  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.
