Amplitudes for space-like separations and causality
This paper explores whether quantum eld theory allows the events of emission and absorption of a single particle to be separated by a space-like interval without violating Lorentz symmetries and causality. Although the answer is indeed armative, tradition- ally such eects have been considered negligible. We show that for suciently light mass eigenstates such processes can become signicant over macroscopic length scales. A critical review of the historical literature reveals various shortcomings of the standard methods; specically, one nds that they are restricted to states for which the expectation value of momentum vanishes. Furthermore, the results obtained here correct Feynman's analysis of this subject. A formalism is thus developed that allows the description of states with non-zero momentum, which is then applied to the OPERA and ICARUS neutrino-speed experiments. For OPERA we choose a mass in the nano electron-volt range and nd that although our formalism predicts a non-zero detection probability for an early arrival time of 60 ns, the predicted event distribution is maximal on the light-cone. Consequently, our prediction does not reproduce the peak at 60 ns reported by the OPERA collabora- tion. Turning to the ICARUS experiment, we note that while the collaboration reported an average time of ight that is consistent with the speed of light, the event data with its associated uncertainties nevertheless indicates that some of the detection events are separated from their corresponding emission events by a space-like interval. For a micro electron-volt mass range, this is in agreement with the here reported formalism. We thus raise the possibility of employing high-precision neutrino-speed experiments to determine the absolute masses of neutrino mass eigenstates. Finally, it is argued that the predicted space-like amplitudes are consistent with the emperical data on SN1987a.