I haven't posted in a while because I've been preoccupied rewriting my paper at the request of Foundations of Physics. They still haven't sent it to referees but they did send it to a member of the editorial board, apparently, and gave it a revise-before-review status, in mid-January, with a due date of 20 March for a new version. I guess I won't reproduce here what the board member said, which was brief, but the general idea was that it was not written appropriately for a journal on the foundations of physics and would I please make it so. This I was entirely willing and happy to do, as it was originally written for a letters journal (Physics Letters A, as I have already posted about), and not tailored much for FOOP. I probably would have done more on this account, except when I got the rejection letter from PLA I was only two days away from departing on a month-long overseas assignment for my engineering job which I knew would be demanding, and didn't have time to revise it much, but at the same time wanted to have somebody else looking at it based on what I thought were encouraging words from the PLA editor in spite of not wanting to publish it. It was nice on that assignment to not have to worry about it or work on it and yet my project could still make progress by having it be considered by illustrious others. Another factor is that it's a difficult chore for me to build a narrative around an analysis, for an audience that I know is generally much more sophisticated than I am. I'm happier just pushing the equations around.
In any case I have given it my best attempt, I feel, and used the available time as best I could, rewriting it to a large extent, and then going over it a lot of times and long past the point where I was getting tired of re-reading words that I am still not all that happy with. Hopefully in the end it will sink or swim based on the physics contained within.
About the physics of my paper, what I wanted to mention is that since I noticed how the magnetic force between to classical spinning particles could apparently cancel the Coulomb force, and even before I realized that that is similar to the Bohmian quantum force, I knew that this result followed very readily from work done by Rivas at least ten years ago. So far as I have been able to determine he has not published explicitly that magnetic forces can cancel Coulomb forces, but some of his figures that show numerical modeling results, both in his book and published papers, are certainly very close to realizing this to be the case. It's surprising to me that these results seemingly have not attracted more attention. So, one of the things I attempted to do in the re-write is to be more clear about how much of what I wrote in the first version of the paper is actually prior work of Rivas in showing that the time-averaged acceleration field of a luminally-circulating charge can reconstitute, as it were, the usual electric and magnetic fields of a static charge and magnetic dipole. I found this result astonishing from the first time I really noticed it in his book, which was after I decided that I had to calculate these fields for myself. But, I was only planning on calculating the velocity fields and for the case of motion that was only asymptotically close to luminal, not exactly luminal. When I found that Rivas had already addressed this problem, I saw right away that he had both done a far better job than I probably could ever have done, and also that the result was quite surprising and not at all what I was anticipating.
As I try to say more clearly in the new version, given that Rivas has already shown that the average electric acceleration fields of a luminally circulating charge are identical to the Coulomb field of a static charge, and given that with luminal motions for both the field source charge and the charge being acted on, it should not be surprising that the magnetic interaction can have an inverse square dependence on interparticle separation and be of similar magnitude to the Coulomb interaction. It is less obvious, to me at least, that it should end up being radial. That it should also depend on the phase differences in the luminal motions and that this difference has to account for retardation is at least obvious once pointed out. So, perhaps what I foind is not news after all and if so, I will be happy to see Martin Rivas get 100% of the credit he deserves. On the other hand, if I truly am the first to notice this, I will be very proud, but still want to say that I probably would never have figured this out on my own, and that Rivas deserves most of the credit for it. I hope I have made that clear enough in the version I sent to FOOP last Monday.
I posted a new version on arxiv that is not quite the final version that I sent to FOOP, but fairly close. The new arxiv version has all of the minor math corrections I found (none of which affected the original thesis) and the general overall rewrite. The FOOP version has still a newer title, however, and at least another week's worth of word-smithing which I think (or hope at least) further improved its read-ability. Here's the current arxiv version: Similarity of the Magnetic Force between Dirac Particles to the Quantum Force of Bohmian Mechanics
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