Quantum clock: A critical discussion on spacetime

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 Δ t that this clock can measure scales as the inverse of its size Δ r. This implies an uncertainty relation between space and time: Δ r Δ t > G ℏ / c4, where G, ℏ, 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.