Sunday, July 5, 2015

Brief Response to Reviewer 3

Yesterday I posted the three reviews of my paper sent me last week by Foundations of Physics. I'm responding to Reviewer 3 first because I have no substantial disagreement with this review, and it raises an interesting question, which I will enjoy expanding on in my resubmission. Here is the Reviewer 3 comment:

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.

In response to remark 1, I will look into not simply stating something is beyond the scope of the paper.  I think in at least most cases there is a good reason why whatever is being referred to isn't relevant to the paper or otherwise shouldn't be included, and that reason can (perhaps should have been) stated.  I thank Reviewer 3 for the helpful remark.

I think remark 2 is most interesting.  Rather than trying to define an experiment that might falsify the hypothesis that Bohm's quantum force is a consequence of the magnetic force, though, it will be more to the immediate point to better determine what the correspondence is.  I already point out the quantum force cannot be directly equated to (even just one part of) the magnetic force between two Dirac particles.  What's needed here is to derive the quantum force from the classical Hamilton-Jacobi equation by incorporation of the magnetic interaction.  Bohm's original paper shows how the Schroedinger equation can be put in a form that can be regarded as the classical Hamilton-Jacobi equation with an additional term he named the quantum mechanical potential.  The quantum force is then derived in the usual fashion, as a gradient of the quantum potential.  So, it should be possible, if the hypothesis is correct, to derive the quantum potential from the magnetic interaction between two Dirac particles.

A derivation of the quantum potential from classical principles would be a very powerful result that would greatly improve my paper, but I doubt I can do it within the two months proposed by FOOP for the creation of a revised submission.  Not that I'm unwilling to try, but one reason the journal might want to publish is so that other people who might be more qualified than I am to carry this out can attempt it if they're interested.

In remark 3,

Reviewer 3 is referring to what is the appendix in the arxiv version.  (It's also placed at the end of submitted version, but the compilation for some reason gave it a section number of 6, which I didn't notice to fix.  Perhaps it would have helped had it said Appendix as intended.)  I stated three reasons I included it in the opening paragraph:
... the quantum force is not usually evaluated explicitly in the literature, since it is not needed to obtain the physical results of interest ({\em e.g., } that the electron momentum vanishes), so for completeness it is evaluated in the following for the hydrogen atom ground state. Also, it serves to illustrate that although magnetic force component described here bears a similarity to the quantum force, it cannot be equated to it directly.  More generally, the quantum force cannot in principle be equatable to the magnetic force, because while the quantum potential is scalar in both its non-relativistic and relativistic \cite{HileyCallaghanY12} forms, the magnetic force must be derived from a vector potential.
This relates directly to my response to Reviewer 3's remark 2).   I can refine and perhaps expand this discussion for my re-submission.

There's not much to say in response to remark 4 except to apologize for letting obvious errors slip through and thanking Reviewer 3 for pointing them out.     

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