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On the cognitive experiments to test quantum-like behaviour of mind

Andrei Yu. Khrennikov

Published May 15, 2002• 10 citations
OpenAlex

Abstract

We describe cognitive experiments (based on interference of probabilities for mental observables) that could verify quantum-like structure of mental measurements. In principle, such experiments could be performed in psychology, cognitive and social sciences.

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My discussion is articulated under the neurological as well as the psychological profile. I insist in particular on the view that mental events arise in analogy with quantum probability fields. I review some results obtained on quantum cognition discussing in detail those that we obtained on quantum interference in mental states during perception-cognition in ambiguous figures. Frequently, I use the approach to quantum mechanics by Clifford algebra. I insist in particular on two recent results. The first is the justification that I obtain of the von Neumann postulate on quantum measurement and the second relates my Clifford demonstration on the logical origins of quantum mechanics and thus on the arising feature that quantum mechanics relates conceptual entities. The whole discussion aims me to support the conclusion that we think in a quantum probabilistic manner.

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We describe methodology of cognitive experiments (based on interference of probabilities for mental observables) which could verify quantum-like structure of mental information, namely, interference of probabilities for incompatible observables. In principle, such experiments can be performed in psychology, cognitive, and social sciences. In fact, the general contextual probability theory predicts not only quantum-like trigonometric (cos θ) interference of probabilities, but also hyperbolic (cosh θ) interference of probabilities (as well as hyper-trigonometric). In principle, statistical data obtained in experiments with cognitive systems can produce hyperbolic (cosh θ) interference of probabilities. We introduce a wave function of (e.g., human) population. In general, we should not reject the possibility that cognitive functioning is neither quantum nor classical. We discuss the structure of state spaces for cognitive systems.
Recently the mathematical formalism of quantum mechanics, especially methods of quantum probability theory, started to be widely used in a variety of applications outside of physics, e.g., cognition and psychology as well as economy and finances. To distinguish such models from genuine quantum physical models, they often called quantum-like (although often people simply speak about, e.g., "quantum cognition"). These novel applications generate a number of foundational questions. Nowadays we can speak about a new science - foundations of quantum-like modeling. At the first stage this science was mainly about comparison of classical and quantum models, mainly in the probabilistic setting. It was found that statistical data from cognitive psychology violate some basic constraints posed on data by classical probability theory (Kolmogorov, 1933); in particular, the constraints given by the formula of total probability and Bell's type inequalities. Recently another question attracted some attention. In spite of real success in applications, there are no reason to believe that the quantum probability would cover completely all problems of, e.g., cognition. May be more general probability models have to be explored. A similar problem attracted a lot of attention in foundations of quantum physics culminating in a series of experiments to check Sorkin's equality for the triple-slit experiment by Weihs' group. In this note we present a similar test in the cognitive experimental setting. Performance of this test would either give further confirmation of the adequacy of the quantum probability model to cognitive applications or rejection of the conventional quantum model. Thus this note opens the door for a series of exciting experimental tests for the quantum-like model of cognition.
It is proposed to define "quantumness" of a system (micro or macroscopic, physical, biological, social, political) by starting with understanding that quantum mechanics is a statistical theory. It says us only about probability distributions. The only possible criteria of quantum behaviour are statistical ones. Therefore I propose to consider any system which produces quantum statistics as quantum ("quantumlike"). A possible test is based on the interference of probabilities. I was mainly interested in using such an approach to "quantumness" to extend the domain of applications of quantum mathematical formalism and especially to apply it to cognitive sciences. There were done experiments on interference of probabilities for ensembles of students and a nontrivial interference was really found. One could say that the quantum statistical behaviour might be expected. But the problem was not so trivial. Yes, we might expect nonclassical statistics, but there was no reason to get the quantum one, i.e., cos-interference. But we got it!
My discussion is articulated under the neurological as well as the psychological profile. I insist in particular on the view that mental events arise in analogy with quantum probability fields. I review some results obtained on quantum cognition discussing in detail those that we obtained on quantum interference in mental states during perception-cognition in ambiguous figures. Frequently, I use the approach to quantum mechanics by Clifford algebra. I insist in particular on two recent results. The first is the justification that I obtain of the von Neumann postulate on quantum measurement and the second relates my Clifford demonstration on the logical origins of quantum mechanics and thus on the arising feature that quantum mechanics relates conceptual entities. The whole discussion aims me to support the conclusion that we think in a quantum probabilistic manner.