Remarks on the Casimir force for magnetodielectric media

TL;DR

This paper compares the Casimir and Boyer forces in magnetodielectric media, revealing that their differences are governed by the underlying quantum statistics of scattering, with Boyer force exhibiting Fermi-Dirac and Casimir force Bose-Einstein distributions.

Contribution

It derives the Boyer force using stress tensor and dielectric variation methods, and highlights the role of quantum statistics in the force's nature.

Findings

Boyer force is derived using stress tensor and dielectric variation methods.

Spectral distribution in Boyer cavity follows Fermi-Dirac statistics.

Spectral distribution in Casimir cavity follows Bose-Einstein statistics.

Abstract

Boyer showed that a perfect electrically conducting slab repels a perfect magnetically conducting slab, in contrast to the attractive Casimir force between two identical perfect electrically/magnetically conducting slabs. To gain insight for the difference between the Boyer force and the Casimir force, we present the derivation of the Boyer force using the stress tensor method and then using the method of variation in dielectric. The Green dyadic, in terms of electric and magnetic Green's functions, is presented for an electric medium filling half of space and another magnetic medium filling another half of space such that the two half-spaces are parallel and separated by a distance $a$. We make the observation that the spectral distribution of scattering in a Boyer cavity is that of Fermi-Dirac type, while the spectral distribution of scattering in a Casimir cavity is that of Bose-Einstein type. Based on this observation we conclude that the difference between the Boyer force and the Casimir force is governed by the statistics of the possible scattering in the respective cavities.