Saturday, July 13, 2013

A New Version of My Magnetic Force Paper on Arxiv

The new version of my paper explaining the origin of the magnetic force as being a kinematical consequence of Thomas precession has been up for over a week now here. It's similar to the conference version I put on Researchgate and linked to previously, but it has two new appendices, an Errata section, and a change to the explanation of how the magnetic force is related to Thomas precession. 

The conference version of the paper was improved in various ways compared to the previous arxiv version (v5), and so the new posting on arxiv is much better than the last version, I think.  First, it fixes the glaring sign error I mentioned previously.  More importantly, it has a much better description of what is the expected anti-centrifugal force of the Thomas precession, that shows explicitly the inverse-cube dependence on interparticle separation (as necessary to overcome the inverse-square character of electrostatic repulsion), and then it shows how this prediction agrees with existing Maxwell-Lorentz electrodynamics in the case of bound circular motion, getting much better agreement than previously.  Previously I had an extra Lorentz (gamma) factor squared, which would certainly not be negligible given that it is an ultrarelativistic case where the anti-centrifugal or strong magnetic force becomes significant.

The new version, like the conference version, assumes that the correct form for the angular velocity of the Thomas precession, as observed from the laboratory frame, is as given by Jackson and most other authors, as opposed to the formula according Malykin (derived by Ritus, originally, references are in my paper on arxiv).  This was very nice in getting agreement in the ultrarelativistic case on the Lorentz factors, and for a brief while I thought it might also be working better in obtaining the magnetic force in the low velocity limit, but now I am having severe doubts.  Finding the sign error flustered and confused me into thinking I could solve problems with that part too using the Jackson formula, but as I think about it further I'm suspecting that Malykin is nonetheless correct.  It may be possible to reinterpret my anticentrifugal force to be consistent with Malykin, since Malykin does not say that the Jackson formula is wrong, merely that it applies to observations made from the accelerating reference frame rather than from the lab frame.

The Errata section retracts the conjecture of the last two versions that the expected magnetic-like force due to kinematical consequences of acceleration of the field-source charge, that I call a quasi-magnetic force, might account for the electron gyromagnetic ratio being (about) twice the classically-expected value.  The doubling of the strength of the spin-orbit coupling it predicts would only happen in positronium atoms, not in hydrogen atoms.  The Errata section also mentions my doubts about the correctness of using the Jackson Thomas precession angular velocity formula.  I hope to get it resolved pretty soon.  The fully relativistic derivation should answer the question.  I already have quite a lot of it done, and it seems to strongly support Malykin, still, to me.  I'm eager to return to working on it in earnest, but next I have to make the slides for my conference talk, and then give the talk.  When I have the slides I plan to make them generally accessible.

The new appendices together are an explicit demonstration of the relativistic-kinematical character of the magnetic force, and how it can always be related to a Coulomb force between two charges in at least one inertial reference frame.  This should not be controversial or any kind of surprise, but I have never seen this derivation in any textbook, so I thought it worth putting in.  It doesn't involve the Thomas precession explicitly.

Another thing perhaps worth mentioning: the conference version of the paper has some different expository content than the arxiv version.  The abstract and introduction in the conference version were written from scratch, and I didn't copy that content into the arxiv version.  I did shorten the introduction of the arxiv version, though, compared to previous, since it was saying a lot of things would be done in the paper that haven't been done yet.  I'll bring that part back when they are.