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Foundations of Physics

, Volume 30, Issue 9, pp 1431–1444 | Cite as

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

  • Guido Bacciagaluppi
Article

Abstract

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.

Keywords

Coherence Quantum Mechanic Continuous Model Characteristic Length Basic Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

  1. 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
  2. G. Bacciagaluppi, “Kochen–Specker theorem in the modal interpretation of quantum mechanics,” Internat. J. Theoret. Phys. 34, 1206–1215 (1995).Google Scholar
  3. G. Bacciagaluppi, Modal Interpretations of Quantum Mechanics (Cambridge University Press, Cambridge), to appear.Google Scholar
  4. G. Bacciagaluppi, “The role of decoherence in quantum theory,” in The Stanford Encyclopedia of Philosophy, to appear.Google Scholar
  5. G. Bacciagaluppi and J. Barrett, “How to weaken the distribution postulate in pilot-wave-theories,” to appear.Google Scholar
  6. Bacciagaluppi and M. Dickson, “Dynamics for modal interpretations,” Found. Phys. 29, 1165–1201 (1999).Google Scholar
  7. 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
  8. G. Bacciagaluppi and M. Hemmo, “Modal interpretations, decoherence and measurements,” Studies in History and Philosophy of Modern Physics 27, 239–277 (1996).Google Scholar
  9. J. Bub, “Quantum mechanics without the projection postulate,” Found. Phys. 22, 737–754 (1992).Google Scholar
  10. A. O. Caldeira and A. J. Leggett, “Path integral approach to quantum Brownian motion,” Physica A 121, 587–616 (1983).Google Scholar
  11. R. Clifton, “Independently motivating the Kochen–Dieks modal interpretation of quantum mechanics,” Brit. J. Phil. Sci. 46, 33–57 (1995).Google Scholar
  12. R. Clifton, “The properties of modal interpretations of quantum mechanics,” Brit. J. Phil. Sci. 47, 371–398 (1996).Google Scholar
  13. D. Dieks, “Resolution of the measurement problem through decoherence of the quantum state,” Phys. Lett. A 142, 439–446 (1989).Google Scholar
  14. 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
  15. D. Dieks, “The modal interpretation of quantum mechanics, measurement and macroscopic behaviour,” Phys. Rev. D 49, 2290–2300 (1994b).Google Scholar
  16. D. Dieks and P. E. Vermaas, eds., The Modal Interpretation of Quantum Mechanics (Kluwer, Dordrecht, 1998).Google Scholar
  17. M. J. Donald, “Discontinuity and continuity of definite properties in the modal interpretation,” in Dieks and Vermaas (1998), pp. 213–222.Google Scholar
  18. 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
  19. 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
  20. B. C. van Fraassen, Quantum Mechanics: An Empiricist View (Clarendon Press, Oxford, 1990).Google Scholar
  21. 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
  22. R. Healey, The Philosophy of Quantum Mechanics: An Interactive Interpretation (Cambridge University Press, Cambridge, 1989).Google Scholar
  23. 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
  24. 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
  25. H. Krips, The Metaphysics of Quantum Theory (Clarendon Press, Oxford, 1987).Google Scholar
  26. L. I. Schiff, Quantum Mechanics, 3rd ed. (McGraw–Hill, New York, 1968).Google Scholar
  27. A. Sudbery, to appear.Google Scholar
  28. W. G. Unruh, private communication, Minneapolis, May 1995.Google Scholar
  29. 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
  30. 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
  31. 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
  32. P. E. Vermaas, A Philosopher's Look at Quantum Mechanics (Cambridge University Press, Cambridge, 1999).Google Scholar
  33. 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
  34. H. D. Zeh, “On the interpretation of measurement in quantum theory,” Found. Phys. 1, 69–76 (1970).Google Scholar
  35. H. D. Zeh, “Toward a quantum theory of observation,” Found. Phys. 3, 109–116 (1973).Google Scholar
  36. 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
  37. W. H. Zurek, “Environment-induced superselection rules,” Phys. Rev. D 26, 1862–1880 (1982).Google Scholar
  38. W. H. Zurek, “Decoherence and the transition from quantum to classical,” Phys. Today 44, 36–44 (1991).Google Scholar
  39. W. H. Zurek, “Reply to criticism,” Phys. Today 46, 84–90 (1993).Google Scholar
  40. W. H. Zurek, S. Habib, and J. P. Paz, “Coherent states via decoherence,” Phys. Rev. Lett. 70, 1187–1190 (1993).Google Scholar
  41. 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

Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • Guido Bacciagaluppi
    • 1
  1. 1.Department of PhilosophyUniversity of California at BerkeleyBerkeleyUSA;

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