Equivalence principle violation from large scale structure

TL;DR

This paper investigates how extended uncertainty principles, incorporating spacetime curvature effects, lead to violations of the weak equivalence principle by making inertial mass position-dependent in quantum systems.

Contribution

It demonstrates that under extended uncertainty relations, the inertial mass becomes position-dependent, indicating a violation of the weak equivalence principle in quantum regimes.

Findings

Inertial mass varies with position under extended uncertainty relations.

The gravitational mass remains unaffected by the extended uncertainty principle.

The ratio of inertial to gravitational mass remains unchanged in the analyzed scenarios.

Abstract

We explore the interplay between the equivalence principle and a generalization of the Heisenberg uncertainty relations known as extended uncertainty principle, that comprises the effects of spacetime curvature at large distances. Specifically, we observe that, when the modified uncertainty relations hold, the weak formulation of the equivalence principle is violated, since the inertial mass of quantum systems becomes position-dependent whilst the gravitational mass is left untouched. To obtain the above result, spinor and scalar fields are separately analyzed by considering the non-relativistic limit of the Dirac and the Klein-Gordon equations in the presence of the extended uncertainty principle. In both scenarios, it is found that the ratio between the inertial and the gravitational mass is the same.