I have received three reviews from Foundations of Physics on my paper about the similarity of the magnetic force between relativistically-circulating charges to the quantum force of Bohmian mechanics. I didn't get a final decision; they requested "major" revisions. I'm willing to make any reasonable revisions, but I don't think certain of the revisions requested by two of three reviewers are well justified or reasonable. So I don't consider the revisions I'll be making all that major.

Maybe I will discuss my disagreements and objections to the reviews briefly here soon but not in this post. For now I will just post the reviews. In any case I will be creating both a revised version of the paper and a specific response to the reviews, as requested by FOOP, and can post that response when it's available. Also, I might mention that I recently posted on arxiv a version of the paper that is identical to the submittal to FOOP that the reviews apply to, except for being in two-column APS-like format rather than the FOOP format. So, the page references in the reviews may not line up exactly. Here's the (re-)submittal that was reviewed: http://arxiv.org/abs/1409.8271v5

Now the reviews:

COMMENTS TO THE AUTHOR:

Reviewer #1: The topic of the paper is interesting. Indeed, the rapidly oscillating behaviour associated to the Dirac equation, named by Schrödinger Zitterbewegung, has provided in the past interesting descriptions (at a classical level) of quantum phenomena, but many aspects of the theory deserve more thorough investigations. The author proposes a study of the classical electric and magnetic fields associated to the zitterbewegung interpreted as a charged particle rotating at the speed of light and radius equal to half the reduced Compton length. He raises the possibility that the quantum force of Bohmian mechanics may be attributed to the zitterbewegung classical electrodynamics. Such a possibility was already shown by Rivas, cited by the author, by means of the Lagrangian formalism (the Lagrangian formalism should be preferable in modern physics since it is more compact and elegant, nevertheless the investigation of the magnetic and electric fields has a pedagogical interest having a lower level of abstraction). The main result of the paper is therefore not new, even though it is obtained in a different way. As far as I can say the calculations presented in the paper are correct and the approximations are sound. As well-known, classical electrodynamics predicts the emission of an electromagnetic radiation (synchrotron radiation) for rotating charged particles, ruling out Kepler-like models for atomic orbitals. To avoid this problem a quantum force exactly cancelling the Coulomb force is conjectured in Bohmian mechanics. The author shows that similar arguments can be extended to the zitterbewegung. As far as I can tell the Bohmian quantum force argument is weak (if it cancels the Coulomb force than what bound the electron around the nucleus or in the zitterbewegung motions?). Nevertheless, having estimated the electric and magnetic fields, a vanishing synchrotron radiation should emerge directly and more generally from the author analysis, bypassing Bohmian arguments.

In conclusion, I believe that the author analysis is interesting but the solution of central problem of the synchrotron radiation in terms of Bohmian quantum force is not fully convincing in the present form to motivate publication. I invite the author to clarify this weak point by adding more convincing arguments, for instance, with an explicit (or qualitative) analysis of the energy radiated (Poynting's Vector) starting from the results already given in the paper. With this additional and more general content the paper should be reconsidered for publication.

Reviewer #2: 50 years ago, while at a celestial mechanics workshop at Stanford, I had the opportunity to tour the then new linac at SLAC. After viewing a section of the accelerator, the guide asked for questions, and I asked about the focusing of the beam owing to Coulomb forces that might be expected to defocus the beam. The guide beamed, and allowed to the other tourists that I was not a plant in the audience to ask this obvious question. He then noted that in the lab frame, the magnetic part of the Lorentz force between two electrons moving in the same direction at essentially light speed exactly cancels the Coulomb repulsion between them.

I mention this incident because in both versions of this manuscript, this elementary observation on the interaction of identical charged particles moving essentially at light speed seems to have been ignored. Two such particles orbiting a common center are not effective current elements moving in the same direction where an attractive magnetic interaction obtains. Rather, exactly the opposite is the case, and instead of a force that cancels the repulsive Coulomb interaction, a force that doubles the Coulomb repulsion should be expected. Changing the sign of one of the charges doesn't help. Neither does fudging with effects of retardation. Introducing spins for the constituent charges is unacceptable, for the whole point of the model is to address spin as a consequence of the orbital motion -- and adding spin to the constituents amounts to explaining something in terms of itself is a tautology.

Before recommending that this paper be published, I would like to see a simple, compelling explanation of how the Lorentz force can be used as the author wishes. Absent such an explanation, it seems to me that the proposed model is simply wrong. After all, were the interaction as the author would have it, Poincare' stresses would not have been necessary to stabilize the classical electron model.

Reviewer #3: The paper presents the computation of a magnetic force between two Dirac particles where the spin is interpreted as coming from Zitterbewegung. The idea follows from the earlier work by Rivas.

Here are my remarks.

1) Many of the interesting questions are left out and only mentioned as "beyond the scope of the paper" - this makes the results rather restricted. I'd suggest that the author explains why this is not touched.

2) I have some doubts how this results affects interpretation of quantum mechanics.

The result is nice and (as a matter of fact) rather easy to obtain.

It might be interesting to see whether such computations would make any predictions that would enable to falsify it (say in atom spectroscopy).

3) I fail to see the relevance of the part of Section 6 (evaluation of the quantum force).

Would the author, please, relate it to the other results ?

Mixing the nonrelativistic quantum mechanics with relativistic computation of classical force is slightly dangerous.

4) I would suggest the author to correct the language - there are many prepositions missing, some of the sentences are also a bit awkward.

Example " p3 lines 6-7 "has also" should read: "has also been...". P11 line 38 "An evaluation" etc etc.

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Happy holidays

6 hours ago

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