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In the final few years of his life, Julian Schwinger proposed that the``dynamical Casimir effect'' might provide the driving force behind thepuzzling phenomenon of sonoluminescence. Motivated by that exciting suggestion,I have computed the static Casimir energy of a spherical cavity in an otherwiseuniform material with dielectric constant $\epsilon$ and permeability $\mu$. Asexpected the result is divergent; yet a plausible finite answer is extracted,in the leading uniform asymptotic approximation. That result gives far toosmall an energy to account for the large burst of photons seen insonoluminescence. If the divergent result is retained (which is different fromthat guessed by Schwinger), it is of the wrong sign to drive the effect.Dispersion does not resolve this contradiction. However, dynamical effects arenot yet included.

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