  In 1948 H.B.G.Casimir predicted that an attractive force between two
perfectly conducting neutral plates exists due to changes in the
electromagnetic vacuum energy caused by the influence of the plates. In 1956
E.M. Lifshitz derived an extension of Casimir's expression applicable to finite
temperatures and arbitrary dielectric constants for the two half-spaces and the
gap in between them. It is shown in this brief report that, while the Lifshitz
formula predicts an attractive force for the case of identical dielectric
constants for the two half-spaces, a repulsive force results in some
circumstances when the dielectric constants are not identical. The reason for
the repulsive force and possible applications will be considered.
