THE
INSULIN PROJECT
Aiming to solve the dynamic structure of insulin.
I don’t have diabetes. But I know someone who does. To help, I proposed an art auction to raise funds for
diabetes research. But I found that as a physical scientist I could help directly, in a more profound way
than I had ever imagined, with medical physics.
In early 2012, I had just finished a monumental task - calculating the size of every ion of every element in
every bond environment known in crystals. Using the momentum of atoms, I discovered the dynamic
quantum structure of crystals. Regular atomic motion creates structure and form!
Life events prompted me to consider dynamic motion in the insulin molecule. But I must say that no one
looks at insulin quite like I do! We are made of ancient elements from long-gone stars. I see that insulin
has harnessed ions from salt water as elements of communication, and this inorganic part of the structure
seems pseudo-crystalline. The dynamic structure could be solved using these inorganic elements of
insulin, finally giving a mechanism for glucose attachment and delivery to cells.
This past century, scientists failed to solve dynamic molecular structures using basic physics. By claiming
that atoms are non-local - everywhere and nowhere at once - a definite structure of moving atoms cannot
be solved! But atoms are local: the strong force confines nucleons in a miniscule volume. We simply
need fresh ideas and a renewed determination to solve these active molecular structures.
I have faith that the dynamic structure of insulin is indeed determinate. To benefit medicine, I aim to
solve it using the new quantized values of force and energy found for moving ions in quantum crystals.
And I plan to build a new type of instrument - optical scanners - to probe the molecular structure by using
local photons that refract through insulin at a specific level of energy.
Contributions to THE INSULIN PROJECT are needed and welcome. At present, seed financing is
required to establish a local office and register a charitable not-for-profit organization.
Sincerely,
Dr. David K. Teertstra, Ph.D. M.Sc. University of Manitoba B.Sc. Queens University
Sept. 9, 2012, Burnaby, BC.
Email: en369@ ncf.ca tel. (604) 561-5859
INTRODUCTION
What is insulin made of? How is the molecule constructed? What elements of the universe and of Earth
are required for health? What ingredients must we eat? What does a malfunctioning molecule look like?
A broad look at insulin (and matter in general) answers some of these questions.
Modern medicine is done by educated guesswork because no one can predict how molecules form
and will react. Biopsies and chemical tests take time, yet no one can use light to scan and instantly
recognize molecules like insulin. Overall, there are few tests and instruments available for use, and access
to quality information remains an issue. How does a molecule form? What is its shape? How does one
molecule recognize and attach to another? Is your insulin different from the single synthetic crystal
studied structurally? Does calcium in a rock bond differently from calcium in a molecule? Are parts of
organic structures functionally similar to crystalline structures?
The basic problem is this: even if given the composition of a molecule or crystal (e.g. H2O water
or NaCl salt), we cannot predict the bonded structure or what the material should look like. Or, if given
the structure, we cannot predict chemical compositions. We cannot predict new products and we cannot
predict if a drug will work for you. It’s hit or miss. How does insulin bond to glucose? At this scale, we
don’t really know. One problem is that current descriptions of molecular structure do not include motion
or use the known forces to describe bonding. Physical problems from a century ago remain stagnant and
unsolved.
Molecules and crystals require specific elements in specific sequences to form the structure.
Other elements are definitely rejected. In the dynamic Earth, the rejected elements go on to form valuable
ore deposits. Solving this fundamental problem of molecular formation is very important to mining as
well as medicine and manufacturing. But current models predict only dilution and dispersion of elements,
not their concentration into ordered structures.
I have a long history of tackling and solving problems in science but this past decade withdrew to
consider certain fundamental problems underlying science, industry, medicine and health. Topics of
atomic motion, force, composition, structure…. Now I’m back from this jungle (hopefully more like Jane
Goodall than Kurtz!), returning to society with something to say.
I do not believe in “dumbing down” anything. I believe that anyone can look at the complexity of
a tree or a night sky and get the gist of it. You may not understand everything written here, but realize that
with all of science combined we understand only a small sliver of what there is to know. Much remains to
be discovered, described, invented. Here I discuss some topics mathematically (as required for select
readers), but I’ve written the text so you can skip ahead. I also discuss mental and spiritual components of
our human microcosm which are important to health but which the scientific reader interested only in the
physical may want to skip.
Science is quite amazing in its capacity, but does not come even close to describing our human
experience. It’s not like we need science to get through the day. Consider this problem.
Imagine a glass of ice water. You can see it, right? The glass, the condensation, the surface of
water, an ice cube floating. We can assess the real thing in a split second. Now, take everything science
has and try to do the same. Nope, nothing. Barely a dent in the problem. What is light? What is glass?
How does light get through glass? What is water? How does water turn to ice? What is the structure of
ice? We cannot predict the hexagonal (snowflake) structure! How did ice exclude the many other
elements that can be dissolved in water?
At the grocery store, the optical scanner requires a bar code to recognize what we know perfectly
well is a banana. That’s how primitive our technology is.
We can study electricity, magnetism, wave theory, atomic structure, throw all sorts of technology
at the problem and we still can’t calculate what ice, water or glass should look like. An outsider is not
surprised that science needs new theory, but scientists often are.
THE INSULIN PROJECT uses medical physics to determine the dynamic structure and function of
the insulin molecule. Certain old topics of science get thrown to the wolves. Truly sorry, but those
favourite old slippers were just not getting the job done. But there is plenty of good existing science that
works quite well for this job. What we are getting rid of are just select parts of science that scientists
themselves admit are crazy, illogical and counter-intuitive. You know, the stuff that popular science
magazines dwell on, the unworkable quantum absurdities, the arguments from a century ago. Scientists
are bound to scream and complain, but may I redirect you to the glass of water problem? Or, how does a
molecule form? We have some serious work to do here!
We begin by looking at the structure of insulin strictly as a matter of curiosity. Consider insulin as
an object - like a photo of a galaxy or a work of art. This is a globular cluster of atoms with the
proportions of a fat gummy bear. Drawn as a ribbon diagram, insulin qualifies as an abstract work of art,
but with a structural formalism more like Wassily Kandinsky than Jackson Pollack. Looking closer, one
sees spiral corkscrew structures and also hexagonal rings which are clearly not the work of gravity. Selfsimilar fractal structures are absent. The geometry varies from mathematically tight to loose. This
structure is certainly not random. It has purpose, function.
Insulin is rather like a balled-up bead necklace. Actually, it’s two necklace strands balled
together. But each bead represents a distinct amino acid, so the molecule is really more like a charm
bracelet wherein each charm is specifically placed with special significance. As this folded structure
determines the surface shape and topology that attracts glucose (and then delivers glucose to a cell), we
need to determine the force and dynamic motion of atoms that generates a specific shape and form.
Some say it is too difficult to solve the dynamic structure of a molecule. But I like to aim high.
By aiming high, all sorts of other good solutions appear. To me, science has gone off on a strange tangent,
with too much focus on intangible aspects while reasonable solutions are either unsought or ignored in the
current scientific culture.
The fundamental unsolved problem is that no one knows why specific elements form a molecule.
Molecular shape and size cannot be predicted from composition, and no one really knows how one
molecule docks and attaches to another. The answers must lie in the physical properties of atoms and ions
including mass, speed, electron-orbital structure, charge and magnetism.
For example, the insulin hexamer forms in the presence of divalent zinc ions. What is so special
about divalent zinc? Why not divalent calcium, or iron? Or, what are the dynamic consequences of any
other amino-acid sequence in insulin? It’s clearly not random, but why that sequence in the first place?
You can spend many years asking and delving into the literature and still not have an answer.
So here we have a fundamental problem of major interest to medical and pharmaceutical
companies. The same problem of bonding and structure plagues the mining industry, as they do not know
why certain elements gather together to form a particular mineral structure while other elements are
actively rejected and concentrated into ore. Existing quantum and thermodynamic theory predicts that
mines should not exist! How does insulin differ from a mineral? We clearly need some new science, even
though new science is strongly resisted.
I spent a decade working in basic science, learning facts and theory, instruments and techniques.
Even as a student, I published more than most professors. I then spent another decade largely removed
from worldly concerns to tackle a series of fundamental problems, some of which you have read about in
popular science books. These most difficult problems are neglected because years could be spent without
discovering a solution, and few scientists can afford that risk. But I did it, to great benefit.
If you read about the discovery of insulin, you find that Dr. Frederick Banting read an intriguing
idea and was curious enough to pursue it. It was intuitive, radical research that paid off. Even though the
experts thought it couldn’t be done, even though others had tried and failed, a renewed effort won the
prize! THE INSULIN PROJECT is also radical research seeking a radical breakthrough.
The experts often want to argue science. They fine-tune details while ignoring major problems.
But when you are sick, you want real results. You want to know that everything possible is being done.
Although we have seven billion people on the planet, the fact is that very few are actually working on
problems of major importance to society. In diabetes research, for example, you can quickly find every
person working on the problem in Canada and soon discover each vein of research.
So much remains unknown about even the simplest molecule that I found it necessary to revisit
fundamental notions of atoms, motion and bonding. Over the past decade, I did a lot to describe the
dynamic structures of molecules and crystals using the known forces and physical constants. I required no
new equations; instead, certain older concepts in science have been overextended while some great new
science has been overlooked.
I believe it is now possible to use the existing laws of physics to solve the dynamic structure of
complex molecules like insulin. This is the goal of THE INSULIN PROJECT.
FIVE CATEGORIES OF PROBLEMS
Five categories of physical problems that have been long-ignored as scientists rush off to new discoveries
are solved here using local models:
1) Local action-reaction predicted by Einstein is required because the strong force of quark theory
requires a local atomic nucleus, thus giving each moving atom a specific path or trajectory. The diameter
of the nucleus is far smaller than the de Broglie wavelength of motion. Many problems of physics occur
due to separate equations for waves and moving objects.
2) Light cannot be a wave spread out across time and space because individual atoms absorb and generate
individual photons. Here, a local photon is produced if electromagnetic energy oscillates locally with
mass. A plane wave is generated over time. An electric monopole is perpendicular to the direction of
motion and to dipole loops of magnetic flux (Teertstra 2005, 2008a,b). A local photon attached to a
particle with rest mass gives a mechanism of motion and gives the moving particle polarity.
3) In the stable resonant quantum structure of a molecule, angular momentum is quantized. A consistent
structure is generated by consistent atomic motion, not by random chaotic motion.
4) The powerful Coulomb force must explain all bond distances in a system of charges in motion. The
nuclear center of mass is also the center of charge of an ion. The volume occupied by an ion depends on
the volume of its electron orbitals (Waber & Cromer 1965) and on the quantized radius of motion and
electron orbitals of adjacent ions do not overlap.
5) The de Broglie wavelength of a moving ion is similar to the wavelength of a diffracted X-ray and local
interactions of photons and atoms are required to explain diffraction. Local models are also required for
atomic absorption, and emission and refraction also depends on the radius of motion of ions.
The fact is, few analytical methods are absolute and few analytical instruments are quantitative.
The relations between composition and structure are known within about 1 to 2 percent error (at best). We
lack a theory for the composition and structure of the material being analyzed. Considering shape, force
and motion over the last decade, I discovered that atomic motion must be regular and quantized. Regular
motion generates distinct radii of ions in crystals, and this data can be used to solve for the insulin
structure solution.
THE STRUCTURE SOLUTION
We’ve all read about how atoms are here and there and everywhere at once, always vibrating and
oscillating. Or how atoms are always madly rushing about, smashing and colliding in a continual series of
random chaotic collisions that cause irreversible mixing. Or, how the world around us and the whole
universe is decaying, dispersing, losing heat, wearing down to nothing. Such drama makes great press,
but is it true?
You see, we’ve also read about how the body uses the elements of salty ocean water – sodium,
potassium and calcium – as the elements of cellular communication. One reads about cells controlling
calcium in molecular channels, or cells concentrating potassium … but wait a minute! Weren’t these
elements irreversibly mixed? How could a molecule select calcium (Ca2+) from a disordered mixture and
concentrate it for a specific purpose? How did our bodies increase order and structure in the universe? Or,
how did a mineral such as calcite (CaCO3) select specific elements for its structure?
What you may have not read about is a description of the strong force. Positive protons ought to
repel one another, but if they get close enough, they fuse together to form the nucleus of an atom. The
strong force binds quarks together as if in a tiny bag, and then protons and neutrons are also bound
together. That makes nuclear mass local! The nucleus is definitely not “anywhere and everywhere at
once”! Like a planet, each moving atom has a distinct and definite trajectory. The real problem is that we
have separate sets of equations for waves and particles. But what is oscillating? I consider an oscillatory
exchange of electromagnetic energy with mass to generate a photon, and then a moving particle has an
attached “photon motor”.
Are atoms oscillating? I tried to find evidence for this in bond distances between ions in
crystalline structures, but all plots of the data showed that atomic motion is regular, ranging from circular
to elliptical. Angular momentum is quantized! A definite ordered structure arises from regular atomic
motion, not from random chaotic collisions. Crystals are periodic quantum structures.
I also tackled the question of time, of longevity. The oil in your car may be a hundred million
years old! Distinct structures must be maintained by oil molecules. Furthermore, individual crystals are
known to have existed for over four billion years. Such incredibly strong and stable structures show no
signs of “wearing down”. The Earth itself has evolved a distinct layered structure, and our solar system is
also distinctly structured and stable. It looks like the energy of the universe is being used to build many
interesting and elegant structures.
Einstein said that the planets move along paths of zero net force. This means that the outward
centripetal force of a planet is met at all points by a force of attraction toward the Sun (plus minor terms
for other planets). On a stable orbit, the planets don’t experience acceleration. This principle may apply to
moving atoms as well, except that atoms have two types of charge, positive and negative. A moving
charge experiences both attractive AND repulsive forces and the resulting dielectric structures definitely
do not look like those formed by gravity.
An ion moving along a curved trajectory of zero net force does not experience acceleration and
therefore does not lose momentum by radiation. This curved trajectory is stable, as is motion in a straight
line when no force is applied. Whereas an oscillating ion goes from full speed to a complete halt and
could generate considerable braking radiation.
All our past focus on random statistics and probability waves has done nothing to solve even the
simplest of structures. Oh, sure, you can fudge some numbers to replicate a simple structure like hexane
(C6H14) or table salt (NaCl), but no one can use the basic rules of physics to predict such structures to
begin with. Using free variables to fudge an individual structure gives results that are not universally
applicable. The theory of oscillation, for example, has never generated a table of ionic radii or been able
to predict the structure and symmetry of crystals.
The structure of insulin is quite complex, but such complex structures contain the full set of
organizational rules. These rules result from the known physical forces and constants and the properties of
time, distance, mass, speed and charge of moving atoms. Getting rid of some old concepts that physicists
themselves call crazy and counter-intuitive, we do indeed have enough knowledge to solve this distinct
dynamic structure. The results will benefit all of science, including drug development and cancer and
diabetes research.
WE ARE THE EARTH
We are stardust, we are clay. Most of all, we are plants. Our bodies poorly synthesize nine of the twentytwo common amino acids needed to build proteins, enzymes and hormones. Only certain foods – meat,
dairy and eggs – contain all essential amino acids. The rest we get from plants - from greens to grains to
beans - and we need a varied diet to source all essential amino acids along with other critical nutrients
(mostly cations, sometimes loosely called ‘minerals’). Insulin requires seven of these nine essential amino
acids as well as sulphur anions.
We literally are what we eat. The components in our food become the components of our physical
bodies. If we eat an animal, its protein becomes our protein. We are mostly water, yes, but more like salty
ocean water rich in sodium, potassium and calcium, and anions of chlorine, carbonate and sulphate.
Ultimately, our bodies reflect the composition of the Earth. The environment is not something “out there”.
There’s no dividing line. We are the environment.
The academic separation of life sciences from inorganic and physical chemistry has left a major
void in the holistic education of health scientists. Students of organic chemistry are introduced to the
easily-depicted structures of oils and fats (from saturated to unsaturated), and then to other major
biochemicals from carbohydrates to proteins to nucleic acids. The essential inorganic components are
ignored, even though these components allow the molecule to be carried in our water-based blood.
Although the insulin hormone is built from amino acids, it is also built from essential inorganic
components that make it a somewhat soluble salt. Water and its dissolved salts surround, adhere to and
stabilize the active insulin molecule. Although insulin is significantly inorganic structurally and
somewhat crystalline, health scientists are not trained to recognize the crystalline structural components
of organic molecules. These components are the inorganic ingredients of the Earth.
Considering our bodies as a direct product of the universe, a different picture of life emerges. A
quick glance at the chemical composition of our bodies reveals that we are constructed using low-mass
elements that were produced in abundance in the earliest stars. These are mainly carbon (6C), nitrogen
(7N) and oxygen (8O), the subscript indicating that each element contains one additional nuclear proton.
The elements are named according to the number of nuclear protons. Why is hydrogen not in this list?
Well, hydrogen is simply the proton, produced long before stars could exist, along with electrons and
neutrons and a great many other particles. These ancient protons and neutrons are primary ingredients that
later fused together inside stars to create the heavier elements. I find it quite interesting that our physical
bodies are made from matter as old as the origin of the universe itself.
Note that there are tremendous mysteries concerning the physical origins of the universe. These
include the nature and origin of mass, the equal concentrations of positive and negative charge, the
positive charge belonging to high-mass protons with an equal and opposite negative charge of low-mass
electrons, and the nature of the forces. Our bodies operate at the molecular scale using quantum rules
which are only partly understood. Quantized motion is just part of the mystery.
Hydrogen is especially important to us, in the form of atomic hydrogen (the proton-electron pair),
as hydrogen gas (the two-proton – two-electron molecule), and as a proton which is attracted to the
electrons of carbon, nitrogen and oxygen (e.g. H2O). Organic chemists are primarily concerned with the
location of electrons and protons about the heavier atomic nuclei. Organic chemistry is all about the theft
of protons. After the nucleus of an element has attracted its orbital electrons, those electrons may also
attract an outer proton (loosely considered here as an element, hydrogen). Any outer proton must remain
distant from the nucleus because it is moving at significant speed and is also repelled by the nuclear
protons. Because the nucleus of an atom contains almost all the mass of a molecule, the lower-mass
components enter into stable orbitals about each high-mass nucleus which acts as the inertial center of
mass.
We should never imagine that atoms in molecules are motionless; in fact, all the atoms are always
in motion. It’s just that the speed of the lightweight outer components is high relative to the heavier and
sluggish nuclear core. We may use the thermal speed of atoms to calculate a quantized radius of motion.
Our bodies are not merely composed of elements, but of elements in structured motion that are
continually interacting to create shape and form.
Our bodies also use many elements heavier than oxygen. Essential elements include phosphorus,
sulphur, chlorine, sodium, magnesium, potassium and calcium. These elements were formed within stars
that synthesized the elements up to iron. A later generation of stars was required to form elements heavier
than iron, of which copper and zinc are especially important nutritional trace elements.
If we consider that the Earth formed from mixed stardust that collected, aggregated and
eventually melted to a magmatic liquid, these elements ought to be completely dispersed and diluted. If
one studies only liquid states, it would appear that mixing is irreversible. One could extend this theory of
mixing and claim that the entire universe is becoming increasingly disordered and chaotic. Doing so, no
one can then predict the appearance of highly structured and ordered molecules or crystals that have very
specific compositions and dimensions. That is, given the many elements available in a mixed disordered
liquid, only a few elements are selected to form very specific molecules while all others are rejected.
So the real problem here is that we have no theory to predict molecular structure. Or, if given a
structure, we cannot predict composition. In the structure of insulin, no one has an explanation for the
sequence of amino acids and certainly not for the location of specific elements within an amino acid. Why
does the hexamer crystallize with zinc and not with another divalent cation such as calcium or iron?
Consider boron (5B) as an example of the influence of the Earth on the composition of plants and
our bodies. The most abundant elements formed by nuclear fusion have even numbers of protons and
neutrons, but boron has five protons and is of very low universal abundance. The Earth itself has very
little boron. But the structure of the Earth has evolved such that heaviest elements such as iron have
settled to form the core while the lightest elements from lithium to oxygen have fractionated into the
lowest-density outer crust. We live on the surface of this very thin crust of the Earth and our bodies are
formed using these lightest of elements. We require air and water but use very few of the heavy elements
which are present in the rocks and soil underfoot.
Minerals and rocks contain very little boron, yet boron is essential to our joints, bones and teeth.
Boron also affects cell membrane communications and allows Ca, Mg and P to function properly. But
plants biomagnify (or concentrate), recycle, retain and redistribute boron from the extremely low
concentrations found in rock, soil and groundwater. We get an amazing 2.06 mg from just 100 g of
avocado and 1.82 mg from a mere 130 g of red kidney beans. Many other plants give us about 1 mg per
100 grams.
Boron is bio-concentrated in so many edible plants that we need not be concerned about getting
enough boron in our diets. The point is that we get this essential micronutrient from plants, and they get it
from the crust of a planet which itself has a long and complex history of compositional and structural
evolution. Chemically, one is hard pressed to say where the Earth ends and we begin.
Boron is absent from the known structure of insulin. But the insulin structure is determined by
crystallizing many molecules and analyzing the X-ray diffraction data of a single crystal. The refinements
are not that accurate. The near-identical scattering power of X-rays by elements with similar numbers of
electrons (B, C, N, O) means that composition must be determined by bond lengths, but these have not
been corrected for motion. In the structure refinement, the structural characteristics of molecules are
recognized (e.g. by the dimensions of six-membered rings and individual amino acids), but we lack a
theory that proves structure refinement as a method of compositional analysis.
Better resolution of hydrogen coordinates comes from neutron diffraction, but we still need a
definitive physical theory to prove any claim of full site occupancy (indicating just one type of atom fully
occupying a crystallographic site). And of course we also need a fundamental explanation of thin-sheet
diffraction, but a local theory can be developed by considering that the wavelength of diffracted X-rays is
similar to the de Broglie wavelength of a moving ions.
[A note on crystals. In the example of halite, NaCl, equal numbers of sodium and chlorine form
each cubic unit cell. These small cubes stack together to make a larger crystal. One small barely-visible
single crystal of halite contains about Avogadro’s number of atoms which is about equal to the number of
stars in the known universe. In wave theory, X-rays diffract at specific angles from the layers of atoms in
halite.]
Using other methods of chemical analysis, it remains difficult to prove that boron is absent from
the insulin structure. Or if boron is present, is it simply a chemical impurity or a surface residue? Boron
would not be present in a pure synthetic molecule, but is it present in a natural molecule or in a
malfunctioning insulin molecule? We could easily miss a one-percent boron substitution that may be
significant to the biological function of the molecule. I don’t mean to pick on boron here, as one could
also consider beryllium or phosphorus or any other element, but the main point is that the accuracy of
compositional measurement by structure refinement is at present relatively low, at best about 1%. We
need new tools of measurement such as optical scanners to probe the composition and structure of matter.
The amino acids are not randomly linked to form the insulin molecule. Instead, their specific
sequence defines a particular length and surface topology. One can consider that the resonant wavelength
of each component atom contributes to the length of each amino acid and to the overall dimensions of the
molecule, but this remains to be investigated. This problem cannot be solved without a general physical
theory relating composition to the dynamic structure.
SCIENCE IN OUR SOCIETY
Some of the biggest problems of science require a special season of dedication and focus to solve, but we
don’t have a social structure that permits this. Many of the true problems of science don’t make a top-ten
list in popular-science magazines like Discovery or Scientific American. Some problems aren’t even
recognized, and others are rarely mentioned because no one knows how to deal with them. The most
difficult ones are embedded in the literature in a strange or convoluted form. Most scientists try to explain
their data in socially acceptable terms even though a radical new explanation is required. So we rely on
independent inventors and scientists as the “X-factor” to drive innovation.
Einstein proposed quantized linear oscillation of atoms in solids to explain the use of integers in
the Planck equation for the spectrum of blackbody radiation. But he did so before the discovery of X-rays
and before solution of the crystal structure of halite or any other crystal. Linear oscillation is easy to
visualize (you can tie a rock to a spring and set it in motion), but is very difficult to calculate using a
distance-squared force law. Nevertheless, the idea of oscillation is embedded in many areas of science,
including optics. Only a few specialists do these complex calculations, and they have never produced
tables of ionic radius, tables of bond distances, dimensions of polyhedral structures or predictions of the
symmetry of crystals.
Starting in 2010, I attempted to look for evidence of quantized oscillation in the polyhedral bond
distances of crystals. Ion pairs such as Si-O have distinct bond distances that increase with the number of
coordinating oxygen ions, from SiO4 to SiO6. I found distinct increments of the Si radius that indicated
quantization and supported the use of integers in the blackbody equation, but the factor of h/2
consistently appeared. The Planck constant h is expected and required for quantization, but the
appearance of pi indicates circular oscillation. The data indicate that ions in crystals are indeed confined
spherically! The X-ray scattering is isotropic (Bragg 1930) and the electron-density cross-sections are
circular (Fumi & Tosi 1964). Linus Pauling (1929) noted that each cation is commonly surrounded at a
radius by several anions. So the quantized radius of a cation confined to move across a spherical surface
suits the structure of crystals as well as the bond distances. Einstein was right about quantized oscillation;
it’s just not linear.
In linear oscillation, the ion comes to a complete halt, reverses direction and attains maximum
speed as it crosses the center of motion (the crystallographic coordinate). But a decelerating ion must
generate significant radiation and lose momentum. This state of motion is unstable, yet oils like hexane
are known to be hundreds of millions of years old, and crystals like garnet have ages of up to four billion
years. Instead, the bond-distance data in crystals indicate that each confined ion continually changes
direction. The simplest movement is circular to elliptical. In this case, the outward centripetal force must
be continually counteracted by the confining force of numerous surrounding ions. The ion does not
generate radiation because it does not experience acceleration! Angular momentum is quantized and the
ion moves along a curved path of zero net force. For a local ion, this is calculated as a geodesic trajectory.
If one studies gases and liquids, the theory of a continual series of random and chaotic collisions
makes sense. The structure is chaotic. Mixing is irreversible. But if one studies molecules and crystals
with a distinct and definite ordered structure, the motion of atoms must be quite regular and orderly to
make the structure stable over geological time. Using circular to elliptical modes of motion, it is now
extremely easy to generate tables of ionic radii that give accurate bond distances for all ions in all
crystals. Force and bond energy is also quantized and simply calculated. But you’d be surprised at the
number of people who prefer the old theory, even if they don’t use it!
Some themes in science are easy to promote. For example, we cite Isaac Newton’s “clockwork
universe” as if it were a distillation of wisdom, as if Newton were not dealing with mysteries as profound
as those promoted today! Yes, he wrote an equation F = ma (force equals mass times acceleration) that
defines mass as a constant property of any low-speed object (m = F/a = constant) but he knew perfectly
well that what we call mass is simply our experience of the world. Mass itself remains undefined and
mysterious.
What we are actually doing is using light to see where something is. Seeing two objects, we can
define a unit of length. If an object changes position regularly, we use that regular motion to define a
length of time. The only reason we consider a clockwork solar system is because the observed motion
actually is regular and periodic. The rise of the sun, the period of the moon, the swing of a pendulum.
No one really knows the mass of the sun or the moon! Instead, planetary mass is a variable m
which is adjusted to suit a distance-squared equation for gravity (and recently adjusted ever-so-slightly to
suit Einstein’s field equations for gravity). Newton’s distance-squared equation also describes
acceleration, such as the fall of an apple to Earth, which can be measured in experiments here on Earth.
But we really need an independent theory of mass.
There are tremendous social obstacles to developing new science. The greatest work of Newton
and Einstein was accomplished during years of uninterrupted focus. Whereas the typical professor that is
so tied up with grants, committees, departmental politics, graduate students, running a laboratory and
teaching has barely a moment to read or think. A major problem may take a decade of solitary work (e.g.
general relativity). Therefore, researchers stick with known fields of study for guaranteed publications.
They tend to not use old theory, even if it works well, or to solve old problems - even though modern
theory is built on multiple layers of historical assumptions. And they can’t get published if they say
anything out of their field or too different from the mainstream! A complex theory that yields steady but
ambiguous results is favoured (to generate successful grant applications), whereas fundamental problems
that require major exploratory effort and may not be immediately resolved get pushed aside and ignored.
We currently have this social conundrum in which scientists at universities, research councils and
industry are not in an environment which allows them to tackle a significant problem of uncertain
outcome for an extended period of time (an important exception may be The Perimeter Institute for
Theoretical Physics in Waterloo, Ontario). I solved this by periodically renovating or building houses; the
physical labour refreshes the mind, but the work is not so demanding that one cannot think. Such work
would buy me a few months here and there to do some serious reading, writing and computing. I also
took some great advice written by Isaac Newton. He solved the dynamic structure of the solar system with
a single equation for gravity developed while in isolation during the plague years. You must work on a
problem full-time with minimal distractions. Be a dog with a bone to get it done.
BACKGROUND TO THE SCIENCE
Sometimes it takes years of probing into the unknown before discovering simple and clear solutions.
Nature is incredibly complex. What rules govern this jungle? If you were to remove one species from a
jungle, what would the consequences be? The only possible way to find out is to enter the jungle, live
there, and really study it. That takes time.
I’ve been considering this interesting problem. Look around right now, and you can see and name
dozens to hundreds of different materials. Glass, steel, plastic, ice, water, gold, cement, hair. “Well,” you
may say, “they look different because they have different compositions”. True, but try to calculate it from
a composition! We have hundreds of textbooks and optics journals, all with quite amazing theory, yet no
one can calculate what even the simplest materials should look like. No one can predict the structure from
the composition. Even if given the structure, no one can predict the composition.
This is a very practical matter affecting many industries. Going to a grocery store, you can
instantly recognize a banana and say an awful lot about its condition of health. But optical technology is
so primitive that an optical scanner at the checkout can only recognize a barcode! What if we wanted to
identify an object optically, or use light to measure glucose in blood? Or to see a virus? Good luck with
that!
In this particular jungle we must deal with atomic motion (whether random or regular), issues of
local action-reaction versus non-local action at a distance, questions of how to measure distance or time
for objects too small to see, plus theories of light and electricity, thermodynamics and statistics, plus
probabilities and errors of concept. All are major fields of scientific endeavour. Optical absorption, for
example, is entirely described using a complicated theory of linear harmonic oscillation of atoms.
For example, all the evidence points to a local photon, but we have only the wave model wherein
light is spread across space and time. Therefore we have scientific descriptions written in terms of nonlocality. Perhaps the early workers could only imagine a spread-out wave, like a water wave. The nearest
mathematical tool at hand is a sine function. But using a sine function, we do not actually need a spreadout wave. We simply need two conserved quantities that exchange with one another. This could be a local
oscillation, like electromagnetic energy with transient mass (changing from zero to a maximum). This
gives a local photon with wave properties over time.
I have on my desk a large chunk of glass, faceted like a diamond. Now I’ve been immersed in the
problems of describing motion and bonding in crystals for many months straight, years in total. One day,
I realize that light is actually passing through all of the atoms sequentially and then to my eye. We see
directly through oxygen atoms to silicon atoms, then through silicon to oxygen, sodium, oxygen, silicon
and so on. Each atom has its own specific contribution to what the material looks like. An optical
signature, if you will. Mathematically, we can add up all these contributions to calculate what the glass
looks like. Or, working backwards to calculate the composition of the glass from the optical
measurements, we now have an optical scanner. The photons refract through the atoms of each material
intact at a specific level of energy. This works quite nicely, but it’s not in any textbook!
If we take this basic mathematical property of additivity, we find that other properties of solids
are also additive. Ionic radii are calculated by additivity. Bond energy is calculated by additivity.
Ultimately, force is additive (as a vector sum, depending on angle and direction) and the refraction of
polarized light also depends on angle and direction. The optical properties of materials depend on some
fundamental feature of nature. The trick is finding what is most fundamental in this jungle.
The most fundamental theory contains variables of time, distance, mass and charge, and uses
simple equations that contain fundamental physical constants. A poorer sort of theory tacks on free
variables which are fudge factors that reduce the difference between calculation and observation (this is
the problem with models of oscillation). But sometimes the fundamental physical theory is so well hidden
that we go entirely to empirical models. Such models allow practical progress and generate trends that
may eventually reveal an underlying physics. The trickiest beast to deal with uses a complex mix of
fundamental theory in unusual form.
I first studied minerals and crystals because they have simpler compositions and structures than
do molecules. Atoms in crystals are ordered and arrayed in geometric patterns. The salt halite, NaCl,
forms a simple cube, a square tile pattern on the side. As many minerals have the halite structure, from
LiCl to KCl to BN (boron nitride) and so on, it should be possible to find the contribution of each ion to
the optical properties. This turned out to be approximately true. But the optical properties vary with the
volume of the material, so we need to know the sizes of atoms and how they bond. And so into the jungle
I went!
AN ORDERED STRUCTURED UNIVERSE
After many years of study, I realized that disorder in the universe has been over-emphasized. Distinct
structures of solar systems and galaxies (or molecules and crystals) can only form from regular patterns of
motion - not from disordered random chaotic motion. The problem is that disordered gas and liquid was
the most easy to study and understand, historically, whereas the highly ordered dynamic structure of
molecules and crystals has proven curiously difficult to solve!
Many early breakthroughs in physical science came from studies of gas. Continual collisions of
gas atoms against the walls of its container generate pressure. Atoms and molecules in gas continually
collide with one another because the collisions do not produce permanent bonds. The irreversible mixing
of two gases such as O2 and N2 are statistically and thermodynamically modelled using a continual series
of random chaotic collisions. Gas has a random structure and no form.
This gas model extends to liquids with weakly bonded and highly disordered structures. Liquids
also take on the shape of their container and exhibit irreversible mixing. Consider a cup of coffee, which
is hot due to the kinetic energy of many water molecules. If you add cream to these jostling molecules,
there’s no going back! You can never restore the cream to its original condition.
These ideas of temperature, atomic motion and mixing are so powerful that some scientists claim
the entire universe is becoming increasingly mixed, diluted, chaotic and disordered. And yet we see that
gravity acts to collect materials together and to produce distinctly organized structures such as our solar
system and our galaxy. But the equations for gravity contain no terms for entropy. The equations for the
structure of atomic hydrogen contain no terms for disorder. And Earth itself has evolved and developed a
distinct layered structure due to separation of materials, due to unmixing.
Although such models of disorder apply to liquids, they may not apply to the stable structure of a
molecule within a liquid. Different rules must apply at the atomic scale to create structure. Regular
motion creates the form of a molecule. The thermodynamic models of disordered gas and liquid also
completely fail to predict the highly ordered structure of crystals.
Unlike liquids, crystals make their own container. We have perfect cubes of halite or pyrite,
hexagonal snowflakes, octagons of fluorite, a rhomb of calcite and the distinct form of a quartz crystal.
Crystals are natural mathematical objects. Crystals have extracted specific ingredients from the disordered
mix available in liquid, and specifically rejected many other components not necessary for their growth.
Crystallization reverses what we thought was an irreversible process of mixing. Crystallization
actually separates elements at the elemental scale! It would appear that the energy of the universe is being
used to create highly ordered structures. The insulin molecule is a fabulous example of a distinct structure
with a specific biological purpose. To form and maintain such a distinct structure, the dynamic atomic
motion has to be periodic and regular.
In addition to continually colliding, the ions in crystals were also thought to be oscillating. I
attempted to find evidence for quantized linear oscillation in the bond distances and polyhedral structures
of crystals, but instead discovered evidence for quantized circular oscillation! The specific changes of
ionic radius (Shannon 1976) and bond distance (Pauling 1947) are consistent with ions with a quantized
radius of motion confined to move across the surface of a sphere. In the general case of elliptical motion
across the surface of a triaxial ellipsoid, one can calculate bond distances using conservation of angular
momentum.
As the electron-orbital radius of an ion is significantly smaller than its effective ionic radius (by
1.6 to 3.2 times; Slater 1964), there can be no electron-orbital overlap of adjacent ions. Hybrid orbitals (in
Pauling’s valence-bond theory) cannot occur. Instead, there is Pauli exclusion between closed-shell ions
having the stable electric structure of an inert gas. Ionic radii are additive due to minimized distances
between adjacent cations and anions (with Pauli exclusion), and due to the allowed increments of ionic
radius!
The direct relation between atomic motion and form or structure is neglected in the modern
scientific literature. In descriptions of crystalline structure to date, thermal motion is an afterthought. I
started considering motion on realizing that in the most regular polyhedral (such as the SiO4 tetrahedron
with four equal <Si-O> distances) the anions lie on a radius about a higher-mass cation. For ions in
motion, the heavy cation could be a stable center of inertia. The high-valence cation forcefully attracts a
small number of low-valence anions, but the cation is also forcefully encaged by anions!
Like many scientists, I thought that the electron orbitals of an ion explained its size. But the
electron-orbital radii are much smaller than the effective ionic radii. Instead of requiring a new electronorbital structure in each polyhedron, the ion simply increases its radius of motion on entering a larger site.
The encaged cation rolls across an electric surface of its surrounding anions.
The calculations of force, motion and structure indicate that the thermal motion of ions accounts
for much of the volume of an ion in a mineral and in rocks that form the crust of the Earth. And of course
I’ve calculated the volume of the crust of the Earth, but that’s another story! Regular periodic motion is
responsible for the distinct geometric structure of molecules and crystals. These are highly-structured
highly-ordered resonant quantum crystals!
As ionic radius is quantized - no longer a continuous variable - we now have a finite set of
solutions for force and energy in the dynamic structure of molecules and crystals.
MODELS OF BONDING
Modern science builds on previous science, yet new findings have shed light on the original assumptions.
After Niels Bohr solved the dynamic structure of atomic hydrogen and cracked open the hidden quantum
world, physical chemists immediately tried to solve the structures of molecules and crystals. But they
assumed oscillatory modes of motion or considered that the charges of protons and ions were fixed
motionless at specific coordinates. The calculated values of bond energy are then too low compared to
measurement. To increase bond energy, Linus Pauling embraced the new idea that electrons are
delocalized and suggested that all ionic bonds have a percent covalent character. This is an excellent
empirical solution if the actual physics cannot be solved!
Using delocalized orbital electrons, an ion loses its own distinct local charge and one can no
longer use the Coulomb equation to calculate force or energy from the center of charge. But I failed to
find evidence that the distant surrounding ions in a crystal can ever exert sufficient force to disturb the
stable and strongly-bonded electron-orbital structure of the central encaged ion. Quite the opposite! The
vector sum of electric force on the encaged ion must be zero or the resultant force would cause the ion to
migrate and leave the structure. [Note here that mirror planes in crystals commonly indicate the symmetry
requirement of a zero vector sum of force. Conversely, each heavy high-valence cation attracts a
symmetric arrangement of surrounding anions to generate this symmetry.]
Decades later, solutions of the electron-orbital radii revealed that atoms and ions were far too
small to explain the long polyhedral bond distances in crystals (Slater 1964, Waber & Cromer 1965). The
observed cation-anion distances or the electron density maps (Fumi & Tosi 1964, Shannon 1976) are far
too long to allow covalent bonds! Furthermore, recent descriptions of the strong force verify that the
atomic nucleus is held within such a small volume that nuclear mass can only be local and not spread out
across space. This finding is completely consistent with the original model of atoms indicated in the
Rutherford scattering experiments. Considering the small size of electron orbitals, there is plenty of room
for the thermal motion of ions in crystals.
Nuclear mass is also the origin of positive charge. If the nucleus is in motion, its attached orbital
electrons are also in motion. Kinetic theory requires that the entire ion moves. The ionic structure stays
intact because the speed of electrons is a significant fraction of the speed of light whereas the speed of the
nucleus is just one to two times the speed of sound. So Einstein was right – we really do need a local
model of atoms with local action-reaction - but this old idea of non-local particles is still highly embedded
in the way we describe nature. I am one of the few scientists to agree with Einstein on this matter, but I
have good reason to do so. The main problem is that non-local science has failed to explain or predict the
composition, structure and dimensions of dynamic molecules and crystals.
If one considers the typical bond distances of cation-anion pairs in crystals, it is found that the
specific changes of bond distance match the quantized increments of ionic radius expected from Bohr’s
equation. The lowest-mass ions such as Li+ have the largest increments of radius and the highest average
thermal speed. Subtracting the electron-orbital radius Rorb (Waber & Cromer 1965) from the effective
ionic radius Reff (Shannon 1976) indicates the radius of motion of the nucleus Rmotion. Plotting n/ms against
Rmotion generates a straight line of slope h/2, where n is a positive integer, m is the mass of an ion and s
its average thermal speed, h is the Planck constant and is 2Rmotion the circumference of motion. The bond
distance data for crystals indicate that the angular momentum of ions is quantized!
Quantized motion is also consistent with polyhedral structures in which each ion is surrounded by
several other ions, often at a radius (Pauling 1929, Bragg 1930). Note that Pauling (1947) calculated the
specific bond distances in crystals using an equation containing integers. These integers represent the
number of coordinating species (such as anions, protons, electrons and ligands in general), so this is a
general coordination theory. Students of organic chemistry are now trained to account for each changed
location of an electron, proton, ion, molecule etcetera because the resulting change of structure and bond
distance is well-documented.
Bond distances in crystals also depend on coordination number and are calculated exactly using a
quantized radius of motion of the nucleus plus the electron-orbital radius. Here, the significant variable is
the integer quantum number n, and the n of a cation increases with the number of coordinating anions to
increment the radius. This leaves little difference between the calculated quantized radii and the measured
ionic radii and bond distances. These residual differences of radius relate to a magnetic quantum number.
Both the bond-distance data (Pauling 1947, Shannon 1976) and the polyhedral structures are
consistent with the quantized motion of an ion confined to move across a spherical surface. If ions move
across this curved electric isopotential surface (as the electron moves around the proton in atomic
hydrogen) no work is done and the ion neither radiates a photon nor changes radius. But one still has
these positive integers n in crystalline condensed states of matter which are required in the Planck
equation for the spectrum of blackbody radiation.
With ions rotating about a central crystallographic coordinate (and not static or motionless), we
can quickly calculate an increased force and bond energy that explains both structure and energy of
crystallization. With rotation, cations are actually quite close to anions. Whereas by using the commonlyheld notion that ions are continually vibrating or oscillating, the resulting equations contain so many free
variables that we can neither generate a set of ionic radii nor predict bond distances or polyhedral
structures. These equations are complex because under a distance-squared law, force is not simply
proportional to displacement. But scientists are famous for ignoring any actual evidence and sticking to
difficult old theory!
Although everyone sees that the energy of the universe is being used to create some very elegant
structures ranging from molecules to galaxies, scientists still claim that “the laws of thermodynamics
require that disorder is increasing somewhere in the universe”. All I can say is “no, you are overextending the properties of gas and liquid. Different rules apply to generate the ordered structures of
molecules and crystals”. The only thing happening as structures are being built is the generation of new
photons. I agree with the common sense of the average person when I say that our bodies are highly
structured, highly organized and purposeful at all scales! Do you really think that disordered atomic
motion can generate a perfect cube of pyrite?
Of course it hardly matters what theory we use if we are talking about formulae for paint or glue.
So here I tackle something that matters - the structure of insulin - even though I expect numerous groans
and complaints from the old guard! Any valid complaints are welcome. Seriously. If someone finds a way
to predict composition and structure using basic physics, they should go ahead and solve this complex and
dynamic structure before I finish it all!
It is important to produce a clear model – here it is of local ions moving at specific radii in
dielectric crystal structures subject to the Coulomb force - which can be tested against measured structural
dimensions. For example, the observed carbon-oxygen bond distances in CO32- carbonate minerals are
mathematically equal to the smallest allowed n = 1 radius of motion of a C4+ ion and its electron orbitals
(Reff = Rorb + h/2ms). There is no evidence for the shorter bonds of a hybrid orbital expected by Pauling’s
valence-bond theory. If this specific ionic distance is also observed in a similar organic structure we
might consider ionic rather than covalent bonding. Any distances shorter than the smallest allowed ionic
radius of motion of C4+ (Rorb + h/2ms, with no free variables!) must be calculated using the covalent
model. This simply means that the electronic structure has adopted a lower-energy configuration.
In conclusion, this analysis of ionic radii and polyhedral bond distances in crystals generates an
excellent electro-dynamic model (of local ions in local motion bound by Coulomb forces) that we can test
and compare directly to similar structures observed in organic molecules including insulin.
LOCAL PHOTONS LOCAL ATOMS
Of the four known forces, the only force strong enough to explain chemical bonds in molecules and
crystals is the electric Coulomb force. No one has yet found a way to calculate bond strength using the
Coulomb equation because ions have been considered as motionless charges fixed at coordinates (e.g.
Born & Zemann 1964). Charge has also been considered a variable! But under a distance-squared force
law, an increase of bond strength is found for a charge rotating at a radius. Magnetic interactions may
modify bond distances slightly (cf. the Lorentz force law), but magnetism is by far weaker than the
electric force between charges. A century ago, physical chemists like Linus Pauling gave up trying to
solve this fundamental problem and instead developed qualitative models of bonding.
Here, I consider as valid an old idea that ions gain the stable electron-orbital structure of an inert
gas. They maintain this structure even if entering a polyhedral of increased volume. The ions simply gain
an increased volume in which to move, but only quantized increments of radius are allowed. A quantized
increment of radius commonly allows an additional coordinating ligand. In this model, the orbital
electrons move at speeds far greater than that of the thermal speed of ions. The orbital electrons move at a
considerable fraction of the speed of light, whereas atoms move at one to two times the speed of sound.
So the structure of electron orbitals is maintained as the ion moves. The Coulomb force that bonds an ion
in a crystal is insufficient to disturb this electric structure as the total vector sum of force on a
permanently-confined ion is zero. The bonded structure of a system of moving charges can now be
solved using fundamental equations of physics.
Local models are required for both photons and atoms to explain phenomena like atomic
absorption or the production of photons by individual atoms. Refraction also requires contributions from
individual local atoms, depending on their volume of motion. Local photons must interact with the
bonded structure of molecules and crystals, but this problem isn’t even on the map! To solve it, one has to
understand both light and its interaction with materials. I took three years to sufficiently frame the
problem and another four to discover a solution: we need a local model of light, no two ways about it.
The evidence indicates that electromagnetic light is refracted and absorbed by the electric charge
of individual ions (Teertstra 2005, 2008a,b). Light cannot be a wave spread out across space and time.
Yet in the current model, light is like a water wave at the beach, and atoms have the relative size of a
grain of sand. Consider that the wavelength of light absorbed (or generated) by atomic hydrogen is tens of
thousands of times greater than the diameter of the hydrogen atom. And yet somehow the full energy of
the wave gets absorbed by a single atom? Nonsense. Photons must be local particles, smaller than atoms.
Single atoms not only generate photons, they do so at a specific level of energy within the atom, at a
specific radius. The reason modern physics is called crazy or counter-intuitive by physicists is because
these “counter-intuitive” non-local models are incorrect. We simply have an unexplained aspect of nature.
When X-rays were first discovered, no one knew if they were particles or waves. Hence the ‘X’.
At the same time, no one really knew the bonded structure of crystals. For example, halite could be
composed of individual NaCl molecules. But the diffraction pattern formed by a beam of X-rays through
an ordered crystal solved both problems at once. X-rays are high-energy light AND crystals contain
periodic arrays of atoms. In the crystalline halite structure, each Na is surrounded by six Cl at equal
distance while each Cl is surrounded by six Na at equal distance. This is a polyhedral structure in which
moving positive and negative ions mutually confine one another. It’s totally dynamic!
We also need local interactions of X-rays with local ions. Diffraction of X-rays by crystals was
originally explained (by Bragg) by a similarity of the X-ray wavelength with the distance between planes
of atoms. Considering local X-ray photons, we now note that the X-ray wavelength is similar to the de
Broglie wavelength of a moving ion.
To explain the refraction data of dielectric crystals like halite, we need local serial interactions of
light with each ion in a crystal. The photon travels intact (without changing colour or energy) through the
bonded polyhedral structure of Na+ and Cl- ions at a specific level of energy. As with X-rays, two
problems are solved at once: light must consist of a stream of local photons, and moving ions must also
be locally confined in the periodic crystal structure. Photons traveling through crystals are refracted by
alternating sequences of cations and anions. That’s what makes salt look like salt and not like diamond.
But how can we to solve a dynamic bonded structure?
SOLVING DYNAMIC STRUCTURES
Given the many elements that could be in a liquid, no one has come close to predicting the molecular or
crystalline structures that will form or precipitate. In fact, there hasn’t been a good model of ions or ionic
bonds in these structures, and certainly not one that includes high-speed atomic motion. This is because
the empirical models of bonding (e.g. Pauling’s scale of electronegativity) consider high-speed atomic
motion as an afterthought, not as an essential aspect of creating form and structure.
Did you know that at the temperature of your body, oxygen moves at twice the speed of sound?
The bonds holding high-speed oxygen atoms within liquid or solid must be quite stable and strong. The
properties of oxygen do not change just because oxygen moves from an oxide mineral in a rock or into
water or into a molecule in your body. It’s still oxygen, and oxygen has very few choices of motion and
bonding.
Then there are elements like sodium and potassium, or calcium and zinc, found in rock or ocean
water or in your blood, which have just one type of bonding, ionic. Using these positively-charged cations
as reference states, the bond environments in minerals, bones and teeth are directly comparable to those in
organic molecules like insulin. From the force required to confine moving ions in simple mineral
structures, we can find the force requirements of the surrounding organic components.
Zinc is an essential ion in our bodies. A pair of zinc ions encourages insulin molecules to cluster
into a stable hexagonal snowflake-like arrangement. Symmetric forces stabilize this crystalline
arrangement, and these forces are specific to zinc (not iron or calcium). Although we can solve atomic
coordinates from crystallized insulin, these coordinates do not directly give the dynamic structure of a
free and active insulin molecule. So how does insulin recognize and attach to glucose? What are the
specific forces of attraction? To answer that, we need to solve the shape and form generated by moving
atoms and charges in insulin. We need to solve the dynamic structure.
If a mineral or molecule has high electrical resistance it does not conduct electricity (or does so
very poorly), and this indicates equal quantities of positive and negative charge in the structure. This also
means that we can pick up a rock without a shock. Most methods of chemical analysis assume or require
electroneutrality. The formula of the mineral is explained by considering reactions between ions. Why is
this compositional constraint of electroneutrality so exacting? A comparison of the strength of the
Coulomb force to the strength of gravity (both of which are distance-squared laws) indicates that the
electric force is far far stronger than the force of gravity. A free positive charge would attract a negative
charge, even if that charge had to travel a million miles! Mind you, the closest ions get there first.
In crystals, we have this situation where each high-valence high-mass cation has attracted a finite
number of anions to a radius. The anions commonly have lower valence and mass, so the heavy cation is
the center of inertia. The neighboring cation has generated a similar polyhedron. If separated, the two
polyhedral both have a net negative charge. But polyhedral connect by sharing anions to make the heteropolyhedral structure electroneutral.
But for a dynamic structure, we also require that the total angular momentum is zero. Otherwise
the molecule or crystal rotates. In a polyhedral structure common to many minerals, silicon is surrounded
by four oxygen atoms, this is SiO4. One also sees similar tetrahedral or square planar structures in
molecules. These structures are stable if anions alternate directions of rotation. Adjacent anions must be
spin-coupled!
But one also has an array of Si atoms, so a crystal structure has zero angular momentum if
adjacent Si atoms are spin-coupled. If ions are confined to move across the electric isopotential surface of
a sphere, over time, the entire structure has zero total angular momentum. So this is a powerful new
constraint on the structure formed by moving charges!
For example, suppose we have a six-membered ring in which all atoms are identical. A
symmetric structure is generated if all atoms have equal size. The symmetry is strongly enforced if the
structure consists of both positive and negative charges. But if one atom in the ring is replaced by another
element, the net angular momentum cannot be zero. The symmetry is broken. Instead, the non-zero
angular momentum must be counter-acted by a nearby atom (inside or outside of the ring structure). We
have this situation in six-membered carbon rings, in which one carbon is replaced by nitrogen. Nitrogen
must connect to an extra-ring species, not only for the sake of electroneutrality but also for spin coupling
which preserves the electromechanical stability of the ring.
The Si6O18 ring structures in minerals like beryl strongly resist substitution by other ions. These
substitutions are subject to constraints of electroneutrality, but the main problem is that even an
electroneutral substitution would reduce symmetry. This also increases the compositional and structural
complexity of the BeO4 tetrahedra and AlO6 octahedra that connect stacks of six-membered Si6O18 rings!
Sometimes Be2+ is replaced by Li1+ (as these ions have near-identical de Broglie wavelengths and
electron-orbital radii), but Na1+ must appear near the six-membered ring to maintain electroneutrality.
Even so, there remains a residual non-zero total angular momentum which is counteracted by the presence
of a neutral H2O molecule.
In these examples, the radius of motion of each ion must suffice to generate a polyhedron with
dimensions that allow polyhedral polymerization. Only by considering the dynamic motion of the
constituent ions can we determine the shape and size of the structure.
THE SCIENTIFIC PROBLEM
I found that bond distances in crystals can be calculated simply and accurately if ions have a quantized
radius of motion. The ions (consisting of a nucleus and its orbital electrons) are in high-speed motion
around the vacant crystallographic coordinate. This coordinate is the center of electron density and also
the focus of motion. The electron orbitals of adjacent ions do not overlap due to Pauli exclusion between
closed-shell orbitals. Low values of force and energy result from considering ions as motionless charges,
but force and energy increase for an ion in motion. My calculations are currently the most accurate in the
world, plus or minus 0.1%. So I began to wonder if the ions in minerals, which are also used in the
molecules of life for communication, may also have similar bond environments allowing quantized states
of circular motion (or elliptical states that conserve angular momentum). If so, the confining force is
easily calculated and the bond energy has a specific value for each quantized radius of motion. These
specific values would solve part of the dynamic structure in molecules like insulin that acts as anion.
These are the structural components that act like a crystalline salt.
But crystals are notably symmetric. They contain symmetry components like mirror planes that
require that the vector sum of force on a confined ion is zero. There is no resultant force which would act
to drive the ion out of the structure. This is exactly what happens in the inactive “storage” hexamer phase
of insulin. Six insulin molecules close-pack around a pair or zinc ions such that each zinc ion is
symmetrically encaged, as in minerals. But in the biologically active monomer, a single insulin molecule,
the snowflake-like symmetry is removed and the molecule has residual forces of attraction that allow
glucose to dock and attach.
The insulin structure is determined after crystallization in the presence of zinc. Two zinc ions
attract six insulin molecules with a combined effective valence of -4 (in one-electron valence units). This
is the stable snowflake structure, although the symmetry is a little less than perfectly hexagonal. However,
the dynamic reactivity of the insulin molecule requires an asymmetric structure. And this molecule
reminds one of globular galaxies - until highly-structured six-membered rings are seen!
The main problem then is to calculate a dynamic structure in which all atoms and protons are in
motion, and to use this motion to calculate the form and shape of the molecule. To do this, we consider
that the strong force holds all nucleons together in a very small volume such that their location cannot be
smeared across space. We use evidence from nuclear magnetic resonance indicating that electrons are not
delocalized in ring structures but experiencing local electromagnetic confinement. We use the core aspect
of thermodynamic theory which gives the average speed of an atom or ion from its kinetic energy. We use
the original calculations of the radius of electron orbitals from the two workers that defined the textbook
examples of orbital structure, Waber & Cromer (1965). But mainly I use the ideas of Einstein, who knew
that interatomic reactions must be local and that a photon must be local. He didn’t arrive at a theory, but
he stuck to his guns knowing that much more remained to be discovered in science. Much more has
indeed been discovered, but evidence of local physics ranging from atomic absorption to optical tweezers
has been suppressed. It is not at all popular to agree with Einstein!
It is known that particles have wave properties. Neutrons, for example, diffract. Now most people
can only imagine a wave as being spread out. The smallest wave shape is indicated by one wave length.
The simplest mathematical function for a wave is sinusoidal. But in this trigonometric function, one
quantity that grows from zero to a maximum is conserved with another quantity moving from a maximum
to zero. If we say that one quantity is the electromagnetic component of light, the other conserved
quantity could be mass. The two values are related by conservation of energy. Such a photon is local,
having wave properties over time, but this photon has no rest mass. We can consider such a photon as
being attached to a particle such as a neutron to provide polarity and a mechanism of motion. No new
rules of physics are introduced but we now have a local photon.
The present state of modern non-local theory is insufficient to tackle the most fundamental
problems of bonding and structure. Much modern theory has been constructed using layer upon layer of
historical assumptions which are rarely re-examined. I have spent the last decade doing just such a reexamination. I have personally tried out a great many existing theories, developed a few of my own, but
the problem is this. Given the elements sodium and chlorine, no one can predict the salt structure. No one
can calculate what salt should look like. This is a ridiculous situation. Existing theory must have serious
problems. We can’t solve it? You’ve got to be kidding. We must solve it.
SOME USEFUL PHYSICS
Consider the dynamic structure of an oil molecule such as six-carbon hexane in which protons move
around the electrons of a chain of carbon atoms. From the viewpoint of physics, this stable structure is
utterly fascinating. The proton is electrically attracted to the electrons but is also repelled by the nuclear
protons. Any charge experiencing acceleration radiates and loses speed, so a non-radiating proton must
move across a curved electric surface of zero net force, thus defining the outer shape of the molecule.
The components of this oil molecule are separated into distinct regions. A heavy positive nucleus
is surrounded by a layer of low-mass negative electrons moving at very high speed, and then by an outer
layer of positive protons moving at moderate speed. The nuclear cores are the slowest of all. As all
particles are in motion, we can calculate a wavelength or frequency from the speed of each particle (the
nucleus, the electrons, the outer protons). This gives organic molecules a layered dielectric structure of
short-wavelength high-mass elements with electron orbitals that are surrounded by long-wavelength lowmass protons. In other complex molecules, atoms of carbon, nitrogen and oxygen may be in thermal
equilibrium (such that their contact gives each atom the same average kinetic energy), in which case the
de Broglie wavelength of motion decreases as mass increases.
Motion of the atomic nucleus, the orbital electrons and outer protons creates molecular shape and
form.
When we talk about wave lengths (preferring a distance calculation over an energy calculation), we are
talking about how motion creates shape. When we talk about charge, we are talking about an electric
property of mass in which the Coulomb force between centers of charge varies with reciprocal distance
squared. Newton used a near-identical distance-squared force law to solve the dynamic structure of the
solar system, just as we wish to solve the dynamic structure of molecules. The difference is that Newton
could see distinct objects such as the moon and gather data on distance and time (and their ratio, speed)
whereas we cannot use light to see and locate atoms. As a result, solving the structure of a system of
moving charges is difficult.
One of the major theoretical problems is that for a moving electron, one cannot locate the center
of mass within one de Broglie wavelength. The statistical solution is to use a wave function to indicate the
probability of locating the moving electron. Using statistics, this center of mass and charge could be
anywhere and everywhere at once! This gives probable or likely structures, but the uncertainty is
significant.
In organic chemistry, this idea of delocalized electrons is widespread. The electrons are said to be
delocalized in benzene, but it would appear that the electrons are actually localized. Bond distances in this
cyclical C6H6 structure are consistent with J-coupled nuclear spins due to the influence of bonding
electrons on the magnetic field between two nuclei (Gerrat, Raimondi & Cooper 1987).
Over a century ago, chemists gave up on using physics and the Coulomb force equation and out
of necessity developed numerous qualitative models of bonding. The progress has been spectacular, but
the fundamental problem of calculating complex molecular structures using the known forces and
physical constants remains outstanding. The continuing problem is that non-local theory cannot be used to
generate a definite structure. But non-local theory is incorrect for atoms because the nucleus is local and
cannot be smeared across space.
Einstein considered local action-reaction to be essential to the solution of these complex
structures and he realized that much remains to be discovered. Consider the problem of mass. Isaac
Newton gave a wonderful description of our experience of mass (which can be tested in experiments). We
push on an object and it resists acceleration. If two objects are given an equal push (meaning the same
force), the one with higher acceleration has lower mass. We simply define the ratio of force to
acceleration as mass. But that’s it for the theory of mass. We do know that the nuclear mass occupies a
very small volume. Experimentally, most neutrons fired at a thin sheet of gold foil pass directly through,
but a few are deflected at high angle. Theoretically, two positively-charged protons ought to repel one
another and fly apart, but a strong force has recently been proposed that overcomes the repulsive
Coulomb force between protons at short range.
Protons are held together with neutrons as if in a tiny bag. Nuclear mass is confined within a
diameter much less than the de Broglie wavelength of motion. For the elements starting at helium, no one
can claim that their mass is spread across time and space. The strong force requires a local nuclear
mass. A moving atom has a definite trajectory and is subject to Newton’s laws of motion. Einstein’s
insistence on local action-reaction must be correct - although it is currently unpopular to say so.
The strong force indicates that we need to consider local action-reaction mechanisms and trajectories
of local particles to solve dynamic molecular structures.
Scientists relying on popular quantum-theory arguments from the early 1900s do not realize that
the strong force requires a local theory for the motion of atoms. They get quite upset by use of
terminology such as “atomic trajectories”, claiming by rote that electrons are delocalized, “atoms” do not
exist and local “trajectories” are impossible! Even ionic bonding has become a vague concept. Ignoring
the strong force and claiming that atoms can be in two places at once, scientists working with non-local
theory cannot solve (much less predict) the dynamic structure of even the simplest molecules without
using free variables that “push” the calculations toward a reasonable result. Even then, the results are
ambiguous. But the main problem is that people gave up trying to use physics to solve dynamic
structures.
GOALS
The overall goal of THE INSULIN PROJECT is to calculate the dynamic structure of insulin. Here, it is
thought that the structure is formed by the regular motion of numerous particles. For moving charges
(protons and ions), the non-radiative trajectories must correspond to curved (geodesic) surfaces of zero
net force. If motion is quantized, force may be calibrated using known values for ions in crystals. The
final molecular topology gives both residual forces and dimensions that must match the glucose structure.
The first task is to determine the radius of motion of zinc in the structure. This depends in part on
the repulsive Zn-Zn force between two moving Zn2+ ions. The net attractive force of the six surrounding
insulin molecules is also calculable as it must equal the outward force of the moving zinc ions. Note that
the confining force is quite specific to the dimensions of zinc, as the hexamer does not crystallize in the
presence of other divalent ions such as calcium, magnesium or iron which are present in abundance.
Next, the bond environment around the disulphide ion is calculated and examined for structural
similarity in sulphide minerals; disulphide is also thought to occur in the minerals with the pyrite
structure. The radius of oxygen can be calculated using the electron-orbital radius and the quantized
angular momentum. The smallest n = 1 quantized radius of motion of carbon has been defined for the
ionic C-O bond in carbonate minerals. If the motion of these heavy atoms relates directly to their thermal
speed, it may be possible to re-refine the diffraction data using motion-corrected scattering cross-sections.
This may better resolve the dynamic structure.
My initial calculations suggest that the speed of protons varies with force such that the local
structure becomes independent of collisional interactions (as in atomic hydrogen). In the examples of OH, H2O and H3O+, it would appear that the entire molecule exchanges momentum with surrounding
molecules; therefore, one can calculate the thermal speed of the molecule as a distinct entity.
Individual bonds in each amino acid must be assessed for the possibility of oscillatory motion. It
may be that adjacent atoms (for example in C-C linkages) are simply spin-coupled. That is, they have
opposite directions of motion that give a six-membered ring a zero sum of angular momentum. In that
case, short bond distances must relate directly to a constant axis of rotation rather than random motion
across a spherical isopotential surface. If N replaces C, the distinct difference in angular momentum
requires a nearby OH group to maintain the electromechanical stability of the molecule. This provides
constraints on the radius of motion of OH and thus on the bond strength.
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