304 Last modified August 22, 2016

Hofstadter's Shells Revisited

Vernon Brown

Consider that the proton is composed of three electromagnetic shells. Each shell is a single photon of electromagnetic energy trapped in a cavity defined by its own electric field. The field develops when a photon changes direction. Strength of the fields increase being weakest on the outer shell and strongest on the innermost shell. This field strength follows a mathematical rule set out in the Square of the Shells Rule.

The charge of a proton's outer shell is positive. A smaller shell inside the outer shell is negative. A much smaller shell inside that shell is positive. So going from the innermost to the outermost shell you find a charge sequence of positive, negative, positive. Since there are two positive shells and only one negative shell, the proton's overall charge is positive.

A neutron is a proton that has an extra negatively charged outer shell. The field strength of the neutron's outer shell is weaker than a proton's outer shell being only about two and a half times stronger than that of an electron. Left alone, neutrons loose their outer shell and become protons. The outer shell flashes away as a gamma-ray photon.

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Square Of The Shells Rule
Discovered by Vernon Brown in 1991

A proton is composed of three shells and a neutron is the same except it has an extra outer shell. This outer shell's mass is the difference between proton and neutron mass. Measurements show this to be about 2.5 electron masses. We can extend the decimal of this difference to 2.54992206745 electron masses so that when this number is repeatedly squared and summed the result exactly matches the measured mass of a proton.

In order to see this, first square the number 2.54992206745, and square the result, then square the result of that, to obtain, 6.50210, 42.27734, and 1787.37327. These three results added together total 1836.1527, which is very close to the exact mass of a proton in electron masses. Add the starting number and the result is 1838.7026, which is very close the exact mass of a neutron.

Scientists of the time thought that they would eventually show mass to be reducible to smaller and smaller constituents until they found a smallest-possible piece. At the turn of the 20th century, most people believed that this smallest piece, the final irreducible constituent, of all physical reality was the electromagnetic field.

There were very compelling reasons why most scientists believed this and these reasons have never been explained by other ideas. H. A. Lorentz worked out a theory of relativity years before Einstein. The Lorentz version of relativity had material things change shape with motion. H. Ziegler was a student of the Lorentz version of relativity. H. Ziegler discussed this with Einstein, Planck, and Stark.

If these scientists were right, Hofstadter's shells would be made of photons, and each shell would exist in its most simple state as just one sine-wave cycle of electromagnetic energy. Since such photon shells must complete their loops at the speed of light in one wavelength, and we know the mass of each shell, and their wavelength is determined by their energy content in accord with mass-energy equation, we can calculate the diameter that each shell would be if it were a circle.

Shell diameters

The diameter of shell 1, the neutron's outer shell, is 3.3170 x 10-11 centimeters. The next shell in, shell 2, the proton's outer shell, is 1.1889 x 10-11 centimeters. The next shell, shell 3, the middle shell of the proton, is 1.82854 x 10-12 centimeters. Shell 4, the final and most inward shell of both the proton and neutron, is 4.32511 x 10-14 centimeters.

The most simple pattern would be a circle of one wave length. This pattern would repeat at the speed of light and rotate to form a sphere. The path of a photon around the circumference of the sphere would be a pattern caused by its balanced negative and positive charge.

Tracing a path through space, a photon in a self resonant shell would follow a path representing particle spin. The first spin state is the photon loop that must spin at the photon's constant speed--the speed of light. The second state is a flat wise spin perpendicular to the first so that each loop forms a sphere.

This combination provides the rich diversity of spin states necessary to satisfy Dr. Hofstadter's observations of hadronic spectra. There is a spin-up, and spin-down possibility, (clockwise, or counterclockwise), and a flat wise spin left, or spin right. In combination, there is also the possibility that adjacent shells may spin alike, or different, in the spin-up,-spin-down state, and likewise in the spin-left,-spin-right state. However they do relate, this should be an important and useful law of nature that is now not known.

Since each shell is charged, the inside shell and the next-to-inside shell form a doublet that taken together is charge neutral. The next shell out provides the proton's positive charge, and is associated with another outer shell in the neutron. The two outside shells of the neutron thus form another doublet associated by charge. All these spin states, associations, and doublets provide the rich and diverse nuclear spectra observed at electron-impact energies below 1000 MeV.

An electron's mass is .51099906 MeV. This amount of energy is also present in a photon whose frequency is 1.2344046 x 1020 HZ, and whose wavelength is 2.286399 x 10-10 centimeters. If this photon were curled into a loop whose circumference was equal to its wavelength, it would form a circle whose diameter would be 7.730601 x 10-11 centimeters.

This is much larger than an electron is supposed to be. Dr. Samuel Chao Chung Ting of MIT failed to find a solid electron structure larger than about 10-16 meters. His methods could not detect structure smaller than that, so he concluded that an electron must exist as a point charge smaller than 10-16 meters.

There are problems with all measurements of particle size. Physicists assume that somewhere in particle structure there exists something solid that a probe can detect. Constructed only of electric and magnetic fields, there is no solid something in particles. The detecting mechanism punches right through the outer shells and bounces off the inner most proton shells. Redesigned tests would relate energy of the detecting beam to the expected energy structure of the shell to be measured.

Electrons possess a strange characteristic. It is not possible to predict the exact location that a single electron will impact on a flat screen. They seem to exist in a "fuzzy" area most easily described by a probability potential that the electron is located at any certain point within a sphere of about 7 x 10-11 cm. in diameter.

This phenomenon is consistent with the idea that an electron may be composed of a gamma ray photon spinning in a primary spin state at the speed of light and in a secondary spin state forming a sphere of 7.730601 x 10-11 cm. in diameter.

According to the standard photon model prior to 1980, photons did not interact with the fields of other photons and certainly not with their own fields as would be necessary if a stable photon loop were possible. After 1980 this changed.

Nicolaas Bloembergen, Arthur Schawlow, and AK Siegbahn shared the 1981 Nobel Prize in Physics for their contribution to this change. They helped develop laser spectroscopy, a tool used to investigate photon-photon interaction in the new science of non-linear optics.

Although this science is very new, it is now certain that photons do interact with their own electromagnetic fields and with those of other photons. All the ingredients necessary to cause photons to form stable loops are present. These include resonance, electric charge due to the asymmetry caused by the bent path of the photon in the loop, and positive feedback resulting from the electric charge.

Feedback and resonance make the loop stable when the loop circumference is one wavelength of an electron-photon's frequency. Some shorter wavelengths can form unstable loops that quickly unwind into photons again, giving rise to the multitude of unstable particles observed downstream of collisions in particle accelerators.

Electrons have antimatter counterparts called positrons that were first observed by Dr. Carl D. Anderson at the California Institute of Technology in 1932. Scientists soon discovered that when electrons and positrons collided at very low energies, they became photons of energies equivalent to their mass or, 1.234404 x 1020 HZ. This is consistent with the idea that electrons and positrons are composed of photon shells.

That mass can become energy, and energy can become mass is so generally accepted today that people give little thought to the process. But there must be a process, and it must be a reasonable process for those of us who believe that nature must operate by reasonable processes.

If mass is composed of photon shells, the observed transformation of mass into electromagnetic energy is a reasonable process; otherwise, a reasonable process for this transformation still needs definition.

At high energies, colliding electrons and positrons generate much more than just two photons. Electron-positron collider today produce many unstable particles as well as more electrons, and even protons, neutrons, and their anti-matter counterparts. Even a casual observer must see that these particles are created by the process. They can not possibly come from the colliding particles which are orders of magnitude less massive.

What then is the significance of short-lived unstable particles created in these processes. It seems a very dangerous assumption to suppose that because such particles may be created, they must exist in stable mass. It seems even more dangerous to suppose that they somehow form the basis of nuclear structure. The danger is that we are building an ever-more complex and wobbly foundation for fundamental physics. Such a foundation cannot possibly survive. It cannot survive because it was admittedly unreasonable from the start.

Einstein warned us of this. He said, "There is no doubt that quantum mechanics has seized hold of a beautiful element of truth, and that it will be a test stone for any future theoretical basis. However, I do not believe it will be the starting point in the search for this basis, just as, vice versa, one could not go from thermodynamics (resp. statistical mechanics) to the foundations of mechanics."

When in a one-wavelength loop, the electrical field of a photon, changing as it does with time, must complete its negative-positive swing as it moves around the circle. A maximum-negative-amplitude point moves around the circle changing with time, but since it must traverse a circumference described by the same sine function that governs its rate of change, the negative field of the photon must remain toward the outside of the circle all the way around the loop. This gives the electron an overall negative charge originating at its circumference and spreading outward in a field that decreases in amplitude with distance.

Electron charge is a constant; why so has been a mystery to scientists of the twentieth century. Now, we know that this constant charge is the result of the constant amplitude of the electron's photon from which both the electron's charge and Planck's constant derive.

A photon in a loop smaller than an electron's circumference must complete the trip around the loop more often than an electron's photon around an electron's loop. It therefore must present its constant amplitude at any certain point around its circumference more often, and so must exhibit a more powerful force at its circumference. We could then devise a square-of-distance gauge calibrated to one-electron force at the radius of the electron's shell and measure the force of charge on the circumference of the inner photon shells. The inner-shell charge is greater, but since the force originates at a smaller radius and diminishes as the square of distance, it is the same as an electron's force when gauged at an electron's radius.

Strong Nuclear Interaction

Consider two protons, each consisting of three shells. Assume that they may merge together until their outer shells pass through each other and come into close proximity with their next-to-outer shells. Four shells then have other shells of opposite charge in close proximity, and the electric forces of these shells, as calculated by the square-of-the-shells rule are, 6.50210, 42.27734, 6.50210, and 42.27734. Added together, these forces total 97.55888, electron forces, the value of the strong nuclear interaction.

All this may be mere coincidence, but coincidence like this would be like watching a thousand buffalo stampeding through your lawn leaving buffalo chips and hide and hair torn on splintered shrubs and hoof-print tracks from the way they came to the way they went. They do it every day, and you can invite anyone to watch them do it. Would you believe any such guest who told you those buffalo did not exist? Have we come so far down the unreasonable path that Einstein warned us about that we can no longer even consider the correct and reasonable one?


Maxwell's equations may be arranged to calculate the speed of light from two constants of empty space. These were known as electric permittivity and magnetic permeability. They are only constants in the absence of electric and magnetic charge. When charge is present, the value of the constants increase to slow the speed of light. Electric and magnetic fields from all photons in the universe extend outward forever from photon central points. Since massive objects consist of photons, the strength of the fields must necessarily be greater near massive objects, and diminish as the square of distance away from the massive objects. These fields affect the electric and magnetic constants to make them greater near massive objects. Electric permittivity and magnetic permeability thus convey the force of gravity.

The two constants, which really are variables, represent the impedance, Z, of space. They act to impede the formation of electric and magnetic fields and thus determine the speed of light. The path of light bends toward the direction of more impedance. Material things comprised of light must gravitate toward that same direction.

Gravity is thus an electromagnetic phenomenon but separate from and outside the normal electromagnetic field equations. It is a simple refraction of light. It comes about because the impedance of empty space follows a gradient away from massive objects. This is a wide open area. No one has yet formulated the relationship between the electromagnetic constants and gravity.

Scientists have ignored the implications of Hofstadter's findings for decades, but the implications are still there. Some things are possible given this makeup of mass, and other things are not possible. Not possible, for example, is a one-photon loop with anything other than one unit of electric charge. What then is a quark? What then, is a big-bang type of singularity? None of these are possible.