10,048 research outputs found
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
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Oppositions and Paradoxes: Philosophical Perplexities in Science and Mathematics
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 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
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
Maxwell-Huygens, Newton-Cartan, and Saunders-Knox Spacetimes
I address a question recently raised by Simon Saunders [Phil. Sci. 80(2):
22-48 (2013)] concerning the relationship between the spacetime structure of
Newton-Cartan theory and that of what I will call "Maxwell-Huygens spacetime".
This discussion will also clarify a connection between Saunders' work and a
recent paper by Eleanor Knox [Brit. J. Phil. Sci. 65(4): 863-880 (2014)].Comment: 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
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