Is the Metric Signature Really Electromagnetic in Origin?

Abstract

The program of "pre-metric electromagnetism," developed by Hehl and collaborators, seeks to derive certain aspects of the spacetime geometry of the world (in particular, metrical signature) from elementary, empirically informed axioms regarding electromagnetic fields. The program should, therefore, be of profound interest to both empiricist and relationalist philosophers. Up to this point, however, pre-metric electromagnetism has received very little attention within the philosophy of physics; this paper seeks to rectify the situation, by engaging in a detailed foundational study of the program. In particular, in this article, we (a) present a streamlined version of the program, identifying key input assumptions, (b) consider the connections between this program and other notable projects in the foundations of spacetime theories, for example, (i) the dynamical approach to spacetime and (ii) constructive axiomatics, and (c) consider in detail the extent to which this program can be generalized beyond electromagnetism.In achieving these tasks, we hope to open up to philosophers an extraordinarily fecund-but lamentably little-known!-project within the foundations of physics.