The Refractive Index of Curved Spacetime: the Fate of Causality in QED

Understand

It has been known for a long time that vacuum polarization in QED leads to a superluminal low-frequency phase velocity for light propagating in curved spacetime.

• Assuming the validity of the Kramers-Kronig dispersion relation, this would imply a superluminal wavefront velocity and the violation of causality.
• Here, we calculate for the first time the full frequency dependence of the refractive index using world-line sigma model techniques together with the Penrose plane wave limit of spacetime in the neighbourhood of a null geodesic.
• We find that the high-frequency limit of the phase velocity (i.e.