Abstract
A number of recent proposals on 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. Secondly, the lack of a fundamental spacetime renders 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 the evolution of quantum networks with no a priori geometric notions as models for emergent geometry and gravity. In this paper, we review two such models. The first model 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 the 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 that we illustrate with a toy black hole, and exhibits entanglement between matter and geometry and thermalization of the quantum geometry.
Highlights
Research in quantum gravity is currently at a very interesting point
The Hamiltonian for this model is an extension of the string network condensation mechanism of Wen and collaborators for emergent matter, which we review before extending it to dynamical lattices
The question is to what extend this captures elements of gravitational behavior and we study it by looking at a toy black hole
Summary
An essential aspect of geometry, is fixed in spin systems such as the Ising model. Back to the state space Hgraph, we note that, for very large N , the regular cubic lattice is a subgraph of KN , which means a particular state in Hgraph Using these two extremal cases we can sketch out the basic idea behind our models. The model can be used to investigate questions in emergent gravity, such as time vs emergence, and develop new tools for emergent gravity physics in an explicit context In this direction, we have already studied several subjects, including mergence of (flat) geometry and matter [12, 13], deriving the speed of light from first principles [35], matter/geometry interaction and entanglement and issues in quantum cosmology [15], as well as fundamental vs geometric time [16]. We will review the two models of [12, 13] and [15]
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