The equilibrium classical scatter spectrum of waves

TL;DR

This paper derives the Planck spectrum from classical wave train superpositions and Doppler shift effects, challenging traditional quantum interpretations by emphasizing classical wave interactions and Lorentz invariance.

Contribution

It demonstrates that the Planck spectrum can be obtained through classical wave train superpositions and Doppler effects, providing a new perspective on radiation spectra without quantum assumptions.

Findings

Doppler shifts shape the Planck spectrum

Classical wave trains are fundamental radiation entities

Lorentz invariance of Doppler shifts is essential for correct spectrum

Abstract

Regardless of the unspecific notions of photons as light complexes, radiation bundles or wave packets, the radiation from a single state transition is at most a single continuous wave train that starts and ends with the transition. The radiation equilibrium spectrum must be the superposition sum of the spectra of such wave trains. A classical equipartition of wave trains cannot diverge since they would be finite in number, whereas standing wave modes are by definition infinite, which had doomed Rayleigh's theory, and concern only the total radiation. Wave trains are the microscopic entities of radiation interacting with matter, that correspond to molecules in kinetic theory. Their quantization came from matter transitions in Einstein's 1917 derivation of Planck's law. The spectral scatter of wave trains by Doppler shifts, which cause the wavelength displacements in Wien's law used for the frequency dependence in Einstein's derivation, is shown to yield the shape of the Planck spectrum. A Lorentz transform property of Doppler shifts discovered by Einstein is further shown equivalently necessary and sufficient to have corrected Rayleigh's theory.