Combinatorial Spacetime from Loop Quantum Gravity

TL;DR

This paper reformulates loop quantum gravity purely in terms of matter fields, addressing a conceptual controversy by defining spacetime without matter, inspired by Penrose's combinatorial spacetime idea.

Contribution

It introduces a novel reformulation of loop quantum gravity that eliminates the need for a background spacetime, focusing solely on matter fields.

Findings

Spacetime can be described as relations between matter fields.

Reformulation aligns with Penrose's combinatorial spacetime concept.

Addresses foundational issues in quantum gravity theories.

Abstract

Loop quantum gravity is a perspective candidate for the quantum theory of gravity. However, there is a conceptual controversy in it: having started from the Einstein-Hilbert action and describing spacetime without matter, we can hardly define spacetime as anything other than a set of relations between matter fields. Here, following the Penrose idea of combinatorial spacetime we reformulate loop quantum gravity theory solely in terms of the matter fields.