Problem of Time: Facets and Machian Strategy

TL;DR

This paper clarifies the facets of the Problem of Time in quantum gravity, reconceptualizes them at the classical level, and proposes a Machian local resolution applicable to simplified models, outlining future research directions.

Contribution

It reinterprets the facets of the Problem of Time, links them to classical analogs, and introduces a Machian resolution scheme for simplified models, advancing the conceptual understanding of quantum gravity.

Findings

Most facets of the Problem of Time occur at the classical level.

A Machian local resolution is proposed for simplified models.

The paper outlines future steps toward resolving the Problem of Time in full GR.

Abstract

The Problem of Time is that `time' in each of ordinary quantum theory and general relativity are mutually incompatible notions. This causes difficulties in trying to put these two theories together to form a theory of Quantum Gravity. The Problem of Time has 8 facets in canonical approaches. I clarify that all but one of these facets already occur at the classical level, and reconceptualize and re-name some of these facets as follows.The Frozen Formalism Problem becomes Temporal Relationalism, the Thin Sandwich Problem becomes Configurational Relationalism, via the notion of Best Matching. The Problem of Observables becomes the Problem of Beables, and the Functional Evolution Problem becomes the Constraint Closure Problem. I also outline how each of the Global and Multiple-Choice Problems of Time have their own plurality of facets. This article additionally contains a local resolution to the Problem of Time at the conceptual level and which is actually realizable for the relational triangle and minisuperspace models. This resolution is, moreover, Machian, and has three levels: classical, semiclassical and a combined semiclassical-histories-timeless records scheme. I end by delineating the current frontiers of this program toward resolution of the Problem of Time in the cases of full GR and of slightly inhomogeneous cosmology.