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Quantum Logic and the Interpretation of Quantum Mechanics

Published online by Cambridge University Press:  28 February 2022

R.I.G. Hughes
R.I.G. Hughes*
Affiliation:
Princeton University
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Extract

There is no such thing as “The Quantum Logical Interpretation of Quantum Mechanics”. Rather, there is a cluster of interpretations, all of which can be described as “quantum logical”. Here I provide a general framework for discussing interpretations of this kind, and then locate various suggestions within it. The presentation owes much to van Fraassen (see, in particular, van Fraassen 1974 ); his “modal interpretation” is one of those I discuss, along with those of Jauch, Putnam and Kochen. I begin by rehearsing some orthodox quantum theory.

Within quantum mechanics we deal with a set 0 of measurable quantities, or observables (position, momentum, components of spin and so on). Experiment can determine the value of an observable for a given system: the values so determined will be real numbers. A maximal amount of information about what the result would be for a given system, whatever experiment we chose to perform on it, is available once we know the state of the system.

Type
Part II. Quantum Logic and the Interpretation of Quantum Mechanics
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1980 , Issue 1: Volume One: Contributed Papers 1980 , 1980 , pp. 55 - 67
Copyright
Copyright © 1980 by the Philosophy of Science Association

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Footnotes

1

I would like to thank Ed Levy and Bas van Fraassen for their comments on a previous draft of this paper.

References

Bub, J. (1974). The Interpretation of Quantum Mechanics. (University of Western Ontario Series in Philosophy of Science, Vol. 3.) Dordrecht, Holland: Reidel.Google Scholar
Demopoulos, W. (1974). “What is the Logical Interpretation of Quantum Mechanics?” In PSA 1974: Proceedings of the 1974 Biennial Meeting of the Philosophy of Science Association. Edited by Cohen, R.S. et al. Boston: Reidel. Pages 721-28.Google Scholar
Einstein, A., Podolsky, B. and Rosen, N. (1935). “Can Quantum Mechanical Description of Physical Reality be Considered Complete?” Physical Review 47: 777–80.CrossRefGoogle Scholar
Fano, G. (1971). Mathematical Methods of Quantum Mechanics. New York: McGraw Hill.Google Scholar
Friedman, M. and Glymour, C. (1972). “If Quanta Had Logic.” Journal of Philosophical Logic 1: 16–29.CrossRefGoogle Scholar
Healey, R. (1979). “Quantum Realism: Naivete is no Excuse.” Synthese 42: 121–44.CrossRefGoogle Scholar
Heelan, P. (1970). “Quantum and Classical Logic: Their Respective Roles.” Synthese 21: 2–33.CrossRefGoogle Scholar
Holland, S.S. Jr., (1970). “The Current Interest in Orthomodular Lattices.” In Trends in Lattice Theory. Edited by Abbott, J.C. New York: Van Nostrand. Pages 41–116.Google Scholar
Hughes, R.I.G. (1980). “Realism and Quantum Logic.” In Proceedings of the Erice Workshop on Quantum Logic. Edited by Beltrametti, E. et al. London: Plenum Press. In Press.Google Scholar
Jauch, J.M. (1968). Foundations of Quantum Mechanics. Reading, MA: Addison Wesley.Google Scholar
Kochen, S. and Specker, E.P. (1965). “Logical Structures Arising in Quantum Theory.” In Symposium on the Theory of Models. Edited by Addison, J. et al. Amsterdam: North Holland. Pages 177–189.Google Scholar
Kochen, S. and Specker, E.P. (1967). “The Problem of Hidden Variables in Quantum Mechanics.” Journal of Mathematics and Mechanics 17: 59–87.Google Scholar
Kochen, S. and Specker, E.P. (1979). “The Interpretation of Quantum Mechanics.” Unpublished Manuscript.Google Scholar
Putnam, H. (1969). “Is Logic Empirical?” In Proceedings of the Boston Colloquium for the Philosophy of Science. 1966/1968. (Boston Studies in the Philosophy of Science. Vol. V.) Edited by Cohen, R.S. and Wartofsky, M.. Boston: Reidel. Pages 216–241.Google Scholar
Teller, P. (1979). “Quantum Mechanics and the Nature of Continuous Physical Quantities.” Journal of Philosophy 76: 346–61.CrossRefGoogle Scholar
van Fraassen, B.C. (1972). “A Formal Approach to the Philosophy of Science.” In Paradigms and Paradoxes: the Philosophical Challenge of the Quantum Domain. (University of Pittsburgh Series in the Philosophy of Science, Vol. 5.) Edited by Colodny, R. Pittsburgh: University of Pittsburgh Press. Pages 303–366.Google Scholar
van Fraassen, B.C. (1973). “Semantic Analysis of Quantum Logic.” In Contemporary Research in the Foundations and Philosophy of Quantum Theory. (University of Western Ontario Series in Philosophy of Science, Vol. 2.) Edited by Hooker, C.A. Dordrecht, Holland: Reidel. Pages 80–113.Google Scholar
van Fraassen, B.C. (1974). “The Einstein-Pololski-Rosen Paradox.” Synthese 29: 291–309.CrossRefGoogle Scholar
von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik. Berlin: Springer. (Translated by R.T. Beyer as The Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press, 1955.)Google Scholar