Emergent General Relativity

This article wants to be two things. On the one hand it wants to review a number of approaches to the problem of quantum gravity that are new and have not been widely discussed so far. On the other hand it wants to offer a new look at the problem of quantum gravity. The different approaches can be organized according to how they answer the following questions: Is the concept of a spacetime fundamental? Is a background time used? Are Einstein’s equations assumed or derived? (See figure 1.1). In string theory, loop quantum gravity, and most other approaches reviewed in this book spacetime plays a fundamental role. In string theory a given spacetime is used to formulate the theory, in loop quantum gravity one tries to make sense of quantum superpositions of spacetimes. It is these spacetimes in the fundamental formulation of the theory that are directly related to the spacetime we see around us. In this broad sense these approaches treat spacetime as something fundamental. Here we want to focus our attention on approaches that take a different view. In these approaches spacetime emerges from a more fundamental theory. The next questions concern the role of time. The models that we will be looking at will all have some sort of given time variable. They differ though in the way they treat this time variable. One attitude is to use this time variable in the emergent theory. The goal of quantum gravity in this context could then be to find a massless spin two particle in the excitation spectrum of the Hamiltonian corresponding to the given time. We will see in section 1.2.1 a solid state physics inspired approach due to G. Volovik that takes this point of view. The other possible attitude towards the background time is that it is