Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-25T18:53:10.924Z Has data issue: false hasContentIssue false
  • English
  • Français

Epr, Bell, and Collapse: A Route Around “Stochastic” Hidden Variables

Published online by Cambridge University Press:  01 April 2022

Geoffrey Hellman
Geoffrey Hellman*
Affiliation:
Department of Philosophy, Indiana University
Get access Rights & Permissions [Opens in a new window]

Abstract

Two EPR arguments are reviewed, for their own sake, and for the purpose of clarifying the status of “stochastic“ hidden variables. The first is a streamlined version of the EPR argument for the incompleteness of quantum mechanics. The role of an anti-instrumentalist (“realist”) interpretation of certain probability statements is emphasized. The second traces out one horn of a central foundational dilemma, the collapse dilemma; complex modal reasoning, similar to the original EPR, is used to derive determinateness (of all spin components of two spin-½ particles in the singlet state) from just (a form of) weak locality, result definiteness, and an assumption on propensities based on conservation. Theories meeting these conditions are therefore constrained by the Bell inequalities. Neither controversial assumptions of “strong locality” (“factorability”) nor of determinism are employed in the derivation. The categories of “stochastic hidden variables” are then analyzed; one can focus on “quasi-definite” theories, without loss of generality. A means of excluding these is proposed, based on a demand that certain ideal cases be accurately treated. Theorems from quantum measurement theory, sometimes cited as showing that such cases are not physically possible, are found inapplicable.

Type
Research Article
Information
Philosophy of Science , Volume 54 , Issue 4 , December 1987 , pp. 558 - 576
Copyright
Copyright © 1987 by the Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

I am grateful to Harvey Brown, Jeffrey Bub, Michael Friedman, and Michael Redhead for helpful discussion of an earlier version of this paper, and to Arthur Fine and Abner Shimony for helpful correspondence.

References

Aharonov, Y., and Albert, D. (1980), “States and Observables in Relativistic Quantum Field Theories”, Physical Review D 21: 3316–3324.CrossRefGoogle Scholar
Araki, H., and Yanase, M. (1961), Physical Review 129: 940.Google Scholar
Aspect, A.; Dalibard, J.; and Roger, G. (1982), “Experimental Test of Bell's Inequalities Using Time-Varying Analyzers”, Physical Review Letters 49: 1804–1807.CrossRefGoogle Scholar
Belinfante, F. J. (1973), A Survey of Hidden Variables Theories. Oxford: Pergamon.Google Scholar
Bell, J. S. (1964), “On the Einstein Podolsky Rosen Paradox”, Physics 1: 195–200.CrossRefGoogle Scholar
Bell, J. S. (1971), “Introduction to the Hidden Variables Question”, in d'Espagnat, B. (ed.), Foundations of Quantum Mechanics. New York: Academic Press, pp. 171–181.Google Scholar
Bohm, D. (1951), Quantum Theory. Englewood Cliffs, N.J.: Prentice Hall.Google Scholar
Clauser, J. F., and Horne, M. A. (1974), “Experimental Consequences of Objective Local Theories”, Physical Review D 10: 526–535.CrossRefGoogle Scholar
Clauser, J. F., and Shimony, A. (1978), “Bell's Theorem: Experimental Tests and Implications”, Reports on Progress in Physics 41: 1881–1927.CrossRefGoogle Scholar
Eberhard, P. H. (1977), “Bell's Theorem Without Hidden Variables”, Il Nuovo Cimento 38B: 75–80.
Einstein, A. (1948), “Quantenmechanik und Wirklichkeit”, Dialectica 2: 320–324.CrossRefGoogle Scholar
Einstein, A.; Podolsky, B.; and Rosen, N. (1935), “Can the Quantum-Mechanical Description of Physical Reality Be Considered Complete?”, Physical Review 47: 777–780.CrossRefGoogle Scholar
d'Espagnat, B. (1975), “Use of Inequalities for the Experimental Test of a General Conception of the Foundations of Microphysics”, Physical Review D 11: 1424–1435.CrossRefGoogle Scholar
Fine, A. (1969), “On the General Quantum Theory of Measurement”, Proceedings of the Cambridge Philosophical Society 65: 111–122.CrossRefGoogle Scholar
Fine, A. (1981a), “Correlations and Physical Locality”, in Giere, R. N. and Asquith, P. D. (eds.), Philosophy of Science Association Proceedings 1980, vol. 2. East Lansing, Mich.: Philosophy of Science Association, pp. 535–562.Google Scholar
Fine, A. (1981b), “Einstein's Critique of Quantum Theory: The Roots and Significance of EPR”, in Barker, P. and Shugart, C. (eds.), After Einstein. Memphis: Memphis State University Press, pp. 147–158.Google Scholar
Hellman, G. (1982), “Stochastic Einstein-Locality and the Bell Theorems”, Synthese 53: 461–504.CrossRefGoogle Scholar
Jarrett, J. (1984), “On the Physical Significance of the Locality Conditions in the Bell Arguments”, Noûs 18: 569–589.CrossRefGoogle Scholar
Malin, S. (1982), “Observer Dependence of Quantum States in Relativistic Quantum Field Theories”, Physical Review D 26: 1330–1334.CrossRefGoogle Scholar
Pascazio, S. (1985), “A Careful Estimation of Photon Rescattering in Atomic Cascade Experimental Tests of Bell's Inequality”, Il Nuovo Cimento 5D: 23–39.CrossRefGoogle Scholar
Redhead, M. (1982), “Nonlocality and Peaceful Coexistence”, in Swinburne, R. (ed.), Space, Time, and Causality. Dordrecht: Reidel, pp. 151–189.Google Scholar
Selleri, F. (1982) “Generalized EPR-Paradox”, Foundations of Physics 12: 645–659.CrossRefGoogle Scholar
Shimony, A. (1981), “Critique of the Papers of Fine and Suppes”, in Giere, R. N. and Asquith, P. D. (eds.), Philosophy of Science Association Proceedings 1980, vol. 2. East Lansing, Mich.: Philosophy of Science Association, pp. 572–580.Google Scholar
Stalnaker, R. C. (1968), “A Theory of Conditionals”, in W. L. Harper, R. Stalnaker, and G. Pearce (eds.) (1980), Ifs. Dordrecht: Reidel, pp. 41–55.CrossRefGoogle Scholar
Stapp, H. P. (1971), “S-Matrix Interpretation of Quantum Theory”, Physical Review D 3: 1303–1320.CrossRefGoogle Scholar
Stein, H., and Shimony, A. (1971), “Limitations on Measurement”, in d'Espagnat, B. (ed.), Foundations of Quantum Mechanics. New York: Academic Press, pp. 55–76.Google Scholar
Suppes, P., and Zanotti, M. (1976), “On the Determinism of Hidden Variable Theories with Strict Correlation and Conditional Statistical Independence of Observables”, in Suppes, P. (ed.), Logic and Probability in Quantum Mechanics. Dordrecht: Reidel, pp. 445–455.CrossRefGoogle Scholar
Wessels, L. (1981), “The ‘EPR’ Argument: A Post-Mortem”, Philosophical Studies 40: 3–30.CrossRefGoogle Scholar
Wessels, L. (1985), “Locality, Factorability, and the Bell Inequalities”, Noûs 19: 481–519.CrossRefGoogle Scholar
Wigner, E. P. (1952), “Die Meussung Quantenmechanischer Operatoren”, Zeitschrift Für Physik 133: 101–108.CrossRefGoogle Scholar
Wigner, E. P. (1970), “On Hidden Variables and Quantum Mechanical Probabilities”, American Journal of Physics 38: 1005–1009.CrossRefGoogle Scholar