Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle

Abstract

We study influence of noncommutativity of coordinates and noncommutativity of momenta on the motion of a particle (macroscopic body) in uniform and non-uniform gravitational fields in noncommutative phase space of canonical type with preserved rotational symmetry. It is shown that because of noncommutativity the motion of a particle in gravitational filed is determined by its mass. The trajectory of motion of a particle in uniform gravitational field corresponds to the trajectory of harmonic oscillator with frequency determined by the value of parameter of momentum noncommutativity and mass of the particle. The equations of motion of a macroscopic body in gravitational filed depend on its mass and composition. From this follows violation of the weak equivalence principle caused by noncommutativity. We conclude that the weak equivalence principle is recovered in rotationally invariant noncommutative phase space if we consider the tensors of noncommutativity to be dependent on mass. So, finally we construct noncommutative algebra which is rotationally invariant, equivalent to noncommutative algebra of canonical type, and does not lead to violation of the weak equivalence principle.

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Cited by in corpus (8)

• Energy-dependent noncommutative quantum mechanics
• Parameters of noncommutativity in Lie-algebraic noncommutative space
• System of interacting harmonic oscillators in rotationally invariant noncommutative phase space
• Squeezed coherent states for gravitational well in noncommutative space
• Effects of wave propagation in canonical Poisson gauge theory under an external magnetic field
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
• Harmonic oscillator chain in noncommutative phase space with rotational symmetry
• Features of description of composite system's motion in twist-deformed space-time