The Geometry of Conventionality

TL;DR

This paper investigates whether different spacetime geometries can be explained by new force fields within classical theories, finding that Newtonian gravity allows this while relativity does not.

Contribution

It clarifies the conditions under which geometry can be considered conventional in classical theories of space and time.

Findings

In Newtonian gravity, different geometries can be explained by new force fields.

In relativity, geometry cannot be accommodated by additional force fields.

The answer depends on the specific classical theory of space and time.

Abstract

There is a venerable position in the philosophy of space and time that holds that the geometry of spacetime is conventional, provided one is willing to postulate a "universal force field". Here we ask a more focused question, inspired by this literature: in the context of our best classical theories of space and time, if one understands "force" in the standard way, can one accommodate different geometries by postulating a new force field? We argue that the answer depends on one's theory. In Newtonian gravitation the answer is "yes"; in relativity theory, it is "no".