Notes on Rindler wave packets in Minkowski spacetime

We consider wave packets of a massless scalar field that have well-localized Rindler energy, and examine how their energy appears to a Minkowski observer to study how the classical gravitational redshift formula is modified quantum mechanically. We derive, by using the saddle point approximation, an analytic expression for the Minkowski momentum distribution of such Rindler wave packets. We find a universal lower bound on the uncertainty in the Minkowski momentum; the momentum distribution can never become arbitrarily sharp.