I extracted from my longer paper on arxiv all the parts about the massive composite photon, and how it leads to a correction to the Planck-Einstein relation and explains the spin-orbit coupling anomaly without invoking Thomas precession, and put it together into a short paper. I submitted the paper to Foundations of Physics a couple of days ago. Now I have posted it on Researchgate: Composite Photon Energy-Frequency Relation.
I have finally figured out how to reconcile the composite massive photon model, that gives E equals h nu over 2, with the Planck-Einstein law, E equals h nu. It's a very simple reconcilation that requires no modification of Planck's blackbody spectrum, or of the value of the Planck constant h.
When Einstein realized that quantization of light explained the photoelectric effect, he assumed that the light quanta carried energy in accordance with Planck's assumption that the standing wave electromagnetic modes inside a cavity had energy quantized as integer multiples of h nu, where h is as found by Planck (and to within a few percent by Planck himself). However, a photon must necessarily carry momentum E/c, where c is the speed of light, while electromagnetic standing waves in a cavity and at therrmodynamic equilibrium cannot possess net linear momentum. Therefore the quantized energy value of a standing wave mode in multiples of h nu and the number of photons in the cavity at frequency nu cannot be directly equated. Rather, since a standing wave can be regarded as a superposition of two oppositely-traveling waves of equal amplitude, the expected number of photons is twice the number of energy multiples of h nu. This is in agreement, to within all measurements of the speed of light to date, with the frequency-to-energy relationship for the composite photon, which is easily derivable based on the relativistic Doppler effect.
After having thought about the possible ways that a photon of half the currently-accepted energy can be reconciled with established physics, if at all, this seems best to me. In particular, it does not require revision of the value of h, which would lead to changes in the size of atoms (as far as I can see), in addition to many other problems. On the other hand, retaining the Planck blackbody spectrum while reducing the photon energy by half, and retaining that the angular momentum of a photon is h-bar=h/(2 pi), requires only an energy recalibration. To begin with energy levels on emission spectra can be divided by two. This leads immediately to a resolution of the spin-orbit coupling anomaly that does not need to invoke the Thomas precession. It is also straightforward to modify the Schroedinger equation to be in agreement with the photon carrying half the energy.
A new version of my paper is slated to appear at midnight GMT tonight, that will reflect my new point of view. It will be version 7 here: https://arxiv.org/abs/1609.04446
I've been considering my hypothesis that Planck's constant is really twice the accepted value, based on that the photon energy is related to its frequency by half the accepted amount, for the composite photon, as I proposed two posts ago. The hypothesis fails in an obvious way. Since it implies the electron g-factor is actually unity, it is inconsistent with the Zeeman effect, where it is essential that the electron g-factor be (close to) two, in order to agree with observation.
I now have an alternative hypothesis about the photon energy being half the accepted amount in relation to its frequency. That hypothesis is that it explains the spin-orbit coupling anomaly as well or better than the Thomas precession does, while also not otherwise differing noticeably from observation.
If the photon energy for a given atomic transition is half that currently assigned (that is, if the current energy assigned is twice the correct value), then the measure of the spin-orbit coupling energy from emission spectra will appear to be doubled as well. So, correcting the transition energy to be half the accepted value will recover the spin-orbit coupling energy consistent with the original prediction. There will be no need to apply the Thomas factor of one-half in order to find agreement with observation.
As I think I have stated previously, and various people have been pointing out for many decades, it makes no sense that the Thomas precession, a purely kinematical effect, can alter the interaction energy.
Halving the energy per photon has another consequence of halving the expected magnitude of the Zeeman effect generally. I'm not sure if this would be noticeable or not.
This version (v5) obtains that the modulating factor on the inverse-square radial magnetic force between equal mass and parallel-spin zitter particles satisfies the three-dimensional time-dependent Schroedinger equation, except that hbar multiplying the partial derivative with respect to time is replaced by hbar/2. This equation implies an angular momentum spectrum in terms of integer multiples of hbar, but an energy spectrum in terms of integer multiples of hbar/2. This is consistent both with the energy per photon as derived in the same paper for a composite photon to be h/2 times the photon frequency, and so that the accepted value of Planck's constant (h) is only half the correct value. This also implies that the electron g-factor is approximately unity, rather than approximately 2 as currently thought.
Next I will go over everything in it again and try to shorten it, and then submit it to a journal. Since Foundations of Physics published my earlier paper from which this one derives, I plan to submit there.
There is much more I would like to do on it, in particular to try to derive the same result using Hamilton-Jacobi theory, but I have no idea if I can succeed at that or how long it might take, so I think it is a good enough time to submit. I hope at least they will review it.
It's because the generally accepted value of Planck's constant is only half the correct value.
The quantity h-bar in the Schroedinger equation is actually h-bar/2. That's because it represents the spin of the electron, not of the photon, as implicitly assumed by de Broglie and carried forward by Schroedinger, and everyone else.
This fact has been overlooked because it was not recognized that the photon frequency is related to its energy not as E = h nu, but as E = h nu /(1 + v_l/c), where c is the limiting velocity of relativity theory, and v_l is the velocity of the photon, which is only very slightly less than c.
Although I derived that the energy of a composite photon is half the accepted value several months ago, and posted it about here previously, I didn't realize the implications until a few days ago, when I realized that the modulating factor on the Coulomb-like magnetic force between zitter particles satisfies the Schroedinger equation for a free particle in one spatial dimension. Except, the hbar must be replaced by hbar/2. This makes the energy difference between atomic energy levels half as large as previously thought, consistent with the photon energy being half the accepted value. However, simply replacing the hbar in the SE by hbar/2 leads obviously also to an angular momentum spectrum in multiples of hbar/2 rather than hbar. This cannot be, and the photon energy being hbar/2 can only be correct if, in addition to hbar being twice the currently-accepted value, hbar remains the quantum unit of angular momentum. So, the form of the SE has to change from its current form.
The modulation factor that I derived is equivalent to the Schroedinger wavefunction in one dimension, but not in three dimensions. There is a preferred dimension defined by the null four-displacement between the zitter particles. It is essentially the relativistic Doppler effect along the radial direction that gives rise to the modulating factor that can be equated with the de Broglie wave if hbar is replaced by hbar/2. (De Broglie was reasoning by analogy with the photon without knowing of the intrinsic angular momentum difference of the electron. Had he known of the difference, he would have expected the hbar/2.) In the cross-radial direction, though, the modulation goes over to a de Broglie wavelength (rather than half it for radial motion), as I showed in my FOOP paper. So it seems plausible that the Schroedinger-like equation based on the magnetic force modulation could lead to an energy spectrum in terms of multiples of hbar/2 but an angular momentum spectrum that agrees with observation, but that is work to do at the moment.
This is the complete sequel to my previously published paper in Foundations of Physics. The first two versions on arxiv only concerned the similarities of time-symmetric zitterbewegung radiation to the de Broglie wave. The new version (v3) continues on, and at least triples the length.
I still plan to rewrite the abstract and add some bits to the introduction, and generally go over all of the narrative and citations, and then submit it to Foundations of Physics, hopefully within the next few weeks.
The new version incorporates all of the extensions of my previous paper that were posted on arxiv as new versions beyond what was in Found Phys. I will therefore soon be updating that paper on arxiv as well, reverting to the published version with corrections. I posted that previously as v11 (v10 is the version in Found Phys, except for formatting). v12 is extended and has some considerable material that is now in the paper linked above. When I post v13, it will be the corrected version that was v11, but I will add the erratum I have written but not yet posted or provided to Foundations of Physics. I plan to submit the erratum and the new paper to Foundations of Physics at about the same time, although as separate submittals. Here is to the latest:
I have just uploaded it to arxiv, so it won't be public there for a few days. But I anticipate they may flag it and question me about my lack of an institution, as they did with my previous paper (although they approved it eventually), so I have also uploaded it already to Researchgate. It's linkable here:
I will be looking it over and very likely making some tweaks in the next day or so, since it won't get posted to arxiv until probably Tuesday midnight GMT at the earliest.
It's still a bit rough but I've been eager to post something since about a week ago when I was successful in obtaining the de Broglie wave correct superluminal phase velocity, as well as the correct group velocity and wavelength.
It is actually the beginning of a longer paper I've been writing as a sequel to my previous paper, that was published in Foundations of Physics. Figuring this new bit out has changed my understanding (for the better I believe) and so I now want to revise the rest of it to reflect the better understanding. Then I will replace the current version with the expanded version, and I plan to submit the full version to Found. Phys. Also, I made an erratum to offer them. But the (full version of the) new paper notes the problem (as mentioned in previous blogger posts and already fixed on the arxiv version) in any case.