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Synthese

, Volume 188, Issue 1, pp 85–116 | Cite as

On A- and B-theoretic elements of branching spacetimes

  • Matt Farr
Article

Abstract

This paper assesses branching spacetime theories in light of metaphysical considerations concerning time. I present the A, B, and C series in terms of the temporal structure they impose on sets of events, and raise problems for two elements of extant branching spacetime theories—McCall’s ‘branch attrition’, and the ‘no backward branching’ feature of Belnap’s ‘branching space–time’—in terms of their respective A- and B-theoretic nature. I argue that McCall’s presentation of branch attrition can only be coherently formulated on a model with at least two temporal dimensions, and that this results in severing the link between branch attrition and the flow of time. I argue that ‘no backward branching’ prohibits Belnap’s theory from capturing the modal content of indeterministic physical theories, and results in it ascribing to the world a time-asymmetric modal structure that lacks physical justification.

Keywords

Branching time A series B series C series Branch attrition Supertime BST Indeterminism Direction of time Open future 

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References

  1. Aharonov Y., Albert D., Vaidman L. (1988) How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Physical Review Letters 60(14): 1351–1354CrossRefGoogle Scholar
  2. Aharonov Y., Bergmann P., Lebowitz J. (1964) Time symmetry in the quantum process of measurement. Physical Review 134: 1410–1416CrossRefGoogle Scholar
  3. Aharonov Y., Popescu S., Tollaksen J. (2010) A time-symmetric formulation of quantum mechanics. Physics Today 63: 27–33CrossRefGoogle Scholar
  4. Albert D. Z. (2000) Time and chance. Harvard University Press, Cambridge, MAGoogle Scholar
  5. Arntzenius F., Greaves H. (2009) Time reversal in classical electromagnetism. British Journal for the Philosophy of Science 60(3): 557–584CrossRefGoogle Scholar
  6. Belnap N. (1992) Branching space–time. Synthese 92(3): 385–434CrossRefGoogle Scholar
  7. Belnap N., Perloff M., Xu M. (2001) Facing the future: Agents and choices in our indeterminist world. Oxford University Press, OxfordGoogle Scholar
  8. Black M. (1959) The “direction” of time. Analysis 19(3): 54–63CrossRefGoogle Scholar
  9. Davies P. (1977) The physics of time asymmetry. University of California Press, Berkeley, CAGoogle Scholar
  10. Earman J. (1986) A primer on determinism. D. Reidel, DordrechtCrossRefGoogle Scholar
  11. Earman J. (2002) What time reversal invariance is and why it matters. International Studies in the Philosophy of Science 16(3): 245–264CrossRefGoogle Scholar
  12. Earman J. (2008) Pruning some branches from “branching spacetimes”. In: Dieks D. (eds) The ontology of spacetime II. Elsevier Science, Oxford, pp 187–205CrossRefGoogle Scholar
  13. Elga A. (2001) Statistical mechanics and the asymmetry of counterfactual dependence. Philosophy of Science 68(3): 313–324CrossRefGoogle Scholar
  14. Farr, M. (2011). Temporal ontology on the two-time framework. Unpublished manuscript.Google Scholar
  15. Farr, M., & Reutlinger, A. (2011). Difference making and the direction of time. Unpublished manuscript.Google Scholar
  16. Hawking S. (1989) A brief history of time: From the big bang to black holes. Bantam Books, LondonGoogle Scholar
  17. Ladyman J. (2000) What’s really wrong with constructive empiricism? Van Fraassen and the metaphysics of modality. British Journal for the Philosophy of Science 51(4): 837–856CrossRefGoogle Scholar
  18. Ladyman J., Ross D. (2007) Every thing must go. Oxford University Press, OxfordCrossRefGoogle Scholar
  19. Lewis D. (1979) Counterfactual dependence and time’s arrow. Noûs 13(4): 455–476CrossRefGoogle Scholar
  20. Malament D. (2004) On the time reversal invariance of classical electromagnetic theory. Studies in History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics 35(2): 295–315CrossRefGoogle Scholar
  21. Maudlin T. (2007) The metaphysics within physics. Oxford University Press, OxfordCrossRefGoogle Scholar
  22. McCall S. (1976) Objective time flow. Philosophy of science 43(3): 337–362CrossRefGoogle Scholar
  23. McCall S. (1984) A dynamic model of temporal becoming. Analysis 44(4): 172–176CrossRefGoogle Scholar
  24. McCall S. (1994) A model of the universe. Clarendon Press, OxfordGoogle Scholar
  25. McCall S. (1998) Time flow does not require a second time dimension. Australasian Journal of Philosophy 76(2): 317–322CrossRefGoogle Scholar
  26. McTaggart J. M. E. (1908) The unreality of time. Mind 17(68): 457–474CrossRefGoogle Scholar
  27. McTaggart J. M. E. (1927) The nature of existence. Cambridge University Press, CambridgeGoogle Scholar
  28. Meiland J. (1974) A two-dimensional passage model of time for time travel. Philosophical Studies 26(3): 153–173CrossRefGoogle Scholar
  29. Montague R. (1974) Deterministic theories. Yale University Press, New HavenGoogle Scholar
  30. Müller, T. (2009). Eliminating modality from the determinism debate? Models vs. equations of physical theories. In A. Hieke & H. Leitgeb (Eds.), Reduction–abstraction–analysis. Proceedings of the 31th international Ludwig Wittgenstein symposium (pp.~47–62). Frankfurt: Ontos Verlag.Google Scholar
  31. Nerlich G. (1998) Falling branches and the flow of time. Australasian Journal of Philosophy 76: 309–316CrossRefGoogle Scholar
  32. Øhrstrøm P., Schärfe H., Ploug T. (2010) Branching time as a conceptual structure. In: Croitoru M., Ferré S., Lukose D. (eds) Conceptual structures: From information to intelligence. Springer, Berlin, pp 125–138CrossRefGoogle Scholar
  33. Placek, T., & Belnap, N. (2010). Indeterminism is a modal notion: Branching spacetimes and Earman’s pruning. Synthese. doi: 10.1007/s11229-010-9846-8
  34. Placek T., Müller T. (2007) Counterfactuals and historical possibility. Synthese 154(2): 173–197CrossRefGoogle Scholar
  35. Price H. (1996) Time’s arrow and Archimedes’ point: New directions for the physics of time. Oxford University Press, OxfordGoogle Scholar
  36. Prior A. N. (1967) Past, present and future. Clarendon Press, OxfordCrossRefGoogle Scholar
  37. Reichenbach H. (1956) The direction of time. University of California Press, BerkeleyGoogle Scholar
  38. Schlesinger G. (1980) Aspects of time. Hackett Publishing Company, CambridgeGoogle Scholar
  39. Smart J. J. C. (1980) Time and becoming. In: Van Inwagen P. (eds) Time and cause: Essays presented to Richard Taylor. Reidel, Dordrecht, pp 3–15Google Scholar
  40. Smart J. J. C. (1995) Review of McCall (1994). Australasian Journal of Philosophy 73(1): 161–163Google Scholar
  41. Wronski L., Placek T. (2009) On Minkowskian branching structures. Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics 40(3): 251–258CrossRefGoogle Scholar
  42. Zeh D. (2007) The physical basis of the direction of time. Springer, BerlinGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of BristolBristolUK

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