Flat Spacetime Gravitation with a Preferred Foliation

TL;DR

This paper explores a flat spacetime gravitational theory incorporating a preferred foliation, analyzing its physical interpretation and implications for the flow of time, while addressing its observability and potential physical applications.

Contribution

It introduces a formalism for flat spacetime gravitation with a preferred foliation, extending prior work and analyzing its physical significance and potential necessity.

Findings

Preferred foliation may be unobservable.

Flowing theory of time requires a preferred foliation.

Certain physics areas may need a preferred foliation.

Abstract

Paralleling the formal derivation of general relativity as a flat spacetime theory, we introduce in addition a preferred temporal foliation. The physical interpretation of the formalism is considered in the context of 5-dimensional ``parametrized'' and 4-dimensional preferred frame contexts. In the former case, we suggest that our earlier proposal of unconcatenated parametrized physics requires that the dependence on $\tau$ be rather slow. In the 4-dimensional case, we consider and tentatively reject several areas of physics that might require a preferred foliation, but find a need for one in the process (``flowing'') theory of time. We then suggest why such a foliation might reasonably be unobservable.