_{1}

When analyzing an Electron’s orbit’s and movements, a “classical” bare g-factor of “1” must be used, but when analyzing just the Electron itself, a bare g-factor and gyromagnetic ratio of twice the “classical” value is needed to fit reality. Nobody has fully explained this yet. By examining the electromagnetic wave nature of the electron, it is possible to show a simple reason why its bare g-factor must be 2, without resorting to superluminal velocities or dismissing it as mystically intrinsic. A simple charged electromagnetic wave loop (CEWL) model of the electron that maintains the same electromagnetic wave nature as the high-energy photons from which electron-positron pairs form, will have exactly half of its energy in the form of magnetic energy who’s field lines are perpendicular to the direction of the charge rotation, which leads to the conclusion that only half of the electron’s electromagnetic mass is rotational mass, from which it is easy to calculate a bare g-factor of 2 using Feynman’s equation for the electron’s g-factor.

The g-factor for an electron [

What is the electron’s g-factor? The g-factor is a part of the calculation for the gyromagnetic ratio [

L = angular momentum.

Therefore,

A problem arose in the early days of trying to make quantum mechanical equations fit reality. It became apparent from experiments that the electron’s internal g-factor (as opposed to it’s orbital g-factor) needed to be 2 instead of 1.

i.e. the electron’s Gyromagnetic ratio =

When Uhlenbeck and Goudsmit first discovered electron “spin”, they proposed that an electron has a magnetic moment due to a physically spinning sphere [

Note: See section 3 of the Discussions at end of paper for Dirac’s later insight into the mathematical necessity for the g-factor of 2 as well as the Thomas correction.

When Uhlenbeck and Goudsmit realized that the surface of their sphere would need to exceed the speed of light in order to produce the correct magnetic moment they had no explanation for how this could work, so they just submitted a note in their spin paper [

For a sphere of; M = mass,

For the same sphere, if charge Q resides only on the surface, the magnetic moment “u” is:

Therefore

If the surface-charged-spherical model produces a g-factor of 5/3 instead of the necessary 2, then it can’t be correct. But in those early years of quantum mechanics this mistake was not known, and since it looked right, people moved on with the right answer of 2 for the wrong reason. The superluminal conflict was dismissed at the time by just saying the electron has an “intrinsic” spin that can’t be understood classically.

Both the erroneous g-factor explanation and the superluminal velocity issues go away if the Charged-Elec- tromagnetic-Wave-Loop (CEWL) Model is used, i.e. the charge can now rotate within Einstein’s laws of relativity, and the g-factor of 2 can easily be derived from the model. It can also be demonstrated that no other shape or diameter besides the CEWL model can get rid of the superluminal violations of relativity. The CEWL model, as described in the paper “An Electron Model Consistent with Electron-Positron Pair Production from High Energy Photons” [

The CEWL model starts with the premise that since electron-positron pairs form from purely electromagnetic photons (of energy > 1.022 Mev [

Note: Maxwell was the first to be able to calculate the speed of light “c” with his equation

and

Modern modelling of photons generally focuses on the “potential” E and B fields (Electric and Magnetic fields), but as Maxwell first envisioned a photon, it is actually composed of a charge separation spiralling through space at the speed of light [

When high energy gamma ray photons (of at least 1.011 Mev energy) collide with matter, they produce elec-

tron-positron pairs [

The CEWL model for electron positron pair production is shown below by the transition from a high energy photon in

The simplest definition of the g-factor of an electron is that it represents the ratio between the radius of the rotating charge, and the radius of the rotating mass. For example if we look at an electron orbiting in a circle, we know that it will generate a bare g-factor of one because the mass and the charge are both orbiting at the same radius around the atom. The CEWL electron model may look similar, with a rotating charged component, but unlike the case where an electron orbits a nuclei (where all the mass of the electron contributes to rotational mass), in the CEWL model only half the electron’s mass contributes to rotational mass. The electric energy, i.e. the rotating charge component, contributes to the rotational mass, but the magnetic energy, because the direction of its components only act in a plane perpendicular to the direction of the charge, as shown in

MIT Physics professors’ emeriti Slater & Frank have solved Maxwell’s Electromagnetic equations for the general case of plane wave propagation of photons to show that the total Electro-Magnetic Energy Density in free space, i.e. with no resistive component is:

As further explained by Slater & Frank, the average magnetic component (the B half of this equation) is only greater than the average Electric component when a resistive component is present [

Using

Note: Using Maxwell’s

Electromagnetic Stress-Energy tensor form for mass used in Einstein’s General Relativity [

Electromagnetic Tensor equation for Mass:

Since only half the electromagnetic mass contributes to angular momentum, then we can simply substitute L/2 for L into Feynman’s electron gyromagnetic equation, Equation (2) above, and we get:

The electron g-factor

Note: See the Conclusions section for a more detailed explanation.

This is similar to the Faraday Paradox in which a magnet rotating inside a conductive loop can impart no rotational energy out to the loop. [

The fact that the Tensor equations of general relativity show that the space time distortions due to electromagnetic energy density are no different from the space time distortions of “mass” suggests that they are one and the same. Furthermore, if we invoke some mystical “other” form of mass such as a sphere or disk on which the charge rotates, we run into a problem; If there is another form of “mass” (besides the electromagnetic energy components), then by Einstein’s

No other diameter except a circular loop of exactly the CEWL diameter can fit reality. This is because unless the charge is rotating in a circular loop of diameter

1) When the Grand Master of Physics Lorentz first heard of Uhlenbeck’s and Goudsmit’s ground-breaking spin paper, he pointed out a possible problem; i.e. since the magnetic energy is roughly the magnetic moment squared

divided by the radius cubed, i.e.

had also reinforced the concept that the spin must be “intrinsic” and physics moved on. But apparently Lorentz’s only objection to that size was that it conflicted with the then current estimates of atomic nuclei cross sections, and since he was aware that electron’s can be emitted from nuclei (beta decay), hence the size didn’t make sense to him. But the original CEWL model paper shows that the Muon and Tau higher energy states of the electron have a much smaller size [

2) Two other distinguished physicists have suggested the same diameter as that of the CEWL model: Just before publishing the original paper, a book by Mac Gregor [

Another paper [

3) A few years after Uhlenbeck’s and Goudsmit’s ground breaking spin paper, the famous physicist Dirac was able to derive an amazing 4 × 4 matrix version of quantum mechanics which included relativity corrections, and was able to show that both the g-factor of 2 as well as the Thomas correction of 2 could both be inferred as necessary from his more advanced mathematical descriptions of the electron [

The CEWL model matches all known values for the electron, so it is compatible with the amazing equations of quantum mechanics, but it goes a step further by proposing an internal structure for the electron itself. Quantum mechanical equations were developed to fit the known spectral line data generated by quantum energy jumps of electrons as they transition between orbital levels within the ecosystems of atoms (electrons have characteristic wavelengths as they move through space, and because of this, only atomic orbits whose circumferences are integer values of these wavelengths are stable). The quantum energy jump equations address the energy level jumps within the ecosystem of an atom, but do not address the internal structure of the electron itself. Richard Feynman, one of the founders of QED theory, (one of the most advanced forms of quantum mechanics), lamented at the end of his 1985 book on QED that there is no theory that explains the masses of particles [

4) The CEWL model addresses the previously mysterious g-factor of 2 needed to make quantum mechanical equations fit reality, but how does this fit with the mysterious Pauli’s exclusion principle of quantum mechanics? And is it compatible with the mysterious “superposition of spin” demonstrated by the Stern Gerlach experiment [

The heavier neutrons and protons of the nuclei have magnetic moments too, they are just much heavier than an electron. Imagine strapping a pound of lead to the needle of one of the compasses (assuming the heavy compass could still rotate freely); the two compasses would still align themselves as before, except that the lighter “electron” would respond to a magnetic field quicker than the heavy “nuclei”. In any atom, the first electron in any orbital pair would align itself with the nuclei, and the second would align itself with the first, and each successive electron pair in an atomic “ecosystem” would do likewise. The Stern-Gerlach experiment consisted of shooting randomly oriented silver atoms (which have one unpaired electron in the outer shell) through a strong magnet [

result was that the stream of silver atoms split into two streams and this result was used to demonstrate that electrons exist in a “superposition”. “Superposition” implies something mystical about an electron, but it’s not really that mysterious; what was really happening was that the heavy nuclei didn’t have time to react while going through the magnet, but the unpaired electron did. If the heavier nuclei were already somewhat aligned with the magnet, the electron flipped out of its normal state opposing the nuclei spin, and into a spin state closer to that of the nuclei (adding to the total magnetic moment). If on the other hand the nuclei happened to already be aligned somewhat opposite to the magnet, then the final orientation of the electron subtracted from the nuclei magnetic moment. The net effect is two magnetic states (of the atomic ecosystem) depending on whether the electron now adds to, or subtracts from, the original nuclei magnetic moment after going through the magnet (an electron by itself would not show a two state “superposition” since it would simply rotate into full alignment with the magnet).

5) The circular loop of the CEWL electron model is similar to the nature of an inductive loop antenna [

By investigating the antenna nature of the CEWL model it may be possible to investigate, among other things, the directionality and polarity of the “virtual” photons of QED theory that are emitted (and immediately reabsorbed) in the vicinity of electrons. As semiconductors shrink down to sizes where ever smaller numbers of electrons are channelled through ever smaller channels, CEWL modelling of the antenna and spin characteristics at scales close to the CEWL size of the electron may provide insight into how to further reduce resistance losses in semiconductors.

6) The electron’s g-factor of 2 represents the highest gyromagnetic moment of any form of matter and this is most likely connected to the fact that the electron is an indivisible unit of matter and a building block for other forms of matter [

This same arbitrary equation:

Is used for neutrons and protons and all nuclei “For simplicity and consistency” [

By looking at how Feynman derived the electron’s gyromagnetic ratio in equation #2 from his equation #1, it is easy to see that when investigating an electron’s orbit around an atom, where both all the mass and all the charge of the electron orbit at the same radius around the atom, the bare g-factor must be exactly 1, so it has been a mystery why a bare g-factor of 2 is needed to make quantum mechanical equations fit reality. This paper shows that if a simple Charged-Electromagnetic-Wave-Loop (CEWL) model is used for the electron itself, whereby the electron maintains the same electromagnetic characteristics as the photon from which it originated, then it follows that only half of the electron’s mass contributes to the angular momentum inside the electron. This is due to the fact that the magnetic field lines inside the electron are perpendicular to the direction of the charge rotation internally (see

The CEWL model, in addition to explaining why a bare g-factor of 2 is needed for calculations involving the electron’s internal spin, also explains all other known values for the electron as well as showing how electron- positron pairs can form from high energy photons.

Many thanks to Robert V. Mulkern PhD for reviewing this paper as well as for the calculations to demonstrate that a surface charged spherical model can’t work, and for helpful discussions.

Donald Bowen, (2016) The Real Reason Why the Electron’s Bare g-Factor Is 2 Times Classical. Journal of Modern Physics,07,1200-1209. doi: 10.4236/jmp.2016.710109