Spin systems as toy models for emergent gravity
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 initiate a study of such problems using toy models for emergent geometry and gravity based on evolution of quantum networks with no a priori geometric notions.
In this talk we present two 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, and exhibits entanglement between matter and geometry and thermalization of the quantum geometry.
A recent review paper of some of this work is http://arxiv.org/abs/0911.5075