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The GTR-model: a universal framework for quantum-like measurements. (English) Zbl 1356.81017

Aerts, Diederik (ed.) et al., Probing the meaning of quantum mechanics. Superpositions, dynamics, semantics and identity. Based on the first international meeting on quantum mechanics and quantum information: physical, philosophical and logical approaches, Cagliari, Italy, July 23– 25, 2014. Hackensack, NJ: World Scientific (ISBN 978-981-3146-27-3/hbk; 978-981-3146-29-7/ebook). 91-140 (2016).
Summary: We present a very general geometrico-dynamical description of physical or more abstract entities, called the general tension-reduction (GTR) model, where not only states, but also measurement-interactions can be represented, and the associated outcome probabilities calculated. Underlying the model is the hypothesis that indeterminism manifests as a consequence of unavoidable fluctuations in the experimental context, in accordance with the hidden-measurements interpretation of quantum mechanics. When the structure of the state space is Hilbertian, and measurements are of the universal kind, i.e., are the result of an average over all possible ways of selecting an outcome, the GTR-model provides the same predictions of the Born rule, and therefore provides a natural completed version of quantum mechanics. However, when the structure of the state space is non-Hilbertian and/or not all possible ways of selecting an outcome are available to be actualized, the predictions of the model generally differ from the quantum ones, especially when sequential measurements are considered. Some paradigmatic examples will be discussed, taken from physics and human cognition. Particular attention will be given to some known psychological effects, like question order effects and response replicability, which we show are able to generate non-Hilbertian statistics. We also suggest a realistic interpretation of the GTR-model, when applied to human cognition and decision, which we think could become the generally adopted interpretative framework in quantum cognition research.
For the entire collection see [Zbl 1352.81007].

MSC:

81P05 General and philosophical questions in quantum theory
81P15 Quantum measurement theory, state operations, state preparations
81P16 Quantum state spaces, operational and probabilistic concepts
81Q65 Alternative quantum mechanics (including hidden variables, etc.)
00A79 Physics
91E10 Cognitive psychology
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