Eur. Phys. J. C (2016) 76: 30
https://doi.org/10.1140/epjc/s10052-016-3884-4

Regular Article - Theoretical Physics

Time crystals from minimum time uncertainty

¹ Department of Physics and Astronomy, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
² Department of Electrical Engineering, Alexandria University, Alexandria, 12544, Egypt
³ Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, AB, T1K 3M4, Canada

^* e-mail: moh.m.khalil@gmail.com

Received: 2 October 2015
Accepted: 5 January 2016
Published online: 21 January 2016

Abstract

Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra and show that this leads to corrections to all quantum mechanical systems. We also demonstrate that such a deformation implies a discrete spectrum for time. In other words, time behaves like a crystal. As an application of our formalism, we analyze the effect of such a deformation on the rate of spontaneous emission in a hydrogen atom.