I've been working for the last week or so to extend my paper (although not in the direction suggested by Reviewer 1) and I think I've made some real progress. I was thinking that I might be able to obtain the Bohr velocity as the speed where the phase difference between the retarded and advanced zitter motions is pi. This would tend to cancel the zbw magnetic force. It turned out it worked; I got (pi over 2 times) the Bohr velocity if the separation is the Bohr radius. It's a completely distinct relationship between range and velocity than the circular orbit Coulomb attraction one, so it's not a trivial thing.
A couple of days later I got to thinking that probably the de Broglie wavelength relationship was implicit in what I had done, and when I looked at my equations, I could see it right away. So I cleaned it up a little and stuck it up on arxiv. It's got an extraneous factor of a half in it, however, that I hope to resolve soon. Also all I did was add a new section (V) and one sentence to the abstract. I'll be making a more extensive revision soon enough for resubmittal to FOOP and will replace it again in any case, and certainly I will relace it promptly if I can resolve the excess factor of a half.
As of this writing the version is 6. Here is the link to the newest version: http://arxiv.org/abs/1409.8271
Wednesday, July 15, 2015
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,
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,
Saturday, July 4, 2015
New Reviews
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:
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:
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