Let A and B be two atoms or, more generally, a ''source'' and a ''dete
ctor'' separated by some distance R. At t = 0 A is in an excited state
, B in its ground state, and no photons are present. A theorem is prov
ed that in contrast to Einstein causality and finite signal velocity t
he excitation probability of B is nonzero immediately after t = 0. Imp
lications are discussed.