Noncommutative geometry of the quantum clock

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.

arXiv comment7 pages, version accepted for publication on Phys. Lett. A. A discussion of the motion of a particle in a Schwarzschild background has been added