Advertisement

UnfinishedWork: A Bequest

  • Abner Shimony
Chapter
Part of the The Western Ontario Series in Philosophy of Science book series (WONS, volume 73)

The following is a list of projects on which some results have been achieved but are still incomplete. Participants in this Conference and their students and colleagues are invited to carry investigations further: (1) A quantum mechanical limitation upon the possibility of exact measurement due to the existence of additive conserved quantities; (2) The apparent impossibility of achieving a quantum mechanical mixture of definite measurement outcomes by means of a measurement procedure that is reliable or even approximately reliable if the initial state of the object is a superposition of eigenstates with different eigenvalues; (3) The extension to a system of n particles, with n greater than two, of an established complementarity relation between one-particle and two-particle interferometric visibilities in a two-particle system; (4) The refinement and performance of a proposed experiment for testing the hypothesis that the validity of the Pauli Exclusion Principle is a time dependent phenomenon, holding with increasing accuracy with the aging of an ensemble of fermions; (5) The resolution of the conflict between the locality implied by the special theory of relativity and the non-locality exhibited by violations of Bell's Inequalities in entangled quantum mechanical systems.

Keywords

Complete State Pauli Exclusion Principle Standard Quantum Mechanic Fringe Visibility Versus Pair 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E.P. Wigner, “Die Messung quantenmechanischer Operatoren,” Zeitschrift f. Physik 133, 101–108 (1952).zbMATHCrossRefADSMathSciNetGoogle Scholar
  2. 2.
    H. Araki and M. Yanase, “Measurement of quantum mechanical operators,” Physical Review 120, 622–626 (1960).zbMATHCrossRefADSMathSciNetGoogle Scholar
  3. 3.
    H. Stein and A. Shimony, “Limitations on measurement,” in B. d'Espagnat (ed.) Foundations of Quantum Mechanics (Academic, New York/London, 1971), 56–76.Google Scholar
  4. 4.
    A. Shimony and H. Stein, “A problem in Hilbert space theory arising from the quantum theory of measurement,” American Mathematical Monthly 86, 292–293 (1979).zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    E.P. Wigner, “The problem of measurement,” American Journal of Physics 31, 6–15 (1963).zbMATHCrossRefADSMathSciNetGoogle Scholar
  6. 6.
    A. Shimony, “Approximate measurement in quantum mechanics—II,” Physical Review D 9, 2321–2323 (1974). Reprinted in Search for a Naturalistic World View, vol. 2 (Cambridge University Press, Cambridge, UK, 1993), 41–47.CrossRefADSGoogle Scholar
  7. 7.
    H. Stein, “Maximal extension of an impossibility theorem concerning quantum measurement,” in R.S. Cohen, M. Horne, and J. Stachel (eds.) Potentiality, Entanglement and Passion-at-a-Distance (Kluwer Academic, Dordrecht/Boston/London, 1997), 231–243. Theoretical Physics 64, 719 (1980).Google Scholar
  8. 8.
    P. Busch, P. Lahti, and P. Mittelstaedt, The Quantum Theory of Measurement, 2nd ed. (Springer, Berlin-Heidelberg, 1996), 6.zbMATHGoogle Scholar
  9. 9.
    P. Busch and A. Shimony, “Insolubility of the quantum measurement problem for unsharp observables,” Studies in the History and Philosophy of Modern Physics 27B, 399 (1997).Google Scholar
  10. 10.
    S. Machida and M. Namiki, “Theory of measurement of quantum mechanics—mechanism of reduction of wave packet” I, II, Progress in Theoretical Physics 63, 1457–1473, 1833– 1843 (1980).CrossRefADSGoogle Scholar
  11. 11.
    H. Araki, “A remark on Machida-Namiki theory of measurement,” Progress in Theoretical Physics 64, 719–730 (1980).zbMATHADSMathSciNetGoogle Scholar
  12. 12.
    M. Namiki and S. Pascazio “Quantum theory of measurement based on the many-Hilbert-space approach,” Physics Reports 232, 302–411 (1993).CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    R.B. Griffiths, Consistent Quantum Theory (Cambridge University Press, Cambridge, UK, 2002).zbMATHGoogle Scholar
  14. 14.
    R. Omnès, Quantum Philosophy (Princeton University Press, Princeton, NJ, 1999).Google Scholar
  15. 15.
    M.A. Horne, A. Shimony, and A. Zeilinger, “Two particle interferometry,” Physical Review Letters 62, 2209–2212 (1988).CrossRefADSGoogle Scholar
  16. 16.
    A.F. Abouraddy, M.B. Nasr, B.E.A. Saleh, A.V. Sergienko, and M.C. Teich, “Demonstration of the complementarity of one- and two-photon interference,” Physical Review A 63, 8031– 8036 (2001).CrossRefGoogle Scholar
  17. 17.
    R.B. Griffiths, Consistent Quantum Theory (Cambridge University Press, Cambridge, UK, 2002), 85.zbMATHGoogle Scholar
  18. 18.
    G. Jaeger, A. Shimony, and L. Vaidman, “Two interferometric complementarities,” Physical Review A 51, 63 (1995).CrossRefADSGoogle Scholar
  19. 19.
    M. Horne, “Complementarity of fringe visibilities in three-particle quantum mechanics,” in D. Greenberger, W. Reiter, and A. Zeilinger (eds.) Epistemological and Experimental Perspectives on Quantum Physics (Kluwer Academic, Dordrecht/Boston/London, 1999), 211–219.Google Scholar
  20. 20.
    E. Corinaldesi, “Model of a dynamical theory of the Pauli Principle,” Supplemento al Nuovo Cimento serie I 5, 937–943 (1967).Google Scholar
  21. 21.
    A. Shimony, “Proposed experiment to test the possible time dependence of the onset of the Pauli Exclusion Principle,” Quantum Information Processing 5, 277–286 (2006).zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    W. Pauli, “The connection between spin and statistics,” Physical Review 58, 716–722 (1940).zbMATHCrossRefADSGoogle Scholar
  23. 23.
    J.S. Bell, “On the Einstein-Podolsky-Rosen Paradox,” Physics 1, 195–200 1964. Reprinted in J.S. Bell, Speakable and Unspeakable in Quantum Mechanics, 2nd ed. (Cambridge University Press, Cambridge, UK, 2004), 14–21.Google Scholar
  24. 24.
    J. Clauser, M.A. Horne, A. Shimony, and R.A. Holt, Proposed experiment to test local hidden-variable theories,” Physical Review Letters 23, 880–884 (1969).CrossRefADSGoogle Scholar
  25. 25.
    J.S. Bell, “The theory of local beables,” in Speakable and Unspeakable in Quantum Mechanics, 2nd ed. (Cambridge University Press, Cambridge, UK, 2004), 56–57, 64–65.Google Scholar
  26. 26.
    J. Jarrett, “On the physical significance of the locality conditions in the Bell arguments,” Noû s 18, 569 (1984).CrossRefMathSciNetGoogle Scholar
  27. 27.
    N. Gisin, “Bell's inequality holds [note: should read “is violated”] for all non-product states,” Physics Letters A 154, 201–202 (1991).CrossRefADSMathSciNetGoogle Scholar
  28. 28.
    S. Popescu and D. Rohrlich, “Generic quantum nonlocality,” Physics Letters A 166, 293–297 (1992).CrossRefADSMathSciNetGoogle Scholar
  29. 29.
    P. Eberhard, “Bell's theorem and the different conceptions of locality,” Nuovo Cimento B 46, 392–419 (1978).CrossRefADSMathSciNetGoogle Scholar
  30. 30.
    G.-C. Ghirardi, A. Rimini, and T. Weber, “A general argument against super-luminal transmission through the quantum mechanical measurement process,” Lettere al Nuovo Cimento 27, 293–298 (1980).CrossRefMathSciNetGoogle Scholar
  31. 31.
    D. Page, “The Einstein-Podolsky-Rosen physical reality is completely described by quantum mechanics,” Physics Letters A 91, 57–60 (1982).CrossRefADSMathSciNetGoogle Scholar
  32. 32.
    J. S. Bell, “La Nouvelle Cuisine,” in Speakable and Unspeakable in Quantum Mechanics, 2nd ed. (Cambridge University Press, Cambridge, UK, 2004).Google Scholar
  33. 33.
    M. Heller, “Cosmological singularity and the creation of the universe,” Zygon 35, 665–685 (2000); M. Heller, W. Sasin, and D. Lambert, “Groupoid approach to noncommutative quantization of gravity,” Journal of Mathematical Physics 38, 5840–5853 (1997).CrossRefGoogle Scholar
  34. 34.
    A. Connes, Noncommutative Geometry (Academic, New York, 1994).zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V 2009

Authors and Affiliations

  • Abner Shimony

There are no affiliations available

Personalised recommendations