How Existence of Intrinsic Spin Might Explain the Non-Classical Character of Atomic Radiation

Bohr's Correspondence principle tells us that in the limit of large quantum numbers, quantum physics will agree with classical physics. For example, the simple Rutherford atom model of hydrogen, where a point charge electron orbits a point charge proton in a classical Keplerian orbit, will increasingly agree with observation, in terms of rate of radiative decay and frequency of transition radiation, as the electron orbital energy and angular momentum is raised. (The study of so-called Rydberg atoms, that is, atoms where the outer electron is excited to a high energy level compared to the rest, confirms this.) The frequency of the electromagnetic radiation becomes in the limit of large quantum number simply the frequency of revolution of the electron in its classical orbit. The rate of energy loss is also calculable from the radiation intensity predicted for an accelerating point charge according to classical electrodynamics.

At lower energy levels, and apart from the issue of quantized energy levels, the classical model of radiative decay of the system of bound point charges deviates significantly from observation. There are at least two obvious differences from what the classical model predicts. The transition time between two defined energy levels is less than the classical model predicts, and the frequency of the radiation is inconsistent with the classical expectation. The classical expectation is that the radiation of decay between two energy levels will start at the orbital frequency of the higher energy level and end at the (higher) orbital frequency of the lower. Observation however shows that transition radiation is essentially monochromatic, with the frequency predictable based on simply the energy difference between the levels. These seemingly inexplicable differences with the expectations of classical physics led to some despair at the time of their discovery. The initial triumph of quantum theory, even the early quantum theory of Bohr and Sommerfeld, and later the modern version developed particularly by Heisenberg, Schroedinger, and Dirac, was its ability to accurately describe atomic spectra including these features.

Understanding the Origin of Quantum Behavior by Study of the Positronium Atom

For several years now I have been of a belief that if there is an explanation of quantum behavior in the classical electrodynamics consequences of the existence of intrinsic spin, then the Positronium atom is the ideal system for its elucidation. This belief grew out of my study of spin-orbit coupling in the quasiclassical hydrogen atom,

Status Update

I am disappointed that Physica Scripta has withdrawn my paper from consideration after receiving a response from only one referee. That referee observed that I state in my concluding remarks that the analysis should be taken as only a plausibilty argument, and therefore it should not be published on that grounds alone.

I want to say that although I do consider that paper to be only a preliminary analysis, and that there are relativistic effects omitted that could negate it (which is why I say it is only a plausibilty argument) it is nonetheless a quantitative argument that both the magnetic and strong forces are direct consequences of the Thomas precession. As such I believe it is of sufficient interest to warrant publication in its own right, or at least review.

That said, I'm not entirely upset because it was just my first attempt, and the next will be much more relativistically precise.

Status Report, and an Old Review

My paper linked in the previous post was sent back without review by Physics Letters A. This is what the general physics editor said:

Dear Mr. Lush,

I regret that your article is not suitable for publication in Physics Letters A as it does not satisfy our criteria of urgency and timeliness. Please consider submitting your work to a regular journal having a more pedagogical bias.

Thank you for submitting your work to our journal.

Yours sincerely,
(the general physics editor)

I then submitted it to Physica Scripta. Their status shows it sent out to three referees, as of a week ago, with one already having returned a report.

Meanwhile, here is an old review for amusement, of essentially version 3 of my paper about L. H. Thomas' 1927 paper: http://arxiv.org/abs/0905.0927v3

The journal is Studies in the History and Philosophy of Modern Physics.

Origin of the Strong Force?

I placed a new paper on arxiv on 22 August: " Does Thomas precession cause rotational pseudoforces in particle rest frames?"

The paper investigates the plausibility that the magnetic force can be viewed as being caused directly by the Thomas precession (TP), as a kinematical force that must exist if there are no inertial forces of rotation due to the TP. For example, if an observer in a (translating and accelerating) reference frame rotating due to TP does not observe Coriolis forces in her frame, then it will appear both to her and to a laboratory frame observer that an anti-Coriolis force is acting. This force can be identified with the magnetic force (although, interestingly, not generally).

I replaced the initial version with version 2 on 5 September. This update has an additional section that considers the case of a missing centrifugal force in Thomas-precessing frames. I was anxious to make the update when I realized suddenly that, rather than being negligible as it is in the minimally-relativistic case I initially analyzed, it could become very significant in the highly relativistic case. In fact, a lack of centrifugal force in a Thomas-precessing frame implies an always-attractive anticentrifugal force that might overcome Coulomb (i.e. electrostaitc) repulsion and explain the binding of quarks into nucleons.

It turned out to be a simple matter to calculate the scale where the anticentrifugal force overcomes Coulomb repulsion in a system with relativsitic mass about equal to a proton's. The answer is at the scale of about one one-hundredth of the measured proton size.

I was disappointed to have obtained too small a value, but only for a little while until I realized that it's naive to use the Coulomb force in that regime. The actual electrodynamic repulsion in such a highly relativistic case becomes considerably weaker, and so the value I obtained is only an idealized bound, and the proton size is consistent with it.

The calculation is made easy by the facts that there's a limiting speed as the scale shrinks, which is of course the speed of light, and that the total relativistic mass can be taken to be simply the proton mass.

It's fun to think about how the anticentrifugal force appears to an observer in a Thomas-precessing reference frame. She sees objects appearing to orbit around her, which she can interpret as that there is a force holding them in orbit.  This is the centripetal force in her frame.  She can easily calculate how strong the force is based on how far away the objects are and how fast they orbit. The strength is of course equal to that of the centripetal force she calculates in her frame. As the rate of TP in her frame increases, eventually it must overcome electrostatic repulsion.

I submitted version 2 to Physics Letters A on 5 September as well. As of 18 September, it is registering as "with editor". I'm not sure but I'd expect it to say "out for review" or something similar if it were. In any case that's the current status and I consider no news is good news. The same journal and editor rejected my Bohr radius paper in three days.

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.

New Support for Angular Momentum Nonconservation due to Thomas Precession

Vladimir Hnizdo has now posted a pre-print of a paper that finds, as I did, that angular momentum is not conserved in the spin-orbit interaction:

http://arxiv.org/abs/1103.4092

I'm very happy with this outcome. Not only does it agree with my results, and using an entirely different approach (Lagrangian and Hamiltonian mechanics, which will probably be more convincing to physicists than my cruder methods), and cite my work, but it also shows how the result can be reconciled with the result from quantum theory that angular momentum is conserved in spin-orbit interaction. It turns out, the angular momentum that is constructed using the generalized momentum of Hamiltonian mechanics is conserved. Since quantum mechanics is constructed using the Hamiltonian description, it naturally arrives at the same result of angular momentum conservation. However I think it is nonetheless very important and remarkable that the ordinary angular momentum is not conserved in the spin-orbit interaction.

From a practical standpoint, this should remove a problem I've had in getting published, that no reviewer or journal editor seemingly can get past a statement that angular momentum conservation is violated. I expect that Hnizdo's paper will pass peer review and find publication in a mainstream journal, and at least at that point anyone who disagrees with the angular momentum nonconservation statement can take it up with that journal. I expect that won't happen though because Hnizdo's explanation is very elegant and straightforward and convincing.

In my positronium paper I put on arxiv last December, I lamented explicitly that the problem of angular momentum nonconservation exhibited would cause my entire analysis, which has many other interesting findings, to be disregarded. Now I can thank Vladimir Hnizdo for making it possible for these findings to be fairly examined.