Classical Geometry from a Physical State in Canonical Quantum Gravity

TL;DR

This paper constructs a quantum state in loop quantum gravity that approximates a degenerate classical 3-metric and shows how classical non-degenerate geometries can emerge from it through evolution.

Contribution

It demonstrates that a quantum weave state can represent a degenerate metric and evolve into a non-degenerate classical geometry within canonical quantum gravity.

Findings

A weave state approximates a degenerate 3-metric at large scales.

Classical evolution can transform degenerate metrics into non-degenerate ones.

The quantum state solves all quantum constraints in loop quantum gravity.

Abstract

We construct a weave state which approximates a degenerate 3-metric of rank 2 at large scales. It turns out that a non-degenerate metric region can be evolved from this degenerate metric by the classical Ashtekar equations, hence the degeneracy of 3-metrics is not preserved by the evolution of Ashtekar's equations. As the s-knot state corresponding to this weave is shown to solve all the quantum constraints in loop quantum gravity, a physical state in canonical quantum gravity is related to the familiar classical geometry.