Time uncertainty in quantum gravitational systems

Abstract

It is generally argued that the combined effect of the Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We consider a simple family of gravitational models, including the Einstein-Rosen waves, in which the (nonlinearized) inclusion of gravity changes the normalization of time translations by a monotonic energy-dependent factor. In these circumstances, it is shown that a maximum time resolution emerges nonperturbatively only if the total energy is bounded. Perturbatively, however, there always exists a minimum uncertainty in the physical time.