Modified Special Relativity on a fluctuating spacetime

TL;DR

This paper demonstrates that deformed special relativity (DSR) effects can emerge from averaging quantum gravitational fluctuations in a fluctuating spacetime, linking stochastic metric fluctuations to nonlinear momentum relations.

Contribution

It explicitly shows how DSR-like nonlinear momentum relations can result from averaging stochastic spacetime fluctuations, connecting quantum gravity effects to observable relativistic deformations.

Findings

DSR-like relations emerge from averaging stochastic fluctuations.

Averaging over de Broglie wavelength scale produces nonlinear momentum relations.

Physical implications of stochastic spacetime fluctuations are discussed.

Abstract

It was recently proposed that deformations of the relativistic symmetry, as those considered in Deformed Special Relativity (DSR), can be seen as the outcome of a measurement theory in the presence of non-negligible (albeit small) quantum gravitational fluctuations [1,2]. In this paper we explicitly consider the case of a spacetime described by a flat metric endowed with stochastic fluctuations and, for a free particle, we show that DSR-like nonlinear relations between the spaces of the measured and classical momenta, can result from the average of the stochastic fluctuations over a scale set be the de Broglie wavelength of the particle. As illustrative examples we consider explicitly the averaging procedure for some simple stochastic processes and discuss the physical implications of our results.