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Delocalized Properties in the Modal Interpretation of a Continuous Model of Decoherence

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I investigate the character of the definite properties defined by the Basic Rule in the Vermaas and Dieks' (1995) version of the modal interpretation of quantum mechanics, specifically for the case of the continuous model of decoherence by Joos and Zeh (1985). While this model suggests that the characteristic length that might be associated with the localisation of an individual system is the coherence length of the state (which converges rapidly to the thermal de Broglie wavelength), I show in an exactly soluble case that the definite properties that are possessed with overwhelming probability in this modal interpretation are delocalized over the entire spread of the state.

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REFERENCES

  • D. Albert and B. Loewer, “Wanted dead or alive: Two attempts to solve Schro– dinger's paradox,” in Proceedings of the 1990 Biennial Meeting of the Philosophy of Science Association, Vol. 1, A. Fine, M. Forbes, and L. Wessels, eds. (Philosophy of Science Association, East Lansing, 1990), pp. 277–285.

    Google Scholar 

  • G. Bacciagaluppi, “Kochen–Specker theorem in the modal interpretation of quantum mechanics,” Internat. J. Theoret. Phys. 34, 1206–1215 (1995).

    Google Scholar 

  • G. Bacciagaluppi, Modal Interpretations of Quantum Mechanics (Cambridge University Press, Cambridge), to appear.

  • G. Bacciagaluppi, “The role of decoherence in quantum theory,” in The Stanford Encyclopedia of Philosophy, to appear.

  • G. Bacciagaluppi and J. Barrett, “How to weaken the distribution postulate in pilot-wave-theories,” to appear.

  • Bacciagaluppi and M. Dickson, “Dynamics for modal interpretations,” Found. Phys. 29, 1165–1201 (1999).

    Google Scholar 

  • G. Bacciagaluppi, M. J. Donald, and P. E. Vermaas, “Continuity and discontinuity of definite properties in the modal interpretation,” Helv. Phys. Acta 68, 679–704 (1995).

    Google Scholar 

  • G. Bacciagaluppi and M. Hemmo, “Modal interpretations, decoherence and measurements,” Studies in History and Philosophy of Modern Physics 27, 239–277 (1996).

    Google Scholar 

  • J. Bub, “Quantum mechanics without the projection postulate,” Found. Phys. 22, 737–754 (1992).

    Google Scholar 

  • A. O. Caldeira and A. J. Leggett, “Path integral approach to quantum Brownian motion,” Physica A 121, 587–616 (1983).

    Google Scholar 

  • R. Clifton, “Independently motivating the Kochen–Dieks modal interpretation of quantum mechanics,” Brit. J. Phil. Sci. 46, 33–57 (1995).

    Google Scholar 

  • R. Clifton, “The properties of modal interpretations of quantum mechanics,” Brit. J. Phil. Sci. 47, 371–398 (1996).

    Google Scholar 

  • D. Dieks, “Resolution of the measurement problem through decoherence of the quantum state,” Phys. Lett. A 142, 439–446 (1989).

    Google Scholar 

  • D. Dieks, “Objectification, measurement and classical limit according to the modal interpreta-tion of quantum mechanics,” in Symposium on the Foundations of Modern Physics 1993, P. Busch, P. Lahti, and P. Mittelstaedt, eds. (World Scientific, Singapore, 1994a), pp. 160–167.

    Google Scholar 

  • D. Dieks, “The modal interpretation of quantum mechanics, measurement and macroscopic behaviour,” Phys. Rev. D 49, 2290–2300 (1994b).

    Google Scholar 

  • D. Dieks and P. E. Vermaas, eds., The Modal Interpretation of Quantum Mechanics (Kluwer, Dordrecht, 1998).

    Google Scholar 

  • M. J. Donald, “Discontinuity and continuity of definite properties in the modal interpretation,” in Dieks and Vermaas (1998), pp. 213–222.

  • H. Everett, III, “ ‘Relative State’ formulation of quantum mechanics,” Rev. Mod. Phys. 29, 454–462 (1957). Repr. in Quantum Theory and Measurement, J. A. Wheeler and W. H. Zurek, eds. (Princeton University Press, Princeton, 1983), pp. 315–323.

    Google Scholar 

  • B. C. van Fraassen, “Semantic analysis of quantum logic,” in Contemporary Research in the Foundations and Philosophy of Quantum Theory, C. A. Hooker, ed. (Reidel, Dordrecht, 1973), pp. 180–213.

    Google Scholar 

  • B. C. van Fraassen, Quantum Mechanics: An Empiricist View (Clarendon Press, Oxford, 1990).

    Google Scholar 

  • D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.-O. Stamatescu, and H. D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin, 1996).

    Google Scholar 

  • R. Healey, The Philosophy of Quantum Mechanics: An Interactive Interpretation (Cambridge University Press, Cambridge, 1989).

    Google Scholar 

  • E. Joos and H. D. Zeh, “The emergence of classical properties through interaction with the environment,” Z. Physik B 59, 223–243 (1985).

    Google Scholar 

  • S. Kochen, “A new interpretation of quantum mechanics,” in Symposium on the Foundations of Modern Physics 1985: 50 Years of the Einstein–Podolski–Rosen Gedankenexperiment, P. Lahti and P. Mittelstaedt, eds. (World Scientific, Singapore, 1985), pp. 151–169.

    Google Scholar 

  • H. Krips, The Metaphysics of Quantum Theory (Clarendon Press, Oxford, 1987).

    Google Scholar 

  • L. I. Schiff, Quantum Mechanics, 3rd ed. (McGraw–Hill, New York, 1968).

    Google Scholar 

  • A. Sudbery, to appear.

  • W. G. Unruh, private communication, Minneapolis, May 1995.

  • W. G. Unruh and W. H. Zurek, “Reduction of a wave packet in quantum Brownian motion,” Phys. Rev. D 40, 1071–1094 (1989).

    Google Scholar 

  • P. E. Vermaas, “A no-go theorem for joint property ascriptions in the modal interpretation of quantum theory,” Phys. Rev. Lett. 78, 2033–2037 (1997).

    Google Scholar 

  • P. E. Vermaas, “Expanding the property ascriptions in the modal interpretation of quantum theory,” in Quantum Measurement: Beyond Paradox, R. Healey and G. Hellman, eds., Minnesota Studies in the Philosophy of Science, Vol. XVII (University of Minnesota Press, Minneapolis, 1998).

    Google Scholar 

  • P. E. Vermaas, A Philosopher's Look at Quantum Mechanics (Cambridge University Press, Cambridge, 1999).

    Google Scholar 

  • P. E. Vermaas and D. Dieks, “The modal interpretation of quantum mechanics and its generalization to density operators,” Found. Phys. 25, 145–158 (1995).

    Google Scholar 

  • H. D. Zeh, “On the interpretation of measurement in quantum theory,” Found. Phys. 1, 69–76 (1970).

    Google Scholar 

  • H. D. Zeh, “Toward a quantum theory of observation,” Found. Phys. 3, 109–116 (1973).

    Google Scholar 

  • W. H. Zurek, “Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?,” Phys. Rev. D 24, 1516–1525 (1981).

    Google Scholar 

  • W. H. Zurek, “Environment-induced superselection rules,” Phys. Rev. D 26, 1862–1880 (1982).

    Google Scholar 

  • W. H. Zurek, “Decoherence and the transition from quantum to classical,” Phys. Today 44, 36–44 (1991).

    Google Scholar 

  • W. H. Zurek, “Reply to criticism,” Phys. Today 46, 84–90 (1993).

    Google Scholar 

  • W. H. Zurek, S. Habib, and J. P. Paz, “Coherent states via decoherence,” Phys. Rev. Lett. 70, 1187–1190 (1993).

    Google Scholar 

  • W. H. Zurek and J. P. Paz, “Decoherence, chaos, the quantum and the classical,” in Symposium on the Foundations of Modern Physics 1993, P. Busch, P. Lahti, and P. Mittelstaedt, eds. (World Scientific, Singapore, 1994), pp. 458–472.

    Google Scholar 

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Bacciagaluppi, G. Delocalized Properties in the Modal Interpretation of a Continuous Model of Decoherence. Foundations of Physics 30, 1431–1444 (2000). https://doi.org/10.1023/A:1026453817453

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