Notes on Rindler wave packets in Minkowski spacetime

TL;DR

This paper analyzes how localized Rindler wave packets of a massless scalar field are perceived by Minkowski observers, revealing a fundamental limit on the precision of their momentum distribution due to quantum effects.

Contribution

It provides an analytic expression for the Minkowski momentum distribution of Rindler wave packets and uncovers a universal lower bound on momentum uncertainty.

Findings

Minkowski momentum distribution derived analytically

Universal lower bound on momentum uncertainty established

Quantum effects modify classical gravitational red-shift interpretation

Abstract

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 red-shift 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.