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A Generalized Manifold Topology for Branching Space-Times

Published online by Cambridge University Press:  01 January 2022

Thomas Müller
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Abstract

The logical theory of branching space-times, which provides a relativistic framework for studying objective indeterminism, remains mostly disconnected from discussions of space-time theories in philosophy of physics. Earman has criticized the branching approach and suggested “pruning some branches from branching space-time.” This article identifies the different—order-theoretic versus topological—perspective of both discussions as a reason for certain misunderstandings and tries to remove them. Most important, we give a novel, topological criterion of modal consistency that usefully generalizes an earlier criterion, and we introduce a differential-geometrical version of branching space-times as a non-Hausdorff (generalized) manifold.

Type
General Philosophy of Science
Information
Philosophy of Science , Volume 80 , Issue 5 , December 2013 , pp. 1089 - 1100
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

Research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement 263227 and from the Dutch Organization for Scientific Research, grant NWO VIDI 276-20-013. Thanks to Nuel Belnap and Tomasz Placek for many stimulating discussions.

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