Influence of Noncommutativity on the Motion of Sun-Earth-Moon System and the Weak Equivalence Principle

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.

Weak equivalence principle in quantum space

“…The equivalence principle was examined in the context of a noncommutative algebra of canonical type in (Bastos et al, 2011;Gnatenko, 2013;Saha, 2014;Bertolami and Leal, 2015;Tkachuk V., 2017b, Gnatenko Kh. andTkachuk, V. 2018a). The weak equivalence principle in noncommutative phase space was studied in (Bastos et al, 2011;Bertolami and Leal, 2015;Tkachuk V., 2017b, Gnatenko Kh.…”

“…The weak equivalence principle in noncommutative phase space was studied in (Bastos et al, 2011;Bertolami and Leal, 2015;Tkachuk V., 2017b, Gnatenko Kh. andTkachuk, V. 2018a). The authors of (Bertolami and Leal, 2015) concluded that the equivalence principle holds in the quantized space in the sense that an accelerated frame of reference is locally equivalent to a gravitational field, unless the parameters of noncommutativity are anisotropic (η xy ≠ η xz ).…”

“…44-46 and find the way to preserve the weak equivalence principle (Gnatenko, 2013;Tkachuk V., 2017b, Gnatenko Kh. andTkachuk, V. 2018a). The equations of motion of a particle with mass m in a uniform gravitational field with Hamiltonian…”