Quantum Gravity as an Information Network: Self-Organization of a 4D Universe

TL;DR

This paper introduces a quantum gravity model where space-time emerges from information bits organized as a network, exhibiting phase transitions and self-organization into a 4D universe without singularities.

Contribution

It presents a novel network-based quantum gravity model using Ising interactions that self-organizes into a 4D universe and describes its phase transitions and emergent properties.

Findings

The universe's large-scale structure has a Hausdorff dimension of 4.

Space-time dissolves into disordered bits at a second quantum phase transition.

The model predicts black hole-like excitations with horizons and lower spectral dimensions.

Abstract

I propose a quantum gravity model in which the fundamental degrees of freedom are information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension 4. The spectral dimension is lower than the Hausdorff dimension: it coincides with the Hausdorff dimension 4 at a first quantum phase transition corresponding to an IR fixed point while at a second quantum phase transition describing small scales space-time dissolves into disordered information bits. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. At finite temperatures the universe graph emerges without big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe graph unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits topological black hole excitations corresponding to graphs containing holes with no space-time inside and with "Schwarzschild-like" horizons with a lower spectral dimension.