Gravitational and Inertial Mass of Casimir Energy

Abstract

It has been demonstrated, using variational methods, that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. This conclusion holds independently of the orientation of the plates. We review these arguments and add further support to this conclusion by considering parallel semitransparent plates, that is, $δ$-function potentials, acting on a massless scalar field, in a spacetime defined by Rindler coordinates. We calculate the force on systems consisting of one or two such plates undergoing acceleration perpendicular to the plates. In the limit of small acceleration we recover (via the equivalence principle) the situation of weak gravity, and find that the gravitational force on the system is just $M\mathbf{g}$, where $\mathbf{g}$ is the gravitational acceleration and $M$ is the total mass of the system, consisting of the mass of the plates renormalized by the Casimir energy of each plate separately, plus the energy of the Casimir interaction between the plates. This reproduces the previous result in the limit as the coupling to the $δ$-function potential approaches infinity. Extension of this latter work to arbitrary orientation of the plates, and to general compact quantum vacuum energy configurations, is under development.