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

TL;DR

This paper supports the idea that quantum vacuum energy, including Casimir energy, obeys the equivalence principle by analyzing the gravitational force on semitransparent plates in accelerated frames, confirming previous findings.

Contribution

It extends prior work by considering semitransparent plates in Rindler spacetime, demonstrating that Casimir energy gravitates according to the equivalence principle in this more general setting.

Findings

Gravitational force on Casimir systems equals Mg in the weak acceleration limit.

Casimir energy contributes to the system's mass and gravitational interaction.

Results agree with previous perfect conductor plate analyses in the appropriate limit.

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, delta-function potentials, acting on a massless scalar field, in a spacetime defined by Rindler coordinates (tau,x,y,xi). Fixed xi in such a spacetime represents uniform acceleration. We calculate the force on systems consisting of one or two such plates at fixed values of xi. In the limit of large Rindler coordinate xi (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 delta-function potential approaches infinity.