September 7, 2008

A simple model of electrons, protons, neutrons and their antiparticles

© 2008

A strictly classical model of electrons, protons, neutrons and their antiparticles is presented. The model explains mass, spin and charge for each particle. An approximation of the value of the elementary charge can be calculated, and is found to be 0.956 times that of the measured value. Further, the model strongly suggests why neutrons can be unstable. A structure of the atomic nuclei is proposed, which explains why the ratio N:Z for stable nuclides follows a limited range as Z increases. Only the electromagnetic force is needed to support the model.

General hypothesis
It is hypothesized that an elementary particle is simply a standing enclosed electromagnetic wave with a half or whole number of wavelengths (λ). For each half number of λ the wave will twist 180° around its travel path, thereby giving rise to chirality. As for photons, the Planck constant (h) can be applied to determine the total energy (E): E = nhc/λ, where n = 1/2, 1, 3/2, 2, etc., and c is the speed of light in vacuum. The mass (m) can be expressed as a function of λ, since E = mc2 gives m = nh/cλ from the formula above.

A particle will possess no charge if the electric field of the looping wave is effectively canceled out by electric field vectors in opposite directions. If the sum of electric field vectors differ from zero the particle will be charged. Negative and positive values of charge arise from opposite chiralities.

Like electric currents flowing in the same direction attract each other, also loops of electromagnetic waves attract. They align with the waves moving in the same direction and with their magnetic moments merging.

The electron and positron
The electron represents an enclosed electromagnetic wave of 1/2 λ, analogous to a Möbius band because of the 180° twist. The mass is determined by the wavelength. The incomplete wave period causes an asymmetry in the standing wave and allows a given fraction of the electric field to escape.

The wave can release potential energy by coiling upon itself once, making a double loop and switching chirality in the process. An attempt to compute the value of the elementary charge suggests that the coiled structure is the one occurring naturally.

By convention, the charge of the electron is negative and the electric field points toward it. This implies that the electromagnetic wave processes in a left hand mode through the internal twist. One full twist will take two loops, explaining the 1/2-spin attribute of electrons.

The positron has the same half wavelength, structure, mass and spin as the electron, but opposite charge because of right hand twisting.

The proton and antiproton
The proton and antiproton are built like the positron and electron, respectively. But they have a much higher total energy, giving them a shorter wavelength and more mass.

The neutron and antineutron
The simplest elementary particle with no charge consists of 1 λ, and the neutron apparently does. The measured mass of the neutron is just slightly larger than that of the proton, implying a λ nearly twice that of the proton. It has like the electron a measured negative magnetic moment, suggesting left hand twisting.

The observed 1/2-spin of free neutrons seems to contradict the whole λ, but can be explained by folding. Because of the internal 360° twist, tension is released in the neutron if it folds into two lobes (like converting the number 0 to an 8). In a common plane, the formed two lobes have opposite spins and magnetic moments. By folding again, perpendicular to the intersection, the neutron aligns upon itself and releases potential energy in the process. It now resembles two parallel waves with a 180° twist each, and therefore appears with a 1/2 spin. Locally, at the “hinge” region, a strain is created which makes the neutron unstable. Eventually it breaks down in beta decay, forming new waves.

It is likely that the two lobes of the neutron go through coiling, analogous to that of the 1/2-λ particles. In that case the neutron will consist of two antisymmetric double-loops, with opposite twist compared to the uncoiled neutron.

The antineutron should materialize and behave like a neutron, but with an opposite twist.

Approximate calculation of the elementary charge
The measured elementary charge (e) of 1.602176487 × 10−19 C can be approximated theoretically fairly well by assuming that the charged particle appears in a coiled configuration and that the 180° twist is effectively concentrated near the node of the enclosed wave.

In the electromagnetic wave making an elementary particle, the value of the total electric field (|Etotal|) can be derived from the total energy. Using radians, one can let |Etotal| be represented by the definite integral

, where a is a constant. Letting the integral curve twice around the circumference of a circle, the 1/2-λ wave encloses a sphere of radius (r) λ/8π and volume (V) λ3/384π2.

Only a fraction of the vectors in Etotal is not canceled out in effect by vectors in the opposite direction, and contributes to the charge. This fraction can be approximated by assuming a perfect double circular path and neglecting the effect of the internal 180° twist. Because of symmetry around the line crossing the node + peak (0 and π/2, respectively) and π/4 + 3π/4, the vector sum of Etotal will be parallel to this line. This net electric field (Eapprox) will point in the direction of π/4 + 3π/4, and its fraction can be expressed as:

= (−a/30)(5 cos(3π) − 3 cos(5π) − 5 cos(0) + 3 cos(0)) / a(− cos(π) + cos(0))
= (−a/30)(− 5 + 3 − 5 + 3) / 2a = 15−1

The effect of not taking into account the 180° twist concentrated near the node will be to underestimate the fraction of escaping field vectors. This is because some of the vectors subtracted from the sum in the computation, actually are perpendicular to the net sum.

Gauss’ law for electric field gives:

hc / λV=ε0|Etotal|2
|Etotal|2=384hcπ2 / λ4ε0
|Etotal|=(384hc)1/2π / λ2ε01/2

, where ε0 is the electric constant. Also, Coulomb’s law applied on a point charge gives the electric field associated with it:

|E|=Q / 4πε0r2

, where Q is the charge of the particle.

An approximation of the absolute value of the charge (Qapprox) carried by the particle can now be found. Since 15−1|Etotal| = |Eapprox|, we have:

15−1(384hc)1/2π / λ2ε01/2=Qapprox / 4πε0r2
16(3hc)1/2π / 15λ2ε01/2=64π2Qapprox / 4πε0λ2
(3hc)1/2 / 15λ2ε01/2=Qapprox / ε0λ2
Qapprox=(3hcε0)1/2 / 15
Qapprox=1.531376790 × 10−19 C

So, Qapprox/e ≈ 0.956. Apart from the already mentioned cause of underestimation, deviations from a perfect double circular path and possibly other factors as well, can make the approximated elementary charge at variance with the measured value.

As is shown, the absolute value of the charge does not depend on λ in a double circular wave. It will not for wave particles of other shapes either.

The atomic nucleus
For an element above hydrogen in the periodic table, the nucleus consists of a defining number of protons (Z) in a framework of neutrons (N). The “8-configuration” of the neutron is apparently stabilized if a proton aligns with one of the lobes. This may be due to the electric field topology of the proton. The opposite lobe is free to align with another proton and/or other neutron lobes. Thus, several neutrons can build a structure holding the protons. The positions of a proton in a neutron lobe may be restricted by the electric fields from other protons in the nucleus. Protons may therefore share different binding energies with their neutrons.

In a stable nuclide, there must be sufficient framework (N) to prevent overlapping of the electric field vectors from the charged units (Z). On the other hand, if the ratio N:Z is too high there will not be enough protons to stabilize all the neutrons. A neutron will eventually fold onto itself and go through beta decay. A too large Z will destabilize the structure as the separate electric fields more frequently conflict each other, and thereby repel the protons.

By accounting for nuclear spin and nuclear magnetic moment, and also fitting binding energy into the model, it should be possible to find likely configurations for any nuclide. Different configurations may correspond to alternative excitement states of the nucleus.

The presented model, or a modification of it, should shed light on the structure of other elementary particles as well.

The model suggests that both the electromagnetic force and gravitation can only originate from electromagnetic waves. This may give insight into understanding the intrinsic structure of these only two forces of nature.

Several testable predictions can be made from the model, making it falsifiable.

HyperPhysics (; Department of Physics and Astronomy, Georgia State University, Atlanta, GA, USA) was an excellent source when exploring basic concepts in physics, and Wolfram Mathematica Online Integrator (; Wolfram Research, Inc.) was a helpful tool when calculating the integrals.


Anonymous said...

For a rotating field, there must be a frequency associated with it. If the field is stable, the frequency is constant. Several years ago, I discovered a correlation between the charge of the electron and a fixed frequency that falls within the range of feasibility. What frequency have you associated with your rotating field of the electron?

What has led you to believe that the field wave is closed, other than assumed chirality? It would make more sense to me to associated the force field of the electron (Coulomb's Law) with the rotating field, especially for the correlation described above.

Rebel said...

Thanks for the comments!

I have not associated any frequency with the electron.

The closed wave explains the two kinds of charges (right-handed and left-handed). Also, the absolute value of the charge is identical for a big particle (proton) and a small one (electron) with the same shape.

As I see it:

Open EM wave: radiation

Closed EM wave: particle

Rebel said...

Actually, according to the model the electron are bigger than the proton diameter-wise, but the electron is much less energy dense. Sorry for the confusion! (And for not detecting it earlier!)

zv said...

"Several testable predictions can be made from the model, making it falsifiable."

... for example...

Rebel said...

I can come up with three obvious predictions:

1. Elementary particles should be (almost) two-dimensional.

2. Also the atomic nucleus should be two-dimensional according to the model.

3. It should be possible to draw a schematic structure for every nuclide, which explains the observed nuclear spin and nuclear magnetic moment for that particular nuclide.

Please feel free to make predictions that will challenge the model! Because the model is so simple, and fundamentally different from the Standard Model, that should be an easy task for opponents and others.

It may even be possible to disprove that electromagnetic waves can form loops with a 180° twist for each half period, which is the very premise for the model. Only that description can allow for half-period closed waves, since the Möbius property makes positive and negative amplitudes identical.

Anonymous said...

How does this theory explain Quantum Entanglement?

Rebel said...

It doesn't.

Rebel said...

In a (heated) discussion at about the presented model an erroneous statement in the text was pointed out to me. It has now been changed. Sources to misconceptions also became evident, and have been/will be reformulated or elaborated. This includes showing more steps in the calculations.

All the conclusions are still the same, as is the validity of the calculations.

Imperator said...

A model similar to yours is described in J.G. Williamson and M.B. van der Mark "Is the electron a photon with toroidal topology?" 1997.

Here is a link

or google it.

The model has problems though.

Ehrich said...

Sorry to get in on this so late but would you say that your hypothesis is in parallel with Carver Mead's "wave-only" view of the atom?

I've been working on this same hypothesis since around 2002 and I see lots of evidence to back it up including the interference pattern that seems to be present in the current model of the "electron cloud". Unfortunately I deal with more of the abstract concepts and not the math as much but your work here is very promising.

greg alexander said...

Pardon my amateurness. I think this is fundamentally a better approach (though I suspect the details are wrong, naturally) than quantum mechanics. I think once we actually understand what an electron _is_ (and surely it is nothing but "waves" in some sense), all of the nonsense and "spooky" parts will simply melt away.

However, I have a basic question. What is a closed wave?

This is probably way off the mark, but the only way I can conceptualize of a standing wave that is not infinite is demonstrated by (I replicated a physics lecture I sat in on once). Otherwise you need to have "something" at the two "ends" of the wave reflecting energy back?

carlosmoya79 said...

While I barely know anything at all about the subject, I couldn't but notice that this model doesn't seem to depict nucleons as composite particles. Thus, if I may ask, where does this leave the quarks?

Martin said...


In light of the proton size update article that you commented on, how does your calculation change? Does it predict this exactly? Please show.

Also, your explanations are very unclear without images depicting the geometries you describe. Even just a parametric plot in Wolfram Alpha would suffice if you don't have the proper software.

Rebel said...

Thanks for the link - the article is very encouraging! To me it seems that my own model is almost a special case of their toroid, except for the introduced 180° twist which also allows for 1/2-wavelength particles...

When googling the paper I also stumbled across another interesting work: The nature of the electron

I don’t know of Carver Mead's view, but my approach to elementary particles is certainly “wave-only” :-)

Like you I think there is lots of “evidence” of such particles, and I find it strange that so few people are digging more into it!

Greg Alexander:
A closed wave just means that it is looping, i.e. there are no “ends”.

Remember, EM waves can both twist and bend!

Who needs quarks? Oh yeah, the standard model of course...

Quarks have never been detected, e.g. by measuring their alleged fractional charges. They are just inferred in the light of the models that requires them! The same can be said about weak and strong nuclear forces.

Rebel said...

I have not made any calculations. I neither have all the details from the mentioned experiment (The proton shrinks in size) nor the mathematical capacity to perform such calculations! I would be great, and also more credible, if somebody else cared to perform the calculation and falsify my suggestion.

I agree with you that images of the geometries would benefit the description of the model, and hopefully I will manage to make some decent figures in the near future... Until then you will have to imagine it visually. A self-made Möbius strip may help...

Ehrich said...

Well, I'll give you the same visualization that my friend who started me down this path gave me and maybe it'll help you as well...

Imagine a body of water that is still. Now drop in a pebble and watch the water ripple. Now drop in several pebbles at the same time in the same general area and notice the interference pattern looks incredibly like the current model of the atom. Just to test the idea, I found a wave interference visualization app, gave it two waves to represent the waves that would be 2 electrons in a "typical" hydrogen atom and lo and behold there was an interference pattern that looked EXACTLY like the "probability densities" for the electrons in a hydrogen atom as seen here:

That's where I started and ever since I've been taking apart the idea that waves are interfering with one another to make our matter. These days I realize that "pebbles" isn't a good analogy since it's more like a steady stream of water for each pebble and that maybe gravity was one of those waves but your idea of a closed wave makes a lot of sense here as well so I'm going to ponder this a bit and see where my brain takes me.

Ehrich said...

I must have missed this when it came out...regardless, it comes pretty close to your ideas..

Anonymous said...

A photon is described as an electric field interacting with a magnetic field in a self supporting manner along the direction of propagation, often diagrammed as two orthogonal sine waves. Can you create a similiar visualization and/or animation which explains how the E and M fields are interacting in order to produce the described shape in a stable manner? Can you determine a "path" configuration which computes as "stable" using the EM equations in simulation software?

Anonymous said...

Hello! Great to see someone throwing some math AND thought into physics. I unfortunately lack the skills in the first.. But wave only models captured a lot of my thoughts lately.
The "model" I currently work on operates on phase-change: space is filled with liquid aether, which force is applied on. Once the energy reaches the critical point, gaseous aether - matter emerges. Thus it has no fixed position, it appears and disappears with energy, staying only in stable configurations for some time.
The electron is a point phase change. Once it expands, it is crushed by incoming waves. If it is in a stable configuration, it reappears again and again, giving the illusion of a particle.
The rest is complex fluxes of energy, with self reinforcing properties. Once such system emerges, it perpetues on incoming energy. Thus matter is structured energy, and we are at the boiling point of aether.
With enough energy, we should see bubbles in aether - center of the Sun, earth, etc, surrounded by a foam, clouds of "matter", keeping the energy compacted.

Makes any kind of sense? :-)