The Problem of Hidden Variables in Quantum Mechanics

  • Simon Kochen
  • E. P. Specker
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    Bohm, D., ‘Quantum Theory in Terms of “Hidden” Variables I’, Phys. Rev. 85 (1952), 166–179.CrossRefGoogle Scholar
  2. [2]
    Bohm, D., ‘A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables II’, Phys. Rev. 85 (1952), 180–193.CrossRefGoogle Scholar
  3. [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. [4]
    Broglie, L. de, Non-Linear Wave Mechanics, Elsevier, 1960.Google Scholar
  5. [5]
    Freistadt, H., The Causal Formulation of the Quantum Mechanics of Particles’, Nuovo Cimento Suppl., Ser. 10, 5 (1957), 1–70.Google Scholar
  6. [6]
    Gleason, A., ‘Measures on Closed Subspaces of Hilbert Space’, J. of Math, and Mech. 6 (1957), 885–893.Google Scholar
  7. [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.CrossRefGoogle Scholar
  8. [8]
    Halmos, P., Lectures on Boolean Algebras, Van Nostrand Studies, 1963.Google Scholar
  9. [9]
    Hermann, G., Die naturphilosophischen Grundlagen der Quantenmechanik, Abhandlungen der Fries’schen Schule, 1935.Google Scholar
  10. [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. [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. [12]
    Neumark, M. A., ‘Operatorenalgebren im Hilbertschen Raum’, in Sowjetische Arbeiten zur Funktionalen Analyse, Verlag Kultur and Fortschritt, Berlin, 1954.Google Scholar
  13. [13]
    Pryce, M. H. L., ‘A Modified Perturbation Method for a Problem in Paramagnetism’, Phys. Soc. Proc. A, 63 (1950), 25–29.CrossRefGoogle Scholar
  14. [14]
    Schiff, L., Quantum Mechanics, 2nd ed., McGraw-Hill, 1955.Google Scholar
  15. [15]
    Schwartz, J., ‘The Wiener-Siegel Causal Theory of Quantum Mechanics’, in Integration of Functional, New York University, 1957.Google Scholar
  16. [16]
    Siegel, A., and Wiener, N., ‘The Differential Space of Quantum Theory’, Phys. Rev. 101 (1956).Google Scholar
  17. [17]
    Specker, E., ‘Die Logik nicht gleichzeitig entscheidbarer Aussagen’, Dialectica 14 (1960), 239–246.CrossRefGoogle Scholar
  18. [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.CrossRefGoogle Scholar
  19. [19]
    Neumann, J. von, Mathematical Foundations of Quantum Mechanics, P.V.P., 1955.Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1975

Authors and Affiliations

  • Simon Kochen
    • 1
    • 2
  • E. P. Specker
    • 1
    • 2
  1. 1.Cornell UniversityUSA
  2. 2.Eidgenössische Technische HochschuleZürichSwitzerland

Personalised recommendations