Resolution of the problem of time in quantum gravity

TL;DR

This paper proposes a radical solution to the problem of time in quantum gravity by removing space-like separation, describing fields on an observer's trajectory, and connecting to the Virasoro algebra extension, which aligns with the standard model in four dimensions.

Contribution

It introduces a novel approach to quantum gravity by eliminating space-like separation and utilizing p-jet fields on an observer's trajectory, linking to the Virasoro algebra extension.

Findings

The limit p -> infinity exists only in 4 dimensions.

The relation between fermions and bosons matches the standard model.

The approach provides a consistent quantum extension of general relativity.

Abstract

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.