Quantum Gravity and a Time Operator in Relativistic Quantum Mechanics

TL;DR

This paper explores the introduction of a dynamical time operator in relativistic quantum mechanics to address the problem of time in quantum gravity, analyzing its potential to reconcile quantum mechanics and general relativity.

Contribution

It proposes a novel dynamical time operator in RQM and examines its role in the canonical quantization of gravity, offering a new perspective on the problem of time.

Findings

The dynamical time operator can be defined within RQM.

It provides insights into the conditional interpretation of quantum gravity.

Potential to bridge the conceptual gap between QM and GR.

Abstract

The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in General Relativity (GR) are seen as mutually incompatible notions. The introduction of a dy- namical time operator in relativistic quantum mechanics (RQM), that in the Heisenberg representation is also a function of the parameter t (iden- tifed as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of the canonical quantization approach toquantum gravity is developed. 1