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Unbounded Operators and the Incompleteness of Quantum Mechanics

Published online by Cambridge University Press:  01 April 2022

Adrian Heathcote
Adrian Heathcote*
Affiliation:
Department of Philosophy, Australian National University
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Abstract

A proof is presented that a form of incompleteness in Quantum Mechanics follows directly from the use of unbounded operators. It is then shown that the problems that arise for such operators are not connected to the non-commutativity of many pairs of operators in Quantum Mechanics and hence are an additional source of incompleteness to that which allegedly flows from the EPR paradox. Finally, it will be argued that the problem is not amenable to some simple solutions that will be considered.

Type
Discussion
Information
Philosophy of Science , Volume 57 , Issue 3 , September 1990 , pp. 523 - 534
Copyright
Copyright © 1990 by the Philosophy of Science Association

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Footnotes

†

I wish to express my gratitude to Alan Carey for lengthy correspondence on the subject of this paper; also to the two anonymous referees of this journal whose comments led to a significant improvement of the argument.

References

Dirac, P. A. M. (1930), The Principles of Quantum Mechanics. Oxford: Oxford University Press.Google Scholar
Einstein, A., Podolsky, B. and Rosen, N. (1935), “Can Quantum-Mechanical Description of Reality be Considered Complete?”, Physical Review 47: 777–780. Also in S. Toulmin (ed.), 1970.CrossRefGoogle Scholar
Emch, G. C. (1972), Algebraic Methods in Statistical Mechanics and Quantum Field Theory. New York: Interscience.Google Scholar
Emch, G. C. (1984), Mathematical and Conceptual Foundations of 20th Century Physics. Amsterdam: North Holland.Google Scholar
Geroch, R. (1985), Mathematical Physics. Chicago: University of Chicago Press.Google Scholar
Glimm, J. and Jaffe, A. (1985), Quantum Field Theory and Statistical Mechanics. Berlin: Birkhauser.Google Scholar
Jauch, J. M. (1968), Foundations of Quantum Mechanics. Reading: Addison-Wesley.Google Scholar
Jauch, J. M. (1972), “On Bras and Kets”, in A. Salam and E. P. Wigner (eds.), Aspects of Quantum Theory. Cambridge: Cambridge University Press.Google Scholar
Mackey, G. W. (1963), The Mathematical Foundations of Quantum Mechanics. New York: W. A. Benjamin.Google Scholar
Naimark, M. A. (1960), Normed Rings. Groningen: P. Noordhoff N.V.Google Scholar
Reed, M. and Simon, B. (1972), Methods of Modern Mathematical Physics Vol. I. Functional Analysis. New York: Academic Press.Google Scholar
Reed, M. and Simon, B. (1975), Methods of Modern Mathematical Physics Vol. II. Fourier Analysis, Self-Adjointness. New York: Academic Press.Google Scholar
Stein, H. and Shimony, A. (1971), “Limitations on Measurement”, in B. d'Espagnat (ed.), Proceedings of the International School of Physics; “Enrico Fermi”. New York: Academic Press.Google Scholar
Toulmin, S. (ed.) (1970), Physical Reality. New York: Harper Row.Google Scholar
Wigner, E. P. (1973), “Epistemological Perspective on Quantum Theory”, in C. Hooker (ed.), Contemporary Research in the Foundations and Philosophy of Quantum Theory. Dordrecht: D. Reidel.Google Scholar