Casimir self-stress in a dielectric sphere

TL;DR

This paper introduces a new method for calculating the Casimir self-stress in dielectric spheres with arbitrary properties, clarifying the nature of Casimir forces beyond pairwise interactions.

Contribution

It develops a general computational approach for Casimir self-stress in homogeneous dielectric spheres, extending previous special cases and challenging existing dilute-limit assumptions.

Findings

Reproduces known repulsive Casimir force for perfect reflectors

Disagrees with literature in the dilute limit

Argues Casimir forces arise from wave reflections, not pair interactions

Abstract

The dielectric sphere has been an important test case for understanding and calculating the vacuum force of a dielectric body onto itself. Here we develop a method for computing this force in homogeneous spheres of arbitrary dielectric properties embedded in arbitrary homogeneous backgrounds, assuming only that both materials are isotropic and dispersionless. Our results agree with known special cases; most notably we reproduce the prediction of Boyer and Schwinger et al. of a repulsive Casimir force of a perfectly reflecting shell. Our results disagree with the literature in the dilute limit. We argue that Casimir forces can not be regarded as due to pair-wise Casimir-Polder interactions, but rather due to reflections of virtual electromagnetic waves.