Wednesday, July 15, 2015

Did I explain the de Broglie wavelength?

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:

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,

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:

Now the reviews:

Friday, March 20, 2015

Status Update and What Martin Rivas Did

I haven't posted in a while because I've been preoccupied rewriting my paper at the request of Foundations of Physics.  They still haven't sent it to referees but they did send it to a member of the editorial board, apparently, and gave it a revise-before-review status, in mid-January, with a due date of 20 March for a new version.  I guess I won't reproduce here what the board member said, which was brief, but the general idea was that it was not written appropriately for a journal on the foundations of physics and would I please make it so.  This I was entirely willing and happy to do, as it was originally written for a letters journal (Physics Letters A, as I have already posted about), and not tailored much for FOOP.   I probably would have done more on this account, except when I got the rejection letter from PLA I was only two days away from departing on a month-long overseas assignment for my engineering job which I knew would be demanding, and didn't have time to revise it much, but at the same time wanted to have somebody else looking at it based on what I thought were encouraging words from the PLA editor in spite of not wanting to publish it.  It was nice on that assignment to not have to worry about it or work on it and yet my project could still make progress by having it be considered by illustrious others.  Another factor is that it's a difficult chore for me to build a narrative around an analysis, for an audience that I know is generally much more sophisticated than I am.  I'm happier just pushing the equations around.

In any case I have given it my best attempt, I feel, and used the available time as best I could, rewriting it to a large extent, and then going over it a lot of times and long past the point where I was getting tired of re-reading words that I am still not all that happy with.  Hopefully in the end it will sink or swim based on the physics contained within.

About the physics of my paper, what I wanted to mention is that since I noticed how the magnetic force between to classical spinning particles could apparently cancel the Coulomb force, and even before I realized that that is similar to the Bohmian quantum force, I knew that this result followed very readily from work done by Rivas at least ten years ago.  So far as I have been able to determine he has not published explicitly that magnetic forces can cancel Coulomb forces, but some of his figures that show numerical modeling results, both in his book and published papers, are certainly very close to realizing this to be the case.  It's surprising to me that these results seemingly have not attracted more attention. So, one of the things I attempted to do in the re-write is to be more clear about how much of what I wrote in the first version of the paper is actually prior work of Rivas in showing that the time-averaged acceleration field of a luminally-circulating charge can reconstitute, as it were, the usual electric and magnetic fields of a static charge and magnetic dipole.  I found this result astonishing from the first time I really noticed it in his book, which was after I decided that I had to calculate these fields for myself.  But, I was only planning on calculating the velocity fields and for the case of motion that was only asymptotically close to luminal, not exactly luminal.  When I found that Rivas had already addressed this problem, I saw right away that he had both done a far better job than I probably could ever have done, and also that the result was quite surprising and not at all what I was anticipating.

As I try to say more clearly in the new version, given that Rivas has already shown that the average electric acceleration fields of a luminally circulating charge are identical to the Coulomb field of a static charge, and given that with luminal motions for both the field source charge and the charge being acted on, it should not be surprising that the magnetic interaction can have an inverse square dependence on interparticle separation and be of similar magnitude to the Coulomb interaction.  It is less obvious, to me at least, that it should end up being radial.  That it should also depend on the phase differences in the luminal motions and that this difference has to account for retardation is at least obvious once pointed out.  So, perhaps what I foind is not news after all and if so, I will be happy to see Martin Rivas get 100% of the credit he deserves.  On the other hand, if I truly am the first to notice this, I will be very proud, but still want to say that I probably would never have figured this out on my own, and that Rivas deserves most of the credit for it.  I hope I have made that clear enough in the version I sent to FOOP last Monday.

I posted a new version on arxiv that is not quite the final version that I sent to FOOP, but fairly close. The new arxiv version has all of the minor math corrections I found (none of which affected the original thesis) and the general overall rewrite.  The FOOP version has still a newer title, however, and at least another week's worth of word-smithing which I think (or hope at least) further improved its read-ability. Here's the current arxiv version: Similarity of the Magnetic Force between Dirac Particles to the Quantum Force of Bohmian Mechanics

Friday, October 31, 2014

Is the Quantum Hamilton-Jacobi Equation just the Classical Hamilton-Jacobi Equation Properly accounting for Magnetic Interactions?

Wikipedia has a nice description of the quantum potential of Bohmian Mechanics, and the more I read it, the more I think it can fit in with the idea that quantum behavior is just the classical electrodynamical consequences of elementary particles being charges circulating at the speed of light.   In the quantum potential article, it is already discussed that the quantum potential can be equated to the internal energy of the zitterbewegung.  What better way for this to influence the motion than via magnetic interactions?

However, de Broglie-Bohm theory is, like quantum mechanics generally, a non-local theory.  Classical electrodynamics is of course Einstein-local, but it's also widely recognized that time-symmetric electrodynamics, while remaining Einstein local, has a substantial similarity to non-locality. Wheeler and Feynman famously used time-symmetric interactions with the rest of the universe to explain radiation reaction. So, the classical time-symmetric Hamilton-Jacobi equation accounting for magnetic zitterbewegung interactions may lead to a theory that has the apparent non-locality of quantum mechanics.

So far I've been focusing on just one small part of the total magnetic interaction; the part that's radially-directed and has a non-vanishing average and falls off inverse-squarely at long distance.  There are many other terms that would also need to be taken into account, particularly at distances where the separation is not large compared to the Compton radii of the interacting particles.  On the other hand, those that fall off less than inverse squarely will have a longer-range character, and when treated time-symmetrically, can plausibly interact significantly and seemingly non-locally with, say, slits in an obstructing plane.

A couple of days ago I got my paper returned from Physics Letters A.  Here is what the editor said:

Ms. Ref. No.:  PLA-D-14-02082
Title: Radially Acting, Relative Spin Phase and Polarization Modulated, Inverse Square Law Magnetic Force Between Spinning Charged Particles
Physics Letters A

Dear Mr. Lush,

Thank you for submitting your work to our journal.
I have read your manuscript with interest.
I regret that it is not suitable for publication in Physics Letters A since it does not satisfy our criteria of urgency and timeliness.
Please consider submitting your work to a journal which has a more pedagogical bias.

Yours sincerely,

{name removed)

I think I will take the kind editor's advice and submit it to a different journal, but first I'm going to add some speculation about the quantum force and the quantum Hamilton-Jacobi equation.

Thursday, October 30, 2014

Is the Quantum Force of Bohmian Mechanics the Magnetic Force Between Spinning Dirac Particles?

In Bohmian mechanics there is a quantum potential, and from its gradient
can be obtained a "quantum force."  A few days ago I calculated the quantum force for the ground state of hydrogen and got that it's equal and opposite the Coulomb force between two charges.   This is consistent with what I remembered about Bohmian mechanics, that in the s states the electron is stationary.  This seemed far-fetched to me.  However, it is not entirely unlike my recent finding regarding the magnetic force between two spinning charged particles where their spin is a consequence of circulatory motion of the charges at the speed of light.

In any case, if we have two particles that are going around in little circles at the speed of light (what I called zitter particles in my new paper, but Rivas refers to in the electron case as a Dirac electron, if I understand him correctly) then it's easy to have that the magnetic force between them exactly cancels the Coulomb force expected if the were static charges, if the circular motion centers stay fixed.  The phase relationship between the two particles' positions in their circulatory motions however must be evaluated accounting for the propagation delay.  This means that the phase relationship including retardation changes with separation, modulating the inverse square law magnetic force radially-acting part. The modulation wavelength is the Compton wavelength.

It's not obvious to me how this might correspond precisely to the quantum force of Bohmian mechanics but it's at least reminiscent of it.  Of course, a classical force corresponding to the quantum force cannot cancel the Coulomb force precisely everywhere.          

Saturday, September 27, 2014

My new paper on relative spin phase modulated magnetic force

When I was thinking it was necessary to take a difference between retarded and advanced fields to have a time-symmetric electrodynamics that's Lorentz covariant, I investigated whether a magnetic interaction between point charges moving in little circles at or near the speed of light could play the role of the Coulomb force in binding atoms.  Really it can't, but it's remarkable how close it comes.

I needed a force that was radial and of the same strength and range dependence as the Coulomb force.  Rivas shows in his book, Kinematical Theory of Spinning Particles, how the electric acceleration field of a point charge moving in a circle of an electron Compton wavelength radius has an average that is inverse square like the Coulomb force and of the same strength.  (That is pretty surprising given that the acceleration field falls off explicitly only directly inversely with distance, hence it's characterization as the radiation field.)  But, since the magnetic field in Gaussian units is just the electric field crossed by a unit vector, the magnetic acceleration field for a charge doing the relativistic circular motion has the same strength as the electric field.

If we have a magnetic field that's just as strong as a Coulomb field, and the charge moving in it is moving at the speed of light, then v/c for the charge is one and the resulting magnetic force via the Lorentz force law is just as strong as the Coulomb force.  So, if we suppose the test charge is going in the same type of little circle as the field-generating charge, if the two motions are exactly aligned and in phase, then it turns out there's a purely radial component of the force that's constant in time and just as strong as the Coulomb force. If the circular motions of the two particles are out of phase, then the strength varies sinusoidally with the phase difference, and so it could either double or cancel the electric force.  But the phase difference has to include the time delay of propagation from one circulating particle to the other. (It's important to realize that the charges aren't orbiting around each other, but each doing their little  circular motions separately, with the circle centers many (Compton wavelength) diameters apart.)  So there can be a very substantial influence on the motion of the center of the test charge's circular motion due to the magnetic force, if it is already also moving because of the electric field, due to the relative orientation of the charges plane of motion (which translates to the spin polarization) and the difference in phase of the internal motions of their spins.  The phase of the zitterbewegung motion of the Dirac electron has already been shown by David Hestenes to correspond to the phase of the wave function of a free electron.  So for bound particles, it doesn't seem unreasonable to suppose that the wavefunction involves the relative zitterbewegung phase of the interacting particles.

In the process of putting the story together about this magnetic force as an alternative to the Coulomb force in the time-symmetric picture, I realized (see the previous post) that I missed a sign change in going from retardation to advancement of the magnetic field, so that it does not change sign, and so the magnetic force does not need to replace the Coulomb force but only augment it, in order to plausibly explain quantum behavior.

I'm looking forward to understanding how this picture plays out, but that will take a while, so for now I am putting out what I have.  It will appear on arxiv tomorrow, but I have already posted it to Researchgate here.