The Quantum Nature of Identity in Human Thought: Bose-Einstein Statistics for Conceptual Indistinguishability

Diederik Aerts,Sandro Sozzo,Tomas Veloz

doi:10.1007/s10773-015-2620-4

Diederik Aerts, Sandro Sozzo + Show 1 more

Open Access

https://doi.org/10.1007/s10773-015-2620-4

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Abstract

Increasing experimental evidence shows that humans combine concepts in a way that violates the rules of classical logic and probability theory. On the other hand, mathematical models inspired by the formalism of quantum theory are in accordance with data on concepts and their combinations. In this paper, we investigate a novel type of concept combination were a number is combined with a noun, e.g., `Eleven Animals. Our aim is to study 'conceptual identity' and the effects of 'indistinguishability' - in the combination 'Eleven Animals', the 'animals' are identical and indistinguishable - on the mechanisms of conceptual combination. We perform experiments on human subjects and find significant evidence of deviation from the predictions of classical statistical theories, more specifically deviations with respect to Maxwell-Boltzmann statistics. This deviation is of the 'same type' of the deviation of quantum mechanical from classical mechanical statistics, due to indistinguishability of microscopic quantum particles, i.e we find convincing evidence of the presence of Bose-Einstein statistics. We also present preliminary promising evidence of this phenomenon in a web-based study.

Highlights

There has been accumulated evidence in experimental psychology for decades indicating that the probabilistic aspects of human decision making are nonclassical, in the sense that, when attempted to model them, classical probabilistic theories fail
That we find quantum theory to be able to model concepts in a way it models identical quantum entities, is a strong new element for quantum cognition, but might incorporate a new way to reflect about this mysterious and not at all understood behaviour of identical quantum entities
We investigated the type of statistics underlying a conceptual combination of a number and a noun

Summary

Introduction

There has been accumulated evidence in experimental psychology for decades indicating that the probabilistic aspects of human decision making are nonclassical, in the sense that, when attempted to model them, classical probabilistic theories fail. In our SCoP formalism, a concept is an ‘entity in a specific state changing under the influence of a context’, rather than a ‘container of instantiations’, as in the traditional approaches [5, 6] This made it possible to elaborate a quantummechanical model which successfully represents different sets of data collected on conjunctions and disjunctions of two concepts [7, 8, 12, 13, 22]. The same linguistic expression can elicit the thought about eleven objects, present in space and time, each of them being an instantiation of Animal, and distinguishable from each other Is this intuitive difference between concepts and objects the reason why the first behaves following BE statistics and the second following MB statistics? Since Bohmian mechanics is equivalent to standard quantum mechanics, identity and indistiguishibility will give rise to BE statistics [27], and we would not be amazed that the non-local potential in Bohmian theory is at the origin of this quantum behavior with respect to identity and indistiguishibility

Identity and indistinguishability in physics

Identity and indistinguishability if concepts are considered

Psychological evidence of indistinguishability in concepts

Preliminary study of indistinguishability in concepts on the web

Conclusions