Towards Noncommutative Quantization of Gravity

TL;DR

This paper introduces a noncommutative geometric framework for quantum gravity, quantizing a space-time-based groupoid, with implications for understanding cosmological constants and the emergence of space and time.

Contribution

It presents a novel noncommutative geometric approach to quantum gravity, quantizing a space-time groupoid and linking quantum observables to correlations of distant phenomena.

Findings

Predicts vanishing cosmological constants in the classical limit

Provides a toy model based on finite groups

Suggests quantum gravitational observables are non-local

Abstract

We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid constructed on space-time rather than space-time itself. Both space and time emerge in the transition process to the commutative case. Our approach clearly suggests that quantum gravitational observables should be looked for among correlations of distant phenomena rather than among local effects. A toy model is computed (based on a finite group) which predicts the value of "cosmological constants" (in the quantum sector) which vanish when going to the standard space-time physics.