Composite system in noncommutative space and the equivalence principle

TL;DR

This paper investigates how noncommutative geometry affects the motion of composite systems and the validity of the equivalence principle, providing conditions for its preservation in noncommutative space.

Contribution

It derives the effective noncommutative parameters for composite systems and establishes conditions to restore the weak equivalence principle in noncommutative space.

Findings

Coordinates of the center-of-mass satisfy noncommutative algebra

Weak equivalence principle is violated in non-uniform gravitational fields

Conditions for the principle's recovery are proposed

Abstract

The motion of a composite system made of N particles is examined in a space with a canonical noncommutative algebra of coordinates. It is found that the coordinates of the center-of-mass position satisfy noncommutative algebra with effective parameter. Therefore, the upper bound of the parameter of noncommutativity is re-examined. We conclude that the weak equivalence principle is violated in the case of a non-uniform gravitational field and propose the condition for the recovery of this principle in noncommutative space. Furthermore, the same condition is derived from the independence of kinetic energy on the composition.