Philosophy of Physics Seminar (Thursday - Week 7, TT25)

Abstract:  will present a hierarchy of spacetime asymmetry conditions within the context of general relativity. The weakest condition -- known as "rigidity" (Geroch 1969) -- captures a sense in which a spacetime is free of symmetry “holes” of a certain type. The rigidity condition is necessary for some strong forms of determinism (Belot 1995). Because all standard models of general relativity are rigid (Halvorson and Manchak 2022), one can show that various collections of spacetimes count as deterministic in ways not fully appreciated until just recently (Halvorson, Manchak, and Weatherall 2025). On the other extreme, the strongest condition in the asymmetry hierarchy is satisfied whenever a model is completely devoid of all symmetries. In these "Heraclitus" spacetimes, no pair of distinct points can be isometrically mapped (even locally) into one another (Manchak and Barrett 2023). One can show that such spacetimes exist (indeed, they are likely generic) and that there are senses in which their global properties (e.g. topology) are completely determined by their local properties (Manchak and Barrett 2025). Throughout the presentation, I will pose a number of precise open questions that could help to clarify the role of asymmetry within the context of general relativity.