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

## Sunday, June 25, 2017

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