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Towards a Revised Probabilistic Basis for Quantum Mechanics

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Part of the book series: Synthese Library ((SYLI,volume 78))

Abstract

Quantum mechanics (QM) supplies quantitative probabilities for the occurrences of physically significant events. Historically the probabilistic interpretation of the Schrödinger wave function arose almost as an afterthought. When Schrödinger proposed his equation for the wave function Ψ he had an electromagnetic analogy in mind (Jammer, 1966). When Born (1926) suggested that Ψ be given a probabilistic interpretation he only related probability to |Ψ|2 in a remark added in proof. The curious origins of the probability interpretation notwithstanding, Born’s suggestion quickly took virtually unchallenged hold throughout physics. The famous challenges by Einstein were not to a probabilistic interpretation for Ψ but rather to the completeness of the description of physical reality offered by QM (Einstein et al., 1935).

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References

  • Arthurs, E. and Kelly, J. L., Jr., ‘On the Simultaneous Measurement of a Pair of Conjugate Observables’, Bell Systems Technical Journal 44 (1965), 725–729.

    Article  Google Scholar 

  • Benioff, P., ‘Some Aspects of the Relationship Between Mathematical Logic and Physics, I’, Journal of Mathematical Physics 11 (1970) 2553–2569.

    Article  Google Scholar 

  • Benioff, P., ‘Some Aspects of the Relationship Between Mathematical Logic and Physics, II’, Journal of Mathematical Physics 12 (1971), 360–376.

    Article  Google Scholar 

  • Birkhoff, G. and von Neumann, J., ‘The Logic of Quantum Mechanics’, Annals of Mathematics 37 (1936), 823–843.

    Article  Google Scholar 

  • Born, M., ‘Zur Quantenmechanik den Stosvorgange’, Zeitschrift für Physik 37 (1926), 865.

    Article  Google Scholar 

  • Born, M., Natural Philosophy of Cause and Chance, Dover, New York, 1964.

    Google Scholar 

  • Born, M., Born-Einstein Letters, Walker, New York, 1971.

    Google Scholar 

  • Einstein, A., Podolsky, B., and Rosen, N., ‘Can Quantum-Mechanical Description of Physical Reality Be Considered Complete’, Physical Review 47 (1935), 777–780.

    Article  Google Scholar 

  • Feynman, R., Leighton, R., and Sands, M., The Feynman Lectures on Physics, I, Addison-Wesley, Reading, Mass., 1963.

    Google Scholar 

  • Fine, T., Theories of Probability, Academic Press, New York, 1973.

    Google Scholar 

  • Foulis, D. J. and Randall, C. H., ‘Operational Statistics’, Journal of Mathematical Physics 13 (1972), 1667–1675.

    Article  Google Scholar 

  • Gordon, J. P. and Louisell, W. H., ‘Simultaneous Measurement of Noncommuting Observables’, in P. L. Kelley, B. Lax, and P. E. Tannewald (eds.), Physics of Quantum Electronics, McGraw-Hill, New York, 1966.

    Google Scholar 

  • Helstrom, C. W. and Kennedy, R. S., Noncommuting Observables in Quantum Detection and Estimation Theory’, IEEE Transactions on Information Theory IT-20 (1974), 16–24.

    Article  Google Scholar 

  • Jammer, M., The Conceptual Development of Quantum Mechanics, McGraw-Hill, New York, 1966.

    Google Scholar 

  • Jauch, J. M., Foundations of Quantum Mechanics, Addison-Wesley, Reading, Mass., 1968.

    Google Scholar 

  • Kaplan, M. A., Extensions and Limits of Comparative Probability Orders, Unpublished Ph.D. dissertation, Cornell University, Ithaca, N. Y., 1973.

    Google Scholar 

  • Kolmogorov, A., Foundations of the Theory of Probability, Chelsea, New York, 1956.

    Google Scholar 

  • Kraft, C., Pratt, J., and Seidenberg, A., ‘Intuitive Probability of Finite Sets’, Annals of Mathematical Statistics 30 (1959), 780–786.

    Article  Google Scholar 

  • Krantz, D., Luce, R., Suppes, P., and Tversky, A., Foundations of Measurement, I, Academic Press, New York, 1971.

    Google Scholar 

  • Messiah, A., Quantum Mechanics, North-Holland, Amsterdam, 1962.

    Google Scholar 

  • Popper, K., ‘The Propensity Interpretation of Probability’, British Journal of Philosophical Science 10 (1959), 25–42.

    Article  Google Scholar 

  • Renyi, A., Foundations of Probability, Holden-Day, San Francisco, 1970.

    Google Scholar 

  • She, C. Y. and Heffner, H., ‘Simultaneous Measurement of Noncommuting Observables’, Physical Review 152 (1966), 1103–1110.

    Article  Google Scholar 

  • Suppes, P., ‘Probability Concepts in Quantum Mechanics’, Philosophy of Science 28 (1961), 378–389.

    Article  Google Scholar 

  • Suppes, P., ‘The Probabilistic Argument for a Non-Classical Logic of Quantum Mechanics’, Philosophy of Science 33 (1966), 14–21.

    Article  Google Scholar 

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© 1976 Springer Science+Business Media Dordrecht

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Fine, T.L. (1976). Towards a Revised Probabilistic Basis for Quantum Mechanics. In: Suppes, P. (eds) Logic and Probability in Quantum Mechanics. Synthese Library, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9466-5_9

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  • DOI: https://doi.org/10.1007/978-94-010-9466-5_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-277-1200-4

  • Online ISBN: 978-94-010-9466-5

  • eBook Packages: Springer Book Archive

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