Sunday, August 21, 2011

About the previous post

I have recently come to realize that Vladimir Hnizdo's paper referred to in my previous post does not support angular momentum nonconservation due to Thomas precession, contrary to the title and assumption of my previous post.

It does find the kinetic angular momentum is nonconserved (although the canonical angular momentum is conserved), but the nonconservation is not attributable to the Thomas precession as it is in my analysis. Offhand I am not sure of the amount of the nonconservation, but I guess it's not the same as in my analysis, because in my analysis the amount is exactly equal to the amount of Thomas precession of the electron spin. That is why in my analysis it's obvious that the Thomas precession is directly responsible for the nonconservation.

I apparently lept erroneously to the conclusion that the recent Hnizdo paper was seeing the same phenomenology seen in my analyses. However on close comparison it does not exhibit the same behavior as seen in my model. Where in my model the electron orbit precesses faster than the spin, I believe in the recent Hnizdo model they precess at the same rate. This is similar at least in this respect to L. H. Thomas's analysis of 1926, that conserves orbit-averaged i.e. secular angular momentum, only. Hnizdo's analysis obtains unlike Thomas that the canonical angular momentum is generally conserved. This continues to seem an important result to me. In particular, it shows how quantum theory can obtain strict angular momentum conservation in spite of the semiclassical model of e.g. Thomas obtaining secular conservation only.

Later on I plan to compare my and the Hnizdo model more closely. At the moment though I have another project drawing to completion, that I'm excited about. I believe I have shown how the magnetic component of the Lorentz force can be regarded as a direct and necessary consequence of the Thomas precession. This analysis also yielded a surprise that I hope will be of general interest. I hope to submit something to arxiv in a few days. I will post a link here when it's publicly viewable, and make some additional comments.