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Author: Andrei Y. Khrennikov
Publisher: Springer Science & Business Media
ISBN: 1402095937
Category : Science
Languages : en
Pages : 354
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Book Description
The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell’s theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed.
Author: Andrei Y. Khrennikov
Publisher: Springer Science & Business Media
ISBN: 1402095937
Category : Science
Languages : en
Pages : 354
Get Book Here
Book Description
The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell’s theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed.
Author: Andrei Y. Khrennikov
Publisher: Springer
ISBN: 9781402096105
Category : Science
Languages : en
Pages : 354
Get Book Here
Book Description
The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell’s theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed.
Author: Andrei Y. Khrennikov
Publisher: Springer Science & Business Media
ISBN: 3642051014
Category : Science
Languages : en
Pages : 226
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Book Description
Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Växjö model) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. This model can be represented in a quantum-like way, namely, in complex and more general Hilbert spaces. In this way quantum probability is totally demystified: Born's representation of quantum probabilities by complex probability amplitudes, wave functions, is simply a special representation of this type.
Author: Harald Atmanspacher
Publisher: Springer
ISBN: 3319286757
Category : Computers
Languages : en
Pages : 293
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Book Description
This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Quantum Interaction, QI 2015, held in Filzbach, Switzerland, in July 2015. The 20 papers together with 2 invited keynotes presented in this book were carefully selected from 27 submissions. Quantum Interaction has developed into an emerging interdisciplinary area of science combining research topics in mathematics, physics, psychology, economics, cognitive science, and computer science.
Author: Adam Forrest Kay
Publisher: Basic Books
ISBN: 1541675770
Category : Science
Languages : en
Pages : 346
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Book Description
An expert researcher argues for a revolutionary new understanding of quantum mechanics The received wisdom in quantum physics is that, at the deepest levels of reality, there are no actual causes for atomic events. This idea led to the outlandish belief that quantum objects—indeed, reality itself—aren’t real unless shaped by human measurement. Einstein mocked this idea, asking whether his bed spread out across his room unless he looked at it. And yet it remains one of the most influential ideas in science and our culture. In Escape from Shadow Physics, Adam Forrest Kay takes up Einstein’s torch: reality isn’t mysterious or dependent on human measurement, but predictable and independent of us. At the heart of his argument is groundbreaking research with little drops of oil. These droplets behave as particles do in the long-overlooked quantum theory of pilot waves; crucially, they showcase quantum behavior while being described by classical physics. And that classical-quantum interface points to a true understanding of quantum mechanics and a reasonable universe. A bold and essential reset of the field, Escape from Shadow Physics describes the kind of true scientific revolution that comes along just once—or less—in a century.
Author: Andre? I?U?r?evich Khrennikov
Publisher: World Scientific
ISBN: 1783267976
Category : Science
Languages : en
Pages : 299
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Book Description
"Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Interrelation of Classical and Quantum Randomness rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their interrelation and interpretational and foundational issues. The book presents the essentials of classical approaches to randomness, enlightens their successes and problems, and then proceeds to essentials of quantum randomness. Its wide-ranging and comprehensive scope makes it suitable for researchers in mathematical physics, probability and statistics at any level"--
Author: Peter Bruza
Publisher: Springer
ISBN: 3642008348
Category : Science
Languages : en
Pages : 324
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Book Description
This book constitutes the refereed proceedings of the Third International Symposium on Quantum Interaction, QI 2009, held in Saarbrücken, Germany, in March 2009. The 21 revised full papers presented together with the 3 position papers were carefully reviewed and selected from numerous submissions. The papers show the cross-disciplinary nature of quantum interaction covering topics such as computation, cognition, decision theory, information retrieval, information systems, social interaction, computational linguistics and finance.
Author: Alberto Casado
Publisher: Frontiers Media SA
ISBN: 2889666417
Category : Science
Languages : en
Pages : 190
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Book Description
Author: Paulo Castro
Publisher: Springer Nature
ISBN: 3031498615
Category :
Languages : en
Pages : 321
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Book Description
Author: Emmanuel Haven
Publisher: Cambridge University Press
ISBN: 1107012821
Category : Psychology
Languages : en
Pages : 305
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Book Description
Written by world experts in the foundations of quantum mechanics, this book shows how elementary quantum mechanical principles can be applied to social sciences problems. Aimed at economists and psychologists, as well as physicists, it explores the exciting field of quantum social science.
