Discreteness of the volume of space from Bohr-Sommerfeld quantization

TL;DR

This paper demonstrates that quantizing space via Bohr-Sommerfeld methods yields a volume spectrum consistent with loop gravity, supporting the idea of directly quantizing space in quantum gravity theories.

Contribution

It provides new evidence that direct quantization of space using Bohr-Sommerfeld rules reproduces key features of loop gravity's space quantization.

Findings

Reproduces loop gravity's space quantization

Calculates the Bohr-Sommerfeld volume spectrum of a tetrahedron

Supports direct quantization of space in quantum gravity

Abstract

A major challenge for any theory of quantum gravity is to quantize general relativity while retaining some part of its geometrical character. We present new evidence for the idea that this can be achieved by directly quantizing space itself. We compute the Bohr-Sommerfeld volume spectrum of a tetrahedron and show that it reproduces the quantization of a grain of space found in loop gravity.