Stochastic Spacetime and Brownian Motion of Test Particles

TL;DR

This paper explores the concept of spacetime fluctuations through the lens of Brownian motion of test particles, linking quantum gravitational effects to observable phenomena like lightcone fluctuations and spectral broadening.

Contribution

It introduces a novel interpretation of quantum spacetime fluctuations as Brownian motion of particles, supported by explicit examples and analogies with electromagnetic phenomena.

Findings

Spacetime fluctuations induce Brownian motion in test particles.

Observable effects include lightcone fluctuations and spectral line broadening.

Fluctuations can cause variations in luminosity and angular blurring.

Abstract

The operational meaning of spacetime fluctuations is discussed. Classical spacetime geometry can be viewed as encoding the relations between the motions of test particles in the geometry. By analogy, quantum fluctuations of spacetime geometry can be interpreted in terms of the fluctuations of these motions. Thus one can give meaning to spacetime fluctuations in terms of observables which describe the Brownian motion of test particles. We will first discuss some electromagnetic analogies, where quantum fluctuations of the electromagnetic field induce Brownian motion of test particles. We next discuss several explicit examples of Brownian motion caused by a fluctuating gravitational field. These examples include lightcone fluctuations, variations in the flight times of photons through the fluctuating geometry, and fluctuations in the expansion parameter given by a Langevin version of the Raychaudhuri equation. The fluctuations in this parameter lead to variations in the luminosity of sources. Other phenomena which can be linked to spacetime fluctuations are spectral line broadening and angular blurring of distant sources.