Saturday, December 30, 2017

The Utility of the Composite Photon

I suppose that the hypothesis of my paper, that the observed frequency of a photon is the frequency of classical electromagnetic fields resulting from the motion of its charged constituents, is perceived as self-contradictory by most physicists.  If the photon is by definition the sole constituent of the electromagnetic field, as a couple of generations of physicists have been taught, then it is not possible that it can itself be a source of electromagnetic fields.  Yet this hypothesis makes possible the derivation of a photon energy-frequency relationship that is arguably more correct than the standard relation proposed by Einstein, as it provides a resolution of the spin-orbit coupling anomaly more plausible than invocation of Thomas precession. (And recognizing that the Thomas precession as a kinematic effect cannot modify energy levels, it becomes possible to recognize it as accounting for the magnetic force and its effects, including previously-unrecognized magnetic binding of charged particles, that occurs irrespective of relative charge polarity.)

However perhaps the greatest explanatory utility of a photon with an electromagnetic structure, and whose interactions are describable through classical electrodynamics, is that it can allow electromagnetism and particularly the magnetic force to account for the so-called wave character of matter, without conflict with quantum electrodynamics and quantum field theory generally.  A composite photon with an electromagnetic structure, interacting with charged matter in accordance with classical electrodynamics, obviates the need to postulate a non-classical wave character of matter, which has been shown by Bohm equivalent to postulating a new force that is of magnitude similar and sometimes equal to the Lorentz force.  Why invent a new force when a known force can plausibly do the job?       

   

Monday, December 25, 2017

Did I Make Algebra Errors?

I don't believe I did, but that's what the Foundations of Physics reviewer said about my photon paper (now posted on arxiv, with only narrative changes compared to the FOOP submittal here: Composite Photon Energy-Frequency Relation).   But said reviewer didn't say anything specific about what the alleged errors are.  I am extremely disappointed with FOOP for passing this off as an actual review.  They apparently cannot be bothered to take a position on whether the composite massive photon does indeed have a derivable energy-frequency relationship that is consistent with the Planck law, when it is taken into account that two photons are needed to constitute a standing-wave mode as used by Planck in developing the first correct blackbody spectrum description.

I will post the review and a more detailed response later.  There was also a second review that is demonstrably not even about my paper.  I received the reviews and reject decision in early October.  I wrote a letter to FOOP soon after asking for more specifics on what the alleged errors are, and pointing out that the other review was not even about my paper, but have not received any reply other than from the Springer front office that my letter would be forward appropriately.

There are several reasons I continue to have confidence that there are no substantive algebraic errors in my paper.  The algebra in the paper is rather simple, and most of it is quite standard and published by others and in mainstream journals, as cited. It seems the reviewer has no familiarity with this literature and couldn't be bothered to look at the relevant references. In the use of the relativistic Doppler effect, the treatment is completely standard and in many textbooks. Algebra associated with Lorentz factors could be a bit surprising perhaps to those unfamiliar with it, but seriously I think it is reasonable to expect a professional physicist to be intimatey familiar with it. I tried to put essentially every step in the derivation embedded in either the narrative text or as numbered equations, to the point that I can check every step just on re-reading the paper.  Rereading it post-review I could not see any errors to correct.

I also spent a lot of time going over the derivation, immediately after obtaining the result, hoping to eliminate the factor of one-half I'd obtained compared to the Planck-Einstein law (i.e. E = h nu).  When I realized I could (probably) calculate an energy-frequency relation for the composite photon (as described in Don Lincoln's Scientific American article, "The Inner Life of Quarks"), I was wondering if I would get the Planck-Einstein relation, and thinking it would be a nice paper if I did.  So I was irritated by the factor of half, which I viewed initially as an obstacle to publication and general acceptance, and looked long and hard for mistakes or a way to get rid of it. The fact that I couldn't get any other result however gave me a suspicion that there might be something more profound about what I'd found.  Still, I set the problem aside for months because I was working on understanding the relativistic interaction between two zitter electrons.

My paper published by FOOP in 2016 only worked out the case of nonrelativistic motion of the interacting zitter particles (which are however intrinsically relativistic objects), and wasn't clear that this restriction was in effect, so I was trying hard to get the full result for submittal as a sequel. In working the interaction problem out more systematically, however, I soon realized that the factor of a half I'd obtained on the photon energy-frequency relationship compared to expectation could be related to the energy eigenvalues that would result from an equation I was able to obtain for the interaction of two zitter electrons.  The equation is identical to a one-dimensional free-particle Schroedinger equation except that the frequency is doubled (its derivation is in the previous arxiv version to the link above, v7, which is a much longer version but has various issues that make it unsuitable for publication until they can be worked out or split off).  This naturally leads to an expectation that photons with energy equatable with the difference between energy eigenvalues will be halved, in agreement with my result for the photon.  It also provides an explanation for the spin-orbit coupling anomaly that doesn't require invoking the Thomas precession, which I have thought for a long time to be an obviously  incorrect and poorly justified explanation.  Halving of all energy levels (which is different than halving the Planck constant, a distinction missed by Reviewer 1) is a much more elegant resolution the spin-orbit coupling anomaly, which can coexist with the Dirac relativistic electron theory, and explain why the Thomas precession does not appear explicitly in the latter, which also does not suffer the anomaly of the semiclssical spin-orbit coupling analysis.

Having things appearing to come together in a more-compelling semiclassical resolution of the spin-orbit coupling anomaly was very exciting, but I was still intimidated by the problem of disagreement with Planck and Einstein, so for months I put off trying to reconcile my photon result with theirs.  This was fine as long as I was making progress on the relativistic zitter particle interaction problem, but when that got bogged down I decided to attempt a reconcilation.  I started with a close examination of how Planck derived successfully the first black-body spectrum.  I wasn't expecting to find a mistake (and I didn't), but I thought maybe I could incorporate negative energy states, as these would not have been recognized as a possibility circa 1900, and by doubling the number of possible energy levels the factor of a half might arise in a convincing way.  However I was unable to build an argument that worked around this idea.  Then I started thinking about and looking at how Einstein incorporated the Planck result into his conjecture that light is corpuscular and realized there is a basic disconnect between a photon that carries nonzero momentum and the energy states in a cavity resonator that were studied by Planck. That is, the states studied by Planck (and Rayleigh and Jeans before him) were standing wave modes and as such cannot possess nonzero momentum.  As is well known, standing waves can be understood as a superposition of two equal-amplitude oppositely traveling waves, which leads naturally to each standing wave mode of quantized energy consisting of an even number of oppositely-traveling photons within the cavity.  This seems perfectly natural to me as a description of the cavity in thermodynamic equilibrium, where for every photon being radiated and absorbed in one direction, there is necessarily another in the opposite direction.  Otherwise, a closed cavity oscillator in isolation will not maintain a constant temperature over its external surface, and will tend to accelerate spontaneously if placed in free space.  So it seems to me that Einstein's adoption of the energy of Planck's quantum of energy for the cavity oscillator modes as the energy of a light corpuscle was not carefully thought out but rather a careless assumption.

Later I will post both of the FOOP reviews and try to comment more specifically on them, but for now I will just mention that I sent the slightly revised version of my paper, along with the FOOP submittal and reviews to EJTP (a peer-reviewed journal without publication fees) and they have acknowledged receiving it.

If anyone can point out any errors in the arxiv version I'd be grateful if they would post them here and/or email them to me.  Unhappy but grateful nonetheless. Moderation is on so comments won't post right away but I promise I will approve any serious comment.