On Einstein Algebras and Relativistic Spacetimes
@article{Rosenstock2015OnEA, title={On Einstein Algebras and Relativistic Spacetimes}, author={Sarita Rosenstock and Thomas William Barrett and James Owen Weatherall}, journal={Studies in History and Philosophy of Modern Physics}, year={2015}, volume={52}, pages={309-316} }
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References
SHOWING 1-10 OF 54 REFERENCES
Categories and the Foundations of Classical Field Theories
- Geology
- 2015
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,…
Einstein algebras
- Mathematics
- 1972
An approach to quantization of general relatively using a reformulation of the classical theory in which the events of space-time play essentially no role is discussed.
Einstein Algebras and the Hole Argument
- PhilosophyPhilosophy of Science
- 2003
Einstein algebras have been suggested (Earman 1989) and rejected (Rynasiewicz 1992) as a way to avoid the hole argument against spacetime substantivalism. In this article, I debate their merits and…
Sheaves of Einstein algebras
- Mathematics, Physics
- 1995
To include all types of singularities into a geometrically tractable theoretical scheme we change from Einstein algebras, an algebraic generalization of general relativity, to sheaves of Einstein…
Einstein algebras and general relativity
- Mathematics, Physics
- 1992
A purely algebraic structure called an Einstein algebra is defined in such a way that every spacetime satisfying Einstein's equations is an Einstein algebra but not vice versa. The Gelfand…
What Price Spacetime Substantivalism? The Hole Story
- Philosophy, PhysicsThe British Journal for the Philosophy of Science
- 1987
Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument…
The Hole Argument
- PhilosophyPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
- 1988
I give an informal outline of the hole argument which shows that spacetime substantivalism leads to an undesirable indeterminism in a broad class of spacetime theories. This form of the argument…
On North's "The Structure of Physics"
- Philosophy
- 2012
Jill North argues that Hamiltonian mechanics provides the most spare -- and hence most accurate -- account of the structure of a classical world. We point out some difficulties for her argument, and…
Are Newtonian Gravitation and Geometrized Newtonian Gravitation Theoretically Equivalent?
- Geology
- 2014
I argue that a criterion of theoretical equivalence due to Glymour (Noûs 11(3):227–251, 1977) does not capture an important sense in which two theories may be equivalent. I then motivate and state an…
Structured spaces and their application to relativistic physics
- Mathematics, Physics
- 1995
A sheaf of functions on a topological space is called a differential structure if it satisfies an axiom of a closure with respect to composition with the Euclidean functions. A differential structure…