Casimir Energy for a Spherical Cavity in a Dielectric: Applications to Sonoluminescence

TL;DR

This paper calculates the static Casimir energy for a spherical cavity in a dielectric medium to evaluate its potential role in sonoluminescence, finding it too small and of the wrong sign to explain the phenomenon.

Contribution

It provides a detailed computation of the Casimir energy in a spherical dielectric cavity and compares it with previous regularization methods, assessing its relevance to sonoluminescence.

Findings

Casimir energy is divergent but a finite approximation is obtained.

The computed energy is too small to explain sonoluminescence.

The sign of the Casimir energy is incompatible with driving the effect.

Abstract

In the final few years of his life, Julian Schwinger proposed that the ``dynamical Casimir effect'' might provide the driving force behind the puzzling phenomenon of sonoluminescence. Motivated by that exciting suggestion, we have computed the static Casimir energy of a spherical cavity in an otherwise uniform material. As expected the result is divergent; yet a plausible finite answer is extracted, in the leading uniform asymptotic approximation. This result agrees with that found using zeta-function regularization. Numerically, we find far too small an energy to account for the large burst of photons seen in sonoluminescence. If the divergent result is retained, it is of the wrong sign to drive the effect. Dispersion does not resolve this contradiction. In the static approximation, the Fresnel drag term is zero; on the mother hand, electrostriction could be comparable to the Casimir term. It is argued that this adiabatic approximation to the dynamical Casimir effect should be quite accurate.