Thermodynamics and Energy

   

Distribution of Photons Under the Control of the Classical Equipartition and Boltzmann Distribution Laws—Resolution of the Ultraviolet Catastrophe Paradox

Authors: Kenichi Akabane

Since Planck’s explanation of blackbody radiation over one century ago, researchers have considered that the law of equipartition does not apply to photons. Furthermore, since the publication of Bose distribution theory, photons have been presumed to follow the Bose distribution (quantum statistics) rather than the Boltzmann distribution. I first show that the mean energy of photons based on Wien’s radiation law, which slightly differs from that of Planck’s law, equals the mean energy 3kT of the lattice vibrations of a solid and hence satisfies the idealized classical law of equipartition (where k is Boltzmann’s constant and T is the equilibrium temperature). However, zero-frequency photons are logically nonexistent because all of their components are zero; accordingly, they must be excluded from the distribution. Using this fact, I demonstrate that Planck’s law is merely Wien’s radiation law with the zero-frequency photons excluded from the distribution, which follows the classical law of equipartition and the Boltzmann distribution law. Additionally, I show that the accepted theory of photons cannot exclude zero-frequency photons from the distribution. The present study might help to elucidate the mechanism of the specific heat of solids mediated by phonons, which (like photons in a cavity) form standing waves.

Comments: 19 Pages. There are no changes to the contents of the manuscript, but for clarity, Fig. 1 has been added and Figs. 4 and 5 have been deleted. Accordingly, the text related to Figs. 4 and 5 has been deleted.

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Submission history

[v1] 2022-10-05 01:13:04
[v2] 2025-01-27 02:14:45

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