Background independent condensed matter models for quantum gravity

TL;DR

This paper explores background-independent quantum gravity models using spin systems and quantum networks, demonstrating emergent space, matter, and gravitational features without predefined spacetime.

Contribution

It introduces two novel models of emergent geometry and matter from non-geometric quantum systems, applying quantum information theory to derive physical properties.

Findings

Derived speed of light from quantum information methods.

Modeled gravitational attraction with a toy black hole.

Showed entanglement between matter and geometry, and thermalization of quantum geometry.

Abstract

A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such approach. At the conceptual level, there is a clash between the "timelessness" of general relativity and emergence. Second, the lack of a fundamental spacetime makes difficult the straightforward application of well-known methods of statistical physics to the problem. We recently initiated a study of such problems using spin systems based on evolution of quantum networks with no a priori geometric notions as models for emergent geometry and gravity. In this article we review two such models. The first is a model of emergent (flat) space and matter and we show how to use methods from quantum information theory to derive features such as speed of light from a non-geometric quantum system. The second model exhibits interacting matter and geometry, with the geometry defined by the behavior of matter. This model has primitive notions of gravitational attraction which we illustrate with a toy black hole, and exhibits entanglement between matter and geometry and thermalization of the quantum geometry.