The quantum clock: a critical discussion on space-time

TL;DR

This paper explores the fundamental limits of measuring very short time intervals using a thought experiment, revealing a space-time uncertainty relation linked to quantum and gravitational constants.

Contribution

It introduces a novel ideal clock model based on random events and derives a space-time uncertainty relation involving fundamental constants.

Findings

Minimum measurable time interval scales inversely with clock size

Derived a space-time uncertainty relation: Delta r Delta t > G   / c^4

Discussed implications for the nature of space-time at small scales

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. 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 principle.