In the current version of my paper on arxiv, http://arxiv.org/abs/1108.4343v5, as well as version 4, I argue that the strength of atomic (at least) spin-orbit coupling should be doubled compared to what is predicted according to Maxwellian electromagnetism, and apart from the electron g-factor being about twice the classically expected value. This caused me to suspect that the doubling of the g-factor could be a mistaken interpretation of the increased strength of the magnetic interaction expected when both interacting particles are free to accelerate. However, as I observe in version 5, the g-factor being closer to one than two is directly contradicted by highly precise "g minus two" experiments that measure the electron (and also muon) g-factor to sufficient precision to measure the g-factor anomaly (that is, the small deviation predicted by quantum electrodynamics of the g-factor from the Dirac value of exactly 2). Because these experiments utilize strong magnetic fields generated by electron currents in neutral wires, there is no doubing of the magnetic field strength expected according to the mechanism of my paper.
The resolution to this problem is to simply pay attention to what my own theory is saying. In hydrogen or other atoms, the nucleus is much heavier than the electron and so the acceleration of the nucleus is much smaller than the acceleration of electron, and the additional magnetic interaction strength is reduced accordingly. I had been thinking of the situation as seen from the electron rest frame, where the proton (in hydrogen, say) is relatively accelerating with the same acceleration as that of the electron seen from an inertial frame, and thinking that this would cause a doubling, but on further reflection it is now clear (and should have been obvious) to me that the proton acceleration seen from the electron rest frame is only just how the usual magnetic field arises and can't cause a doubling. In order for an actual doubling to occur, it would be necessary that the proton acceleration as seen from inertial frames be of the same magnitude as the electron acceleration seen from inertial frames.
I don't know why it took so long for this to become obvious to me but a couple of days ago it did and now I feel foolish.
I'll be updating my paper on arxiv to cover this and some other items including what I have already posted about regarding what is the expected form of the anti-centrifugal force of the Thomas precession. It will probably be within a couple of weeks.
In the meantime, I can mention that based on this proper understanding, it is possible to say what should be the expected effect on the spin-orbit coupling strength due to the effect of both interaction particles being free to accelerate. In positronium, the spin-orbit coupling strength should indeed be doubled compared to that expected according to pure Maxwellian electromagnetics. I haven't done any research yet into whether anyone has ever tried to measure the spin-orbit coupling strength in positronium, but I suspect it would be difficult. In hydrogen, on the other hand, there will be an additional magnetic interaction strength equal to the ratio of the electron to the proton masses. This is about one part in 1836 (if memory serves) and so it might be within the realm of possibility for measurement.
6 hours ago