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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
Bohm, D., ‘Quantum Theory in Terms of “Hidden” Variables I’, Phys. Rev. 85 (1952), 166–179.
Bohm, D., ‘A Suggested Interpretation of the Quantum Theory in Terms of “Hidden” Variables II’, Phys. Rev. 85 (1952), 180–193.
Bopp, F., ‘La méchanique quantique est-elle une méchanique statistique classique particulière?’, Ann. L’Inst. H. Poincaré 15 II (1956), 81–112.
Broglie, L. de, Non-Linear Wave Mechanics, Elsevier, 1960.
Freistadt, H., The Causal Formulation of the Quantum Mechanics of Particles’, Nuovo Cimento Suppl., Ser. 10, 5 (1957), 1–70.
Gleason, A., ‘Measures on Closed Subspaces of Hilbert Space’, J. of Math, and Mech. 6 (1957), 885–893.
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.
Halmos, P., Lectures on Boolean Algebras, Van Nostrand Studies, 1963.
Hermann, G., Die naturphilosophischen Grundlagen der Quantenmechanik, Abhandlungen der Fries’schen Schule, 1935.
Kochen, S. and Specker, E., Logical Structures Arising in Quantum Theory, The Theory of Models, 1963 Symposium at Berkeley, pp. 177–189.
Kochen, S. and Specker, E., The Calculus of Partial Propositional Functions, Logic, Methodology and Philosophy of Science, 1964 Congress at Jerusalem, pp. 45–57.
Neumark, M. A., ‘Operatorenalgebren im Hilbertschen Raum’, in Sowjetische Arbeiten zur Funktionalen Analyse, Verlag Kultur and Fortschritt, Berlin, 1954.
Pryce, M. H. L., ‘A Modified Perturbation Method for a Problem in Paramagnetism’, Phys. Soc. Proc. A, 63 (1950), 25–29.
Schiff, L., Quantum Mechanics, 2nd ed., McGraw-Hill, 1955.
Schwartz, J., ‘The Wiener-Siegel Causal Theory of Quantum Mechanics’, in Integration of Functional, New York University, 1957.
Siegel, A., and Wiener, N., ‘The Differential Space of Quantum Theory’, Phys. Rev. 101 (1956).
Specker, E., ‘Die Logik nicht gleichzeitig entscheidbarer Aussagen’, Dialectica 14 (1960), 239–246.
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.
Neumann, J. von, Mathematical Foundations of Quantum Mechanics, P.V.P., 1955.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Communicates by A. M. Gleason
Rights and permissions
Copyright information
© 1975 D. Reidel Publishing Company, Dordrecht, Holland
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive