Quantum particles and an effective spacetime geometry

TL;DR

This paper investigates how quantum particles, modeled as classical extended objects, can be used to infer an effective spacetime geometry by analyzing the covariant center of mass and its deviation from geodesic motion.

Contribution

It introduces a scheme to extract components of an effective connection from the motion of extended objects' centers of mass, bridging quantum particle behavior and spacetime geometry.

Findings

Proposes a method to determine effective connection components from center of mass trajectories.

Shows that the center of mass generally does not follow background geodesics.

Discusses limitations in obtaining the full effective connection.

Abstract

Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a first step to study how it is possible to read spacetime geometry with quantum particles, we model these particles with classical extended objects. We propose to represent such extended objects by its covariant center of mass, which generically does not follow a geodesic of the background metric. We present a scheme that allows to extract some of components of an "effective" connection, namely, the connection that would be obtained if the locus of the center of mass is regarded as a geodesic. We discuss some issues that arise when trying to obtain all the components of the effective connection and its possible implications.