Wednesday, February 20, 2013

A little more about the electron g factor

I spent a little bit of time reading about the electron "g minus 2" experiments that are referred to in Jackson's Chapter 11, that are based on the BMT or Thomas's equation of motion for the spin.  These do appear to contradict my hypothesis that the electron g-factor being (approximately) 2 is a misunderstanding due to a failure to recognize that the magnetic interaction strength doubles when it is between two equal-mass free particles, compared to that given by Maxwell-Lorentz electrodynamics.  When I make my next revision to my paper I will at least mention this fact.  I may decide to de-emphasize the hypothesis that the doublling of the magnetic interaction strength can explain the electron non-unity g-factor, by removing mention of it from the abstract.

When I finish obtaining the main thrust of the paper, I will look into the matter further.  The problem here is (and I already mention this in the revision I posted on arxiv in January), that if it doesn't account for doubling the g-factor compared to classical expectations, the doubling I found would be an additional and unneeded factor of two. 

If this had been known in 1926 then there would have been no motivation for postulating the electron must have a non-unity g-factor, but now that the g-factor has been measured as being close to 2, it must be reconciled with the doubling of the magnetic interaction strength by other considerations.  There is almost room for such a reconcilation, since Bucher has shown that we should not expect the classical analog of the atomic L=1 quantum state to be a circular orbit.  This means that the Sommerfeld explanation of the anomalous fine structure could be accounting for the extra factor of two.  However, this would also require invoking the Thomas explanation for the (spin-orbit coupling) anomaly, which I believe is not correct.

I just want to register some awareness of the issue.  Right now I am focused on getting the fully relativistic version of my paper finished and reposted on arxiv, and then submitted to a journal.  It is coming along pretty well and perhaps I will be able to repost it within a month or so, or even less.

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