I placed a new paper on arxiv on 22 August: " Does Thomas precession cause rotational pseudoforces in particle rest frames?"
The paper investigates the plausibility that the magnetic force can be viewed as being caused directly by the Thomas precession (TP), as a kinematical force that must exist if there are no inertial forces of rotation due to the TP. For example, if an observer in a (translating and accelerating) reference frame rotating due to TP does not observe Coriolis forces in her frame, then it will appear both to her and to a laboratory frame observer that an anti-Coriolis force is acting. This force can be identified with the magnetic force (although, interestingly, not generally).
I replaced the initial version with version 2 on 5 September. This update has an additional section that considers the case of a missing centrifugal force in Thomas-precessing frames.
I was anxious to make the update when I realized suddenly that, rather than being negligible as it is in the minimally-relativistic case I initially analyzed, it could become very significant in the highly relativistic case. In fact, a lack of centrifugal force in a Thomas-precessing frame implies an always-attractive anticentrifugal force that might overcome Coulomb (i.e. electrostaitc) repulsion and explain the binding of quarks into nucleons.
It turned out to be a simple matter to calculate the scale where the anticentrifugal force overcomes Coulomb repulsion in a system with relativsitic mass about equal to a proton's. The answer is at the scale of about one one-hundredth of the measured proton size.
I was disappointed to have obtained too small a value, but only for a little while until I realized that it's naive to use the Coulomb force in that regime. The actual electrodynamic repulsion in such a highly relativistic case becomes considerably weaker, and so the value I obtained is only an idealized bound, and the proton size is consistent with it.
The calculation is made easy by the facts that there's a limiting speed as the scale shrinks, which is of course the speed of light, and that the total relativistic mass can be taken to be simply the proton mass.
It's fun to think about how the anticentrifugal force appears to an observer in a Thomas-precessing reference frame. She sees objects appearing to orbit around her, which she can interpret as that there is a force holding them in orbit. This is the centripetal force in her frame. She can easily calculate how strong the force is based on how far away the objects are and how fast they orbit. The strength is of course equal to that of the centripetal force she calculates in her frame. As the rate of TP in her frame increases, eventually it must overcome electrostatic repulsion.
I submitted version 2 to Physics Letters A on 5 September as well. As of 18 September, it is registering as "with editor". I'm not sure but I'd expect it to say "out for review" or something similar if it were. In any case that's the current status and I consider no news is good news. The same journal and editor rejected my Bohr radius paper in three days.