Relativity and Radiation Balance for the Classical Hydrogen Atom in Classical Electromagnetic Zero-Point Radiation

TL;DR

This paper emphasizes the importance of special relativity in analyzing the classical hydrogen atom within electromagnetic zero-point radiation, correcting previous errors and demonstrating radiation balance at fundamental frequencies.

Contribution

It introduces a relativistic analysis approach, correcting prior nonrelativistic approximations, and shows radiation balance holds at fundamental frequencies in the classical hydrogen atom.

Findings

Radiation balance holds at fundamental frequencies and overtones.

Nonrelativistic Fourier coefficients are invalid for Coulomb systems.

Relativistic analysis corrects previous misconceptions.

Abstract

Here we review the understanding of the classical hydrogen atom in classical electromagnetic zero-point radiation, and emphasize the importance of special relativity. The crucial missing ingredient in earlier calculational attempts (both numerical and analytic) is the use of valid approximations to the full relativistic analysis. It is pointed out that the nonrelativistic time Fourier expansion coefficients given by Landau and Lifshitz are in error as the electromagnetic description of a charged particle in a Coulomb potential, and, because of this error, Marshall and Claverie's conclusion regarding the failure of radiation balance is invalid. Rather, using Marshall and Claverie's calculations, but restricted to lowest nonvanishing order in the orbital eccentricity (where the nonrelativistic orbit is a valid approximation to the fully relativistic electromagnetic orbit) radiation balance for classical electromagnetic zero-point radiation is shown to hold at the fundamental frequencies and associated first overtones.