Newton's Second Law in a Noncommutative Space

TL;DR

This paper explores how noncommutative geometry modifies Newton's second law, revealing symmetry-breaking effects and a Coriolis-like force in gravitational systems, which could impact our understanding of classical mechanics in quantum regimes.

Contribution

It introduces a correction to Newton's second law arising from noncommutative phase space, linking quantum geometry to classical dynamics and symmetry breaking.

Findings

Correction term breaks rotational symmetry in central force problems

In the Kepler problem, the correction acts like a Coriolis force

Noncommutative effects could influence classical gravitational dynamics

Abstract

In this work we show that corrections to the Newton's second law appears if we assume that the phase space has a symplectic structure consistent with the rules of commutation of noncommutative quantum mechanis. In the central field case we find that the correction term breaks the rotational symmetry. In particular, for the Kepler problem, this term takes the form of a Coriolis force produced by the weak gravitational field far from a rotating massive object.