Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-07T20:25:11.327Z Has data issue: false hasContentIssue false
  • English
  • Français

A Generalized Manifold Topology for Branching Space-Times

Published online by Cambridge University Press:  01 January 2022

Thomas Müller
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.

References

Belnap, N. 1992. “Branching Space-Time.” Synthese 92 (3): 385–434..CrossRefGoogle Scholar
Belnap, N. 2003. “No-Common-Cause EPR-Like Funny Business in Branching Space-Times.” Philosophical Studies 114:199–221.CrossRefGoogle Scholar
Belnap, N., Perloff, M., and Xu, M.. 2001. Facing the Future: Agents and Choices in Our Indeterminist World. Oxford: Oxford University Press.Google Scholar
Butterfield, J. 2005. “Determinism and Indeterminism.” In Routledge Encyclopedia of Philosophy, vol. 3. London: Routledge.Google Scholar
Deutsch, D. 1991. “Quantum Mechanics Near Closed Timelike Lines.” Physical Review D 44 (10): 3197–3217..Google ScholarPubMed
Earman, J. 2006. “Aspects of Determinism in Modern Physics.” In Handbook of the Philosophy of Physics, ed. Butterfield, J. and Earman, J., 1369–1434. Amsterdam: Elsevier.Google Scholar
Earman, J. 2008. “Pruning Some Branches from Branching Space-Times.” In The Ontology of Spacetime II, ed. Dieks, D., 187–206. Amsterdam: Elsevier.CrossRefGoogle Scholar
Hajicek, P. 1971. “Causality in Non-Hausdorff Space-Times.” Communications in Mathematical Physics 21:75–84.CrossRefGoogle Scholar
Lewis, D. K. 1986. On the Plurality of Worlds. Oxford: Blackwell.Google Scholar
Malament, D. 2012. Topics in the Foundations of General Relativity and Newtonian Gravitation Theory. Chicago: University of Chicago Press.CrossRefGoogle Scholar
McCabe, G. 2005. “The Topology of Branching Universes.” Foundations of Physics Letters 18 (7): 665–76..CrossRefGoogle Scholar
Mendelson, B. 1990. Introduction to Topology. 3rd ed. New York: Dover.Google Scholar
Montague, R. 1962. “Deterministic Theories.” In Decisions, Values and Groups, ed. Willner, D., 325–70. Oxford: Pergamon. Repr. in Formal Philosophy, ed. R. H. Thomason (New Haven, CT: Yale University Press, 1974), 303–59.Google Scholar
Müller, T. 2011. “Branching Space-Times, General Relativity, the Hausdorff Property, and Modal Consistency.” Technical report, Theoretical Philosophy Unit, Utrecht University. http://philsci-archive.pitt.edu/8577/.Google Scholar
Penrose, R. 1979. “Singularities and Time-Asymmetry.” In General Relativity: An Einstein Centenary Survey, ed. Hawking, S. W. and Israel, W., 581–638. Cambridge: Cambridge University Press.Google Scholar
Placek, T. 2010. “Bell-Type Correlations in Branching Space-Times.” In The Analytic Way: Proceedings of the 6th European Congress of Analytic Philosophy, ed. Czarnecki, T., Kijania-Placek, K., Poller, O., and Woleński, J., 105–44. London: College Publications.Google Scholar
Placek, T., and Belnap, N.. 2012. “Indeterminism Is a Modal Notion: Branching Spacetimes and Earman’s Pruning.” Synthese 187 (2): 441–69.. doi:10.1007/s11229-010-9846-8.CrossRefGoogle Scholar
Prior, A. N. 1967. Past, Present and Future. Oxford: Oxford University Press.CrossRefGoogle Scholar
Thomason, R. H. 1970. “Indeterminist Time and Truth-Value Gaps.” Theoria 36:264–81.Google Scholar
Visser, M. 1996. Lorentzian Wormholes. New York: American Institute of Physics.Google Scholar
Wroński, L., and Placek, T.. 2009. “On Minkowskian Branching Structures.” Studies in History and Philosophy of Modern Physics 40:251–58.CrossRefGoogle Scholar