Contextual Approach To Quantum Formalism
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Contextual Approach To Quantum Formalism
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Author : Andrei Y. Khrennikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-21
Contextual Approach To Quantum Formalism written by Andrei Y. Khrennikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-21 with Science categories.
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.
Contextual Approach To Quantum Formalism
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Author : Andrei Y. Khrennikov
language : en
Publisher: Springer
Release Date : 2009-08-29
Contextual Approach To Quantum Formalism written by Andrei Y. Khrennikov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-29 with Science categories.
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.
Ubiquitous Quantum Structure
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Author : Andrei Y. Khrennikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-23
Ubiquitous Quantum Structure written by Andrei Y. Khrennikov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-23 with Science categories.
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.
Quantum Probability And Related Topics
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Author : Luigi Accardi
language : en
Publisher: World Scientific
Release Date : 2013
Quantum Probability And Related Topics written by Luigi Accardi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
This volume contains the current research in quantum probability, infinite dimensional analysis and related topics. Contributions by experts in these fields highlight the latest developments and interdisciplinary connections with classical probability, stochastic analysis, white noise analysis, functional analysis and quantum information theory. This diversity shows how research in quantum probability and infinite dimensional analysis is very active and strongly involved in the modern mathematical developments and applications. Tools and techniques presented here will be of great value to researchers.
Advances In Pilot Wave Theory
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Author : Paulo Castro
language : en
Publisher: Springer Nature
Release Date : 2024-06-17
Advances In Pilot Wave Theory written by Paulo Castro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-17 with Science categories.
This book provides a state-of-the-art review of Pilot Wave Theory at the beginning of the XXI century. It contains the best contributions of the first International Conference on Advances in Pilot Wave Theory, held in Lisbon in 2021. The event brought together physicists from the new emerging field of Hydrodynamic Quantum Analogs (HQA) and philosophers of science. Three main themes were discussed: 1. Hydrodynamic quantum analogs, 2. Theoretical advances in pilot wave physics and, 3. Philosophical foundations of pilot wave theory. Recent experimental work in HQA has provided impetus to develop the pilot-wave approach into a realistic basis of quantum mechanics, specifically a dynamical completion of the existing theory of quantum statistics. To that end, the meeting featured theoretical work that advanced Louis de Broglie original pilot wave theory. This collection shows how several aspects of quantum systems have been reproduced in the hydrodynamic environment, and how the power of analogy suggests the possibility of a relatively intelligible quantum realm. Most notably, the notion of memory, as engendered in the pilot-wave-hydrodynamic system, suggests a profitable direction to explore in developing a more complete description of quantum phenomena. This book is expected to be of great interest to physicists, computer scientists and philosophers of science interested in the foundations of Quantum Mechanics. Chapter 1 and Chapter 12 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Chronic Stress And Its Effect On Brain Structure And Connectivity
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Author : Starcevic, Ana
language : en
Publisher: IGI Global
Release Date : 2019-01-11
Chronic Stress And Its Effect On Brain Structure And Connectivity written by Starcevic, Ana and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-11 with Medical categories.
Neuroscientists found that chronic stress and cortisol can trigger long-term changes in brain structure and connectivity in individuals and emphasize the importance of reducing stressful factors in one’s daily life. Early exposure to stressful events can make a person more vulnerable to anxiety and other mood disorders later in their lifetime. Those who take active steps to reduce their stress through various means such as physical activity or therapy can reduce the negative long-term effects on the brain. Chronic Stress and Its Effect on Brain Structure and Connectivity is an essential reference source that presents current information on chronic stress management, the impact of mass media coverage on the human mind, and the effects of post-traumatic stress. Featuring research on topics such as the neurophysiological basis of moods, trauma, quantum cognition, mental health, therapy, and neurobiology, this book is ideally designed for mental health professionals, neuroscientists, neurologists, psychiatrists, researchers, and therapists.
Probability And Randomness
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Author : Andre? I?U?r?evich Khrennikov
language : en
Publisher: World Scientific
Release Date : 2016
Probability And Randomness written by Andre? I?U?r?evich Khrennikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Science categories.
"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"--
Quantum Interaction
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Author : Harald Atmanspacher
language : en
Publisher: Springer
Release Date : 2016-01-07
Quantum Interaction written by Harald Atmanspacher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-07 with Computers categories.
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.
Quantum Social Science
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Author : Emmanuel Haven
language : en
Publisher: Cambridge University Press
Release Date : 2013-01-17
Quantum Social Science written by Emmanuel Haven and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-17 with Psychology categories.
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.
Towards A Local Realist View Of The Quantum Phenomenon
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Author : Alberto Casado
language : en
Publisher: Frontiers Media SA
Release Date : 2021-05-03
Towards A Local Realist View Of The Quantum Phenomenon written by Alberto Casado and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-03 with Science categories.