The Quantum Minimum Time Interval Implies a Heisenberg Uncertainty Relation Between Space and Time: ΔrΔt>Gℏ/c4, and that is a Foundational Problem for Einstein-GR

The Quantum Minimum Time Interval Implies a Heisenberg Uncertainty Relation Between Space and Time: ΔrΔt>Gℏ/c4, and that is a Foundational Problem for Einstein-GR 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 Δtthat this clock can measure scales as the inverse of its size Δr. This implies an uncertainty relation between space and time: ΔrΔt>Gℏ/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.