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The Problem of Hidden Variables in Quantum Mechanics

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Part of the The University of Western Ontario Series in Philosophy of Science book series (WONS,volume 5a)

Abstract

Forty years after the advent of quantum mechanics the problem of hidden variables, that is, the possibility of imbedding quantum theory into a classical theory, remains a controversial and obscure subject. Whereas to most physicists the possibility of a classical reinterpretation of quantum mechanics remains remote and perhaps irrelevant to current problems, a minority have kept the issue alive throughout this period. (See Freistadt [5] for a review of the problem and a comprehensive bibliography up to 1957.) As far as results are concerned there are on the one hand purported proofs of the non-existence of hidden variables, most notably von Neumann’s proof, and on the other, various attempts to introduce hidden variables such as de Broglie [4] and Bohm [1] and [2]. One of the difficulties in evaluating these contradictory results is that no exact mathematical criterion is given to enable one to judge the degree of success of these proposals.

Keywords

  • Pure State
  • Boolean Algebra
  • Commutative Algebra
  • Hide Variable
  • Hide State

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.

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Bibliography

  1. Bohm, D., ‘Quantum Theory in Terms of “Hidden” Variables I’, Phys. Rev. 85 (1952), 166–179.

    CrossRef  Google Scholar 

  2. Bohm, D., ‘A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables II’, Phys. Rev. 85 (1952), 180–193.

    CrossRef  Google Scholar 

  3. Bopp, F., ‘La méchanique quantique est-elle une méchanique statistique classique particulière?’, Ann. L’Inst. H. Poincaré 15 II (1956), 81–112.

    Google Scholar 

  4. Broglie, L. de, Non-Linear Wave Mechanics, Elsevier, 1960.

    Google Scholar 

  5. Freistadt, H., The Causal Formulation of the Quantum Mechanics of Particles’, Nuovo Cimento Suppl., Ser. 10, 5 (1957), 1–70.

    Google Scholar 

  6. Gleason, A., ‘Measures on Closed Subspaces of Hilbert Space’, J. of Math, and Mech. 6 (1957), 885–893.

    Google Scholar 

  7. Griffith, J. H. E. and Owen, J., ‘Paramagnetic Resonance in the Nickel Tutton Salts’, Proc. Royal Society of London, Ser. A, 213 (1952), 459–473.

    CrossRef  Google Scholar 

  8. Halmos, P., Lectures on Boolean Algebras, Van Nostrand Studies, 1963.

    Google Scholar 

  9. Hermann, G., Die naturphilosophischen Grundlagen der Quantenmechanik, Abhandlungen der Fries’schen Schule, 1935.

    Google Scholar 

  10. Kochen, S. and Specker, E., Logical Structures Arising in Quantum Theory, The Theory of Models, 1963 Symposium at Berkeley, pp. 177–189.

    Google Scholar 

  11. Kochen, S. and Specker, E., The Calculus of Partial Propositional Functions, Logic, Methodology and Philosophy of Science, 1964 Congress at Jerusalem, pp. 45–57.

    Google Scholar 

  12. Neumark, M. A., ‘Operatorenalgebren im Hilbertschen Raum’, in Sowjetische Arbeiten zur Funktionalen Analyse, Verlag Kultur and Fortschritt, Berlin, 1954.

    Google Scholar 

  13. Pryce, M. H. L., ‘A Modified Perturbation Method for a Problem in Paramagnetism’, Phys. Soc. Proc. A, 63 (1950), 25–29.

    CrossRef  Google Scholar 

  14. Schiff, L., Quantum Mechanics, 2nd ed., McGraw-Hill, 1955.

    Google Scholar 

  15. Schwartz, J., ‘The Wiener-Siegel Causal Theory of Quantum Mechanics’, in Integration of Functional, New York University, 1957.

    Google Scholar 

  16. Siegel, A., and Wiener, N., ‘The Differential Space of Quantum Theory’, Phys. Rev. 101 (1956).

    Google Scholar 

  17. Specker, E., ‘Die Logik nicht gleichzeitig entscheidbarer Aussagen’, Dialectica 14 (1960), 239–246.

    CrossRef  Google Scholar 

  18. Stevens, K. W. H., ‘The Spin-Hamiltonian and Line Widths in Nickel Tutton Salts’, Proc. Roy. Soc. of London, Ser. A. 214 (1952), 237–244.

    CrossRef  Google Scholar 

  19. Neumann, J. von, Mathematical Foundations of Quantum Mechanics, P.V.P., 1955.

    Google Scholar 

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Communicates by A. M. Gleason

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© 1975 D. Reidel Publishing Company, Dordrecht, Holland

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Kochen, S., Specker, E.P. (1975). The Problem of Hidden Variables in Quantum Mechanics. In: Hooker, C.A. (eds) The Logico-Algebraic Approach to Quantum Mechanics. The University of Western Ontario Series in Philosophy of Science, vol 5a. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1795-4_17

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  • DOI: https://doi.org/10.1007/978-94-010-1795-4_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-277-0613-3

  • Online ISBN: 978-94-010-1795-4

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