A Brief Comment on Maxwell(/Newton)[-Huygens] Spacetime

I provide an alternative characterization of a "standard of rotation" in the context of classical spacetime structure that does not refer to any covariant derivative operator.Comment: 13 page

Categories and the Foundations of Classical Field Theories

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills theories.Comment: 26 pages. Written for a volume entitled "Categories for the Working Philosopher", edited by Elaine Landr

Inertial motion, explanation, and the foundations of classical spacetime theories

I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to "explain" inertial motion. I argue that there is a sense in which both theories may be understood to explain inertial motion, but that the sense of "explain" is rather different from what one might have expected. This sense of explanation is connected with a view of theories---I call it the "puzzleball view"---on which the foundations of a physical theory are best understood as a network of mutually interdependent principles and assumptions.Comment: 41 pages, 2 figures. Invited for inclusion in Towards a Theory of Spacetime Theories, D. Lehmkuhl e

On the Status of the Geodesic Principle in Newtonian and Relativistic Physics

A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16(1), (1975)] provides a sense in which the geodesic principle has the status of a theorem in General Relativity (GR). I have recently shown that a similar theorem holds in the context of geometrized Newtonian gravitation (Newton-Cartan theory) [Weatherall, J. O. "The Motion of a Body in Newtonian Theories." Journal of Mathematical Physics 52(3), (2011)]. Here I compare the interpretations of these two theorems. I argue that despite some apparent differences between the theorems, the status of the geodesic principle in geometrized Newtonian gravitation is, mutatis mutandis, strikingly similar to the relativistic case.Comment: 16 page

Are Newtonian Gravitation and Geometrized Newtonian Gravitation Theoretically Equivalent?

I argue that a criterion of theoretical equivalence due to Clark Glymour [Nous 11(3), 227-251 (1977)] does not capture an important sense in which two theories may be equivalent. I then motivate and state an alternative criterion that does capture the sense of equivalence I have in mind. The principal claim of the paper is that relative to this second criterion, the answer to the question posed in the title is "yes", at least on one natural understanding of Newtonian gravitation.Comment: 27 page

On (Some) Explanations in Physics

I offer one possible explanation of why inertial and gravitational mass are equal in Newtonian gravitation. I then argue that this is an example of a kind of explanation that is not captured by standard philosophical accounts of scientific explanation. Moreover, this form of explanation is particularly important, at least in physics, because demands for this kind of explanation are used to motivate and shape research into the next generation of physical theories. I suggest that explanations of the sort I describe reveal something important about one way in which physical theories can be related diachronically.Comment: 32 pages. Forthcoming in Philosophy of Scienc

Geometry and Motion in General Relativity

A classic problem in general relativity, long studied by both physicists and philosophers of physics, concerns whether the geodesic principle may be derived from other principles of the theory, or must be posited independently. In a recent paper [Geroch & Weatherall, "The Motion of Small Bodies in Space-Time", Comm. Math. Phys. (forthcoming)], Bob Geroch and I have introduced a new approach to this problem, based on a notion we call "tracking". In the present paper, I situate the main results of that paper with respect to two other, related approaches, and then make some preliminary remarks on the interpretational significance of the new approach. My main suggestion is that "tracking" provides the resources for eliminating "point particles"---a problematic notion in general relativity---from the geodesic principle altogether.Comment: 26 pages, 1 figure. Forthcoming in a future volume of the Einstein Studies serie

Fiber Bundles, Yang-Mills Theory, and General Relativity

I articulate and discuss a geometrical interpretation of Yang-Mills theory. Analogies and disanalogies between Yang-Mills theory and general relativity are also considered.Comment: 54 page