Models of Particle Detection in Regions of Spacetime

TL;DR

This paper compares two models of particle detection in spacetime regions, revealing that the probability of detection depends on the measurement device, and connects these models to different probability definitions in quantum mechanics.

Contribution

It introduces and contrasts two measurement models for detecting particles in spacetime, linking one to path integral probabilities and highlighting device dependence.

Findings

Different models predict different detection probabilities.

One model relates to path integral probability definitions.

Detection probabilities are device-dependent.

Abstract

We investigate two models of measuring devices designed to detect a non-relativistic free particle in a given region of spacetime. These models predict different probabilities for a free quantum particle to enter a spacetime region $R$ so that this notion is device dependent. The first model is of a von Neumann coupling which we present as a contrast to the second model. The second model is shown to be related to probabilities defined through partitions of configuration space paths in a path integral. This study thus provides insight into the physical situations to which such definitions of probabilities are appropriate.