Faster than Light Photons in Gravitational Fields II - Dispersion and Vacuum Polarisation

TL;DR

This paper investigates how vacuum polarisation in quantum electrodynamics within gravitational fields affects light propagation, especially whether superluminal photon velocities persist at high frequencies, impacting causality considerations.

Contribution

It extends previous low-frequency analyses by calculating the high-frequency behavior of photon phase velocity in curved spacetime using a comprehensive effective action.

Findings

Superluminal velocities are examined at high frequencies.

The frequency dependence of photon phase velocity is characterized.

Implications for causality in curved spacetime are discussed.

Abstract

Vacuum polarisation in QED in a background gravitational field induces interactions which effectively violate the strong equivalence principle and affect the propagation of light. In the low frequency limit, Drummond and Hathrell have shown that this mechanism leads to superluminal photon velocities. To confront this phenomenon with causality, however, it is necessary to extend the calculation of the phase velocity $\vp(\w)$ to high frequencies, since it is $\vp(\infty)$ which determines the characteristics of the effective wave equation and thus the causal structure. In this paper, we use a recently constructed expression, valid to all orders in a derivative expansion, for the effective action of QED in curved spacetime to determine the frequency dependence of the phase velocity and investigate whether superluminal velocities indeed persist in the high frequency limit.