Approaches to Quantum Gravity

Questions and answers 153was that the question is spurious because an average Lorentz symmetry isalready manifested by the *individual* causet.Perhaps, however, you are implicitly asking whether quantum effects couldproduce a type of “averaging” that would remove the need for an intermediatenonlocality scale, or at least lower that scale down toward the Planck length.That is an important question, but as far as I can see, we don’t yet have thetools for answering it.• Q-D.Oriti-toR.Sorkin:1. I would like to draw your attention to the perspective offered on the issuesyou raise by Deformed Special Relativity models. On the one hand, it seemsto me that they are a counterexample to your statement that the deformation ofthe dispersion relation for matter or gauge fields would necessarily imply theexistence of a state of absolute rest, i.e. a violation of Lorenz invariance. Nosuch state exists in DSR theories, which have a full 10-dimensional symmetrygroup in 4d, despite the deformation of dispersion relations that some of thesemodels predict.2. DSR models also seem good candidates for the effective dynamics of matterfields in discrete approaches to Quantum Gravity like spin foam modelsor group field theories. On the other hand, and exactly because they are fullyLorentz invariant in the above sense, DSR models, which are closely relatedto non-commutative geometry, seem to confirm your conclusion that “discretenessplus Lorentz invariance implies non-locality”. Indeed, as you say regardingnon-commutative geometry-based models, they seem to suggest that, at least insome cases, the modifications coming from Quantum Gravity to usual flat spacefield theories can be encoded in non-local field theory formulations. Also, theexistence of ∗ two ∗ scales of deformation of usual flat space physics, related toa minimal length scale and a maximal length scale (the cosmological constant),has been suggested as natural in the context of so called “doubly deformed (ortriply) special relativity”.3. It would be very interesting in this respect to obtain the dispersion relationfor some matter field propagating on a causal set and then compare this withthose studied in DSR models.4. Do you expect a phenomenon like UV/IR mixing in any field theory oncausal sets, according to the recent results on the D’Alembertian on a causal setthat you have described?5. How does the non-locality of causal sets compare, in your opinion, withthat suggested by Markopoulou, that identifies the discrepancy between macroscopic(i.e. metric-induced) locality and microscopic locality defined in termsof nearest-neighbor relations on the underlying graph (which is not, in itself, ageometric object)?