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.
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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.
G. Bacciagaluppi, “Kochen–Specker theorem in the modal interpretation of quantum mechanics,” Internat. J. Theoret. Phys. 34, 1206–1215 (1995).
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).
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).
G. Bacciagaluppi and M. Hemmo, “Modal interpretations, decoherence and measurements,” Studies in History and Philosophy of Modern Physics 27, 239–277 (1996).
J. Bub, “Quantum mechanics without the projection postulate,” Found. Phys. 22, 737–754 (1992).
A. O. Caldeira and A. J. Leggett, “Path integral approach to quantum Brownian motion,” Physica A 121, 587–616 (1983).
R. Clifton, “Independently motivating the Kochen–Dieks modal interpretation of quantum mechanics,” Brit. J. Phil. Sci. 46, 33–57 (1995).
R. Clifton, “The properties of modal interpretations of quantum mechanics,” Brit. J. Phil. Sci. 47, 371–398 (1996).
D. Dieks, “Resolution of the measurement problem through decoherence of the quantum state,” Phys. Lett. A 142, 439–446 (1989).
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.
D. Dieks, “The modal interpretation of quantum mechanics, measurement and macroscopic behaviour,” Phys. Rev. D 49, 2290–2300 (1994b).
D. Dieks and P. E. Vermaas, eds., The Modal Interpretation of Quantum Mechanics (Kluwer, Dordrecht, 1998).
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.
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.
B. C. van Fraassen, Quantum Mechanics: An Empiricist View (Clarendon Press, Oxford, 1990).
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).
R. Healey, The Philosophy of Quantum Mechanics: An Interactive Interpretation (Cambridge University Press, Cambridge, 1989).
E. Joos and H. D. Zeh, “The emergence of classical properties through interaction with the environment,” Z. Physik B 59, 223–243 (1985).
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.
H. Krips, The Metaphysics of Quantum Theory (Clarendon Press, Oxford, 1987).
L. I. Schiff, Quantum Mechanics, 3rd ed. (McGraw–Hill, New York, 1968).
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).
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).
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).
P. E. Vermaas, A Philosopher's Look at Quantum Mechanics (Cambridge University Press, Cambridge, 1999).
P. E. Vermaas and D. Dieks, “The modal interpretation of quantum mechanics and its generalization to density operators,” Found. Phys. 25, 145–158 (1995).
H. D. Zeh, “On the interpretation of measurement in quantum theory,” Found. Phys. 1, 69–76 (1970).
H. D. Zeh, “Toward a quantum theory of observation,” Found. Phys. 3, 109–116 (1973).
W. H. Zurek, “Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse?,” Phys. Rev. D 24, 1516–1525 (1981).
W. H. Zurek, “Environment-induced superselection rules,” Phys. Rev. D 26, 1862–1880 (1982).
W. H. Zurek, “Decoherence and the transition from quantum to classical,” Phys. Today 44, 36–44 (1991).
W. H. Zurek, “Reply to criticism,” Phys. Today 46, 84–90 (1993).
W. H. Zurek, S. Habib, and J. P. Paz, “Coherent states via decoherence,” Phys. Rev. Lett. 70, 1187–1190 (1993).
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.
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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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DOI: https://doi.org/10.1023/A:1026453817453