Resolution of the problem of time in quantum gravity
Abstract
Description
The metric determines the casual structure of spacetime, but in quantum gravity it is also a dynamical field which must be quantized using this causal structure; this is the famous problem of time. A radical resolution of this paradox is proposed: remove the concept of space-like separation entirely. This can be done by describing all fields in terms on p-jets, living on the observer's trajectory; all points on the trajectory have time-like separations. Such a description is necessary to construct well-defined representations the N-dimensional generalization of the Virasoro algebra Vir(N); this is the natural quantum extension of vect(N), which is the correct symmetry algebra of general relativity in N dimensions. The limit p -> oo, necessary for a field theory interpretation, only exists if N = 4 and there are three fermions for every two bosons, a relation that is satisfied in the standard model coupled to gravity.
Name of paper changed since the term "causality paradox" refers to the problem of time. Material on the generalization of the Virasoro algebra beyond one dimension expanded
Name of paper changed since the term "causality paradox" refers to the problem of time. Material on the generalization of the Virasoro algebra beyond one dimension expanded