Defining a Relativity-Proof Notion of the Present via Spatio-temporal Indeterminism

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In this paper we describe a novel approach to defining an ontologically fundamental notion of co-presentness that does not go against the tenets of relativity theory. We survey the possible reactions to the problem of the present in relativity theory, introducing a terminological distinction between a static role of the present, which is served by the relation of simultaneity, and a dynamic role of the present, with the corresponding relation of co-presentness. We argue that both of these relations need to be equivalence relations, but they need not coincide. Simultaneity, the sharing of a temporal coordinate, need not have fundamental ontological import, so that a relativizing strategy with respect to simultaneity seems promising. The notion of co-presentness, on the other hand, does have ontological import, and can therefore not be relativized to an observer or to an arbitrarily chosen frame. We argue that a formal representation of indeterminism can provide the structure needed to anchor the relation of co-presentness, and that this addition is in fact congenial to the notion of dynamic time as requiring real (indeterministic) change. The resulting picture is one of an extended dynamic present, implying a formal distinction between static (coordinate) simultaneity and dynamic co-presentness. After working out the basics of our approach in the simpler framework of branching time, we provide our full analysis in the framework of branching space-times, which allows for a formal definition of modal correlations. The spatial extension of the dynamic present can reach as far as the modal correlations do. In the limit, the dynamic present could extend across a maximal space-like hypersurface.

Zusammenfassung in einer weiteren Sprache
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100 Philosophie
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Presentism, Extended now, Indeterminism, Branching space-times
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undefined / . - undefined, undefined
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ISO 690MÜLLER, Thomas, 2020. Defining a Relativity-Proof Notion of the Present via Spatio-temporal Indeterminism. In: Foundations of Physics. Springer Science+Business Media. 2020, 50(6), pp. 644-664. ISSN 0015-9018. eISSN 1572-9516. Available under: doi: 10.1007/s10701-019-00267-x
BibTex
@article{Muller2020-06Defin-46274,
  year={2020},
  doi={10.1007/s10701-019-00267-x},
  title={Defining a Relativity-Proof Notion of the Present via Spatio-temporal Indeterminism},
  number={6},
  volume={50},
  issn={0015-9018},
  journal={Foundations of Physics},
  pages={644--664},
  author={Müller, Thomas}
}
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