body.
Fig. 2a Cells density, formula (3) as the function of z and growth factor k, for
k<0.5, a=10 µm, del-1 = λ= size of the tumor. Fig. 2b the same as in Fig 2a but
for k>0.5.
114
Fig. 1a: Cells density, formula (3) as the function of z and growth factor k, for k<0.5, a=1 µm,
del-1 = λ= size of the tumor. Fig. 1b: the same as in Fig 1a but for k>0.5
115
Fig. 2a: Cells density, formula (3) as the function of z and growth factor k, for k<0.5, a=10
µm, del-1 = λ= size of the tumor. Fig. 2b: the same as in Fig 2a but for k>0.5.
116
Appendix
The model equations
Let us define:
u(z, t) = expected density of cells at z and at time t moving to the right,
v(z, t) = expected density of cells at z and at time t moving to the left.
Furthermore, let
δ (z ) = probability of collision occurring between a fixed scattering centre
and a cell moving between z and z + ∆.
Suppose that a collision might result in the disappearance of the moving cell
without new particle appearing. Such a phenomenon is called absorption. Or
the moving particle may be reversed in direction or back-scattered. We shall
agreeing that in each collision at z an expected total of F(z) cells arises moving
in the direction of the original cell, B(z) arise going in the opposite direction.
The expected total number of right-moving cells z1 ≤ z ≤ z 2 at time t is
z2
∫ u( z, t )dz ,
(1)
z1
while the total number of cell passing z to the right in the time interval
t1 ≤ t ≤ t 2 is
t2
w∫ u ( z , t )dt ,
(2)
t1
where w is the particles speed.
Consider the cell moving to the right and passing z + ∆ in the time interval
t1 + ∆w ≤ t ≤ t 2 + ∆w :
t2 + ∆ / w
w
t2
∆

∫ u ( z + ∆, t ' )dt ' = w∫ u z + ∆, t '+ w dt '.
t1 + ∆ / w
t1
117
(3)
These can arise from cells which passed z in the time interval t1 ≤ t ≤ t 2 and came
through ( z, z + ∆ ) without collision
t2
w∫ (1 − ∆δ ( z , t ' ))u ( z , t ' )dt '
(4)
t1
plus contributions from collisions in the interval ( z, z + ∆ ). The right-moving
cells interacting in ( z, z + ∆ ) produce in the time t1 to t2,
t2
w∫ ∆δ ( z , t ' ) F ( z , t ' )u ( z , t ' )dt '
(5)
t1
cells to the right, while the left moving ones give:
t2
w∫ ∆δ( z , t ' ) B( z , t ' )v( z , t ' )dt ' .
(6)
t1
Thus
t2
2
2
∆
⌠ 
w u z + ∆, t '+ dt ' = w∫ u ( z, t ' )dt ' + w∆ ∫ δ ( z, t ' )( F ( z, t ' ) − 1)u ( z, t ' )dt '
w
⌡ 
t1
t1
t
t
t1
(7)
t2
+ w∆ ∫ δ ( z, t ' ) B( z, t ' )v( z, t ' )dt '.
t1
Now, we can write:
∆
1 ∂u

 ∂u

u  z + ∆, t '+  = u ( z , t ' ) +  ( z , t ' ) +
( z , t ' ) ∆
w
w ∂t

 ∂z

(8)
to get
t2
2
⌠  ∂u
 1 ∂u
(
z
,
t
'
)
+
(
z
,
t
'
)
dt
'
=


 ∂z
∫t δ ( z, t ' )(( F ( z, t ' ) − 1)u ( z, t ' ) + B( z, t ' )v( z, t ' ))dt '.
⌡
 w ∂t
1
t
(9)
t1
On letting ∆ → 0 and differentiating with respect to t2 we find
∂u 1 ∂u
+
= δ( z , t )( F ( z, t ) − 1)u ( z , t ) + δ( z , t ) B ( z , t )v ( z , t ).
∂z w ∂t
118
(10)
In a like manner
−
∂v 1 ∂v
+
= δ ( z , t ) B ( z , t )u ( z , t ) + δ ( z , t )( F ( z , t ) − 1)v ( z , t ).
∂z w ∂t
(11)
The system of partial differential equations of hyperbolic type (10-11) is the
Boltzmann equation for one dimensional transport phenomena (Kozlowski,
Marciak-Kozlowska, 2009)
Let us define the total density for cells, ρ( z , t )
ρ( z , t ) = u ( z , t ) + v( z , t )
(12)
and density of cells current
j ( z , t ) = w(u ( z , t ) − v( z , t )).
(13)
Considering equations (10-13) one obtains
∂ρ 1 ∂j
+
= δ( z , t )u ( z , t )( F ( z , t ) − B ( z , t ) − 1) + δ( z, t )v( z , t )( B ( z , t ) − F ( z , t ) + 1). (14)
∂z w2 ∂t
Equation (14) can be written as
∂ρ 1 ∂j δ ( z , t )( F ( z , t ) − B ( z , t ) − 1) j
+
=
∂z w 2 ∂t
w
(15)
or
j=
w
∂ρ
1
∂j
+
.
δ ( z , t )( F ( z , t ) − B( z , t ) − 1) ∂z wδ ( z , t )( F ( z , t ) − B( z , t ) − 1) ∂t
(16)
Denoting, D, diffusion coefficient
D=−
w
δ( z , t )( F ( z , t ) − B( z , t ) − 1)
and τ, relaxation time
τ=
1
wδ ( z , t )(1 − F ( z , t ) − B ( z , t ))
(17)
119
equation (10) takes the form
j = −D
∂ρ
∂j
−τ .
∂t
∂z
(18)
Equation (18) is the Cattaneo’s type equation and is the generalization of the
Fourier equation (Kozlowski, Marciak-Kozlowska, 2009). Now in a like manner we obtain from equation (15 – 18)
1 ∂j 1 ∂ρ
+
= δ ( z , t )u ( z, t )( F ( z , t ) − 1 + B( z, t ))
w ∂z w ∂t
+δ ( z, t )v( z, t )( B( z, t ) + F ( z, t ) − 1))
(19)
∂j ∂ρ
+
= 0.
∂z ∂t
(20)
or
Equation (20) describes the conservation of cells in the transport processes.
Considering equations (19) and (20) for the constant D and τ the hyperbolic
Heaviside equation is obtained:
τ
∂ 2 ρ ∂ρ
∂2 ρ
+
=
D
.
∂t 2 ∂t
∂z 2
(21)
where τ is the relaxation time
In the stationary state transport phenomena dF ( z , t ) / dt = dB ( z , t )dt = 0 and
dδ( z , t ) / dt = 0. In that case we denote F ( z , t ) = F ( z ) = B ( z , t ) = B ( z ) = k ( z ) and equa-
tion (18) and (19) can be written as
du
= δ ( z )(k − 1)u ( z ) + δ ( z )kv( z ),
dz
dv
−
= δ ( z )k ( z )u ( z ) + δ ( z )(k ( z ) − 1)v( z )
dz
(22)
with diffusion coefficient
D=
w
δ (z )
(23)
120
and relaxation time
τ ( z) =
1
.
wδ ( z )(1 − 2k ( z ))
(24)
The system of equations (22) can be written as
d
( δk )
du
d u dz
dδ
δ (k − 1) d (δk ) 

(1 − k ) +
= 0,
−
+ u δ 2 (2k − 1) +
2
dz
δk dz
δk
dz 
dz

(25)
du
= δ ( k − 1)u + δkv( z ).
dz
(26)
2
Equation (26) after differentiation has the form
d 2u
du
+ f (z)
+ g ( z )u ( z ) = 0 ,
2
dz
dz
(27)
1  δ dk dδ 
f ( z) = − 
+ ,
δ  k dz dz 
δ dk
.
g ( z ) = δ 2 ( z )( 2k − 1) −
k dz
(28)
where
For the constant absorption rate we put
k ( z ) = k = constant ≠
1
.
2
In that case
1 dδ
,
δ dz
g ( z ) = δ 2 ( z )( zk − 1).
f ( z) = −
(29)
With functions f(z) and g(z) the general solution of the equation (2. 30) has the
form
u ( z ) = C1e
∫
(1− 2 k )1 / 2 δdz
+ C2e
∫
− (1− 2 k )1 / 2 δdz
.
(30)
In the subsequent we will consider the solution of the equation (28) with f(z)
and g(z) described by (30) for Cauchy condition:
121
u ( 0) = q , v ( a ) = 0 .
(31)
Boundary condition (31) describes the generation of the heat carriers (by illuminating the left end of the strand with laser pulses) with velocity q heat carrier
per second.
The solution has the form:
1


2qe [ f ( 0 )− f ( a ) ] 
(1 − 2k ) 2
 cosh[ f ( x) − f (a )]
u( z) =
1

1 + βe 2 [ f ( 0 ) − f ( a ) ] 
 (1 − 2k ) 2 − (k − 1) 
k −1
+
sinh[ f ( x) − f (a )],
1
(32)
(1 − 2k ) 2 − (k − 1)
u(z) =
( f ( 0 ) − f ( a ))
2qe
1 + βe 2 [ f ( 0 ) − f ( a ) ]
1


2
 (1 − 2k ) + (k − 1) sinh[ f ( x) − f (a )],


k


where
1
f ( z ) = (1 − 2k ) 2 ∫ δdz ,
1
[ ]
[∫ δdz ] ,
f (0) = (1 − 2k ) 2 ∫ δdz ,
0
f (a ) = (1 − 2k )
β=
1
2
(33)
a
1
2
(1 − 2k ) + (k − 1)
1
2
.
(1 − 2k ) − (k − 1)
Considering formulae (12), (13) and (33) we obtain for the density,
ρ( z )
and
current density j(z).
j( z) =
2qwe [ f ( 0)− f ( a ) ]
1 + βe 2 [ f ( 0 ) − f ( a ) ]
1


2
(
1
2
k
)
−

cosh[ f ( z ) − f (a)] 
1


 (1 − 2k ) 2 − (k − 1)



1 − 2k
−
sinh[ f ( z ) − f (a)]
1


2
 (1 − 2k ) − (k − 1)

122
(34)
and
q=
2qe [ f ( 0) − f ( a ) ]
1 + βe 2 [ f ( 0 ) − f ( a ) ]
1


(1 − 2k ) 2

cosh[ f ( z ) − f (a)] 
1


 (1 − 2k ) 2 − (k − 1)
.


1
−

sinh
[
f
(
z
)
−
f
(
a
)
]
1


 (1 − 2k ) 2 − (k − 1)

(35)
Equations (34) and (35) fulfill the generalized Fourier relation
j=−
w ∂ρ
,
δ ( z ) ∂z
D=
W
,
δ( z)
(36)
where D denotes the diffusion coefficient.
Analogously we define the generalized diffusion velocity υD(z)
1


w(1 − 2k ) cosh[ f ( z ) − f (a)] − (1 − 2k ) 2 sinh[ f ( x) − f (a)]
j( z)

.
υD ( z) =
=
1
n( z )
(1 − 2k ) 2 cosh[ f ( x) − f (a)] − sinh[ f ( x) − f (a)]
1
2
(37)
Assuming constant cross section for heat carriers scattering δ ( z ) = δo we obtain
from formula (33)
1
f ( z ) = (1 − 2k ) 2 z ,
f (0) = 0,
(38)
1
f ( a) = (1 − 2k ) 2 a
and for density ρ(z ) and current density j(z)
1
j( z) =
2qwe
− (1− 2 k ) 2 aδ
1
1 + βe
− (1− 2 k ) 2 aδ
1

1


(1 − 2k ) 2

2
cosh
(
2
k
−
1
)
(
x
−
a
)
δ


1



2
 (1 − 2k ) − (k − 1)

1


(1 − 2k )
2
−
sinh (2k − 1) ( x − a)δ  ,
1



(1 − 2k ) 2 − (k − 1)

123
(39)
1
ρ( z ) =
2qe
− (1− 2 k ) 2 aδ
1
1 + βe
− (1− 2 k ) 2 aδ
1

1
δ


(1 − 2k ) 2

2
−
−
cosh
(
2
k
1
)
(
x
a
)


1



2
 (1 − 2k ) − (k − 1)

1


1
2
−
sinh (2k − 1) ( x − a)δ  .
1



(1 − 2k ) 2 − (k − 1)

(40)
Formulae (39) and (40) describe the kinetic of the growth of the cell aggregation-tumor. The development of the tumor strongly depends on the coefficient
k. In the following we will call k-the growth coefficient. For k<0.5 the density
of the cell oscillate, Fig. 1a, 2a. On the other hand for k>0.5 the cell density
grows exponentially, Fig. 2a, 2b.
References
Jemal, A. :The Journal of the American Medical Association, 2005 ; 294 :1255–
1259.
Marusic, M., Bajzer Z, Freyer J. P., and Vuk-Pavlovic S: Analysis of growth of
multicellular tumour spheroid by mathematical models. Cell Prolif. 1994;
27;73-78.
Kozlowski M. Marciak-Kozlowska J., From femto- to attoscience and beyond,
NOVA, USA, 2009.
Sloan Erica, K., et. al., Cancer Res, 2010; 70 (18) 7042-7052.
Sutherland, R. M. Cell and environment interactions in tumor microregions: the
multicell spheroid model. Science, 1988; 240 :177– 184.
124
CHAPTER VIII
EVOLVING CONSCIOUSNESS
In the seminal paper [1] F. Calogero described the cosmic origin of quantization. In paper [4] the tremor of the cosmic particles is the origin of the quantization and the characteristic acceleration of these particles a ≈ 10 m/s2 was
calculated. In our earlier paper [5] the same value of the acceleration was obtained and compared to the experimental value of the measured space-time acceleration [6]. In this paper we define the cosmic force – Planck force, FPlanck
= MP aPlanck (aPlanck ≈ a) and study the history of Planck force as the function of
the age of the Universe.
Masses introduce a curvature in space-time, light and matter are forced to move
according to space-time metric. Since all the matter is in motion, the geometry
of space is constantly changing. A Einstein relates the curvature of space to the
mass/energy density:
G=kT,
(1)
G is the Einstein curvature tensor and T the stress-energy tensor. The proportionality factor k follows by comparison with Newton’s theory of gravity: k =
G/ c4 where G is the Newton’s gravity constant and c is the vacuum velocity of
light; it amounts to about 2.10-43 N-1 expressing the rigidity of space-time.
In paper [5] the model for the acceleration of space-time was developed. Prescribing the -G for space-time and +G for matter the acceleration of space-time
was obtained:
1  π  2 ( N + 34 )2
=−  
AP ,
3
24
M2
1
a Planck
1
(2)
where AP, Planck acceleration equal, viz. ;
1
 c7  2
c
 =
≅ 1051 ms-2.
AP = 
τP
 ℏG 
125
(3)
As was shown in paper [5] the a Planck for N = M = 1060 is of the order of the
acceleration detected by Pioneer spacecrafts [6].
Considering AP it is quite natural to define the Planck force FPlanck
FPlanck = M P AP =
c4
= k −1 ,
G
(4)
where
1
 ℏc  2
MP =   .
G
From formula (4) we conclude that (FPlanck ) = rigidity of the space-time. The
−1
Planck force, FPlanck = c4/G = 1.2·1044 N can be written in units which characterize the microspace-time, i.e. GeV and fm. In that units
k-1 = FPlanck = 7. 6·1038 GeV/fm.
As was shown in paper [5] the present value of Planck force equal
1
Now
Planck
F
1  π 2
c4
GeV
( N = m = 10 ) ≅ −   10 −60
= −10−22
.
24
G
fm
60
(5)
In papers [7, 8] the Planck time τP was defined as the relaxation time for spacetime
τP =
ℏ
M Pc2
(6)
.
Considering formulae (5) and (6) FPlanck can be written as
FPlanck =
M Pc
,
τP
(7)
where c is the velocity for gravitation propagation. In papers [7, 8] the velocities and relaxation times for thermal energy propagation in atomic and nuclear
matter were calculated:
126
υatomic = αem c,
(8)
υnuclear = α s c,
where αem = e 2 /(ℏc) = 1 / 137, α s = 0.15 . In the subsequent we define atomic and nuclear accelerations:
aatomic =
αem c
,
τ atomic
anuclear =
αs c
τ nuclear
(9)
.
2
Considering that τ atomic = ℏ (me αem
c 2 ), τ nuclear = ℏ (m N α s2 c 2 ) one obtains from formula
(9)
3
me c 3αem
,
ℏ
m c 3α 3
= N s.
ℏ
aatomic =
anuclear
(10)
We define, analogously to Planck force the new forces: FBohr, FYukawa
FBohr = me aatomic =
FYukawa = mN anuclear
(m c )
2 2
3
αem
= 5 ⋅ 10 −13
e
ℏc
(m c )
=
2 2
N
ℏc
GeV
,
fm
α s3 = 1.6 ⋅ 10 −2
(11)
GeV
.
fm
Comparing formulae (7) and (11) we conclude that gradients of Bohr and YuNow
kawa forces are much large than FPlanck
, i.e. :
FBohr
5 ⋅ 10 −13
=
≅ 10 9 ,
Now
− 22
FPlanck
10
(12)
FYukawa 10 −2
= −22 ≅ 10 20.
Now
FPlanck 10
The formulae (12) guarantees present day stability of matter on the nuclear and
atomic levels.
As the time dependence of FBohr and FYukawa are not well established, in the subsequent we will assumed that αs and αem [9] do not dependent on time. Considering formulae (11) and (12) we obtain
127
(
)
2
FYukawa
1 mN c 2 αs3
=
T,
1
FPlanck  π  2 M P c 2 ℏ
 
4
(
(13)
)
2
3
FBohr
1 me c 2 αem
=
T.
1
FPlanck  π  2 M P c 2 ℏ
 
4
(14)
As can be realized from formulae (13), (14) in the past FPlanck ≈ FYukawa (for T
= 0.002 s) and FPlanck ≈ FBohr (for T ≈ 10 s), T = age of universe. The calculated
ages define the limits for instability of the nuclei and atoms.
In 1900 M. Planck [10] introduced the notion of the universal mass, later on
called the Planck mass
1
 ℏc  2
MP =   .
G
(15)
Considering the definition of the Yukawa force (11)
FYukawa =
mN υN mN α strong c
=
,
τN
τN
(16)
the formula (16) can be written as:
FYukawa =
mYukawa c
,
τN
(17)
where
mYukawa = m N α strong ≅ 147
MeV
~ mπ .
c2
(18)
From the definition of the Yukawa force we deduced the mass of the particle
which mediates the strong interaction – pion mass postulated by Yukawa in
[11].
128
Accordingly for Bohr force:
FBohr =
mυ
τ Bohr
=
me αem c mBohr c
=
,
τ Bohr
τ Bohr
mBohr = me αem = 3.7
keV
.
c2
(19)
(20)
For the Bohr particle the range of interaction is
γ Bohr =
ℏ
mBohr c
≈ 0.1 nm,
(21)
which is of the order of atomic radius.
Considering the electromagnetic origin of the mass of the Bohr particle, the
planned sources of hard electromagnetic field LASETRON [1] are best suited
to the investigation of the properties of the Bohr particles.
In an important work, published already in 1951 J. Schwinger [12] demonstrated that in the background of a static uniform electric field, the QED spacetime is unstable and decayed with spontaneous emission of e+ e- pairs. In the
paper [12] Schwinger calculated the critical field strengths ES:
me2 c 3
ES =
.
eℏ
(22)
Considering formula (22) we define the Schwinger force:
e
FSchwinger
= eE S =
me2 c 3
.
ℏ
(23)
Formula (23) can be written as:
e
FSchwinger
=
me c
,
τ Sch
(24)
where
τ Sch =
ℏ
me c 2
(25)
129
is Schwinger relaxation time for the creation of e+ e- pair. Considering formulae
(23) the relation of FYukawa and FBohr to the Schwinger force can be established
m
= α  N
 me
2
 e
 FSchwinger , α s = 0.15,
FYukawa

1
3
e
FBohr = αem
FSchwinger
, αem =
,
137
3
s
(26)
and for Planck force
2
FPlanck
M  e
=  P  FSchwinger
.
 me 
(27)
e
, FPlanck, FYukawa and FBohr are presented, all
In Table 5.2 the values of the FSchwinger
in the same units GeV/fm. As in those units the forces span the range 10-13 to
1038 it is valuable to recalculate the Yukawa and Bohr forces in the units natural
to nuclear and atomic level. In that case one obtains:
FYukawa = 16
MeV
.
fm
(28)
It is quite interesting that αv ≈ 16 MeV is the volume part of the binding energy
of the nuclei (droplet model).
Table 5.2: Schwinger, Planck, Yukawa and Bohr forces [GeV/fm]
e
FSchwinger
≈ 10-6
FPlanck
FYukawa
FBohr
≈ 1038
≈ 10-2
≈ 10-13
For the Bohr force considering formula (5.23) one obtains:
FBohr =
50 eV
.
0.1 nm
(29)
Considering that the Rydberg energy ≈ 27 eV and Bohr radius ≈ 0.1 nm formula
(29) can be written as
FBohr =
Rydberg energy
.
Bohr radius
(30)
130
References
[1]
Calogero. F, Phys. Letters, A228, (1997) p. 335.
[2]
Kozlowski M., Marciak-Kozlowska J., Nuovo Cimento, vol, 116B,
(2001) p. 821.
[3]
Anderson J. D. et al., Phys. Rev. Lett. , 81 (1998) p. 2858.
[4]
Marciak-Kozlowska J., Kozlowski M., Foundations of Physics Letters,
vol. 9, (1996) p. 235.
[5]
Kozlowski M., Marciak-Kozlowska J., Foundations of Physics Letters,
vol. 10, (1997) p. 295.
[6]
Kozlowski M., Marciak-Kozlowska J., arXiv/astro-ph/0307 168.
[7]
Planck M. The theory of heat radiation, Dover Publications 1959, p. 173.
[8]
Yukawa H, Proc. Phys. -Math. Soc. Japan, 17, (1935) p. 48.
[9]
Schwinger J., Phys. Rev., 82 (1951) p. 664.
131
Chapter IX
ON THE POSSIBLE NEW BRAIN WAVES ω = 100MHz
AND MICROTUBULE QUANTUM OSCILLATIONS
Introduction
Review and update of a 120-year-old theory of consciousness published in Physics of Life Reviews claims that consciousness derives from deeper level, finer scale
activities inside brain neurons. The recent discovery of quantum vibrations in
"microtubules" inside brain neurons corroborates this theory, according to review
authors Stuart Hameroff and Sir Roger Penrose. They suggest that EEG rhythms
(brain waves) also derive from deeper level microtubule vibrations, and that from
a practical standpoint, treating brain microtubule vibrations could benefit a host
of mental, neurological, and cognitive conditions.
The theory, called "orchestrated objective reduction" ('Orch OR'), was first put
forward in the mid-1990s by eminent mathematical physicist Sir Roger Penrose,
FRS, Mathematical Institute and Wadham College, University of Oxford, and
prominent anesthesiologist Stuart Hameroff, MD, Anesthesiology, Psychology
and Center for Consciousness Studies, The University of Arizona, Tucson. They
suggested that quantum vibrational computations in microtubules were "orchestrated" ("Orch") by synaptic inputs and memory stored in microtubules, and terminated by Penrose "objective reduction" ('OR'), hence "Orch OR". Microtubules
are major components of the cell structural skeleton.
Orch OR was criticized from its inception, as the brain was considered too "warm,
wet, and noisy" for seemingly delicate quantum processes. However, evidence
has now shown warm quantum coherence in plant photosynthesis, bird brain navigation, our sense of smell, and brain microtubules. The recent discovery of warm
temperature quantum vibrations in microtubules inside brain neurons by the research group led by Anirban Bandyopadhyay, PhD, at the National Institute of
Material Sciences in Tsukuba, Japan (and now at MIT), corroborates the pair's
theory and suggests that EEG rhythms also derive from deeper level microtubule
vibrations. In addition, work from the laboratory of Roderick G. Eckenhoff, MD,
at the University of Pennsylvania, suggests that anesthesia, which selectively
132
erases consciousness while sparing non-conscious brain activities, acts via microtubules in brain neurons.
"The origin of consciousness reflects our place in the universe, the nature of our
existence. Did consciousness evolve from complex computations among brain
neurons, as most scientists assert? Or has consciousness, in some sense, been here
all along, as spiritual approaches maintain?" ask Hameroff and Penrose in the
current review. "This opens a potential Pandora's Box, but our theory accommodates both these views, suggesting consciousness derives from quantum vibrations in microtubules, protein polymers inside brain neurons, which both govern
neuronal and synaptic function, and connect brain processes to self-organizing
processes in the fine scale, 'proto-conscious' quantum structure of reality".
After 20 years, "the evidence now clearly supports Orch OR", continue Hameroff
and Penrose. "Our new paper updates the evidence, clarifies Orch OR quantum
bits, or "qubits", as helical pathways in microtubule lattices, rebuts critics, and
reviews 20 testable predictions of Orch OR published in 1998 – of these, six are
confirmed and none refuted".
An important new facet of the theory is introduced. Microtubule quantum vibrations (e.g. in megahertz) appear to interfere and produce much slower EEG "beat
frequencies". Despite a century of clinical use, the underlying origins of EEG
rhythms have remained a mystery. Clinical trials of brief brain stimulation aimed
at microtubule resonances with megahertz mechanical vibrations using transcranial ultrasound have shown reported improvements in mood, and may prove useful against Alzheimer's disease and brain injury in the future.
Lead author Stuart Hameroff concludes, "Orch OR is the most rigorous, comprehensive and successfully-tested theory of consciousness ever put forth. From a
practical standpoint, treating brain microtubule vibrations could benefit a host of
mental, neurological, and cognitive conditions".
"Consciousness depends on nonharmonic vibrations of microtubules inside neurons, similar to certain kinds of Indian music, but unlike Western music which is
harmonic", Hameroff explains.
133
2. Consciousness and Quantum Theory
The issue of observation in QM is central, in the sense that objective reality cannot
be disentangled from the act of observation, as the Copenhagen Interpretation (CI)
nearly states. In the words of John A. Wheeler 1981, we live in an observer-participatory Universe. The vast majority of today's practicing physicists follow CI's
practical prescriptions for quantum phenomena, while still clinging to classical
beliefs in observer-independent local, external reality). There is a critical gap between practice and underlying theory. In his Nobel Prize speech of 1932, Werner
Heisenberg concluded that the atom "has no immediate and direct physical properties at all". If the universe's basic building block isn't physical, then the same
must hold true in some way for the whole. The universe was doing a vanishing
act in Heisenberg's day, and it certainly hasn't become more solid since. (R.
Schild, 2012)
This discrepancy between practice and theory must be confronted, because the
consequences for the nature of reality are far-reaching An impressive body of
evidence has been building to suggest that reality is non-local and undivided.
Non-locality is already a basic fact of nature, first implied by the Einstein-Podolsky-Rosen thought experiment despite the original intent to refute it, and later
explicitly formulated in Bell's Theorem
Moreover, this is a reality where the mindful acts of observation play a crucial
role at every level. Heisenberg again: "The atoms or elementary particles themselves... form a world of potentialities or possibilities rather than one of things or
facts". He was led to a radical conclusion that underlies our own view in this
paper: "What we observe is not nature itself, but nature exposed to our method of
questioning." Reality, it seems, shifts according to the observer's conscious intent.
There is no doubt that the original CI was subjective (R. Schild, 2012)
Quantum theory is not about the nature of reality, even though quantum physicists
act as if that is the case. To escape philosophical complications, the original CI
was pragmatic: it concerned itself with the epistemology of quantum world (how
we experience quantum phenomena), leaving aside ontological questions about
the ultimate nature of reality. The practical bent of CI should be kept in mind,
particularly as there is a tendency on the part of many good physicists to slip back
134
into issues that cannot be tested and therefore run counter to the basic tenets of
scientific methodology.
3. Model
In order to put forward the classical theory of the brain waves we quantize the
brain wave field. In the model (Marciak-Kozlowska, Kozlowski, 2013) we assume (i) the brain is the thermal source in local equilibrium with temperature T.
(ii) The spectrum of the brain waves is quantized according to formula
E = ℏω
(1)
where E is the photon energy in eV, ℏ =Planck constant, ω = 2πν ,ν -is the frequency in Hz. (iii). The number of photons emitted by brain is proportional to the
(amplitude)2 as for classical waves. The energies of the photons are the maximum
values of energies of waves For the emission of black body brain waves we propose the well know formula for the black body radiation.
In thermodynamics we consider Planck type formula for probability P (E) dE for
the emission of the particle (photons as well as particles with m≠0) with energy
(E, E+dE) by the source with temperature T is equal to:
P(E)dE= BE2 e (-E/kT) dE
(2)
where B= normalization constant, E=total energy of the particle, k = Boltzmann
constant=1.3 × 10-23 J K-1. K is for Kelvin degree. However in many applications
in nuclear and elementary particles physics kT is recalculated in units of energy.
To that aim we note that for 1K, kT is equal k1K = K x 1.3 × 10-23 J x K-1= 1.3 ×
10-23 Joule or kT for 1K is equivalent to 1.3 × 10-23 Joule= 1.3 × 10-23/(1.6 10-19)
eV = 0.8 × 10-4 eV. Eventually we obtain 1K= 0.8 × 10-4 eV, and 1eV= 1.2 × 104
K
( − Emax )
dN
2
= BEmax
e T
dE
(2)
where, B is the normalization constant, T is the temperature of the brain thermal
source in eV. The function
dN
describes the energy spectrum of the emitted
dE
brain photons.
135
Until 2014 no one has find the experimental evidence of the cold source of the
brain photons. But recently the new sort of neutrino with the mass of the order 7
keV was experimentally evidenced. The neutrino ν decays according to the
scheme:
ν → 2γ
(3)
where γ denotes x ray photons with energy 3.5 keV. In the paper (Marciak-Kozlowska, Kozlowski, 2013) the comparison of the photon spectra of CBM and the
spectra of brain electromagnetic emission was performed. It occurs that both spectra can be described with formula (2), but with different temperatures. The ratio
of the temperatures is
Tbrain
= 10−10
TCBM
(4)
Following formula (4) we argue that in brain spectra the photons with energy of
the order of
10−10 i3.7103 eV = 3.710−7 eV = 3.710−3 K
(5)
can be observed
In Fig. 1, we present the result of the comparison of the calculated, formula (2),
temperatuta T= 0.8 × 10-14 eV= 0.8 ×10−10 K , and observed spectra of the brain
waves. The calculated spectra are normalized to the maximum of the measured
spectra.
The obtained temperature is the temperature for the brain source in the thermal
equilibrium. The source is thermally isolated (adiabatic well). It must be stressed
that in the paper we abandon the idea that every physical object is either a wave
or a particle. Neither it is possible to say that particles “become” waves in the
quantum domain and conversely that waves are “transformed “into particles. It is
therefore necessary to acknowledge that we have here a different kind of an entity,
one that is specifically quantum. For this reason Levy-Leblond and Balibar developed the name quanton, (Levy-Leblond, Balibar, 1990). Following that idea
the human brain emits quantons with energies E = ℏω . The brain quantons are the
quantum objects that follows all quantum laws: tunneling, the superposition and
Heisenberg uncertainty rule.
136
In Fig. 2 we present the theoretical spectrum of the brain waves with for temperature T = 10−3 K we will call them ψ waves.
Fig. 1: Comparison of experimental and theoretical results for brain vibration
Fig. 2: The model calculation of the ψ wave energy spectrum
137
Beginning in 2009, Anirban Bandyopadhyay and colleagues at the National
Institute of Material Sciences in Tsukuba, Japan, were able to use
nanotechnology to address electronic and optical properties of individual micro
tubules[Anirban Bandyopadhyay, 2013]. The group has made a series of
remarkable discoveries suggesting that quantum effects do occur in microtubules
at biological temperatures. First, they found that electronic conductance along
microtubules, normally extremely good insulators, becomes exceedingly high,
approaching quantum conductance, at certain specific reso- nance frequencies of
applied alternating current (AC) stimulation. These resonances occur in
gigahertz, megahertz and kilohertz ranges, and are particularly prominent in low
megahertz (e.g. 8.9 MHz). Conductances induced by specific (e.g. megahertz) AC
frequencies appear to follow several types of pathways through the microtubule
– helical, linear along the microtubule axis, and ‘blanket-like’ along/around the
entire microtubule surface. Second, using various techniques, the Bandyopadhyay
group also determined AC conductance through 25-nm-wide microtubules is
greater than through single 4-nm-wide tubulins, indicating cooperative, possibly
quantum coherent effects throughout the microtubule, and that the electronic
properties of microtubules are programmed within each tubulin. Their results also
showed that conductance increased with microtubule length, indicative of
quantum mechanisms.
The resonance conductance (‘Bandyopadhyay coherence’ – ‘BC’) through
tubulins and microtubules is consistent with the intra-tubulin aromatic ring
pathways) which can support Orch OR quantum dipoles, and in which anesthetics
bind, apparently to selectively erase consciousness. Bandyopadhyay’s
experiments do seem to provide clear evidence for coherent microtubule quantum
states at brain temperature.
In our model the new ψ wane have the frequency ω =100 MHz in rather good
agreement with Bandyopadhyay measurement. In light of the above it seems
reasonable to argue that the ψ vibration postulated in this paper is the candidate
for the resonances observed in Bandyopadhyay’s experiments
In Table 1 the calculated energy, and wave length according to formulae
E[eV ] = 10 −15 ω[ Hz ] λ [m ] =
10−7
E [ eV ]
138
(6)
TABLE 1: The full spectrum of the brain vibrations with new ψ wave included
WAVE
MAXIMUM
FREQUENCY[Hz]
ENERGY
Wave length [m]
∼ 108
δ
3. 9
[ ×10 eV]
∼ 3. 9
θ
7. 9
∼ 7. 9
∼ 108
α
13. 9
∼ 13. 9
∼ 108
β
ψ
30
∼ 30
108
8
∼ 10
∼ 108
∼1
15
Conclusions
It is obvious that consciousness is not located in space. According to special relativity theory all physically observed phenomena are located in 4 D space-time.
In conclusion the conscious not exist in time also. Consciousness is timeless. The
brain photons are the effect of the interaction of the timeless consciousness with
human brain. The final result of this interaction are the: alpha, beta, delta and
theta and new ψ waves. In the paper we calculated the energy of the new ψ wave
Eψ = 10 −7 eV ,
ω = 100MHz
References
Kevork N. Abazaijan, 2014 Resonantly produced 7 keV sterile nutrino dark matter and the properties of Milky Way Satelites, Phys. Rev. Lett. 112, 161303,
2014.
Stuart Hameroff and Roger Penrose, 2013. Consciousness in the universe: A review of the ‘Orch OR’ theory. Physics of Life Reviews, 2013.
Schild R., 2012. Cosmology of Consciousness, Quantum Physics & Neuroscience
of Mind, Cosmology Science Publishers, Cambridge, 2012.
Sahu S., Ghosh S., Hirata K., Fujita D., Bandyopadhyay, 2013. A Multi-level
memory-switching properties of a single brain microtubule. Appl Phys Lett
2013;102:123701.
Marciak-Kozlowska J., Kozlowski M., 2013, On the Brain and Cosmic Background Photons, Neuroquantology vol 11, 223, 2013
139
Epilogue: Mathematics, Physics, Plants and Fibonacci
Series
Number rules the Universe
Pythagoreans (ca. 530-510 B. C)
Introduction
In the preface to the first (German) Edition of the book “Collected Papers on the
Quantum Mechanics”, Zurich 1926 [1] E. Schrodinger wrote: a young lady friend
recently remarked to the Author (Schrodinger) “When you began this work you
have no idea that anything so clever would come out of it, had you”.
This unorthodox comparison between scientific and purely aesthetic
communication is able to provide a first clue towards criteria distinguishing good
fantasy in science from bad. Science as a crowning intellectual achievement is
essentially disciplined; but it is not always easy to realize the need for an equally
severe discipline in the domain of the imaginative arts. Imagination and intellect,
however, are not always in antithesis to one another. Reason
implies not only a capacity for logical sequence of argument, but also a sensitivity
to balance and contrast a trained intuition without untrained intuition s arrogant
claims to short-circuit the discipline of the intellect When the imagination thus
becomes disciplined, and undertakes the severest obligations inherent in
perfecting the pattern of an art-form, it has taken the essential step towards
security against the weaknesses of fantasy. Structure as disciplined as that of a
mathematical argument is capable of transfiguring the merest nonsense into
divine nonsense.
Modern physics might well be regarded as study of the structure of matter and of
the behavior of radiation. A criterion for success pursuit of the former study
demands that analysis of material structures into atoms and molecules, and of
these into nuclei with groups of associated electrons, must be capable of giving
rise to verifiable prediction of the bulk properties of matter, mechanical, thermal,
chemical, and electrical. Criteria for theories as to the behaviour of radiation are
that the phenomena of light, colour, radio, X-rays, heat radiation, must become
140
explainable by some single mechanism; the only mechanism so far successful has
been the propagation of electric and magnetic quantities with a unique and
universal speed which is accurately measurable. This speed exceeds that of the
fastest material particles, as a limit towards which the latter can only approach.
Within the scope of these two most general schemes, the structure of matter has
been a prime example of pattern since D. Mendeleyev in XIX century arranged
all the then known chemical species or elements into a two-dimensional
framework. Written down in a table of horizontal rows and vertical columns, the
chemical elements were found to repeat certain properties periodically, much as
the harmonic properties of the notes on a piano keyboard repeat themselves at
intervals of octaves. To form the gross substances which we distinguish by touch,
smell, taste, etc., the affinities for chemical combining of atomic species are found
to wax and wane with precise regularity throughout the periods of this table. The
whole assemblage of empirically periodic patterns is now understood as
manifesting the way in which successive electrons can become associated with
atomic nuclei of definite mass: these additions proceed until one after another
their possible federations into electrically and mechanically stable groups or subpatterns are.
There have been eras in which an educated man could only live up to his standard
if he were at the same time a poet and a philosopher and an experimental or
mathematical researcher. E. Schrodinger is a good example. He attended a
gymnasium, which emphasized the study of Greek and Latin classics. His book
Nature and the Greeks published in 1948 is an elegant exposition of ancient
physical theories and their relevance. Schrodinger wrote in 1925 an intensely
account of his beliefs, Seek for the Road. The book was influenced by Hinduism
and is an argument for the essential oneness of human consciousness.
1. The beautiful mathematics / physics
During my work as a lecturer in Physics Department [2], Warsaw University I
like very much the Kepler – Copernicus (Kopernik in Polish) – Newton panorama
of the planet moving. I started as usual with historical facts and write the basic
equations. Considering the FQXI community I left of all steps and start from the
equation :
141
d 2u
m 1 1
+ u = − 2 2 F  ,
2
dΘ
L u u
1
u= .
r
(1)
Equation 1 is the master equation which describes the movement of the body with
mass m in the field of central forces F(1/u). We can imagine the following
functions F(1/u)
1
F   = K1u π ,
u
K 2u 3 ,
K 3u 2 , K 4 u 0.64 ,
K 5u −4.62 .
(2)
We can imagine the “other” universes for which the central forces have the
different F(1/u). But can life be originated and developed in all these universes?
This question is answered by the anthropic principle and will be discussed later
on. For the moment we can say the following:macroscopic structure of the
Universe we live in can be understood with just two forces: Newton and Coulomb.
For both forces
1
F   = Ku 2 .
u
(3)
Why?
With the forces described by formula (3) we obtain for equation (1)
d 2u
Km
+u = − 2 .
2
dΘ
L
(4)
with constant on the right hand side of the equation- only for quadratic in u forces
Only for that force! Can you imagine ! This is miracle, is not ?
This beautiful equation describes the classical motion of the planets, and electrons
round the source of the force F = Ku2. Moreover, the equation (4) in fact is the
harmonic oscillator equation, which can be solved at once The solution to the eq.
(4) can be written as
142
u = A cos(Θ − Θ 0 ) −
mK
,
L2
(5)
or
1
r=
mK
A cos(Θ − Θ 0 ) − 2
L
.
(6)
Equation (6) describes the conic curves: ellipse, parabola and hyperbola
depending on constants A, Θ0, m, K and L. We can choose our coordinate axes so
that Θ0= 0 to simplify things just a little:
r=
1
mK
A cos Θ − 2
L
.
(7)
This is a conic sections. From plane geometry, any conic section can be written
as
r = r0
1+ e
,
1 + e cos Θ
(8)
where e is called the eccentricity of the orbit.
Other dimensions
In any higher organism, a large number of cells must be inter-counted by nerve
fibers. If space had only two dimensions, an organ-ism could be only a twodimensional configuration and its nerve paths would cross. At the intersections,
the nerves would have to penetrate each other, for absence of a third dimension
would not permit a fiber to be led above or below another one. As a consequence
nerve impulses would mutually interfere. The existence of a highly developed
organism having many non-intersecting nerve paths in thus possible only in a
space having at least three dimensions.
As we know both the Newtonian gravitational force and electrostatic force can be
described in the three dimensional space (formula (9))
F=
K
,
r2
n = 3,
(9)
143
where n is the number of dimension of space. For n ≠ 3 the natural generalization
of formula (1.180) is
F = (n − 2 )
K
r n −1
,
n ≠ 2.
(10)
The impossibility of stable planet orbit for n > 3 can be seen in an elementary
way. Let m be the mass of planet and L angular momentum (which is constant for
the central force (1.181))
ɺ = const.
L = mr 2 Θ
(11)
The gravitation potential for the conservative force will be
V =−
K
r n −2
.
(12)
At the extreme distances from the central body for a planet with mass m, we have
dr
= 0.
dt
(13)
The kinetic energy T at such points is then
T=
p2 1 2 ɺ 2
= mr Θ ,
2m 2
(14)
which by equation (15) becomes
T=
L2
.
2mr 2
(16)
By conservation of mechanical energy T + V = constant, or
L2
K
L2
K
−
=
− n−2 ,
2
n−2
2
2mr1
r1
2mr2 r2
(17)
where r1 is the minimum distance from the central body and r2 is the maximum
distance, perihelion and aphelion respectively.
144
The equation (17) shows that for n = 4 there can be a finite, positive solution only
if r2 > r1 For n > 4 it can be shown that an orbit in which r oscillates between two
extremes is likewise ruled out.
In general the centripetal force in a circular orbit is
ɺ 2.
Fc = mr 2 Θ
(18)
Using Eq. (1. 182) this becomes
Fc =
L2
.
mr 3
(19)
In the actual eccentric orbit, the attractive force must be less than this centripetal
force at perihelion, for then the planet is about to move outward. At aphelion, it
is just the other way around.
These conditions can be expressed respectively by the following inequalities
F < Fc
( n − 2) K
L2
<
r1n −1
mr13
or
K
r1n − 2
<
L2
,
(n − 2)mr12
(20) and (21)
L2
.
(n − 2)mr22
(22)
F > Fc
L2
( n − 2) K
>
r2n −1
mr23
or
K
r2n − 2
>
L2
L2
L2
L2
.
−
<
−
2mr12 (n − 2)mr12 2mr22 (n − 2)mr22
(23)
L2  1
L2  1

−1 
(
n
2
)
−
−
<
− (n − 2) −1 .


2
2 
mr1  2
 2mr2  2

(24)
and
This relation obviously cannot be true for n = 4, for then each of the brackets
becomes zero. Remembering that r2 > r1 it also cannot be true for any n > 4, which
makes the values of the brackets less than ½.
145
In conclusion, it may be said that stable elliptical planetary orbits can exist and
support the existence of the highly developed organisms only in three dimensional
space. The second miracle!
The Fibonacci series
The beautiful arrangement of leaves in some plants, called phyllotaxis, obeys a
number of subtle mathematical relationships. For instance, the florets in the head
of a sunflower form two oppositely directed spirals: 55 of them clockwise and 34
counterclockwise. Surprisingly, these numbers are consecutive Fibonacci
numbers. The ratios of alternate Fibonacci numbers are given by the convergents
to , where is the golden ratio, and are said to measure the fraction of a turn
between successive leaves on the stalk of a plant: 1/2 for elm and linden, 1/3 for
beech and hazel, 2/5 for oak and apple, 3/8 for poplar and rose, 5/13 for willow
and almond, etc. A similar phenomenon occurs for daisies, pineapples, pinecones,
cauliflowers, and so on. Lilies, irises, and the trillium have three petals;
columbines, buttercups, larkspur, and wild rose have five petals; delphiniums,
bloodroot, and cosmos have eight petals; corn marigolds have 13 petals; asters
have 21 petals; and daisies have 34, 55, or 89 petals – all Fibonacci numbers.
We have the series of numbers:
• 2 - Gravity and electromagnetic fields,
• 3 - Structure of the Universe, the next must be 5- I suspect!
•
5 - This is the dimension of space time in which gravity and electromagnetic can be unified (Kaluza-Klein scenario). Enough is enough! But wait
!What means 8?
•
8 - N = 8 Supergravity in 4 Dimensions
More generally the term may refer to an eight-dimensional vector space over any
field, such as an eight-dimensional complex vector space, which has 16 real
dimensions. It may also refer to an eight-dimensional manifold such as an 8sphere, or a variety of other geometric constructions. N=8 Supergravity is the
most symmetric quantum field theory which involves gravity and a finite number
of fields. It can be found from a dimensional reduction of 11D supergravity by
making the size of 7 of the dimensions go to zero. It has 8 supersymmetries which
146
is the most any gravitational theory can have since there are 8 half-steps between
spin 2 and spin -2. (A graviton has the highest spin in this theory which is a spin
2 particle). More supersymmetries would mean the particles would have
superpartners with spins higher than 2. The only theories with spins higher than
2 which are consistent involve an infinite number of particles. In botany the
phenomenon of phylotaxis is well known: The leafs are placed according to rules
of Fibonacci series! Does the flowers knows the mathematics? Certainly no !They
do not attend maths or physics classroom. Now we have real problem, who
teaches plants and what about the unreasonable effectiveness of mathematics in
physics, botany, medicine … Take a radical step. There are not medicine, botany,
mathematics, physics. as the separated part of SCIENCE. The Universe has only
four pillars with N= 2, 3, 5, 8 respectively, which can be seen may be at the Level
IV [3]. It is worth to add that the ancient Egyptians depicted a cosmos with a
heavenly roof “ supported by 4 women at the cardinal points”[4].
References
[1] Erwin Schrodinger Collected papers on Wave Mechanics, AMS Chelsea
Publishing, USA, 1982.
[2] M. Kozlowski, PHYSICS. Lecture Notes Science Teacher College, I-Proclaim
Press USA, 2012.
[3] Max Tegmark, Our Mathematical Universe: My Quest for the Ultimate Nature
of Reality, A Knopf, 2014 USA.
[4] E.T. Bell, Numerology, vol. 3 Hyperion Press, USA, 1933.
[5] M. Kozlowski, 2015 http://fqxi. org/community/forum/topic/2321.
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