Sunday, September 27, 2015

A Better Analysis of the De Broglie Wavelength Relationship to the Zitterbewegung

This is the latest version of my paper on the magnetic force between Dirac particles due to the zitterbewegung, which as of this writing is version 8 and was posted late last week.  This version is more successful in getting the de Broglie wavelength exactly as a modulation of the magnetic force for both non-radial and radial relative motion between Dirac particles.

The new version solves the problem of getting a modulation that had a wavelength of half the de Broglie wavelength for radial relative motion.  It also corrects a mistake of the previous two versions, and in what was sent to Foundations of Physics as a requested revision (which was similar to arxiv version 6).  I overlooked the time dependence of the interparticle separation in deriving the preferred velocity and its relationship to the Bohr velocity.  The new version recovers the idea that there is a preferred radial velocity where the advanced magnetic force will cancel the retarded magnetic force, but it is not completely satisfying in that it requires spiral motion.

After I posted the new version to arxiv, I sent the journal an email to let them know in particular about the error in what I sent them.  I'd only realized I'd made the mistake about five days previously.  I haven't heard anything back yet about how they want to handle it, or if they're still interested, but it has only been a couple of days.  Meanwhile, the status is still "under review".    

Saturday, September 12, 2015

Another Connection to the de Broglie Wavelength

I found another connection to the de Broglie wavelength, when I took account of time dilation due to relative motion between Dirac particles.  Assuming (after various authors) that a Dirac particle (such as the electron) consists of a point charge moving in a circulatory motion at the speed of light so that it has angular momentum of h-bar over two, then supposing one Dirac particle is stationary while another is moving, there will be a difference in frequency of the circulatory motion of one particle relative to the other.  It's easy to calculate both the frequency of the circulatory motion and the amount of time dilation, and so also to get a difference in frequency due to the time dilation.  The frequency difference depends on the speed of the relative motion.  It turns out that the de Broglie wavelength can be equated to the time traveled by the moving particle during one period of the difference frequency due to time dilation.

I put a new version of my paper on arxiv to capture just this observation, about three weeks ago.  Then I had to get about preparing a revised version of the same paper for re-submittal to Foundations of Physics.  I had a lot of consternation in getting the revision done, because I'm still sorting things out about this on several fronts.  The extension of the paper to include the connection to the de Broglie wavelength is unsatisfying in several ways, that I will perhaps describe in more detail later.  The worst way is that I'm so far only able to make some sense of things when the spins are aligned; if they are opposite then the model seems to break down.  But also, up to my re-submittal deadline, I was unable to directly explain how the observation about the de Broglie wavelength being related to time dilation could be related and reconciled to my other observation about the de Broglie wavelength as described in my previous post.  So, I didn't include it in the resubmittal.  (The journal would probably have given me an extension to the deadline, but I was eager to get a review of what I had so far, and had no idea when I'd be able to figure things out better.  I'd already spent considerable effort trying to understand it, with scant success.)  Now I want to report that I've made better sense of at least this bit, and was able to combine the new result with my previous derivation of the de Broglie wavelength, which I think is well motivated but gave a result too small by a factor of a half, and get the right result.

I'll be working on a new revision to post on arxiv, hopefully within a week or two, that will make better sense than the one I link to above, which is v7.  So, v8 will be a better version, and I'm also planning to rewrite the narrative somewhat beyond what I did for the re-submittal to FOOP.   Also at that time I will contact the journal to tell them I made a little more progress, to see if they're interested.