Time Uncertainty in Quantum Gravitational Systems

TL;DR

This paper investigates time uncertainty in quantum gravitational systems, showing that non-perturbative effects can lead to a maximum time resolution when energy is bounded, contrasting with perturbative results indicating a minimum time uncertainty.

Contribution

It introduces a non-perturbative analysis of time uncertainty in gravitational models, revealing conditions for maximum time resolution absent in perturbative approaches.

Findings

Non-perturbative analysis shows maximum time resolution with bounded energy.

Perturbative approach confirms a minimum time uncertainty always exists.

Gravity modifies time translation normalization in the models studied.

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.