Between a Stone and a Hausdorff Space
History and Philosophy of Physics
2023-10-24 v2 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
We consider the duality between General Relativity and the theory of Einstein algebras, in the extended setting where one permits non-Hausdorff manifolds. We show that the duality breaks down, and then go on to discuss a sense in which general relativity, formulated using non-Hausdorff manifolds, exhibits excess structure when compared to Einstein algebras. We discuss how these results bear on a class of algebraically-motivated deflationist views about spacetime ontology. We conclude with a conjecture concerning non-Hausdorff spacetimes with no bifurcate curves.
Cite
@article{arxiv.2305.03871,
title = {Between a Stone and a Hausdorff Space},
author = {Jingyi Wu and James Owen Weatherall},
journal= {arXiv preprint arXiv:2305.03871},
year = {2023}
}
Comments
24 pages, including appendix; 1 table. Forthcoming in the British Journal for Philosophy of Science