Quantum Gravity Effects in Geodesic Motion and Predictions of Equivalence Principle Violation

TL;DR

This paper demonstrates that quantum gravity effects induce violations of the Equivalence Principle through non-commutative spacetime and GUP, providing bounds on the quantum gravity scale based on experimental tests of gravitational phenomena.

Contribution

It introduces a novel approach linking quantum gravity-induced spacetime non-commutativity with Equivalence Principle violations and derives bounds on the quantum gravity scale using classical geodesic deviations.

Findings

Bounds on the QG scale parameter $eta$ are consistent with recent literature.

Quantum gravity effects cause measurable deviations in geodesic motion.

Experimental tests of gravitational redshift and free fall constrain quantum gravity models.

Abstract

We show that the Equivalence Principle (EP) is violated by Quantum Gravity (QG) effects. The predicted violations are compared to experimental observations for Gravitational Redshift, Law of Reciprocal Action and Universality of Free Fall. This allows us to derive explicit bounds for $\beta$ - the QG scale. In our approach, there appears a deviation in the geodesic motion of a particle. This deviation is induced by a non-commutative spacetime, consistent with a Generalized Uncertainty Principle (GUP). GUP admits the presence of a minimum length scale, that is advocated by QG theories. Remarkably, the GUP induced corrections are quite robust since the bound on $\beta$ obtained by us, {\it{in General Relativity scenario in an essentially classical setting}} of modified geodesic motion, is closely comparable to similar bounds in recent literature \cite{vag}. The latter are computed in purely {\it{quantum}} physics domain in {\it{flat}} spacetime.