Weak values and consistent histories in quantum theory


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 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 Lüders’ Rule. It is argued that an assumption of reverse causality 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 characterized as multiple-time amplitudes than expectation values, and as such can have little to say about counterfactual questions
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DOI 10.1016/j.shpsb.2003.02.001
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References found in this work BETA

Interpreting the Quantum World.Jeffrey Bub - 1998 - British Journal for the Philosophy of Science 49 (4):637-641.
Time's Arrow and Archimedes' Point: New Directions for the Physics of Time.Huw Price - 1998 - British Journal for the Philosophy of Science 49 (1):135-159.
Weak-Measurement Elements of Reality.Lev Vaidman - 1996 - Foundations of Physics 26 (7):895-906.
Time-Symmetrised Quantum Theory, Counterfactuals and 'Advanced Action'.R. E. Kastner - 1999 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 30 (2):237-259.

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Citations of this work BETA

Quantum Mechanics as a Consistency Condition on Initial and Final Boundary Conditions.David John Miller - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):767-781.
Non-Representative Quantum Mechanical Weak Values.B. E. Y. Svensson - 2015 - Foundations of Physics 45 (12):1645-1656.
The Transactional Interpretation, Counterfactuals, and Weak Values in Quantum Theory.Ruth E. Kastner - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (4):806-818.
Quantum Weak Values and Logic: An Uneasy Couple.Bengt E. Y. Svensson - 2017 - Foundations of Physics 47 (3):430-452.

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