It's here. It isn't the final version, but it has significant improvements compared to previous. Section IIb is improved in the sense that there are no leftover terms in the magnetic force derived as a Coriolis effect of the relative rotation of the lab frame relative to the field source particle rest frame as seen by the test particle co-moving observer (TPCMO). This is a result of having the correct sign on the Thomas precession as observed by the TPCMO, which is opposite of that seen by an inertial observer of an accelerated frame, as usually is provided in textbooks. The explanation of how this happens is at the end of new Appendix A.

The new Appendix A also has a complete derivation of the Thomas precession using very elementary analysis that I hope is more transparent than other derivations, and may be unique in its own right. I needed such a derivation because unlike other derivations that focus on the precession of a spinning particle, this one is focused on kinematics more generally, I'd say, and so obtains directly standard kinematical effects of rotation, such as that the velocity of a particle in a rotating frame is the velocity in the non-rotating plus an angular velocity of the rotation crossed with the radius vector to the particle from the center of rotation. This is particularly important because it has been argued previously (by Bergstrom) that even though the magnetic force is clearly a Coriolis effect of the Thomas precession, it cannot give rise to an anticentrifugal forces because it applies only at a point and not more globally. Bergstrom invents an interpretation that there is a "mosaic" of transformations between non-inertial and inertial reference frames such that the rotation applies only at the center of rotation, but I believe this interpretation is without real basis, and furthermore is disproved by the analysis in my Appendix A of version 7. It seems pretty clear that the sole purpose of Bergstrom's interpretation is to avoid the otherwise obvious conclusion that if the Thomas precession causes a Coriolis effect as the magnetic force, then it must also cause a centrifugal-like force. So, I believe this clears the way for a convincing relativistic argument that there need to be anti-centrifugal and anti-Euler forces.

I also used this update as an opportunity to introduce for the first time on arxiv the hypothesis that the anti-centrifugal force is the ultra-strong force that binds preons to from quarks.

The improvements to section IIb make it fully consistent with that part of the talk I gave at the PIERS conference last August. Unfortunately due to confusion related to finding a sign error at the last minute and the deadline for the paper, they didn't get into the paper published in the conference proceedings. I discussed that sign error in at least one previous post. Later on perhaps I will make a corrected version of that and post it on Reasearchgate. The charts I gave as the talk for the PIERS conference are already posted there. The talk also has an overview of the analysis that is now in Appendix A, but Appendix A is more advanced and more rigorous, in particular in how the partial derivative of time in the TPCMO's frame with respect to source particle rest frame time should be obtained. The version in the talk gets the right result but the reasoning behind it is not quite right. Getting it through a defensible derivation is a very significant improvement, I feel.

The path should now be clear to complete the analysis and obtain a relativistically exact (to order v^2/c^2) derivation of the magnetic force as a Coriolis effect of the Thomas precession. This should also bring along an anti-Euler force of the Thomas precession, if one exists as I think necessary. The anti-centrifugal force with be strongly implied, but can't be proven until the analysis is extended to order v^4/c^4. But of course, as mentioned previously, it can already be found in Maxwell-Lorentz electrodynamics, if one knows where to look.

## Wednesday, November 13, 2013

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