Quantum clock: A critical discussion on spacetime

Abstract

We critically discuss the measure of very short time intervals. By means of a Gedankenexperiment, we describe an ideal clock based on the occurrence of completely random events. Many previous thought experiments have suggested fundamental Planck-scale limits on measurements of distance and time. Here we present a new type of thought experiment, based on a different type of clock, that provide further support for the existence of such limits. We show that the minimum time interval $\Delta t$ that this clock can measure scales as the inverse of its size $\Delta r$. This implies an uncertainty relation between space and time: $\Delta r$ $\Delta t$ $> G \hbar / c^4$; where G, $\hbar$ and c are the gravitational constant, the reduced Planck constant, and the speed of light, respectively. We outline and briefly discuss the implications of this uncertainty conjecture.