Consistent discrete gravity solution of the problem of time: a model

TL;DR

This paper demonstrates how a consistent discrete lattice formulation of canonical general relativity can resolve the problem of time by enabling relational quantization, using a simple model system as a test case.

Contribution

It introduces a constraint-free discrete formulation of gravity that allows for relational quantization, addressing the problem of time in quantum gravity.

Findings

Constraint-free discrete gravity formulation enables relational quantization.

Application to a simple parameterized particle model.

Potential to overcome traditional obstacles in quantum gravity.

Abstract

The recently introduced consistent discrete lattice formulation of canonical general relativity produces a discrete theory that is constraint-free. This immediately allows to overcome several of the traditional obstacles posed by the ``problem of time'' in totally constrained systems and quantum gravity and cosmology. In particular, one can implement the Page--Wootters relational quantization. This brief paper discusses this idea in the context of a simple model system --the parameterized particle-- that is usually considered one of the crucial tests for any proposal for solution to the problem of time in quantum gravity.