Real-time particle-detection probabilities in accelerated macroscopic detectors

Abstract

We construct the detection rate for particle detectors moving along non-inertial trajectories and interacting with quantum fields. The detectors described here are characterized by the presence of records of observation throughout their history, so that the detection rate corresponds to directly measurable quantities. This is in contrast to past treatments of detectors, which actually refer to probes, i.e., microscopic systems from which we extract information only after their interaction has been completed. Our treatment incorporates the irreversibility due to the creation of macroscopic records of observation. The key result is a real-time description of particle detection and a rigorously defined time-local probability density function (PDF). The PDF depends on the scale $\sigma$ of the temporal coarse-graining that is necessary for the formation of a macroscopic record. The evaluation of the PDF for Unruh-DeWitt detectors along different types of trajectory shows that only paths with at least one characteristic time-scale much smaller than $\sigma$ lead to appreciable particle detection. Our approach allows for averaging over fast motions and thus predicts a constant detection rate for all fast periodic motions.