  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.
