QED Vacuum Polarization in a Background Gravitational Field and Its Effect on the Velocity of Photons

We calculate in QED the contribution to the photon effective action from one-loop vacuum polarization on a general curved background manifold, and use it to investigate the corrections to the local propagation of photons. We find that the quantum corrections introduce tidal gravitational forces on the photons which in general alter the characteristics of propagation, so that in some cases photons travel at speeds greater than unity. The effect is nondispersive and gauge invariant. We look at a few examples, including a background Schwarzschild geometry, and we argue that although these results are controversial they do not in fact exhibit any obvious inconsistency.