The Probabilistic Roots of the Quantum Mechanical Paradoxes

Accardi, Luigi

doi:10.1007/978-94-009-6286-6_16

Cited by 75 publications

(67 citation statements)

References 22 publications

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“…Examples of physically meaningful statistical data not admitting a Kolmogorovian model were known since the early days of quantum mechanics (cf. The discussion of the two-slit experiment in [7]); in [9] Bell pointed out another simple example (based on correlations rather than conditinal probabilities )of statistical data not admitting a Kolmogorovian model. This examples was at the origin of a vast literature (cr.…”

Section: The Statistical Invariantsmentioning

confidence: 99%

“…In fact one can show (cf. [7]) that all the so-called paradoxes of quantum theory arise from the application of the usual rules of the Kolmogorovian model to sets of statistical data which do nota dmit such a model.…”

Section: The Statistical Invariantsmentioning

confidence: 99%

“…in § (0.) let us recall that, as shown in [5], [6], [7], the axiomatic formalization of the notion of first kind measurement (or filter), and of the operations which can be perfomed on them, leads naturally to the notion of Schwinger algebra of measurements which, in the notations introduced in § (1. ), is defined as follows:…”

Section: Deduction Of the Quantum Formalism From Heisenberg Principlementioning

confidence: 99%

“…In particular we will not discuss the relevance of the answers to these questions for the old interpretational problems of quantum theory (cf. [7]), nor the important steps that have been made in the last years towards the inner development of the usual quantum probabilistic model (for these we refer to the papers in these proceedings). We believe that once understood the origins and the meaning of quantum probability, it will be easier to go further along the lines of the analysis of more general classes of nonkolomogorovian probabilistic models the deepening of the usual quantum quantum one, as well as the study of the connections between the kolmogorovian and the quantum model.…”

mentioning

confidence: 99%

“…Question II.) has been dealt with extensively in [7] and will not be discussed here; in Sections (3.) and (4.)…”

mentioning

confidence: 99%

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Some trends and problems in quantum probability

Accardi¹

1984

Quantum Probability and Applications to the Quantum Theory of Irreversible Processes

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From the experimental point of view probability enters quantum theory just like classical statistical physics, i.e. as an expected relative frequency. However it is well known that the statistical formalism of quantum theory is quite different from the usual Kolmogorovian one involving, for example, complex numbers, amplitudes, Hilbet spaces... The quantum statistical formalism has been described, developped, applied, generalized with the contributions of many authors; however its theoretical status remained, until recently, quite obscure, as shown by the widely contrasting statements that one can find in the vast literature concerning the following questions.\ud \ud Is it possible to justify the choice of the classical or the quantum statistical formalism, for the description of a given set of statistical data, on rigorous mathematical criteria rather than on empirical ones

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Section: The Statistical Invariantsmentioning

confidence: 99%

Section: The Statistical Invariantsmentioning

confidence: 99%

Section: Deduction Of the Quantum Formalism From Heisenberg Principlementioning

confidence: 99%

mentioning

confidence: 99%

“…Question II.) has been dealt with extensively in [7] and will not be discussed here; in Sections (3.) and (4.)…”

mentioning

confidence: 99%

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Some trends and problems in quantum probability

Accardi¹

1984

Quantum Probability and Applications to the Quantum Theory of Irreversible Processes

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Evolutionary Epistemology, Language and Culture

Boer¹

2006

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Towards a quantum evolutionary scheme: Violating Bell’s inequalities in language

Aerts¹,

Czachor

D’Hooghe³

2006

Evolutionary Epistemology, Language and Culture

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We show the presence of genuine quantum structures in human language. The neo-Darwinian evolutionary scheme is founded on a probability structure that satisfies the Kolmogorovian axioms, and as a consequence cannot incorporate quantum-like evolutionary change. In earlier research we revealed quantum structures in processes taking place in conceptual space. We argue that the presence of quantum structures in language and the earlier detected quantum structures in conceptual change make the neoDarwinian evolutionary scheme strictly too limited for Evolutionary Epistemology. We sketch how we believe that evolution in a more general way should be implemented in epistemology and conceptual change, but also in biology, and how this view would lead to another relation between both biology and epistemology.Keywords: quantum, evolution, language, Bell's inequalities, context IntroductionIn this article we will demonstrate the presence of quantum structures in language by proving the violation of Bell's inequalities 2 . Apart from any specific philosophical theory about language, the presence of quantum structures in language is an interesting finding, particularly to the community of scientists who study the structure of language, and also to those who investigate the working of the human mind, language being one of the mind's major products. In addition to this first-order motivation -as one could call it -, the search for quantum structures in language was equally well guided by the aim of elaborating the global worldviews construction program, which is the main theme of research in the Leo Apostel Centre (CLEA) (Aerts, Apostel, De Moor et al. 1995;Apostel 1995). It is through its relevance for the global worldviews construction program that the material presented in this article becomes relevant for Evolutionary Epistemology (EE), certainly in the broad interpretation that EE was given at the conference where we presented the material of this article. The Stanford Encyclopaedia of Philosophy defines EE thus:EE is the attempt to address questions in the theory of knowledge from an evolutionary point of view. It involves, in part, employing models and metaphors drawn from evolutionary biology in the attempt to characterise and resolve issues arising in epistemology and conceptual change. There are two interrelated but distinct programs which go by the name EE. One focuses on the development of cognitive mechanisms in animals and humans. This involves as straightforward extension of the biological theory of evolution to those aspects or traits of animals which are biological substrates of cognitive activity, e.g. their brains, sensory systems, motor systems, etc. This program has been labelled EEM. The other program attempts to account for the evolution of ideas, scientific theories, epistemic norms and culture in general by using models and metaphors drawn from evolutionary biology, and it has been labelled EET. EE is sometimes given a narrow meaning, according to which it is said to attempt to model epistemolo...

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The Probabilistic Roots of the Quantum Mechanical Paradoxes

Cited by 75 publications

References 22 publications

Some trends and problems in quantum probability

Some trends and problems in quantum probability

Evolutionary Epistemology, Language and Culture

Towards a quantum evolutionary scheme: Violating Bell’s inequalities in language

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