David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Any attempt to construct a realist interpretation of quantum theory founders on the Kochen-Specker theorem, which asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truth-values assigned to propositions are (i) contextual; and (ii) multi-valued, where the space of contexts and the multi-valued logic for each context come naturally from the topos theory of presheaves. The first step in our theory is to demonstrate that the Kochen-Specker theorem is equivalent to the statement that a certain presheaf defined on the category of self-adjoint operators has no global elements. We then show how the use of ideas drawn from the theory of presheaves leads to the definition of a generalised valuation in quantum theory whose values are sieves of operators. In particular, we show how each quantum state leads to such a generalised valuation. A key ingredient throughout is the idea that, in a situation where no normal truth-value can be given to a proposition asserting that the value of a physical quantity A lies in a set D of real numbers , it is nevertheless possible to ascribe a partial truth-value which is determined by the set of all coarse-grained propositions that assert that some function f(A) lies in f(D), and that are true in a normal sense. The set of all such coarse-grainings forms a sieve on the category of self-adjoint operators, and is hence fundamentally related to the theory of presheave.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
David Corfield (2002). Conceptual Mathematics: A First Introduction to Categories. Studies in History and Philosophy of Science Part B 33 (2):359-366.
Similar books and articles
James H. McGrath (1986). Quantum Disjunctive Facts. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:76 - 86.
E. P. (1999). Two No-Go Theorems for Modal Interpretations of Quantum Mechanics. Studies in History and Philosophy of Science Part B 30 (3):403-431.
Itamar Pitowsky (2004). Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem. Studies in History and Philosophy of Science Part B 35 (2):177-194.
Ehud Hrushovski & Itamar Pitowsky (2004). Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem. Studies in History and Philosophy of Science Part B 35 (2):177-194.
Jeremy Butterfield & Chris Isham, A Topos Perspective on the Kochen-Specker Theorem: IV. Interval Valuations.
John Hamilton, Chris Isham & Jeremy Butterfield, A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category.
Added to index2009-01-28
Total downloads34 ( #48,751 of 1,096,632 )
Recent downloads (6 months)8 ( #24,329 of 1,096,632 )
How can I increase my downloads?