Spacetime Curvature in terms of Scalar Field Propagators

TL;DR

This paper explores how quantum field correlators can be used to measure and reconstruct spacetime curvature, and examines the effects of a natural ultraviolet cutoff on the resolution of such measurements.

Contribution

It demonstrates that quantum field correlators encode spacetime metric information and analyzes the impact of a UV cutoff on the precision of curvature measurements.

Findings

Quantum correlators contain sufficient information to reconstruct spacetime metric.

A natural UV cutoff limits the spatial resolution of curvature measurements.

The metric exhibits a peculiar scaling behavior near the UV cutoff scale.

Abstract

We show how quantum fields can be used to measure the curvature of spacetime. In particular, we find that knowledge of the imprint that spacetime curvature leaves in the correlators of quantum fields suffices, in principle, to reconstruct the metric. We then consider the possibility that the quantum fields obey a natural ultraviolet cutoff, for example, at the Planck scale. We investigate how such a cutoff limits the spatial resolution with which curvature can be deduced from the properties of quantum fields. We find that the metric deduced from the quantum correlator exhibits a peculiar scaling behavior as the scale of the natural UV cutoff is approached.