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Springer eBooks

On the Origin of Probabilities in Quantum Mechanics: Creative and Contextual Aspects

Diederik Aerts, Bob Coecke, Sonja Smets

Published Jan 1, 1999• 21 citations
Publisher
DOI
10.1007/978-94-017-2245-2_20

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Summary form only given. Contrarily to the classical physics picture, according to quantum mechanics the observable properties of the objects do not yield defined values, until a measurement is performed. The measurement outcome depends indeed also on the set of observables that is being measured [1]. Such a fundamental aspect of Nature is named quantum contextuality and it has been studied in several experimental systems, including single particles [2, 3]. Interestingly, it was recently suggested that even the non-classical power of quantum computing originates from contextuality [4]. Therefore, it is highly relevant to find experimental evidence of this aspect in technological platforms that may be adopted in future quantum computing devices, such as integrated photonics [5-7]. In this work we investigate experimentally quantum contextuality of a single photon on-a-chip, employing reconfigurable photonic circuits fabricated by femtosecond laser waveguide writing [7, 8].

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Comment on the Paper Titled ’The Origin of Quantum Mechanical Statistics: Insights from Research on Human Language’ (arXiv preprint arXiv:2407.14924, 2024)

Krzysztof Sienicki

This analysis critically examines the application of quantum mechanical concepts—such as entanglement, indistinguishability, and Bose Einstein statistics — to language and cognitive processes as proposed in the paper. While the interdisciplinary approach is creative, significant theoretical and empirical challenges arise when translating quantum principles to human cognition. Key issues include the contextual and qualitative nature of cognitive processes, which differ fundamentally from the predictable, probabilistic behaviors observed in quantum systems. Cognitive phenomena are shaped by factors like emotional state, social context, and personal memory, which have no direct analogy in quantum mechanics. The assumption that words or cognitive "particles" are indistinguishable, as quantum particles are, overlooks the unique and dynamic contextual dependencies in language. Moreover, empirical support for such quantum-cognitive parallels remains limited, and the paper’s application of quantum statistics to word frequency distributions may reflect a coincidental pattern rather than a fundamental process. This assessment suggests that while the paper’s quantum analogies could foster new interdisciplinary discussions, they risk speculative overreach if treated as foundational principles for understanding cognition. Effective interdisciplinary integration would require rigorous empirical validation within cognitive science, as well as caution against reductionist interpretations that might simplify the rich complexities of human thought. Future research may benefit from more context-sensitive and evidence-based models that align more closely with established cognitive theories, thereby maintaining the intellectual richness of both quantum mechanics and cognitive science without forcing an untested theoretical bridge between them.

•Dec 1, 2024•25 citations

Outline of a Contextual Probability Theory A Structural Description of Probability Through Contextual Wholes

Viktoras Rimsha, Laimontas Rimsha

Interpretational paradoxes of quantum mechanics may be associated with the application of the structure of classical probability theory to systems whose probabilistic organization is fundamentally contextual. In this work, we propose an outline of an alternative probability theory in which the primary object is not an elementary outcome but a contextual whole—a class of alternatives defined by a common structural property. In this approach, probability is organized on two levels. The first level describes the probabilities of contextual wholes, while the second level describes the conditional probabilities of alternatives within those wholes. Individual alternatives do not possess autonomous probabilities outside their context. Their probabilities arise only as contextual projections of a more fundamental probabilistic structure. Within this model, quantum mechanics appears as a special case of a more general theory in which contextual wholes are described by superpositions of probability amplitudes. Classical probability theory emerges as a limiting case in which all contexts are mutually compatible and can be combined into a single global description. The proposed framework provides a possible conceptual foundation for understanding quantum probability, contextuality, interference, and hybrid probability distributions within a unified structure.

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Contextuality and probability in quantum mechanics and beyond: a preface

Ehtibar N. Dzhafarov

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Sep 16, 2019•8 citations
Summary form only given. Contrarily to the classical physics picture, according to quantum mechanics the observable properties of the objects do not yield defined values, until a measurement is performed. The measurement outcome depends indeed also on the set of observables that is being measured [1]. Such a fundamental aspect of Nature is named quantum contextuality and it has been studied in several experimental systems, including single particles [2, 3]. Interestingly, it was recently suggested that even the non-classical power of quantum computing originates from contextuality [4]. Therefore, it is highly relevant to find experimental evidence of this aspect in technological platforms that may be adopted in future quantum computing devices, such as integrated photonics [5-7]. In this work we investigate experimentally quantum contextuality of a single photon on-a-chip, employing reconfigurable photonic circuits fabricated by femtosecond laser waveguide writing [7, 8].
This analysis critically examines the application of quantum mechanical concepts—such as entanglement, indistinguishability, and Bose Einstein statistics — to language and cognitive processes as proposed in the paper. While the interdisciplinary approach is creative, significant theoretical and empirical challenges arise when translating quantum principles to human cognition. Key issues include the contextual and qualitative nature of cognitive processes, which differ fundamentally from the predictable, probabilistic behaviors observed in quantum systems. Cognitive phenomena are shaped by factors like emotional state, social context, and personal memory, which have no direct analogy in quantum mechanics. The assumption that words or cognitive "particles" are indistinguishable, as quantum particles are, overlooks the unique and dynamic contextual dependencies in language. Moreover, empirical support for such quantum-cognitive parallels remains limited, and the paper’s application of quantum statistics to word frequency distributions may reflect a coincidental pattern rather than a fundamental process. This assessment suggests that while the paper’s quantum analogies could foster new interdisciplinary discussions, they risk speculative overreach if treated as foundational principles for understanding cognition. Effective interdisciplinary integration would require rigorous empirical validation within cognitive science, as well as caution against reductionist interpretations that might simplify the rich complexities of human thought. Future research may benefit from more context-sensitive and evidence-based models that align more closely with established cognitive theories, thereby maintaining the intellectual richness of both quantum mechanics and cognitive science without forcing an untested theoretical bridge between them.
Interpretational paradoxes of quantum mechanics may be associated with the application of the structure of classical probability theory to systems whose probabilistic organization is fundamentally contextual. In this work, we propose an outline of an alternative probability theory in which the primary object is not an elementary outcome but a contextual whole—a class of alternatives defined by a common structural property. In this approach, probability is organized on two levels. The first level describes the probabilities of contextual wholes, while the second level describes the conditional probabilities of alternatives within those wholes. Individual alternatives do not possess autonomous probabilities outside their context. Their probabilities arise only as contextual projections of a more fundamental probabilistic structure. Within this model, quantum mechanics appears as a special case of a more general theory in which contextual wholes are described by superpositions of probability amplitudes. Classical probability theory emerges as a limiting case in which all contexts are mutually compatible and can be combined into a single global description. The proposed framework provides a possible conceptual foundation for understanding quantum probability, contextuality, interference, and hybrid probability distributions within a unified structure.