Metric fluctuations and the Weak Equivalence Principle

TL;DR

This paper models spacetime fluctuations as metric perturbations, deriving a modified Schrödinger equation that suggests possible violations of the Weak Equivalence Principle and Lorentz invariance due to quantum spacetime effects.

Contribution

It introduces a simple model of spacetime fluctuations leading to an anomalous inertial mass tensor, providing a proof-of-concept for potential violations of fundamental principles.

Findings

Existence of an anomalous inertial mass tensor due to spacetime fluctuations

Potential violation of the Weak Equivalence Principle

Indications of Lorentz invariance violation

Abstract

We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging procedure over a finite space--time scale given by the quantum particle in the non--relativistic limit a modified Schr\"odinger equation. The dominant modification consists in an anomalous inertial mass tensor which depends on the type of particle and on the fluctuation scenario. The scenario considered in this paper is a most simple picture of spacetime fluctuations and gives an existence proof for an apparent violation of the weak equivalence principle and, in general, for a violation of Lorentz invariance.