Conformal and projective structures in general relativity

It is proposed that compatible conformal and projective structures be taken as the basic space-time structures in general relativity, with the symmetry group restricted to unimodular diffeomorphisms. Models of classical massless fields, such as the Maxwell field, interact directly with the conformal structure; while classical bodies composed of massive particles, such as solids and fluids, interact directly with the projective structure. It is suggested that this difference is the classical limit of the respective quantum-gravitational interactions, which should reflect the differing approaches to the quantization of fields and particles when gravity is neglected. Models of general relativity based on compatible conformal and projective structures should be the basis for the exploration of ideal measurement procedures, both classical and quantum.