Towards Gravity from the Quantum

The different approaches to quantum gravity, almost all of which are described in detail in the rest of this volume, can be classified according to what they say about spacetime and gravity. First, there are the quantum field theory-like approaches (string theory, black hole thermodynamics, etc.). It is natural to push quantum field theory to its limits since it is our best theory so far. Results coming from traditional quantum field theory on curved spacetime are clearly limited since the spacetime is not dynamical. String theory obtains the graviton as an effective excitation, but the fundamental quantities of the theory in its current formulation refer to a fixed background. There are indications that there may be indirect ways in which a dynamical spacetime and gravity is present in the theory. It is non-trivial to come to a conclusive verdict but the strategy is that general relativity should arise as an effective theory. The so-called background independent approaches to quantum gravity state that the fundamental quantum theory ought to explicitly possess a dynamical spacetime. Presumably because all these originate in general relativity, spacetime is expected to be fundamental except quantum, in the sense that there are geometric and gravitational degrees of freedom in the fundamental theory. The implementation is either via a strict quantum version of classical gravity (straight quantization as in Loop Quantum Gravity) or a more general quantum superposition of spacetimes (as in traditional causal sets or Causal Dynamical Triangulations). Morally, such approaches stay close to general relativity, in practice, there are difficult issues related to dynamics, observables and, often, an ill-defined path integral. An important recent advance is the new ap-