I just found a sign error in my latest arxiv version (v3) of my paper:http://arxiv.org/abs/1108.4343v3. The second sign from the right on Eq. (20) is wrong. The gamma^2 factor in the denominator of the first term on the right of equation of Eq 21 has to move to the numerator. Also then the equation is an approximation but still good to order (v/c)^2, which is all it ever was good to, at best.
My philosophy is: finding errors is always a good thing, especially when you can find them yourself.
Sorry for letting it slip through.
I was actually looking for an error, because things were not making sense as it was. With this correction, and with what follows it but is unposted so far, I hope to be able to show soon that the magnetic force between two particles of equal mass can be derived exactly and generally from an assumption of no pseudoforces in Thomas-precessing particle rest frames.
As version 3 of the paper correctly shows, the complete magnetic force is present in the anti-Coriolis force of the Thomas precession, but there are extra terms as well. These originate because the velocity in a particle rest frame is relative to the particle, while the magnetic force is proportional to the (other) particle velocity in the inertial frame. This leads to an additional vector triple product term (the last term in the right of Eq. (19)) which then can be split into a sum of two vector terms with dot-product factors (Eq. (20)). One of them contributes a gamma-squared factor (that now has to move to the numerator but can still be subsumed into the full relativistic electrodynamic description, I think) and the other vanishes in the circular orbit case (only). So, if the magnetic force is to result exactly with no leftover terms, something has to cancel that leftover term, or it must get subsumed somehow into the proper relativistic electrodynamic descrption of the electromagnetic two-body problem in an inertial frame. This one I think will get cancelled by the anti-Euler force, in the case of non-circular motion. I got a suitable term from the anti-Euler force, but it was the wrong sign to cancel, hence I was hunting for a sign error.
I may be days away from having everything worked out and ready to get into shape for re-submission. This will take at least a month but perhaps I can post something sooner in rough form if I get everything to work out, and then do a final clean-up prior to submission.
A man with a mission
3 hours ago