Weak equivalence principle in noncommutative phase space and the parameters of noncommutativity

TL;DR

This paper investigates how the weak equivalence principle can be preserved in a noncommutative phase space by identifying specific conditions on noncommutativity parameters, ensuring consistent motion and energy properties.

Contribution

It derives conditions on noncommutativity parameters that restore the weak equivalence principle and preserve physical properties in noncommutative phase space.

Findings

Conditions on noncommutativity parameters restore the equivalence principle.

Center-of-mass and relative motions are independent under these conditions.

Kinetic energy of composite systems is additive and independent of composition.

Abstract

The weak equivalence principle is studied in a space with noncommutativity of coordinates and noncommutativity of momenta. We find conditions on the parameters of noncommutativity which give the possibility to recover the equivalence principle in noncommutative phase space. It is also shown that in the case when these conditions are satisfied the motion of the center-of-mass of a composite system in noncommutative phase space and the relative motion are independent, the kinetic energy of composite system has additivity property and is independent on the systems composition. So, we propose conditions on the parameters of noncommutativity which give the possibility to solve the list of problems in noncommutative phase space.