Geometrizing gravity and vice-versa: the force
of a formulation

Knox, Eleanor (2009) Geometrizing gravity and vice-versa: the force
of a formulation.

Abstract

It is well-known that Newton’s theory of gravity, commonly held to describe
a gravitational force, can be recast in a geometrical form: Newton-
Cartan theory. It is less well-known that general relativity, an apparently
geometrical theory, can be reformulated in such a way that it resembles a
force theory; teleparallel gravity does just this. This raises questions. One
of these concerns theoretical underdetermination. I argue that these theories
do not, in fact, represent cases of worrying underdetermination. On
close examination, the alternative formulations are best interpreted as postulating
the same spacetime ontology. In accepting this, we see that the
ontological commitments of these theories cannot be directly deduced from
their mathematical form. The geometrical nature of a gravitational theory
is not a straightforward consequence of anything internal to that theory as a
theory of gravity. Rather, it essentially relies on the rest of nature (the nongravitational
interactions) conspiring to choose the appropriate set of inertial
frames.