Causality problems for Fermi’s two-atom system

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