Thursday, June 13, 2013

Another sign error and more

There is a sign error in my arxiv paper, "The Magnetic Force as a Kinematical Consequence of the Thomas Precession," versions v4 and v5,  The sign error was apparently introduced when I changed notation slightly between versions 3 and 4, from referring to an electron and positron (or proton) using subscripts e and p, to a field source particle and a test particle using subscripts s and t.  Somehow the sign got switched so that now  Eq. (9) obviously does not follow from Eq. (8), and furthermore the Coulomb force per Eq. (9)  is repulsive for opposite charges. 

The sign was correct in previous versions and had been checked carefully, and the change of notation was not a big deal, so I apparently didn't feel a need to recheck it, unfortunately, because it is pretty obvious under even just a casual perusal.

The reason I'm finding it now, though, is because I got a different clue there might be a sign error in that part, due to the fact that I recently found that if I use the Jackson form for the angular velocity of the Thomas precession, rather than the Malykin form, I can successfully predict the form of what I'm calling the strong magnetic force, including all of the gamma (Lorentz) factors, as the anti-centrifugal force of the Thomas precession.  These gamma factors are highly significant in the highly relativistic case where the strong magnetic force manifests, and so the fact that I was missing them using the Malykin form but getting them all correct using the Jackson form is very significant, I believe.  Up until a few weeks ago, I had thought that the form of the strong magnetic force was supporting that Malykin is correct, so I was quite surprised to see it's apparently the other way around.

I've been using the Malykin form since the first version of this paper, because in my original derivation of the magnetic force, that was the only way it would work.  In the low velocity case it's just a sign change on the angular velocity of the Thomas precession, so finding the sign error after suspecting one appears to confirm that I should be using the Jackson equation (which is also the Moller form, and I believe is the only one consistent with the Bargmann-Michel-Telegdi equation that is experimtally verified by "g minus 2" experiments.  Malykin doesn't seem to see a contradiction there though so maybe I'm missing something about that.) 

My understanding has advanced tremendously (seems like to me anyhow) since my initial derivation, and so having the sign flipping there is only making everything make better sense, not causing new problems, I don't think.  I already knew that the original derivation was incorrect, which was what prompted the creation of version 4 in January of this year.  I'm now working on a new revision (6) that I'll post as soon as I can. 

There was one thing in particular that was troubling me with the derivation of versions 4 and 5, that the opposite sign resolves.  I'm hoping I'll feel good enough about the new version when it's done to want to re-submit this paper to a journal, finally.

Perhaps I should mention that in any case I'm planning to give a talk on it at the PIERS conference in Stockholm in August.  My abstract has been accepted.  I submitted a short version of the paper, with enhancements beyond the v5 posting, similar to what I posted here a few weeks ago, for possible publication in the conference preceedings, that's in peer review.  Unfortunately, that version has the glaring sign error.  I'm working frantically to try to get a revision done that I can send with apologies to the conference people.  I hope I'll have one after this weekend.  I've been very busy with my engineering job recently, including having to travel internationally, which has made it difficult to give my paper the time it deserves.

My attitude about this is that having the right answer is the only thing that matters in the long run, so I'm not letting it get me down.  Things are making better sense all the time.

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