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Bohm-Bell Dynamics in the Modal Interpretation

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Part of the book series: The Western Ontario Series in Philosophy of Science ((WONS,volume 60))

Abstract

There are two aspects to time evolution in the modal interpretation. One is the evolution of the set of definite properties, which, in particular in the version of Vermaas and Dieks (1995), is obviously a deterministic evolution, since in this version the definite properties of a system are given at any instant by the spectral resolution of the reduced state ρ of the system. This aspect has been studied by Bacciagaluppi, Donald and Vermaas (1995), and is treated in this same volume by Donald (hic).

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References

  • Albert, D. (1992), Quantum Mechanics and Experience (Cambridge, Mass.: Harvard University Press).

    Google Scholar 

  • Albert, D. and Loewer, B. (1990), ‘Wanted Dead or Alive: Two Attempts to Solve Schrödinger’s Paradox’, in A. Fine, M. Forbes and L. Wessels (eds), Proceedings of the 1990 Biennial Meeting of the Philosophy of Science Association, Vol. 1 (East Lansing: Philosophy of Science Association), pp. 277–285.

    Google Scholar 

  • Bacciagaluppi, G. (1996a), Topics in the Modal Interpretation of Quantum Mechanics, Doctoral Dissertation, University of Cambridge.

    Google Scholar 

  • Bacciagaluppi, G. (1996b), ‘Delocalised Properties in the Modal Interpretation of a Continuous Model of Decoherence’, preprint.

    Google Scholar 

  • Bacciagaluppi, G. (1998), The Modal Interpretation of Quantum Mechanics (Cambridge: Cambridge University Press), forthcoming.

    Google Scholar 

  • Bacciagaluppi, G., Barrett, J. and Dickson, M. (1997), ‘How to Weaken the Distribution Postulate in Bohm’s Theory’, in preparation.

    Google Scholar 

  • Bacciagaluppi, G. and Dickson, M. (1997), ‘Modal Interpretations with Dynamics’, preprint.

    Google Scholar 

  • Bacciagaluppi, G., Donald, M. J. and Vermaas, P. E. (1995), ‘Continuity and Discontinuity of Definite Properties in the Modal Interpretation’, Helvetica Physica Acta 68, 679–704.

    Google Scholar 

  • Bacciagaluppi, G. and Hemmo, M. (1996), ‘Modal Interpretations, Decoherence and Measurements’, Studies in the History and Philosophy of Modem Physics 27, 239–277.

    Article  Google Scholar 

  • Bacciagaluppi, G. and Hemmo, M. (1997), ‘State Preparation in the Modal Interpretation’, forthcoming in Healey and Hellman (1997).

    Google Scholar 

  • Bacciagaluppi, G. and Vermaas, P. E. (1997), ‘Virtual Reality: Consequences of No-Go Theorems for the Modal Interpretation of Quantum Mechanics’, forthcoming in M. L. Dalla Chiara, R. Giuntini and F. Laudisa (eds), Philosophy of Science in Florence, 1995 (Dordrecht: Kluwer).

    Google Scholar 

  • Bell, J. S. (1976), ‘The Measurement Theory of Everett and de Broglie’s Pilot Wave’, in Bell (1987), pp. 93–99.

    Google Scholar 

  • Bell, J. S. (1981), ‘Quantum Mechanics for Cosmologists’, in Bell (1987), pp. 117–138.

    Google Scholar 

  • Bell, J. S. (1984), ‘Beables for Quantum Field Theory’, in Bell (1987), pp. 173–180.

    Google Scholar 

  • Bell, J. S. (1987), Speakable and Unspeakable in Quantum Mechanics (Cambridge: Cambridge University Press).

    Google Scholar 

  • Berndl, K., Dürr, D., Goldstein, S., Peruzzi, G. and Zanghì, N. (1995), ‘On the Global Existence of Bohmian Mechanics’, Communications in Mathematical Physics 173, 647–673.

    Article  Google Scholar 

  • Bohm, D. (1952), ‘A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables, I and II’, Physical Review 85, 166–193.

    Article  Google Scholar 

  • Bohm, D. (1953), ‘Proof that Probability Density Approaches |ψ|2 in Causal Interpretation of the Quantum Theory’, Physical Review 89, 458–466.

    Article  Google Scholar 

  • Bohm, D. and Vigier, J.-P. (1954), ‘Model of the Causal Interpretation of Quantum Theory in Terms of a Fluid with Irregular Fluctuations’, Physical Review 96, 208–216.

    Article  Google Scholar 

  • Bub, J. (1992a), ‘Quantum Logical Solution to the Measurement Problem of Quantum Mechanics’, International Journal of Theoretical Physics 31, 1857–1871.

    Article  Google Scholar 

  • Bub, J. (1992b), ‘Quantum Mechanics Without the Projection Postulate’, Foundations of Physics 22, 737–754.

    Article  Google Scholar 

  • Bub, J. (1994a), ‘On the Structure of Quantal Proposition Systems’, Foundations of Physics 24, 1261–1279.

    Article  Google Scholar 

  • Bub, J. (1994b), ‘How to Interpret Quantum Mechanics’, Erkenntnis 41, 253–273.

    Article  Google Scholar 

  • Bub, J. (1996), ‘Schrödinger’s Cat and Other Entanglements of Quantum Mechanics’, forthcoming in J. Earman and J. Norton (eds), The Cosmos of Science (Pittsburgh: University of Pittsburgh Press, and Konstanz: Universitäts-Verlag Konstanz).

    Google Scholar 

  • Bub, J. (1997), Interpreting the Quantum World (Cambridge: Cambridge University Press).

    Google Scholar 

  • Bub, J. (hic), ‘Decoherence in Bohmian Modal Interpretations’, this volume.

    Google Scholar 

  • Bub, J. and Clifton, R. (1996), ‘A Uniqueness Theorem for ‘No-Collapse’ Interpretations of Quantum Mechanics’, Studies in History and Philosophy of Modem Physics 27, 181–219.

    Article  Google Scholar 

  • Butterfield, J. (1995), ‘Worlds, Minds and Quanta’, Aristotelian Society Supplementary Volume LXIX, 113–158.

    Google Scholar 

  • Clifton, R. (1994), private communication, Prague, August 1994.

    Google Scholar 

  • Cushing, J. (1995), private communication, Cambridge, June 1995.

    Google Scholar 

  • Dickson, M. and Clifton, R. (hic), ‘Lorentz-Invariance in the Modal Interpretation’, this volume.

    Google Scholar 

  • Dieks, D. (1994a), ‘Objectification, Measurement and Classical Limit According to the Modal Interpretation of Quantum Mechanics’, in P. Busch, P. Lahti and P. Mittelstaedt (eds), Symposium on the Foundations of Modern Physics 1993: Quantum Measurement, Irreversibility and the Physics of Information (Singapore: World Scientific, 1994), pp. 160–167.

    Google Scholar 

  • Dieks, D. (1994b), ‘The Modal Interpretation of Quantum Mechanics, Measurement and Macroscopic Behaviour’, Physical Review D 49, 2290–2300.

    Google Scholar 

  • Dieks, D. (1997), ‘Preferred Factorizations and Consistent Property Attribution’, forthcoming in Healey and Hellman (1997).

    Google Scholar 

  • Donald, M. J. (hic), ‘Discontinuity and Continuity of Definite Properties in the Modal Interpretation’, this volume.

    Google Scholar 

  • Dürr, D., Goldstein, S. and Zanghì, N. (1995), ‘Quantum Physics Without Quantum hilosophy’, Studies in History and Philosophy of Modern Physics 26 B, 137–149.

    Article  Google Scholar 

  • Feller, W. (1940), ‘On the Integro-Differential Equations of Purely Discontinuous Markoff Processes’, Transactions of the American Mathematical Society 48, 488–515

    Article  Google Scholar 

  • Feller, W. (1940) ‘Errata’, Transactions of the American Mathematical Society 58 (1945), 474.

    Google Scholar 

  • Fraassen, B. C. van (1973), ‘Semantic Analysis of Quantum Logic’, in C. A. Hooker (ed.), Contemporary Research in the Foundations and Philosophy of Quantum Theory (Dordrecht and Boston: Reidel), pp. 180–213.

    Google Scholar 

  • Fraassen, B. C. van (1991), Quantum Mechanics: An Empiricist View (Oxford: Clarendon Press).

    Google Scholar 

  • Healey, R. and Hellman, G. (eds) (1997), Quantum Measurement: Beyond Paradox. Minnesota Studies in the Philosophy of Science, Vol. 17, forthcoming.

    Google Scholar 

  • Hemmo, M. and Bacciagaluppi, G. (1996), ‘Many Worlds are Possible in Quantum Theory’, in preparation.

    Google Scholar 

  • Kent, A. (1995), ‘A Note on Schmidt States and Consistency’, Physics Letters A 196, 313–317.

    Google Scholar 

  • Kolmogorov, A. (1931), ‘Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung’, Mathematische Annalen 104, 415–458.

    Article  Google Scholar 

  • Maudlin, T. (1994), ‘The Unbuttoned Empiricist: Van Fraassen Speculates About the Quantum World’, Philosophical Books 35, 94–101.

    Article  Google Scholar 

  • Nelson, E. (1966), ‘Derivation of the Schrödinger Equation from Newtonian Mechanics’, Physical Review 150, 1079–1085.

    Article  Google Scholar 

  • Nelson, E. (1985), Quantum Fluctuations (Princeton: Princeton University Press).

    Google Scholar 

  • Peruzzi, G. and Rimini, A. (1996), ‘Quantum Measurement in a Family of Hidden-Variable Theories’, Foundations of Physics Letters 9, 505–519.

    Article  Google Scholar 

  • Reed, M. and Simon, B. (1978), Methods of Modern Mathematical Physics, Vol. 4 (New York: Academic Press).

    Google Scholar 

  • Vaidman, L. (1994), private communication, Erice, February 1994.

    Google Scholar 

  • Valentini, A. (1991a), ‘Signal-Locality, Uncertainty, and the Subquantum H-Theorem, I’, Physics Letters A 156, 5–11.

    Google Scholar 

  • Valentini, A. (1991b), ‘Signal-Locality, Uncertainty, and the Subquantum H-Theorem, II’, Physics Letters A 158, 1–8.

    Google Scholar 

  • Vermaas, P. E. (1995), talk delivered in the Department of History and Philosophy of Science, University of Cambridge, March 1995.

    Google Scholar 

  • Vermaas, P. E. (1996), ‘Unique Transition Probabilities in the Modal Interpretation’, Studies in the History and Philosophy of Modern Physics 27, 133–159.

    Article  Google Scholar 

  • Vermaas, P. E. (1997), ‘A No-Go Theorem for Joint Property Ascriptions in the Modal Interpretation of Quantum Mechanics’, Physical Review Letters 76, 2033–2037.

    Article  Google Scholar 

  • Vermaas, P. E. (hic), ‘The Pros and Cons of the Kochen-Dieks and the Atomic Modal Interpretation’, this volume.

    Google Scholar 

  • Vermaas, P. E. and Dieks, D. (1995), ‘The Modal Interpretation of Quantum Mechanics and Its Generalization to Density Operators’, Foundations of Physics 25, 145–158.

    Article  Google Scholar 

  • Vink, J. (1993), ‘Quantum Mechanics in Terms of Discrete Beables’, Physical Review, A 48, 1808–1818.

    Google Scholar 

  • Zurek, W. H. (1993), ‘Preferred States, Predictability, Classicality, and the Environment-Induced Decoherence’, Progress in Theoretical Physics 89, 281–312.

    Article  Google Scholar 

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Bacciagaluppi, G. (1998). Bohm-Bell Dynamics in the Modal Interpretation. In: Dieks, D., Vermaas, P.E. (eds) The Modal Interpretation of Quantum Mechanics. The Western Ontario Series in Philosophy of Science, vol 60. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5084-2_7

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  • DOI: https://doi.org/10.1007/978-94-011-5084-2_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6135-3

  • Online ISBN: 978-94-011-5084-2

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