Topology, Decoherence, and Semiclassical Gravity

TL;DR

This paper investigates how the time-dependent Schrödinger equation can emerge from quantum gravity, examining decoherence, anomalies, and $ heta$ states in different quantum gravity frameworks.

Contribution

It provides a detailed analysis of mechanisms like decoherence and anomalies that explain the nonoccurrence of certain superpositions in quantum gravity, aiding in deriving the Schrödinger equation.

Findings

Decoherence via irrelevant degrees of freedom can suppress superpositions.

Gravitational anomalies may influence quantum superpositions.

$ heta$ states could play a role in quantum gravity superposition behavior.

Abstract

We address the issue of recovering the time-dependent Schr\"{o}dinger equation from quantum gravity in a natural way. To reach this aim it is necessary to understand the nonoccurrence of certain superpositions in quantum gravity. We explore various possible explanations and their relation. These are the delocalisation of interference terms through interaction with irrelevant degrees of freedom (decoherence), gravitational anomalies, and the possibility of $\theta$ states. The discussion is carried out in both the geometrodynamical and connection representation of canonical quantum gravity.