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Causal Probabilities in GRW Quantum Mechanics

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New Directions in the Philosophy of Science

Part of the book series: The Philosophy of Science in a European Perspective ((PSEP,volume 5))

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Abstract

The paper constructs modal structures that represent alternative developments of GRW systems. With these modal structures in hand, it shows that GRW probabilities can be read as graded modalities, that is, as numerically specified powers of a system to localize. The construction is intended as offering support for Dorato and Esfeld’s (Stud Hist Philos Mod Phys 41(1):41–49, 2010) project of conceiving GRW theory as an ontology of powers.

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Notes

  1. 1.

    Another illustration of this tendency is the debate over probabilities in the consistent histories quantum mechanics; for an argument that these probabilities can be read as single case causal probabilities – see Müller (2007).

  2. 2.

    See for instance Ghirardi et al. (1986).

  3. 3.

    As GRW theory does not posit particles, “N-particles system” is a misnomer. If the theory is supplemented with a flash ontology, the phrase means that flashes come in kinds, and the system in question involves exactly N kinds of flashes.

  4. 4.

    For more on the conceptual issues arising from combining GRW theory and relativity, see Maudlin (2008).

  5. 5.

    By trivial case I mean here a case with \(\Pi _{e}\) having one element only.

  6. 6.

    See Sylvia Wenmackers’s work, http://www.sylviawenmackers.be

  7. 7.

    For a proof that \(\Pi _{e}\langle \mathbf{O}\rangle\) exists and is unique, see Belnap (2003).

  8. 8.

    For the postulates see, for instance Belnap (2003).

References

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Authors and Affiliations

  1. Institute of Philosophy, Jagiellonian University, Grodzka 52, 31-044, Krakow, Poland

    Tomasz Placek

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  1. Tomasz Placek
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Correspondence to Tomasz Placek .

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Editors and Affiliations

  1. Department of Philosophy and Commmunication, University of Bologna, Bologna, Italy

    Maria Carla Galavotti

  2. Institute for History and Foundations of Science, Utrecht University, Utrecht, The Netherlands

    Dennis Dieks

  3. Faculty of Humanities, University of A Coruña, Ferrol, Spain

    Wenceslao J. Gonzalez

  4. Centre for Mathematical Philosophy, Ludwig Maximilian University of Munich, Munich, Germany

    Stephan Hartmann

  5. School of Social Sciences, University of Manchester, Manchester, United Kingdom

    Thomas Uebel

  6. Department of Philosophy, University of Geneva, Geneva 4, Switzerland

    Marcel Weber

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Placek, T. (2014). Causal Probabilities in GRW Quantum Mechanics. In: Galavotti, M., Dieks, D., Gonzalez, W., Hartmann, S., Uebel, T., Weber, M. (eds) New Directions in the Philosophy of Science. The Philosophy of Science in a European Perspective, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-04382-1_40

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