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Macroscopic observables and the Born rule. I. Long run frequencies

Landsman, Nicolaas P. (2008) Macroscopic observables and the Born rule. I. Long run frequencies. [Preprint]

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Abstract

We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a noncommutative C*-algebra of observables is empirically accessible only through associated commutative C*-algebras. The Born probabilities emerge as the relative frequencies of outcomes in long runs of measurements on a quantum system; it is not necessary to adopt the frequency interpretation of single-case probabilities (which will be the subject of a sequel paper). Our derivation of the Born rule uses ideas from a program begun by Finkelstein (1965) and Hartle (1968), intending to remove the Born rule as a separate postulate of quantum mechanics. Mathematically speaking, our approach refines previous elaborations of this program - notably the one due to Farhi, Goldstone, and Gutmann (1989) as completed by Van Wesep (2006) - in replacing infinite tensor products of Hilbert spaces by continuous fields of C*-algebras. In combination with our interpretational context, this technical improvement circumvents valid criticisms that earlier derivations of the Born rule have provoked, especially to the effect that such derivations were mathematically flawed as well as circular. Furthermore, instead of relying on the controversial eigenvector-eigenvalue link in quantum theory, our derivation just assumes that pure states in classical physics have the usual interpretation as truthmakers that assign sharp values to observables.


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Item Type: Preprint
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Landsman, Nicolaas P.
Keywords: Quantum mechanics, Copenhagen Interpretation, Born rule
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Nicolaas P. Landsman
Date Deposited: 02 May 2008
Last Modified: 07 Oct 2010 15:16
Item ID: 4012
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: April 2008
URI: https://philsci-archive.pitt.edu/id/eprint/4012

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