Approaches to Quantum Gravity

Questions and answers 159of how gravity emerges. In the Fermi liquid example gravity emerges as agenuine spin 2 excitation. I, on the other hand, am not looking for such a spin2 excitation. Apart from this difference the excitations in the Fermi liquidwould do just fine for my purpose.4. The argument leading to Poincaré invariance and Minkowski space isindeed somewhat sketchy so let me try to expand on it a little. The originalidea was to use the coherent excitations of the spin model to define thelight cones of the emergent theory. The linear dispersion of the excitationsthen ensured the constancy of the speed of light and thus the emergence ofrelativity.It might be worthwhile to make a little detour and look at the historyof special relativity. When Lorentz introduced the transformations that nowcarry his name he was looking at the Maxwell equations and asked how onewould actually measure quantities like length and time. As was discovered byHeavyside the field of a charge moving with velocity v is no longer sphericallysymmetric. Instead it is an ellipsoid whose one side is compressed bythe now well known factor γ = √ 1 − v 2 /c 2 . From this observation Lorentzargued that physical bodies like measuring rods will be compressed by thesame factor. The conclusion is thus that a world described by Maxwell equationswill look internally like Minkowski space. What we are proposing is toadopt exactly this kind of attitude towards relativity. Minkowski space is thusnot, as Einstein proposed it, a background on which matter propagates but isitself a consequence of the behavior of matter. Matter and geometry are thusinseparable. One implies the other and vice versa.Where we deviate from Lorentz is that we use a quantum mechanical modelinstead of the classical Maxwell equations. A more interesting model than theone presented here is a model presented by Levin and Wen (hep-th/0507118).This model has fermions and photons as low energy excitations and theirinteractions are described by QED. We thus find the same situation as the onedescribed by Lorentz only that now we are dealing with a quantum theory.• Q - D. Oriti - to R. Percacci:1. What is your take on the issue of continuum versus discrete picture ofspacetime, coming from a renormalization group perspective? If gravity isasymptotically safe, would it imply that a continuum description of spacetimeis applicable at all scales, or one can envisage a role of discrete spacetimestructures even in this case? How would a breakdown of the continuumdescription show up in the ERG approach?2. What differences, in formalism and results, can one expect in the ERGapproach, if one adopts a 1st order (e.g. Palatini) or BF-like (e.g. Plebanski)description of gravity?