  This paper explores whether quantum field 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 affirmative, traditionally such effects have been considered
negligible. We show that for sufficiently light mass eigenstates such processes
can become significant over macroscopic length scales. A critical review of the
historical literature reveals various shortcomings of the standard methods;
specifically, one finds 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 find 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
collaboration. Turning to the ICARUS experiment, we note that while the
collaboration reported an average time of flight 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.
