Noncommutative geometry of the quantum clock

TL;DR

This paper develops a noncommutative geometric model that explains quantum clock uncertainty relations and explores particle dynamics within this framework, including relativistic effects and black hole backgrounds.

Contribution

It introduces a novel noncommutative geometry model linking quantum clock uncertainties with relativistic particle dynamics.

Findings

Derived uncertainty relations from the noncommutative geometry model

Analyzed free particle motion in the model under doubly special relativity

Discussed geodesic motion in a Schwarzschild background within this framework

Abstract

We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of doubly special relativity and discuss the geodesic motion in a Schwarzschild background.