Abstract
I discuss philosophical questions raised by existence of extendible maximal globally hyperbolic spacetimes with non-unique extensions. These spacetimes represent a form of indeterminism in classical general relativity: given fixed initial data and equations of the theory, there exists more than one possible way a spacetime could be. Even though such spacetimes have been investigated in the physics literature for quite some time, a philosophical discussion of their importance is missing. Here I explore their relevance for the notion of physical equivalence, distinction between physically reasonable spacetimes and physically unreasonable ones, relation between determinism and singular spacetimes, connections between some forms of indeterminism and existence of time machines, and question whether cosmic censorship can be understood as expressing determinism of general relativity.
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Notes
- 1.
See, however, Manchak (2016b) for a dissenting view.
- 2.
Sticking to the convention followed by most presentations of Misner spacetime in the literature, I discuss two dimensional Misner spacetime. But this spacetime can be defined in higher dimensions as well.
- 3.
More precisely: two maximal extensions 〈M 1, g 1, Λ 1〉 and 〈M 2, g 2, Λ 2〉 of 〈M, g〉 are Cauchy equivalent wrt \(\Sigma,i\) iff \(\psi \circ \Lambda _{1} \circ i = \Lambda _{2} \circ i\)
- 4.
I am not aware of anyone actually subscribing to this in writing.
- 5.
Similar questions could be asked about Malament-Hogarth spacetimes.
- 6.
For difference between Thornian and Wellsian time machines, see Earman et al. (2016).
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Acknowledgements
The author acknowledges the funding of the research grant ‘Mistrz 2011’ of the Foundation for Polish Science, contract nr 5/2011 for financial support. The work on this paper was partically carried out as a part of the “Probability, Causality and Determinism” Bilateral Mobility Grant of the Hungarian and Polish Academies of Sciences, NM-104/2014. I would also like to thank Dennis Dieks, Erik Curiel, Sam Fletcher, F. A. Muller, Christian Wüthrich, and the audience at BSPS 2014 in Cambridge for helpful feedback. Most of this material has been developed through numerous conversations with Tomasz Placek, to whom I am very grateful.
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Doboszewski, J. (2017). Non-uniquely Extendible Maximal Globally Hyperbolic Spacetimes in Classical General Relativity: A Philosophical Survey. In: Hofer-Szabó, G., Wroński, L. (eds) Making it Formally Explicit. European Studies in Philosophy of Science, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-55486-0_11
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