Approaches to Quantum Gravity

Questions and answers 163allow us to push QFT beyond the Planck scale, up to the next frontier,wherever that may be.• Q - L. Crane - to F. Markopoulou:1. Since you are looking at finite nets of finite dimensional vector spaces,while all the unitary representations of the Poincaré group are infinite dimensional,how will you implement Poincaré invariance?2. I do not see how Poincaré invariance automatically will lead to approximateMinkowski space localization. For instance, a QFT on the group manifold ofthe Poincaré group could easily have Poincaré group invariance, but there isno homomorphism to the Minkowski space (it is canonically a subspace, not aquotient) so no invariant way of assigning localization in Minkowski space toexcitations.– A-F.Markopoulou:1. I am expecting to find approximate Poincaré invariance only.2. Your statement is correct. In our scheme, the (approximate) Poincaré invarianceof the excitations is a necessary condition for an effective Minkowskispace, not a sufficient one.• Q - J. Henson - to F. Markopoulou:1. When referring to the QCH on a graph Ɣ as a basis for a theory with nofundamental variables which we would think of as geometrical, you say that“It is important to note that the effective degrees of freedom will not have acausal structure directly related to Ɣ”. The braid example shows that the effectivecausal structure in the sub-system can indeed be more trivial than that onthe graph. But consider a directed graph made up of two chains which wereotherwise unrelated. Because of the axioms of the QCH, degrees of freedomin the system represented by one chain would never affect the other. How doyou interpret this situation, which would naively look like two causally disconnecteduniverses? It seems that the graph order puts some limits on causalityeven if you intend to derive it at an effective level. If you do not want any suchrestriction on the effective causality, the only graph possible is a single chain,and we are back to a standard discrete-time quantum system (but a completelygeneral one). So, in general, why is the “microcausality” necessary when thereis no “microgeometry”? (I have in mind condensed state systems in which aneffective relativistic dynamics can arise from a non-relativistic system, wherethe “microcausality” is trivial.)2. You explain what you mean by a group-invariant noiseless subsystem, andwhat you would interpret as Poincaré invariance. This applies in the case inwhich the subsystem is strictly noiseless, but in the full theory there will comea point at which the Planckian dynamics becomes relevant, with its different