Time Uncertainty in Quantum Gravitational Systems

Abstract

It is generally argued that the combined effect of 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 (non-linearized) 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 non-perturbatively only if the total energy is bounded. Perturbatively, however, there always exists a minimum uncertainty in the physical time.

(4 pages, no figures) Accepted for publication in Physical Review D

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• Asymptotics of Regulated Field Commutators for Einstein-Rosen Waves
• Quantum time uncertainty in Schwarzschild-anti-de Sitter black holes