Spacetime curvature from ultra rapid measurements of quantum fields

TL;DR

This paper demonstrates how ultra-rapid measurements of quantum fields with particle detectors can be used to directly infer the spacetime curvature, linking quantum measurement outcomes to geometric properties.

Contribution

It introduces a method to express spacetime curvature components through excitation probabilities of smeared Unruh-DeWitt detectors in curved backgrounds.

Findings

Curvature tensors can be derived from detector excitation probabilities.

Short distance expansion relates flat and curved spacetime detector responses.

Method provides a physically measurable way to access spacetime geometry.

Abstract

We write the curvature of spacetime in terms of the excitation probability of particle detectors ultra-rapidly coupled to a quantum field. More precisely, we provide an expansion for the excitation probability of a smeared UDW detector delta-coupled to a real scalar quantum field in a curved background. Using a short distance expansion for the Wightman function, we express the excitation probability of a detector as the transition probability in Minkowski spacetime plus correction terms written as a function of the curvature tensors and the detector size. Comparing the excitation probability in curved spacetimes with its flat analog, we are able to express the components of the Ricci and Riemann curvature tensors as a function of physically measurable excitation probabilities of different shaped detectors.