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
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
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
  • J. Bain
  • Philosophy
    Philosophy 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
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
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
  • J. Earman, J. Norton
  • Philosophy, Physics
    The 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
  • J. Norton
  • Philosophy
    PSA: 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"
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?
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
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
...
...