Last week I posted a version of my paper linking the magnetic and strong forces with the Thomas precession on arxiv here.

The revision was needed to correct several errors and misunderstandings, as I previously described.

The new version doesn't attempt to extend the analysis, it just corrects the recognized errors and reflects my better current understanding. It contains an Errata section identifying the corrections.

I'm still working on extending the analysis beyond the bound, circular orbit case. Any case other than this must invoke an anti-Euler force as well as becoming generally more relativistic in nature. The circular orbit case is greatly simplified by the fact that the force is perpendicular to the velocity, and so the relativistic gamma (or Lorentz) factor doesn't come much into play. Also, the Euler force doesn't come into play since the angular velocity of the Thomas precession is constant. So, relaxing the restriction to circular motion makes the analysis much more complicated, but it should also become much more persuasive if it all comes together in a consistent way, as I believe it must.

Also, I'm still uncertain whether an anti-Euler force implies the existence of hitherto unknown forces, or merely leads to previously-known forces such as the magnetic and weak forces. As I mentioned a couple of posts ago, it gives rise to force terms at order (v/c)^2 that are of course at the same order as the the magnetic force. But, the full relativistic treatment of the classical two-body electromagnetic problem for (spinless) charged particles already has a lot of terms at this order that are not directly recognizable as magnetic force related terms. So, the anti-Euler force terms could simply correspond to terms already present in inertial-frame electrodynamics. Showing this to be the case will make the derivation quite persuasive, seems to me. On the other hand, if there are new forces at the same order as the magnetic force, consistency with observations to date demands they would have to average to zero or be otherwise difficult to notice. Perhaps if they were difficult to notice but gave a hint of where one might look for confirmation, that would be of interest. However at the moment I'm optimistic that the anti-Euler force at order (v/c)^2 will simply be relatable to electrodynamics as it is already understood. The anti-Euler effects at higher order in v/c however I think will have to correspond to either the weak or new forces.

Manchester

2 hours ago