Speed of Light in Non--Trivial Vacua

TL;DR

This paper unifies and extends understanding of how the speed of low-energy photons varies in different vacuum states, revealing a universal relation tied to vacuum energy density differences and analyzing various field theories and Casimir setups.

Contribution

It introduces a universal formula for photon speed changes in modified vacua and systematically studies these effects across multiple field theories and vacuum conditions.

Findings

Photon speed change depends on vacuum energy density difference.

Photons can travel faster than c in Casimir vacuum.

Massless particles show speed modifications only when related to mass or running mass.

Abstract

We unify all existing results on the change of the speed of low--energy photons due to modifications of the vacuum, finding that it is given by a universal constant times the quotient of the difference of energy densities between the usual and modified vacua over the mass of the electron to the fourth power. Whether photons move faster or slower than $c$ depends only on the lower or higher energy density of the modified vacuum, respectively. Physically, a higher energy density is characterized by the presence of additional particles (real or virtual) in the vacuum whereas a lower one stems from the absence of some virtual modes. We then carry out a systematic study of the speed of propagation of massless particles for several field theories up to two loops on a thermal vacuum. Only low--energy massless particles corresponding to a massive theory show genuine modifications of their speed while remaining massless. All other modifications are mass-related, or running mass-related. We also develop a formalism for the Casimir vacuum which parallels the thermal one and check that photons travel faster than $c$ between plates.