Approaches to Quantum Gravity

158 Questions and answerswould seem to me that they would play a crucial role in the definition and propertiesof the excitations you want to use to reconstruct spacetime. How do yourexcitations differ in this respect from those emerging in Fermi liquids?4. I am not understanding how you reconstruct Poincaré symmetry and thusMinkowski space out of the coherent excitations you identified; in particular Ido not understand how the the fact that their speed is left unchanged can sufficeto identify the Poincaré group. How do you reconstruct the dimensionality ofyour space, in the first place? How do you realize, in terms of excitations only,that you are using the Poincaré group as opposed to, say, the conformal groupSO(4,1), which has the same dimensionality? How do you see that you are notusing a non-linear realization of the Poincaré group, or a non-commutative versionof the same, as for example in Deformed Special Relativity models? Canyou please sketch in slightly more detail the argument?– A-O.Dreyer:1. It is not the presence of a background time that is the problem. In fact Iam proposing that one can get a background independent emergent theoryalthough the fundamental theory has a background time. The problem is inthe way gravity appears in Volovik’s model. For him Quantum Gravity is thesearch for a massless spin 2 excitation. Now usually such an excitation doesnot arise naturally. It is usually very hard to get rid of the longitudinal modes.This is why Volovik has to tune one parameter of the theory so that the massof the graviton becomes negligible. It is not clear whether starting from amanifestly background independent theory will cure this problem. The basiccharacter of the modes would seem to be untouched.2. On a superficial level one could take the phrase “it may be no moreappropriate to quantize the Einstein equation than it would be to quantizethe wave equation for sound in air.” from the introduction of T. Jacobson’sarticle as the motto of my approach. In my approach gravity is part of the lowenergy emergent physics and not a part of the more fundamental underlyingtheory. Quantizing the gravitational field thus does not give the fundamentaltheory. The more detailed question of how Jacobson’s derivation of theEinstein equations relates to the proposal here is a more interesting but alsomore difficult question. To answer it one has to identify horizons and thenfind expressions for entropy, heat and temperature in terms of the underlyingtheory of quantum spins. The state of the theory right now does not allowfor this.3. It may be best to answer the first part of this question together withquestion 4.The excitations that I am considering here do not differ from the excitationsin a Fermi liquid. The reason why I am discussing them separately is because