Abstract
This paper will discuss the representation of properties in two modal interpretations of quantum mechanics: Richard Healey’s interactive interpretation (Healey, 1989) and the Kochen-Dieks-Clifton (KDC) interpretation, as presented in Clifton (1995). Like many realist interpretations, these interpretations take the set of a system’s dynamical properties, ordered by some appropriate ordering relation, to be isomorphic to the set of projection operators in the Hilbert space associated with the system. The two interpretations share a further similarity: as i will discuss in Section 3, they both assign to the biorthogonal decomposition theorem (or to a generalization of that theorem) a central role in determining which of a system’s properties are possessed at a given time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bub, J. (1991), “Measurement and ‘Beables’ in Quantum Mechanics”, Foundations of Physics 21: 25–42.
Clifton, R. (1995), “Independently Motivating the Kochen-Dieks Modal Interpretation of Quantum Mechanics”, British Journal for Philosophy of Science 46: 33–57.
Clifton, R. (1996), “The Properties of the Modal Interpretation of Quantum Mechanics”, British Journal for Philosophy of Science 47: 371–398.
Healey, R. (1989), The Philosophy of Quantum Mechanics: An Interactive Interpretation. Cambridge: Cambridge University Press.
Healey, R. (1995), “Dissipating the Quantum Measurement Problem”, Topoi 14: 55–65.
Hellman, G. (1981), “Quantum Logic and Meaning”, in P.D. Asquith and R. Giere, (eds.), Proceedings of the 1980 Biennial Meeting of the Philosophy of Science Association, Vol. 2. East Lansing, Michigan: Philosophy of Science Association, pp. 493–511.
Hughes, R.I.G. (1980), “Quantum Logic and the Interpretation of Quantum Mechanics”, in P.D. Asquith and R.N. Giere, (eds.), Proceedings of the 1980 Biennial Meeting of the Philosophy of Science Association, Vol. 2. East Lansing, Michigan: Philosophy of Science Association, pp. 56–67.
Kochen, S. and E.P. Specker (1967), “The Problem of Hidden Variables in Quantum Mechanics”, Journal of Mathematics and Mechanics 17: 59–87.
Putnam, H. (1969), “Is Logic Empirical?”, in R.S. Cohen and M.W. Wartofsky, (eds.), Boston Studies in the Philosophy of Science, Vol. V. Dordrecht: Reidel.
Redhead, M. (1987), Incompleteness, Nonlocality, and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics. Oxford: Oxford University Press.
Reeder, N. (1995), “Property Composition in Healey’s Interpretation of Quantum Mechanics”, Foundations of Physics Letters 8: 497–522.
Shimony, A. (1989), “Search for a World view Which Can Accommodate Our Knowledge of Microphysics”, in J.T. Cushing and E. McMullin, (eds.), Philosophical Consequences of Quantum Theory. Notre Dame, Indiana: University of Notre Dame Press, pp. 25–37.
Teller, P. (1984), “The Projection Postulate: A New Perspective”, Philosophy of Science 51: 369–395.
Vermaas, P.E. (1997), “A No-Go Theorem for Joint Property Ascriptions in Modal Interpretations of Quantum Mechanics”, Physical Review Letters 78: 2033–2037.
von Neumann, J. (1932), Mathematische Grundlagen der Quantenmechanik. Berlin: Springer. Translated by R.T. Beyer as Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press (1955).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Reeder, N. (1998). Projection Operators, Properties, and Idempotent Variables in the Modal Interpretations. In: Dieks, D., Vermaas, P.E. (eds) The Modal Interpretation of Quantum Mechanics. The Western Ontario Series in Philosophy of Science, vol 60. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5084-2_6
Download citation
DOI: https://doi.org/10.1007/978-94-011-5084-2_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6135-3
Online ISBN: 978-94-011-5084-2
eBook Packages: Springer Book Archive