How does Casimir energy fall? II. Gravitational acceleration of quantum vacuum energy

Abstract

It has been demonstrated that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. We here 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 (τ, x, y, ξ). Fixed ξ in such a spacetime represents uniform acceleration. We calculate the force on systems consisting of one or two such plates at fixed values of ξ. In the limit of a large Rindler coordinate ξ (small acceleration), we recover (via the equivalence principle) the situation of weak gravity, and find that the gravitational force on the system is just Mg, where 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.