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Unreal Observables

Published online by Cambridge University Press:  01 January 2022

Bryan W. Roberts
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Abstract

This article argues that quantum observables can include not just self-adjoint operators but any member of the class of normal operators, including those with nonreal eigenvalues. Concrete experiments, statistics, and symmetries are all expressed in this more general context. However, this more general class of observables also requires a new restriction on sets of operators that can be interpreted as observables at once, called ‘sharp sets’.

Type
Physical Sciences
Information
Philosophy of Science , Volume 84 , Issue 5 , December 2017 , pp. 1265 - 1274
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

Thanks to Jeremy Butterfield for many helpful suggestions about these ideas.

References

Albert, D. Z. 1992. Quantum Mechanics and Experience. Cambridge, MA: Harvard University Press.Google Scholar
Blank, J., Exner, P., and Havlíček, M. 2008. Hilbert Space Operators in Quantum Physics. 2nd ed. New York: Springer.Google Scholar
Conway, J. B. 1990. A Course in Functional Analysis. 2nd ed. Graduate Texts in Mathematics 96. New York: Springer.Google Scholar
Dirac, P. A. M. 1930. The Principles of Quantum Mechanics. 1st ed. Oxford: Clarendon.Google Scholar
Dirac, P. A. M. 1935. The Principles of ‘Quantum’ Mechanics. 2nd ed. Oxford: Clarendon.Google Scholar
Dirac, P. A. M. 1947. The Principles of Quantum Mechanics. 3rd ed. Oxford: Clarendon.Google Scholar
Griffiths, D. J. 1995. Introduction to Quantum Mechanics. Upper Saddle River, NJ: Prentice Hall.Google Scholar
Lévy-Leblond, J.-M. 1976. “Who Is Afraid of Nonhermitian Operators? A Quantum Description of Angle and Phase.” Annals of Physics 101 (1): 319–41.CrossRefGoogle Scholar
Messiah, A. 1999. Quantum Mechanics. 2 vols. bound as 1. New York: Dover.Google Scholar
Penrose, R. 2004. The Road to Reality: A Complete Guide to the Laws of the Universe. London: Cape.Google Scholar
Roberts, B. W. 2016. “Observables, Disassembled.” Unpublished manuscript, PhilSci Archive. http://philsci-archive.pitt.edu/12478/.Google Scholar
Rudin, W. 1991. Functional Analysis. 2nd ed. New York: McGraw-Hill.Google Scholar
Sakurai, J. J. 1994. Modern Quantum Mechanics. Rev. ed. Reading, MA: Addison-Wesley.Google Scholar