The Spacetime Picture in Quantum Gravity

TL;DR

This paper introduces a novel approach combining Loop Quantum Gravity, Topos theory, and Non-commutative Geometry to better understand spacetime in Quantum Gravity, predicting new quantization features of surface areas.

Contribution

It presents a new method for deriving surface area quantization in Quantum Gravity, predicting additional smaller area values and sub-divisions beyond standard LQG results.

Findings

Reproduces known area spectrum from LQG

Predicts smaller and subdivided area values

Interprets area as noncommutative distance between points

Abstract

We propose an approach which, by combining insights from Loop Quantum Gravity (LQG), Topos theory, Non-commutative Geometry \`a la Connes, and spacetime relationalism, provides fertile ground for the search of an adequate spacetime picture in Quantum Gravity. With this approach, we obtain a novel way of deducing the quantization of the possible values for the area of a surface. One gets the same area values than those from the area operator in standard LQG, but our approach makes a further prediction: some smaller values and sub-divisions are also allowed. In addition, the area arises as a noncommutative distance between two noncommutative points, and thus they should be interpreted as irreducible string-like objects at the physical level (where the area interpretation for the noncommutative distance holds).