Understanding the Planck Blackbody Spectrum and Landau Diamagnetism within Classical Electromagnetism

TL;DR

This paper demonstrates that classical electromagnetic theory, when correctly incorporating zero-point radiation and relativistic principles, can explain blackbody radiation and Landau diamagnetism without quantum mechanics.

Contribution

It clarifies how to properly combine relativistic electromagnetism with nonrelativistic mechanics to explain blackbody spectrum and diamagnetism classically.

Findings

Classical zero-point radiation explains blackbody spectrum.

Landau diamagnetism can be derived from classical electromagnetism.

Proper relativistic-nonrelativistic coupling is essential for accurate classical explanations.

Abstract

Electromagnetism is a \textit{relativistic} theory and one must exercise care in coupling this theory with \textit{nonrelativistic} classical mechanics and with \textit{nonrelativistic} classical statistical mechanics. Indeed historically, both the blackbody radiation spectrum and diamagnetism within classical theory have been misunderstood because of two crucial failures: 1)the neglect of classical electromagnetic zero-point radiation, and 2) the use of erroneous combinations of nonrelativistic mechanics with relativistic electrodynamics. Here we review the treatment of classical blackbody radiation, and show that use of Lorentz-invariant classical electromagnetic zero-point radiation can be used to explain both the Planck blackbody spectrum and Landau diamagnetism at thermal equilibrium within classical electromagnetic theory. The analysis requires that relativistic electromagnetism is joined appropriately with simple nonrelativistic mechanical systems which can be regarded as the zero-velocity limits of relativistic systems, and that nonrelativistic classical statistical mechanics is applied only in the low-frequency limit when zero-point energy makes no contribution.