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Abstract

The issue is to seekquantum interference effects in an arbitrary field, in particular in psychology. For this I invent a digest of quantum mechanics over finite-n-dimensional Hilbert space. In order to match crude data, I use not only von Neumann's mixed states but also a parallel notion of unsharp tests. The mathematically styled text (and earlier work on multibin tests, designated MB) deals largely with these new tests. Quantum psychology itself is only given a foundation. It readily engenders objections; hence I develop its plausibility gradually, in interlocking essays. There is also the empirically definite proposal that (state, test, outcome)-indexed counts be gathered to record data, then fed to a “matrix format” (MF) search for quantum models. A previously proposed experiment in visual perception, which has since failed to find significant quantum correlations, is discussed. The suspicion that quantum mechanics is all around us goes beyond MF, and “Schrödinger's cat” symbolizes this broader perspective.

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References

  • Aharonov, Y., and Susskind, L. (1967a).Physical Review,155, 1428.

    Google Scholar 

  • Aharonov, Y., and Susskind, L. (1967b).Physical Review,158, 1237.

    Google Scholar 

  • Attneave, F. (1971).Scientific American,225, No. 6, December, p. 63 and cover.

    Google Scholar 

  • Bargmann, V. (1964).Journal of Mathematical Physics,5, 862.

    Google Scholar 

  • Birkhoff, G., and von Neumann, J. (1936).Annals of Mathematics,37, 823. Reprinted in von Neumann (1962).

    Google Scholar 

  • Bohr, N. (1934).Atomic Theory and the Description of Nature. Cambridge University Press, Cambridge.

    Google Scholar 

  • Bohr, N. (1950).Science,111, 51.

    Google Scholar 

  • Borges, J. L. (1967).A Personal Anthology. Grove Press, especially “A New Refutation of Time.”

  • Chevalley, C. C. (1946).Theory of Lie Groups: I. Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • Colodny, R. G. (ed.). (1972).Paradigms and Paradoxes. University of Pittsburgh Press; Pittsburgh, Pennsylvania.

    Google Scholar 

  • Dirac, P. A. M. (1947).Quantum Mechanics, Third Edition. Oxford University Press; Oxford.

    Google Scholar 

  • Einstein, A. (1949). InAlbert Einstein Philosopher—Scientist, Vol. II., P. A. Schilpp, ed. Harper & Bros., New York.

    Google Scholar 

  • Einstein, A. (1953).The Meaning of Relativity, Fourth Edition. Princeton University Press, Princeton, New Jersey, especially p. 3.

    Google Scholar 

  • Epstein, S. T. (1960).Nuovo Cimento,X16, 362.

    Google Scholar 

  • Everett, H., III. (1957).Reviews of Modern Physics,29, 454.

    Google Scholar 

  • Finkelstein, D. (1963).Transactions of the New York Academy of Sciences,25, 621.

    Google Scholar 

  • Finkelstein, D., Jauch, J. M., Schiminovich, S., and Speiser, D. (1962).Journal of Mathematical Physics,3, 207.

    Google Scholar 

  • Frazer, W. R. (1966).Elementary Particles, Prentice-Hall, Englewood Cliffs, New Jersey, p. 28.

    Google Scholar 

  • Gardner, M. (1973).Scientific American,229, No. 1, July, p. 104.

    Google Scholar 

  • Giles, R. (1970).Journal of Mathematical Physics,11, 2139.

    Google Scholar 

  • Gleason, A. M. (1953).Journal of Mathematics and Mechanics,6, 885.

    Google Scholar 

  • Gregory, R. L. (1966).Eye and Brain. McGraw-Hill, New York.

    Google Scholar 

  • Gregory, R. L. (1968).Scientific American,219, No. 5, November, p. 66.

    Google Scholar 

  • Greidanus, J. H. (1971).Proceedings Koninklijke Akademie van Wetenschappen Series B,74, 445.

    Google Scholar 

  • Groddeck, G. (1961).The Book of the It, tr. V. M. E. Collins. Knopf and Random House, New York, p. 12.

    Google Scholar 

  • Hegerfeldt, G. C., Kraus, K., and Wigner, E. P. (1968).Journal of Mathematical Physics,9, 2029.

    Google Scholar 

  • Jauch, J. M. (1968).Foundations of Quantum Mechanics. Addison-Wesley, Reading, Massachusetts.

    Google Scholar 

  • Jauch, J. M. (1973).Are Quanta Real? A Galilean Dialogue. Indiana University Press, Bloomington, Indiana.

    Google Scholar 

  • Landau, L. D. (1927).Zeitschrift für Physik,45, 430.

    Google Scholar 

  • Latham, R. E. (1951). Lucretius'The Nature of the Universe. Penguin Classics, Toronto.

    Google Scholar 

  • Lubkin, E. (1960).Nuovo Cimento,X16, 1098.

    Google Scholar 

  • Lubkin, E. (1964).Nuovo Cimento,X32, 171.

    Google Scholar 

  • Lubkin, E. (1968).Bulletin of the American Physical Society II,13, 590.

    Google Scholar 

  • Lubkin, E. (1970).Annals of Physics,56, 69.

    Google Scholar 

  • Lubkin, E. (1971).Bulletin of the American Physical Society II,16, 67.

    Google Scholar 

  • Lubkin, E. (1974a).Journal of Mathematical Physics,15, 663.

    Google Scholar 

  • Lubkin, E. (1974b).Journal of Mathematical Physics,15, 673. MB designates (1974a and b).

    Google Scholar 

  • Lubkin, E. (1976), inFoundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. III, W. L. Harper and C. A. Hooker, eds., Reidel, Dordrecht.

    Google Scholar 

  • Lubkin, E. (1977).Abstracts of Contributed Papers, 8th International Conference on General Relativity and Gravitation, August 7–12, 1977, University of Waterloo, Ontario, Canada, duplicated for the conference by the Faculty of Mathematics.

    Google Scholar 

  • Lubkin, E. (1978).Journal of Mathematical Physics,19, 1028.

    Google Scholar 

  • Lubkin, E., and Lubkin, T. (1979a).Bulletin of the American Physical Society II,24, 54.

    Google Scholar 

  • Lubkin, E., and Lubkin, T. (1979b).Computer Physics Communications,16, 207.

    Google Scholar 

  • Lubkin, E. (1979).International Journal of Theoretical Physics,18, 165.

    Google Scholar 

  • Mackey, G. W. (1963).Mathematical Foundations of Quantum Mechanics. Benjamin, New York.

    Google Scholar 

  • Mielnick, B. (1980).Journal of Mathematical Physics,21, 44.

    Google Scholar 

  • Mirman, R. (1969).Physical Review,186, 1380.

    Google Scholar 

  • Mirman, R. (1970).Physical Review D,1, 3349.

    Google Scholar 

  • Mirman, R. (1979).Foundations of Physics,9, 283.

    Google Scholar 

  • Moravec, H. (1979).Analog XCVIX, No. 2, February, p. 59.

    Google Scholar 

  • Neumann, J. v. (1927).Göttinger Nachrichten, 245, reprinted in von Neumann (1961).

  • Neumann, J. v. (1955).Mathematical Foundations of Quantum Mechanics, tr. R. Beyer. Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • Neumann, J. v. (1961).Logic, Theory of Sets and Quantum Mechanics, Vol. I ofJohn von Neumann, Collected Works. Pergamon Press, New York.

    Google Scholar 

  • Neumann, J. v. (1962).Continuous Geometry and Other Topics, Vol. IV ofJohn von Neumann, Collected Works. Pergamon Press, New York.

    Google Scholar 

  • Rolnick, W. (1967).Physical Review Letters,19, 717.

    Google Scholar 

  • Satir, P. (1961).Scientific American,204, No. 2, February, p. 108.

    Google Scholar 

  • Schrödinger, E. (1935).Naturwissenschaffen,48, 52.

    Google Scholar 

  • Schrödinger, E. (1945).What Is Life? Cambridge University Press and MacMillan, London.

    Google Scholar 

  • Schrödinger, E. (1958).Mind and Matter. Cambridge University Press, Cambridge.

    Google Scholar 

  • Stapp, H. P. (1971).Physical Review D,3, 1303.

    Google Scholar 

  • Stapp, H. P. (1972).American Journal of Physics,40, 1098.

    Google Scholar 

  • Weyl, H. (1928).Zeitschrift für Physik,46, 1.

    Google Scholar 

  • Weyl, H. (1946).The Classical Groups. Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • Weyl, H. (1949).Philosophy of Mathematics and Natural Science. Princeton University Press, Princeton, New Jersey.

    Google Scholar 

  • Wheeler, J. A. (1957).Reviews of Modern Physics,29, 463.

    Google Scholar 

  • Wick, G. C., Wightman, A. S., and Wigner, E. P. (1952).Physical Review,88, 101.

    Google Scholar 

  • Wick, G. C., Wightman, A. S., and Wigner, E. P. (1970).Physical Review D,1, 3267.

    Google Scholar 

  • Wigner, E. P. (1952).Zeitschrift für Physik,133, 101, footnote 2, p. 102.

    Google Scholar 

  • Wigner, E. P. (1959).Group Theory. Academic Press, New York, pp. 233–236.

    Google Scholar 

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Lubkin, E. Schrödinger's cat. Int J Theor Phys 18, 519–600 (1979). https://doi.org/10.1007/BF00670383

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  • DOI: https://doi.org/10.1007/BF00670383

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