A note on the quantum of time

Abstract

Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the existence of a nonzero uncertainty in the time variable. The existence of a quantum of time modifies the Heisenberg evolution equation for observables. In this letter we propose and analyse a generalisation of Heisenberg's equation for observables evolving in real time (the time variable measured by real clocks), that takes the existence of a quantum of time into account. This generalisation of Heisenberg's equation turns out to be a delay-differential equation.