Is spacetime as physical as is space?

TL;DR

This paper explores the relationship between space and spacetime, proposing that each reference fluid defines a physical space and examining whether spacetime geometry determines physical laws, concluding it does not.

Contribution

It introduces a framework where each reference fluid defines a physical space and shows spacetime geometry alone does not determine the physics or its relativistic character.

Findings

Each reference fluid defines a physical space as a 3-D manifold.

Spacetime geometry does not uniquely determine the physics.

The same physics can be realized on different spacetime structures.

Abstract

Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a congruence of reference trajectories, defines a physical space. The points of that space are formally defined to be the world lines of the congruence. That space can be endowed with a natural structure of 3-D differentiable manifold, thus giving rise to a simple notion of spatial tensor --- namely, a tensor on the space manifold. The second question is: does the geometric structure of the spacetime determine the physics, in particular, does it determine its relativistic or preferred-frame character? We find that it does not, for different physics (either relativistic or not) may be defined on the same spacetime structure --- and also, the same physics can be implemented on different spacetime structures. Keywords: Affine space; classical mechanics; special relativity; relativistic gravity; reference fluid.