Transmission of information in nonlocal field theories

The signaling between two observers in 3 + 1 dimensional flat spacetime coupled locally to a nonlocal field is considered. We show that in the case where two observers are purely timelike related-so that an exchange of on-shell massless quanta cannot occur-signaling is still possible because of a violation of Huygens' principle. In particular, we show that the signaling is exponentially suppressed by the nonlocality scale. Furthermore, we consider the case in which the two observers are lightlike related and show that the nonlocal modification to the local result is polynomially suppressed in the nonlocality scale. This may have implications for phenomenological tests of nonlocal theories.