Abstract
Analogy between the two slit experiment in quantum mechanics (QM) and the disjunction effect in psychology led to fruitful applications of the mathematical formalism of quantum probability to cognitive psychology. These quantum-like studies demonstrated that quantum probability (QP) matches better with the experimental statistical data than classical probability (CP). Similar conclusion can be derived from comparing QP and CP models for a variety of other cognitive-psychological effects, e.g., the order effect. However, one may wonder whether QP covers completely cognitive-psychological phenomena or cognition exhibits even more exotic probabilistic features and we have to use probabilistic models with even higher degree of nonclassicality than quantum probability. It is surprising that already a cognitive analog of the triple slit experiment in QM can be used to check this problem.
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Notes
- 1.
When the first version of this note was prepared [14]; the authors contacted E. Pothos (City University, London) with the proposal to perform this experiment. He informed us that his group has been already working on the triple slit experiment, but problems of the organizational character postponed its completion. Now the research group of E. Guerci (University of Cote d’ Azur; Nice) also works on preparation of this experiment; unfortunately, it also confronts some problems (to finance completion of the experimental study). So, now we are in the state of exciting expectation of the outputs of these experiments. In principle, we cannot exclude that they would be opposite...
- 2.
Incompatible observables represented by non-commutative Hermitian operators cannot be measured jointly. Therefore the straightforward definition of the joint probability distribution is inapplicable. However, it is possible to explore the definition generalizing representation of the classical joint probability distribution through conditional probability. However, the order structure of observations has to be taken into account, because in general \(p(a=a_i) p(b= b_j\vert a=a_i)\) is not equal to \(p(b= b_j) p(a=a_i \vert b= b_j)\).
- 3.
Its homogeneity is important, because it will be divide into a few subgroups which will be used to collect different blocks of statistical data. And it is important that we can assume that the members of all subgroups have “the same mental state”.
- 4.
Another proposal: Do you think that your application for emigration (to this country) will be successful?
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Acknowledgments
One of the authors (AKH) would like to thank G. Weihs for numerous discussions on the possibility to violate Born’s rule, in particular on the triple-slit experiment, and the possibility to see the lab and performance of this test during the visit to Innsbruck in May 2013 and hospitality during this visit.
This work was supported (A. Khrennikov) by the EU-project “Quantum Information Access and Retrieval Theory” (QUARTZ), Grant No. 721321. It was also supported (I. Basieva) by a Marie Sklodowska-Curie Individual Fellowship, grant agreement 696331.
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Basieva, I., Khrennikov, A. (2017). Testing Boundaries of Applicability of Quantum Probabilistic Formalism to Modeling of Cognition: Metaphors of Two and Three Slit Experiments. In: de Barros, J., Coecke, B., Pothos, E. (eds) Quantum Interaction. QI 2016. Lecture Notes in Computer Science(), vol 10106. Springer, Cham. https://doi.org/10.1007/978-3-319-52289-0_4
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