Quantum corrections to the geodesic equation

TL;DR

This paper argues that when quantum graviton effects are included, classical measurements do not reflect the background spacetime, leading to a quantum-corrected geodesic equation that is gauge-independent.

Contribution

It introduces a quantum-corrected geodesic equation accounting for graviton fluctuations, resolving gauge fixing ambiguities in semiclassical gravity.

Findings

Classical particles do not follow background geodesics when quantum effects are included.

The quantum-corrected geodesic equation is explicitly gauge-independent.

Measurement devices are affected by graviton fluctuations, altering perceived spacetime geometry.

Abstract

In this talk we will argue that, when gravitons are taken into account, the solution to the semiclassical Einstein equations (SEE) is not physical. The reason is simple: any classical device used to measure the spacetime geometry will also feel the graviton fluctuations. As the coupling between the classical device and the metric is non linear, the device will not measure the `background geometry' (i.e. the geometry that solves the SEE). As a particular example we will show that a classical particle does not follow a geodesic of the background metric. Instead its motion is determined by a quantum corrected geodesic equation that takes into account its coupling to the gravitons. This analysis will also lead us to find a solution to the so-called gauge fixing problem: the quantum corrected geodesic equation is explicitly independent of any gauge fixing parameter.