Casimir Energy for a Spherical Cavity in a Dielectric: Toward a Model for Sonoluminescence?

TL;DR

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

Contribution

It provides a leading approximation of the Casimir energy in a dielectric sphere, addressing its possible connection to sonoluminescence and discussing divergence and sign issues.

Findings

The computed Casimir energy is too small to explain sonoluminescence.

The divergent result has the wrong sign to drive the effect.

Dispersion does not resolve the energy sign contradiction.

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, I have computed the static Casimir energy of a spherical cavity in an otherwise uniform material with dielectric constant $\epsilon$ and permeability $\mu$. As expected the result is divergent; yet a plausible finite answer is extracted, in the leading uniform asymptotic approximation. That result gives far too small an energy to account for the large burst of photons seen in sonoluminescence. If the divergent result is retained (which is different from that guessed by Schwinger), it is of the wrong sign to drive the effect. Dispersion does not resolve this contradiction. However, dynamical effects are not yet included.