The Geometry of Conventionality

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".