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Weak Values and Consistent Histories in Quantum Theory

Kastner, Ruth (2004) Weak Values and Consistent Histories in Quantum Theory. [Preprint]

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    ABSTRACT: A relation is obtained between weak values of quantum observables and the consistency criterion for histories of quantum events. It is shown that ``strange'' weak values for projection operators (such as values less than zero) always correspond to inconsistent families of histories. It is argued that using the ABL rule to obtain probabilities for counterfactual measurements corresponding to those strange weak values gives inconsistent results. This problem is shown to be remedied by using the conditional weight, or pseudo-probability, obtained from the multiple-time application of Luders' Rule. It is argued that an assumption of reverse causality (a form of time symmetry) implies that weak values obtain, in a restricted sense, at the time of the weak measurement as well as at the time of post-selection. Finally, it is argued that weak values are more appropriately characterised as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions.

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    Item Type: Preprint
    Additional Information: To appear in Studies in History and Philosophy of Modern Physics, 35, no.1, 57-71, March 2004.
    Keywords: time symmetry, consistent histories, counterfactuals
    Subjects: Specific Sciences > Physics > Quantum Mechanics
    Depositing User: Ruth E. Kastner
    Date Deposited: 28 Dec 2003
    Last Modified: 07 Oct 2010 11:12
    Item ID: 1532

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