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The Infinite Apparatus in the Quantum Theory of Measurement

Published online by Cambridge University Press:  31 January 2023

Don Robinson
Don Robinson*
Affiliation:
University of Toronto
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Extract

It has been suggested that the measuring apparatus used to measure quantum systems ought to be idealized as consisting of an infinite number of quantum systems. Let us call this the infinity assumption. The suggestion that we ought to make the infinity assumption has been made in connection with two closely related but distinct problems. One is the problem of determining the importance of the limitations on measurement incorporated into the Wigner-Araki-Yanase quantum theory of measurement. The other is the measurement problem. These problems are not internal to the quantum mechanical formalism. They arise when we obtain particular formal results in applying the quantum mechanical formalism to measurement interactions. The formal results are problematic because they resist explanation. Various authors have claimed that by making the infinity assumption we can neglect the limitations on measurement. Bub (1988) and (1989) claims it allows us to solve the measurement problem. I will argue that both claims are unjustified.

Type
Part IV. Quantum Theory
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1990 , Issue 1: Volume One: Contributed Papers 1990 , 1990 , pp. 251 - 261
Copyright
Copyright © Philosophy of Science Association 1990

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Footnotes

1

I would like to thank Linda Wessels and Michael Lavin for helpful comments on an earlier draft of this paper.

References

Araki, H. (1986), “A Continuous Superselection Rule as a Model of Classical Measuring Apparatus in Quantum Mechanics”, in Gorini, V. and Frigerio, A. (eds.) Fundamental Aspects of Quantum Theory New York: Plenum Press.Google Scholar
Araki, H. (1987), “On Superselection Rules”, in Namiki, M. et al. (eds.) Proceedings of the Second International Symposium on Quantum Mechanics Tokyo: Physical Society of Japan.Google Scholar
Araki, H. and Yanase, M. (1960), “Measurement of Quantum Mechanical Operators”, Physical Review 120: 622–626, reprinted in Wheeler and Zurek (eds.) (1983) pp. 707-711.CrossRefGoogle Scholar
Ballentine, L.E. (1970), “The Statistical Interpretation of Quantum Mechanics”, Reviews of Modern Physics 42: 358–381.CrossRefGoogle Scholar
Belinfante, F.J. (1975) Measurements and Time-Reversal in Objective Quantum Theory. New York: Pergamon Press.Google Scholar
Bub, J. (1988), “From Micro to Macro: A Solution to the Measurement Problem”, in Fine, A. and Leplin, J. (eds.) PSA 1988, Volume 2. East Lansing: Philosophy of Science Association, pp. 134–144.Google Scholar
Bub, J. (1989), “On the Measurement Problem of Quantum Mechanics” in Kafatos, M. (ed.) Bell’s Theorem, Quantum Theory, and Conceptions of the Universe. Boston: Kluwer.Google Scholar
Daneri, A., Loinger, A., and Prosperi, G. (1962), “Quantum Theory of Measurement and Ergodicity Conditions”, Nuclear Physics 33: 297–319.CrossRefGoogle Scholar
Fine, A. (1969) “On the General Quantum Theory of Measurement”, Proceedings of the Cambridge Philosophical Society 65: 111–122.CrossRefGoogle Scholar
Hellman, G. (1987), “EPR, Bell, and Collapse: A Route Around Stochastic Hidden Variables”, Philosophy of Science 54: 558–576.CrossRefGoogle Scholar
Machida, S. and Namiki, M. (1984), “Macroscopic Nature of Detecting Apparatus and Reduction of the Wave Packet”, in Kamefuchi, S. et al. (eds.) Foundations of Quantum Mechanics in the Light of New Technology. Tokyo: Physical Society of Japan.Google Scholar
Sewell, G.L. (1986), Quantum Theory of Collective Phenomena. Oxford: Clarendon Press.Google Scholar
Stein, H. and Shimony, A. (1971), “Limitations on Measurement”, in D’Espagnat, B. (ed.), Foundations of Quantum Mechanics. New York: Academic Press, pp. 56–76.Google Scholar
Wheeler, J and Zurek, W. (1983), Quantum Theory and Measurement. Princeton: Princeton University Press.CrossRefGoogle Scholar
Wigner, E. (1952), “Die Messung quantenmechanischer Operatoren”, Zeitschrift fur Physik 133: 101–108.CrossRefGoogle Scholar
Wigner, E. (1983), “Interpretation of Quantum Mechanics”, in Wheeler and Zurek (eds.) pp. 260–314.Google Scholar
Yanase, M. (1961), “Optimal Measuring Apparatus”, Physical Review 123: 666–668. Reprinted in Wheeler and Zurek (eds.) (1983) pp. 712-714.CrossRefGoogle Scholar
Yanase, M. (1971), “Optimal Measuring Apparatus”, in d’Espagnat, (ed.) Foundations of Quantum Mechanics. New York: Academic Press.Google Scholar