Approaches to Quantum Gravity

Questions and answers 155causality if it is present at all. (So for example, it probably would not makesense to try to identify the causet nonlocality with the “violations of localcausality” manifested in the Aspect experiment.)• Q - L. Crane - to N. Savvidou:Do you know of any approach to the application of the histories picture togravity which doesn’t assume a global spacelike foliation? Isn’t decoherence alocal process?– A-N.Savvidou:There is no paper yet treating foliations that are not globally spacelike. Itis, however, in principle possible to do so in the histories formalism. Onewould have to suitably redefine the foliation functional employed there. Forexample, in a spacetime that involves topology change, the foliation functionalmay be defined with a dependence on the topology of the spatialslice. The main problem in pursuing such an approach would be to ensurethe proper definability (and interpretation) of the canonical constraints. Concerningdecoherence: in the most general case decoherence refers to theprobabilistic behaviour of histories and as such it primarily refers to thestate of the quantum system (or the decoherence functional in the historiesapproach). For this reason, it is a priori a global rather than a local concept.In my opinion, even decoherence from the environment cannot be said to bea local process, because it involves a separation into system and environmentwhich is not given a priori (especially in cosmology). Moreover, in gravitythe true degrees of freedom are non-local functionals of the spacetime fields(because of the spatial diffeomorphism constraint) and in a theory of QuantumGravity even the definition of the notion of local process is problematic –at least before we know that a specific history (4-metric) has been realized.• Q-J.Henson-toL.Crane:The contribution in this volume of Collins, Perez and Sudarsky calls for a“physical regularisation” of Quantum Field Theory on Minkowski space, meaningone that can be imposed without destroying the symmetries that we observeat low energies. Some discussion of this is also given in Sorkin’s contribution.Does the causal sites idea give new insights in this direction?– A-L.Crane:Causal sites are a new type of mathematical structure whose possibilities havenot been explored. I believe some of these possibilities are closely related toideas arising from renormalization.One possibility I have been exploring is imposing a fixed topologicaldimension via the condition that every cover of a site admit a refinement coverall of whose n + 2 fold intersections are empty. This is a well known propertyof n-manifolds. Call such a cover good.