Electromagnetic Casimir effect and the spacetime index of refraction

TL;DR

This paper explores how the electromagnetic Casimir effect responds to gravitational fields by modeling spacetime as a refractive medium, extending previous scalar field results to virtual photons and calculating the energy density in weak gravity.

Contribution

It explicitly demonstrates the application of the spacetime refractive index conjecture to electromagnetic vacuum, showing consistent frequency shifts for virtual photons and deriving the energy density in a gravitational field.

Findings

Virtual photon frequency shifts match scalar field predictions.

Electromagnetic energy density in weak gravity is calculated.

Spacetime as a refractive medium affects vacuum energy.

Abstract

In [5] we investigated the response of vacuum energy to a gravitational field by considering a Casimir apparatus in a weak gravitational field. Our approach was based on a conjecture involving the interpretation of spacetime as a refractive medium and its effect on vacuum energy composed of virtual massless scalar particles. There it was shown how the case of virtual photons as the constituents of vacuum could be inferred from that of the massless scalar field. Here we explicitly show how the same conjecture applies to the electromagnetic vacuum composed of virtual photons. Specifically we show that the boundary conditions imposed on the components of the vector field, decomposed into two scalar fields, result in the same frequency shift for photons. Using the same decomposition and employing our conjecture, we also calculate the electromagnetic energy density for the Casimir apparatus in a weak gravitational field.