Geometry of magnetic moment correction for electron: reason for number 2
Magnetic moment of electron= Dirac factor + 1st virtual particle coupling correction term = 1 + 1/(2.Pi.137.0...) = 1.00116 Bohr magnetons to 6 significant figures (more coupling terms are needed for greater accuracy). The 137.0... number is usually signified by 1/alpha, but it is clearer to use the number than to write 1 + alpha/(2.Pi).
Anyway, the 1 is the magnetic contribution from the core of the electron. The second term, alpha/(2.Pi) or 1/(2.Pi.137), is the contribution from a virtual electron which is associated with the real electron core via shielded electric force. The charge of the core is 137e, the shielding due to the veil of polarised vacuum virtual charges around the core is 1/137, so the observed charge outside the veil is just e.
The core magnetism of 1 Bohr magneton predicted by Dirac's equation is too low. The true factor is nearer 1.00116, and the additional 0.116% is due to the vacuum virtual particles.
In other words, the vacuum reduces the electron's electric field, but increases its magnetic field! The reason for the increase in the magnetic field by the addition of alpha/(2.Pi) = 1/(2.Pi.137.0...) is simply that a virtual particle in the vacuum pairs up with the real particle via the electric field. The contribution of the second particle is smaller than 1 Bohr magneton by three factors, 2, Pi, and 137.0... Why? Well, heuristic reasoning suggests that the second particle is outside the polarised shield, and is thus subject to a shielding of 1/137.
The magnetic field from the real electron core which is transverse to the radial direction (i.e., think about the magnetic field lines over earth's equator, which run at 90 degrees to the radial direction) will be shielded, by the 137 factor. But the magnetic field that is parallel to the radial direction (i.e., the magnetic field lines emerging from earth's poles) are completely unshielded.
Whereas an electric field gets shielded where it is parallel to another electric field (the polarised vacuum field arrow points outward because virtual positrons are closer to the negative core than virtual electrons, so this outward arrow opposes the inward arrow of electric field towards the real electron core, causing attenuation), steady state magnetic fields only interact with steady state electric fields where specified by Ampere's law, which is half of one of Maxwell's four equations.
Ampere's law states that a curling magnetic field causes an electric current, just like an electric field does. Normally to get an electric current you need an electric potential difference between the two ends of a conductor, which causes electrons to drift. But a curling electric field around the conductor does exactly the same job. Therefore, a curling magnetic field around a conductor is quite indistinguishable from an electric field which varies along a conductor. You might say no, because the two are different, but you'd be wrong. If you have an electric field variation, then the current will (by conventional theory) cause a curling magnetic field around the conductor.
At the end of the day, the two situations are identical. Moreover, conventional electric theory has some serious issues with it, since Maxwell's equations assume instantaneous action at a distance (such as a whole capacitor plate being charged up simultaneously), which have been experimentally and theoretically disproved, despite the suppression of this fact as 'heresy'.
Maxwell's equations have other issues as well, for example Coulomb's law which is expressed in Maxwell's equation as the electric field from a charge (Gauss' law), is known to be wrong at high energies. Quantum field theory and experiments confirming it published by Koltick in PRL in 1997 shows that electric forces are 7% higher at 80 GeV than at low energies. This is because the polarised vacuum is like a sponge foam covering on an iron cannon ball. If you knock such sponge foam covered balls together very gently, you don't get a metallic clang or anything impressive. But if you fire them together very hard, the sponge foam covering is breached by the force of the impact, and you experience the effects of the strong cores to a greater degree!
The polarised vacuum veil around the real electron core behaves a bit like the shield of foam rubber around a steel ball, protecting it from strong interactions if the impacts are low energy, but breaking down in very high-energy impacts.
Anyway, the Schwinger correction term, 1/(2.Pi.137) contains 137 because of the shielding by the polarised vacuum veil.
The coupling is physically interpreted as a Pauli-exclusion principle type magnetic pairing of the real electron core with one virtual positron just outside the polarised veil. Because the spins are aligned to some extent in this process, the magnetic field which is of importance between the real electron core and the virtual electron is the transverse magnetic field, which is (unlike the polar magnetic field) shielded by the 137 factor like the electric field.
So that explains why the magnetic contribution from the virtual electron is 137 times weaker than that from the real electron core: because the transverse magnetic field from the real electron core is reduced by 137 times, and that is what causes the Pauli exclusion principle spin alignment. The two other reduction factors are 2 and Pi. These are there simply because each of the two particles is a spinning loop and has its equator on the same plane to the other. The amount of field each particle sees of the other is 1/Pi of the total, because a loop has a circumference of Pi times the diameter, and only the diameter is seen edge-on, which means that only 1/Pi of the total is seen edge on. Because the same occurs for each particle, each of the two particles (the one real particle and the virtual particle), the correct reduction factor is twice this. Obviously, this is heuristic, and by itself doesn't prove anything. It is only when you add this explanation to the prediction of meson and baryon masses by the same mechanism of 137, and the force strengths derivation, that it starts to become more convincing. Obviously, it needs further work to see how much it says about further coupling corrections, but its advantage is that it is a discrete picture so you don't have to artifically and arbitrarily impose cutoffs to get rid of infinities, like those of existing (continuous integral, not discrete) QFT renormalisation.
One think more I want to say after the latest post (a few back actually) here on deriving the strong nuclear force as 137 times Coulomb's law for low energies. The Standard Model does not indicate perfect force unification at high energy unless there is supersymmetry (SUSY), which requires superpartners which have never been observed, and whose energy is not predictable.
The minimal theory of supersymmetry predicts that the strong, weak and electromagnetic forces unify at 10^16 GeV. I've mentioned already that Koltick's experiments in 1997 were at 80 GeV, and that was pushing it. There is no way you can ever test a SUSY unification theory by firing particles together on this planet, since the planet isn't big enough to house or power such a massive accelerator. So you might as well be talking about UFOs as SUSY, because neither are observable scientifically in any conceivable future scenario of real science.
So let's forget SUSY and just think about the Standard Model as it stands. This shows that the strong, weak, and electromagnetic forces become almost (but not quite) unified at around 10^14 GeV, with an interaction strength around alpha of 0.02, but that electromagnetism continues to rise at higher energy, becoming 0.033 at 10^20 GeV, for example. Basically, the Standard Model without SUSY predicts that electromagnetism continues to rise as a weak (logarithmic type) function of energy, while the strong nuclear force falls. Potential energy conservation could well explain why the strong nuclear force must fall when the electromagnetic force rises. The fundamental force is not the same thing as the particle kinetic energy, remember. Normally you would expect the fundamental force to be completely distinct from the particle energy, but there are changes because the polarised vacuum veil around the core is progressively breached in higher energy impacts.