Combinatorial Quantum Gravity: Geometry from Random Bits

TL;DR

This paper introduces a quantum gravity model where space geometry emerges from random bits through a phase transition driven by combinatorial curvature, connecting discrete graph structures to classical gravity.

Contribution

It presents a novel non-perturbative quantum gravity framework based on random graphs and combinatorial curvature, linking discrete structures to Einstein-Hilbert action.

Findings

Space geometry emerges from random bits at a quantum critical point.

The model reduces to Einstein-Hilbert action in the geometric phase.

Provides a new approach to quantum gravity via combinatorial graph theory.

Abstract

I propose a quantum gravity model in which geometric space emerges from random bits in a quantum phase transition driven by the combinatorial Ollivier-Ricci curvature and corresponding to the condensation of short cycles in random graphs. This quantum critical point defines quantum gravity non-perturbatively. In the ordered geometric phase at large distances the action reduces to the standard Einstein-Hilbert term.