Fermat's principle in quantum gravitational optics

TL;DR

This paper explores how quantum vacuum polarization effects in curved spacetime alter photon trajectories, leading to gravitational birefringence and polarization-dependent superluminal propagation, by modifying Fermat's principle and the spacetime refractive index.

Contribution

It derives a modified Fermat's principle incorporating quantum effects, providing a new expression for the spacetime refractive index affected by vacuum polarization in curved backgrounds.

Findings

Photon trajectories are no longer geodesics due to vacuum polarization.

The spacetime refractive index is proportional to light cone corrections.

Polarization sum rules and light path modifications are analyzed.

Abstract

Interactions incorporating the vacuum polarization effects in curved backgrounds modify the null cone structure in such a way that the photon trajectories would not be the space-time geodesics anymore. The gravitational birefringence introduced as a direct consequence of these effects, will allow shifts in the photon velocities leading to polarization dependent superluminal propagation. Taking these effects into account we study Fermat's principle in the context of the 1+3 (threading) formulation of the space-time decomposition. We find an expression for the modified spacetime refractive index and show it is proportional to the light cone correction to the first order. Consequences of this modification on polarization sum rules and spatial light paths are considered.