OKHEP-95-06 Casimir Energy for a Spherical Cavity in a Dielectric: Toward a Model for Sonoluminescence?

In the nal few years of his life, Julian Schwinger proposed that the \dynamical Casimir e ect" 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 and permeability . As expected the result is divergent; yet a plausible nite 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 di erent from that guessed by Schwinger), it is of the wrong sign to drive the e ect. Dispersion does not resolve this contradiction. However, dynamical e ects are not yet included.