Casimir energy for a spherical cavity in a dielectric: Applications to sonoluminescence

In a series of papers, Schwinger [Proc. Natl. Acad. Sci. U.S.A. 90, 958 (1993); 90, 2105 (1993); 90, 4505 (1993); 90, 7285 (1993); 91, 6473 (1994)] 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 ζ-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 other hand, the electrostriction could be comparable to the Casimir term. It is argued that this adiabatic approximation to the dynamical Casimir effect should be quite accurate.