This is a rotating charge loop model of an electron which explains the electron’s de Broglie base frequency to an accuracy of over 6 decimal places. The model also predicts the magnetic moment of the electron to over 6 decimal places and helps explain the transition from a purely electromagnetic photon to a fermion state of matter. The model also explains how charge and spin are conserved in the transition. Finally, this concept might be extended to explain the muon and tau higher energy states of the electron as well.
In the 19th century, Maxwell showed that light is composed of electromagnetic energy [
The model has two parts: 1) What is the form of an electron, and 2) How does a high energy photon convert into an electron-positron pair?
Many attempts have been made to estimate the size and shape of an electron. At the turn of the 20th century, Lorentz presumed it to have a spherical shape and then calculated its radius to be 2.82 ´ 10−15 m [
The size of an electron unfortunately cannot be measured directly (uncertainty principle), so what other means is there to estimate the diameter of the electron? We know the “Charge” of an electron to at least 7 decimal places, and we also know the bare Magnetic Moment of the electron to about the same accuracy. If we take those two extremely accurate figures and assume that the electron’s charge rotates in a circle at the speed of light, and then solve for the diameter required to generate the magnetic moment of an electron, we arrive at a diameter d = 7.72318492 ´ 10−13 m.
Calculations for above:
Known values and definitions:
Qe (charge of electron) = 1.602176565(35) ´ 10−19 Coulombs [
μe (bare magnetic moment electron) = 9.27400968(20) ´ 10−24 Amp×m2 [
g (g factor correction) = 1.00115965218073 [
Note: see Postulate 4) below for when and why to apply g factor correction.
C (speed of light) = 2.99792458 ´ 108 m/s;
T (transit time at speed C around loop of diameter d) = πd/C;
μl (magnetic moment of current around any circle) = Amperes ´ πd2/4.
For a charge of a single electron going in a circular loop at the speed of light:
Solving for the “d” that satisfies the known bare magnetic moment μe:
What is interesting is that the length around this loop happens to exactly match the wavelength of a photon with equivalent energy to the rest mass of an electron i.e. a 0.510998910 MeV photon (this photon wave length is also exactly 2.426310 ´ 10−12 m).
It is as if an electron is simply a 511 KeV photon that is curving back on itself! But this is hard to believe because a photon is neutral, i.e. it has no net charge. Williamson and van der Mark hypothesized an interesting model showing how a photon might be able to wrap back on itself [
In formulating this model, we have been lead to propose the following postulates:
Postulate 1) A purely electromagnetic photon has “open” magnetic field lines, which oscillate, but never close on themselves, which is why it travels at the speed of light.
Postulate 2) Matter is different from a photon only in that its magnetic field lines close on themselves (allowing the energy of matter to exist at rest).
Postulate 3) The mass of matter arises from the distortion of space due to the concentration of the electromagnetic energy. Note: this is not a new idea; Lorentz and others have suggested this by equating the electromagnetic energy in an electron with its mass (and this also fits Einstein’s view that the “gravity” of mass is due to a distortion of space time itself).
Postulate 4) The de Broglie matter-wave arises from the natural frequency of the electron which generates “virtual” photons of the same frequency. The photons are then reabsorbed as described by Feynman; “the electron goes along for a while and suddenly emits a photon; then (horrors!) it absorbs its own photon” [
de Broglie Frequency:
de Broglie Wavelength:
where
The frequency of this model is
This frequency matches, to over six decimal places, the de Broglie “base” frequency (at electron velocity =0)
Note 1: Feynman used “virtual” photons as a way to calculate the “g” factor correction to the bare electron. The virtual photon contributions that he and others calculated for g/2 added a correction factor of 1.00115965246 to the bare magnetic moment (amazingly close to the experimentally measured value of 1.00115965218 [
Note 2: the concept in Postulate 4) is closely related to the Broglie-Bohm “Pilot Wave Theory” [
We have addressed the electron, but to better understand the transition from photon to matter it is important to understand the nature of the photon as well.
Maxwell:
if we combine Maxwell’s equation with Einstein’s equation
Einstein:
we then get:
All of the terms on the right are electromagnetic, which support Postulate 3) which states that the “mass” formed is due to the distortion of space by the concentration of electromagnetic energy.
Note: the wavelength in
Reality Test 1: One reality test of this model is that it can explain how a positron and an electron can fly away from each other. In order to overcome the extremely high electrostatic attraction between an electron and a positron at 10−13 meter distances, the magnetic alignments must be opposite at the initial formation of the electron positron pair. In this model, we hypothesize that when the photon wave frequency reaches the resonant frequency necessary for the electron and positron loops to form (loop transit frequency 1/T), the newly formed loops become strong static magnets, which due to their opposed alignment at the moment of formation, will then repel apart due to the opposing magnetic field forces. They can fly apart because the magnetic repulsion will be greater than the electrostatic attraction at this length scale.
Calculation for distance at which the magnetic force
For one electron and one positron, aligned for maximum magnetic repulsion, the calculations are:
Solving for “r” at equal force we get: 3.35 × 10−13 meter.
Hence separation can occur because the two charges are already separated by more than this distance during the formation of the loops (see diameter of photon and loops in
Note: the above “r” calculation can also be used to determine at what scale two electrons or two positrons can be forced together (see “quark” comments in discussion at end).
Reality Test 2: Spins add up: a spin of 1 (in photon) becomes a 1/2 spin positron and a 1/2 spin electron (note: all charges, all magnetic fields, and all spins add up).
Reality Test 3: A crucial reality test of this model is that it explains and exactly matches the De Broglie frequency and wavelength (see Postulate 4).
Reality Test 4: This model can also be extended to explain higher energy states of the electron such as the muon and tau.
If we extend the original concept that the loop trajectory of the charge density needs to be exactly one wave length of the original photon of equal energy (the Compton wavelength of a 0.511 KeV photon), and then we look at the possibility of looping that same wavelength several times around a smaller diameter trajectory such that the total circumference of all the smaller loops still adds up to the Compton Wave length, then we have a relationship between energy density (mass) and magnetic moment that exactly matches the muon and tau.
This “Loop de Loop” hypothesis predicts that as the number of loops increases, the electromagnetic energy and hence mass will increase as one electron’s worth of charge is concentrated into a smaller loop. Since the energy and hence mass increases in direct proportion to the inverse of the radius, and since the radius decreases in direct proportion to the number of loops
The area of each loop is proportional to its radius squared, which is inversely proportional to the # of loops, which means that the net magnetic moment is proportional to
This means that as mass increases, the magnetic moment should go down by exactly the same amount:
Let’s check the muon:
which is identical if you take into account the different “g” factor corrections of each.
Notes: if we are correct in our proposal that the mass of the muon is proportional to the # of loops (Equation (16)), then the # of loops in a muon would be the ratio of the muon mass to the electron mass, or 206.8 loops in our time frame (slightly higher in its own time frame). The muon’s magnetic moment decreases relative to the electron by the same ratio, but the muon’s magnetic field strength inside the loops increases by the same ratio.
The tau mass is
(half-life is way too short) but if this model is correct, then the tau magnetic dipole moment should be:
Note, a “g” factor correction would increase this very slightly, just like it would for an electron or muon [
We have recently discovered earlier, similar models of the electron such as A. L. Parson’s Magneton Modelpublished in 1915 [
1) Why does an electron and positron loop close on itself “only” at a diameter of 7.723 ´ 10−13 m (derived from Equation (3))? This is the biggest question. A resonance type solution that involves two variables, which can only be solved simultaneously at the de Broglie basefrequency is one likely explanation. Perhaps Zitterbewegung type oscillations can only “resonate” at the electron’s de Broglie base frequency due to interactions of a cycle of virtual photons/Bosons being created and then reabsorbed, or perhaps a Larmor type precessional frequency exists due to the interaction between the rotating charge and the electron’s own magnetic field. Whatever the solution is, in addition to explaining the electron’s mass, magnetic moment, and spin like this model does, it should also explain the mystery of why the smallest stable electric charge is exactly the same whether it is an electron, positron, proton or anti-proton.
2) The loop diameter of this model is much bigger than some theoretical estimates based on small discrepancies measured in the magnetic “g” factor, and the loop diameter is also bigger than direct measurements of the electron’s cross-section based on high energy collisions, but it is important to note that the loop diameter of this model is not the same as the size of the charged region. We have not addressed the size or shape of the charged region, but it would be this much smaller charged region that would affect transient measurements in high energy collisions due to the fact that when the charged region is in a part of the loop moving away from the observer, it is doing so at the speed of light (can’t be measured) and then when it is moving towards the observer, the gamma correction would make it look smaller to the observer (higher frequency observed, and shorter interaction time).
3) Can this model also help explain protons, neutrons and quarks? We think that when electron-positron pairs first formed from bosons after the Big Bang (only bosons could overlap enough to occupy the initial state), there must have been an equal number of electrons and positrons generated by high energy gamma ray pair-produc- tion. So where did the positrons go? We think the universe had to “tip” one way or the other, towards either predominantly regular matter or predominantly antimatter (a stable universe of both can’t coexist), and in the process of tipping towards regular matter, the primordial positrons became bound up inside protons and neutrons. How? If you lay onto the palm of one hand 3 very strong spherical magnets of about 2 cm in diameter, and then drop 2 or 3 more magnets onto the others as shown in
4) It is interesting to note that the ratio of the radius given by this model, to the Bohr radius [
electron orbital in a hydrogen atom, has a value of:
1/137.036, i.e. this ratio is exactly the same as the fine structure constant. This connection to the fine structure constant is probably related to the electron’s “amplitude for absorption of a photon”.
5) This model looks classical, but we feel that it does not contradict quantum mechanical models. One argument against a “classical” loop model is that the quantum mechanical calculation of the gyromagnetic ratio is only 1/2 the “classical” value. The error in this argument lies in the fact that it has been assumed that the mass of the electron would rotate at the same radius as the rotating charge. In our model the mass and gravity are due to the distortion of space time created by the electromagnetic energy densities, and since most of the electromagnetic energy lies well within the loop diameter, most of the mass would also lie inside the loop diameter. Another argument we have encountered contradicting the viability of this model is Bell’s theorem. We feel that this argument is a similar straw-man comparison; i.e. if done properly, the misaligned spin of an electron would need a cosine correction when it encounters a detector, just the same as a quantum model would generate. A full discussion would more properly be reserved for a subsequent paper.
6) At first glance this model doesn’t account for linearly polarized photons. The general form of all photons however is elliptical [
A photon’s ellipticity is also not constant; for example a (mostly) linear photon can easily be changed into a (mostly) circularly polarized photon by sending it through a quarter wave plate or other non-linear optics. The process of forming matter from photons is undoubtedly very nonlinear. It is possible that a certain degree of ellipticity may enhance the formation of matter, and future experiments testing this variable may give some interesting additional insight into the process of how matter is formed from photons.
Electrons and positrons by contrast are most likely not elliptical. We believe that they are made of the same electromagnetic ingredients as the 1.022 MeV photon that they originated from, but the electron and positron loops resort to circular loops once the magnetic field lines can close back on themselves (photon magnetic field lines don’t close on themselves). Once the magnetic field lines can close, the field lines trapped inside the loop will exert an outward force on the rotating charge, and since the distance around the loop is the Compton wavelength of a 511 KeV photon, i.e. a fixed distance, the loop will be pushed out to a circular orbit which is the only orbit at which it would exactly match the magnetic moment of the electron/positron (for a given Compton wavelength perimeter, any other shape would generate too small of an area and hence too small of a magnetic moment).
7) There are many arguments in favour of this model: a) the interesting connection to the fine structure constant, b) a recent experiment that has shown that photons have a mass that is off-center [
Graph 1. Electron-positron pair production in aluminum [
We would like to thank Walid Kyriakos PhD for helpful discussions.
DonaldBowen,Robert V.Mulkern, (2015) An Electron Model Consistent with Electron-Positron Pair Production from High Energy Photons. Journal of Modern Physics,06,1334-1342. doi: 10.4236/jmp.2015.69138