Introduction

The different approaches to Quantum Gravity can be classified according to the role that spacetime plays in them. In particular, we can ask two questions of each approach. (1) Is spacetime geometry and General Relativity fundamental or emergent? (2) Is spacetime geometry, if present, dynamical or fixed?

Reviewing the different approaches we find that they split into four categories. First, there are the Quantum Field Theory-like approaches, such as string theory and its relatives. Here General Relativity is to be an emergent description; however, the spacetime that appears in the initial formulation of the theory is fixed and not dynamical. Next are the so-called background independent approaches to Quantum Gravity, such as loop quantum gravity, spin foams, causal sets and causal dynamical triangulations. Geometry and gravity here are fundamental, except quantum instead of classical. These approaches implement background independence by some form of superposition of spacetimes, hence the geometry is not fixed. Third, there are condensed matter approaches (see). While it is clear that relativity is to be emergent, there is confusion on question (2) above. These are condensed matter systems, so it seems clear that there is a fixed spacetime in which the lattice lives; however, it can be argued that it is an auxiliary construction, an issue we shall not resolve here.

Our main focus in this chapter is a new, fourth, category that is currently under development and constitutes a promising and previously unexplored direction in background independent Quantum Gravity.