Maximal velocity of photons in non-relativistic QED

TL;DR

This paper proves that in non-relativistic QED, the probability of photons traveling faster than the speed of light diminishes over time, establishing a maximal photon velocity consistent with relativistic constraints.

Contribution

It demonstrates that photons in non-relativistic QED cannot propagate faster than the speed of light when the matter system is localized.

Findings

Photon propagation probability beyond speed c vanishes over time.

Photon velocity is effectively bounded by the speed of light.

Results hold for matter systems below ionization energy.

Abstract

We consider the problem of propagation of photons in the quantum theory of non-relativistic matter coupled to electromagnetic radiation, which is, presently, the only consistent quantum theory of matter and radiation. Assuming that the matter system is in a localized state (i.e for energies below the ionization threshold), we show that the probability to find photons at time t at the distance greater than ct, where c is the speed of light, vanishes as t goes to infinity as an inverse power of t.