Influence of noncommutativity on the motion of Sun-Earth-Moon system and the weak equivalence principle

TL;DR

This paper investigates how noncommutativity in phase space affects the motion of the Sun-Earth-Moon system, revealing violations of the weak equivalence principle and estimating noncommutativity parameters from lunar laser ranging data.

Contribution

It demonstrates that noncommutativity leads to differences in free fall accelerations, violating the weak equivalence principle, and provides estimates for noncommutativity parameters based on experimental data.

Findings

Noncommutativity causes non-universal free fall accelerations.

Violates the weak equivalence principle in noncommutative phase space.

Estimates the ratio of momentum noncommutativity parameter to mass.

Abstract

Features of motion of macroscopic body in gravitational field in a space with noncommutativity of coordinates and noncommutativity of momenta are considered in general case when coordinates and momenta of different particles satisfy noncommutative algebra with different parameters of noncommutativity. Influence of noncommutativity on the motion of three-body Sun-Earth-Moon system is examined. We show that because of noncommutativity the free fall accelerations of the Moon and the Earth toward the Sun in the case when the Moon and the Earth are at the same distance to the source of gravity are not the same even if gravitational and inertial masses of the bodies are equal. Therefore, the Eotvos-parameter is not equal to zero and the weak equivalence principle is violated in noncommutative phase space. We estimate the corrections to the Eotvos-parameter caused by noncommutativity on the basis of Lunar laser ranging experiment results. We obtain that with high precision the ratio of parameter of momentum noncommutativity to mass is the same for different particles.