  It has been found in several papers that, because of quantum corrections,
light front can propagate with superluminal velocity in gravitational fields
and even in flat space-time across two conducting plates. We show that, if this
is the case, closed time-like trajectories would be possible and, in
particular, in certain reference frames photons could return to their source of
origin before they were produced there, in contrast to the opposite claim made
in the literature.
