Vacuum energy and the spacetime index of refraction: A new synthesis

Abstract

In $1+3$ (threading) formulation of general relativity spacetime behaves analogous to a medium with a specific index of refraction with respect to the light propagation. Accepting the reality of zero-point energy, through the equivalence principle, we elevate this analogy to the case of virtual photon propagation in a quantum vacuum in a curved background spacetime. Employing this new idea (conjecture) one could examine the response of vacuum energy to the presence of a weak stationary gravitational field in its different quantum field theoretic manifestations such as Casimir effect and Lamb shift. As an evidence in favor of the proposed conjecture, employing quantum field theory in curved spacetime, we explicitly calculate the effect of a weak static gravitational field on virtual massless scalar particles in a Casimir apparatus. It is shown that, as expected from the proposed conjecture, both the frequency and renormalized energy of the virtual scalar field are affected by the gravitational field through its index of refraction. Generalizations to weak stationary spacetimes and virtual photons are also discussed.