Time Crystals from Minimum Time Uncertainty

TL;DR

This paper introduces a deformation of the Heisenberg algebra inspired by the Generalized Uncertainty Principle, leading to the concept of time as a discrete crystal and analyzing its effects on quantum systems like hydrogen emission.

Contribution

It proposes a novel deformation of quantum mechanics based on minimum time uncertainty, revealing time's discrete spectrum and its impact on atomic processes.

Findings

Time exhibits a discrete spectrum as a crystal-like structure.

Deformation affects the rate of spontaneous emission in hydrogen.

Corrections to quantum systems due to minimum time uncertainty.

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.