Spacetime geometry fluctuations and geodesic deviation

TL;DR

This paper investigates how quantum fluctuations of spacetime geometry influence the relative motion of test particles, analyzing different quantum states of gravitons and their impact on geodesic deviation.

Contribution

It introduces a calculation of mean squared fluctuations in test particles' relative velocity and separation caused by quantum spacetime fluctuations in various graviton states.

Findings

Quantum fluctuations cause measurable deviations in test particles' trajectories.

Different graviton states produce distinct fluctuation patterns.

The Riemann tensor correlation function characterizes these quantum effects.

Abstract

The quantum fluctuations of the geodesic deviation equation in a flat background spacetime are discussed. We calculate the resulting mean squared fluctuations in the relative velocity and separation of test particles. The effect of these quantum fluctuations of the spacetime geometry is given in terms of the Riemann tensor correlation function. Three different sources of the Riemann tensor fluctuations are considered: a thermal bath of gravitons, gravitons in a squeezed state, and the graviton vacuum state.