Abstract
We extend the topos-theoretic treatment given in previous papers of assigningvalues to quantities in quantum theory, and of related issues such as theKochen–Specker theorem. This extension has two main parts: the use of vonNeumann algebras as a base category and the relation of our generalized valuationsto (i) the assignment to quantities of intervals of real numbers and (ii) the ideaof a subobject of the coarse-graining presheaf.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
C. J. Isham and J. Butterfield (1998). A topos perspective on the Kochen-Specker theorem: I. Quantum states as generalised valuations. Int.J.Theor.Phys. 37, 2669–2733.
J. Butterfield and C. J. Isham (1999). A topos perspective on the Kochen-Specker theorem: II. Conceptual aspects, and classical analogues. Int.J.Theor.Phys. 38, 827–859.
S. Kochen and E. P. Specker (1967). The problem of hidden variables in quantum mechanics. J.Math.Mech. 17, 59–87.
R. Clifton. Beables in algebraic quantum theory. In From Physics to Philosophy, J. Butterfield and C. Pagonis, eds. (Cambridge University Press, Cambridge 1999), pp. 12–44.
H. Halvorson and R. Clifton (1999). Maximal beable subalgebras of quantum-mechanical observables, Int.J.Theor.Phys. 38, 2441–2484.
R. V. Kadison and J. R. Ringrose. Fundamentals of the Theory of Operator Algebras Volume1: Elementary Theory (Academic Press, New York, 1983).
C. Mulvey and J. W. Pelletier (1999). On the quantisation of points. J.Pure Appl.Algebra.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hamilton, J., Isham, C.J. & Butterfield, J. Topos Perspective on the Kochen=nSpeckerTheorem: III. Von Neumann Algebras as theBase Category. International Journal of Theoretical Physics 39, 1413–1436 (2000). https://doi.org/10.1023/A:1003667607842
Issue Date:
DOI: https://doi.org/10.1023/A:1003667607842