Foundations of Physics Letters

, Volume 4, Issue 3, pp 203–216 | Cite as

Superselection rules and fluctuations in the Many-Hilbert-Spaces approach to quantum measurement

  • Mikio Namiki
  • Saverio Pascazio
Article

Abstract

The interaction between a macroscopic detector and a quantum system is studied by means of a simple model in the context of the Many-Hilbert-Spaces approach, and it is shown that statistical fluctuations play a determinant role in the description of the detector. An order parameter is introduced, in terms of which aquantitative definition of wave-function collapse can be given. The meaning of the superselection charges of the Many-Hilbert-Spaces is also clarified, and an inequivalent representation is given in the limit of infinite number of elementary constituents of the detector. Finally, this approach is compared to other proposals in the literature.

Key words

measurement theory fluctuation interference 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. von Neumann,Die Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932).Google Scholar
  2. 2.
    S. Machida and M. Namiki,Prog. Theor. Phys. 63, 1457 (1980);63, 1833 (1980).Google Scholar
  3. 3.
    S. Machida and M. Namiki, inProceedings of the First International Symposium on the Foundations of Quantum Mechanics, S. Kamefuchiet al., eds. (Physical Society of Japan, Tokyo, 1986), p. 136; M. Namiki,Found. Phys. 18, 29 (1988).Google Scholar
  4. 4.
    K. Hepp,Helv. Phys. Acta 45, 237 (1972).Google Scholar
  5. 5.
    R. Fukuda,Phys. Rev. A35, 8 (1987);A36, 3023 (1987);Prog. Theor. Phys. 81, 34 (1989).Google Scholar
  6. 6.
    S. Kudaka, S. Matsumoto, and K. Kakazu,Prog. Theor. Phys. 82, 665 (1989);Google Scholar
  7. 7.
    M. Namiki,Quantum Mechanics of Macroscopic Systems and Measurement Problem (Kyoritsu Publisher, Tokyo, 1985) (in Japanese).Google Scholar
  8. 8.
    H. Araki,Prog. Theor. Phys. 64, 719 (1980).Google Scholar
  9. 9.
    M. Namiki and S. Pascazio,Phys. Rev. A in press.Google Scholar
  10. 10.
    M. Namiki and S. Pascazio,Phys. Lett. 147A, 430 (1990).Google Scholar
  11. 11.
    J. Summhammer, H. Rauch, and D. Tuppinger,Phys. Rev. A36, 4447 (1987); H. Rauch, inProceedings of the Third International Symposium on the Foundations of Quantum Mechanics, S. Kobayashiet al., eds. (Physical Society of Japan, Tokyo, 1989), p. 3.Google Scholar
  12. 12.
    C. K. Hong, Z. Y. Ou, and L. Mandel,Phys. Rev. Lett. 59, 2044 (1987); Z. Y. Ou and L. Mandel,Phys. Rev. Lett. 61, 54 (1988);62, 2941 (1989).Google Scholar
  13. 13.
    M. Namiki and S. Pascazio, Waseda University preprint WU-HEP-90-15.Google Scholar
  14. 14.
    See, for example, R. A. Webbet al., inProceedings of the Second International Symposium on the Foundations of Quantum Mechanics, M. Namikiet al., eds. (Physical Society of Japan, Tokyo, 1986), p. 193.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Mikio Namiki
    • 1
  • Saverio Pascazio
    • 1
  1. 1.Department of PhysicsWaseda UniversityTokyoJapan

Personalised recommendations