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Contextual Approach To Quantum Formalism
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Book Synopsis Contextual Approach to Quantum Formalism by : Andrei Y. Khrennikov
Download or read book Contextual Approach to Quantum Formalism written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Contextual Approach to Quantum Formalism by : Andrei Y. Khrennikov
Download or read book Contextual Approach to Quantum Formalism written by Andrei Y. Khrennikov and published by Springer. This book was released on 2009-08-29 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Foundations of Quantum Mechanics, an Empiricist Approach by : W.M. de Muynck
Download or read book Foundations of Quantum Mechanics, an Empiricist Approach written by W.M. de Muynck and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking a new perspective provided by a generalization of the mathematical formalism encompassing positive operator-valued measures, this book views old and new problems of the foundations of quantum mechanics. It demonstrates the crucial role of the generalized formalism in fundamental issues and practical applications.
Book Synopsis The Formalisms of Quantum Mechanics by : Francois David
Download or read book The Formalisms of Quantum Mechanics written by Francois David and published by Springer. This book was released on 2014-11-06 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and special relativity through their common roots - causality, locality and reversibility, as well as on the relation between quantum theory, information theory, correlations and measurements, and quantum gravity. Quantum mechanics is probably the most successful physical theory ever proposed and despite huge experimental and technical progresses in over almost a century, it has never been seriously challenged by experiments. In addition, quantum information science ha s become an important and very active field in recent decades, further enriching the many facets of quantum physics. Yet, there is a strong revival of the discussions about the principles of quantum mechanics and its seemingly paradoxical aspects: sometimes the theory is portrayed as the unchallenged and dominant paradigm of modern physical sciences and technologies while sometimes it is considered a still mysterious and poorly understood theory, waiting for a revolution. This volume, addressing graduate students and seasoned researchers alike, aims to contribute to the reconciliation of these two facets of quantum mechanics.
Book Synopsis Contextuality From Quantum Physics To Psychology by : Ehtibar N Dzhafarov
Download or read book Contextuality From Quantum Physics To Psychology written by Ehtibar N Dzhafarov and published by World Scientific. This book was released on 2015-11-30 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explores the variety of meanings of contextuality across different disciplines, with the emphasis on quantum physics and on psychology.
Book Synopsis Ubiquitous Quantum Structure by : Andrei Y. Khrennikov
Download or read book Ubiquitous Quantum Structure written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2010-01-23 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum-Like Models for Information Retrieval and Decision-Making by : Diederik Aerts
Download or read book Quantum-Like Models for Information Retrieval and Decision-Making written by Diederik Aerts and published by Springer Nature. This book was released on 2019-09-09 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have been characterized by tremendous advances in quantum information and communication, both theoretically and experimentally. In addition, mathematical methods of quantum information and quantum probability have begun spreading to other areas of research, beyond physics. One exciting new possibility involves applying these methods to information science and computer science (without direct relation to the problems of creation of quantum computers). The aim of this Special Volume is to encourage scientists, especially the new generation (master and PhD students), working in computer science and related mathematical fields to explore novel possibilities based on the mathematical formalisms of quantum information and probability. The contributing authors, who hail from various countries, combine extensive quantum methods expertise with real-world experience in application of these methods to computer science. The problems considered chiefly concern quantum information-probability based modeling in the following areas: information foraging; interactive quantum information access; deep convolutional neural networks; decision making; quantum dynamics; open quantum systems; and theory of contextual probability. The book offers young scientists (students, PhD, postdocs) an essential introduction to applying the mathematical apparatus of quantum theory to computer science, information retrieval, and information processes.
Book Synopsis Beyond Quantum by : Andrei Khrennikov
Download or read book Beyond Quantum written by Andrei Khrennikov and published by CRC Press. This book was released on 2014-04-10 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present wave of interest in quantum foundations is caused by the tremendous development of quantum information science and its applications to quantum computing and quantum communication. It has become clear that some of the difficulties encountered in realizations of quantum information processing have roots at the very fundamental level. To solve such problems, quantum theory has to be reconsidered. This book is devoted to the analysis of the probabilistic structure of quantum theory, probing the limits of classical probabilistic representation of quantum phenomena.
Book Synopsis Quantum Interaction by : Harald Atmanspacher
Download or read book Quantum Interaction written by Harald Atmanspacher and published by Springer. This book was released on 2016-01-07 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Interaction by : Peter Bruza
Download or read book Quantum Interaction written by Peter Bruza and published by Springer. This book was released on 2009-03-18 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Bio-informatics III by : Luigi Accardi
Download or read book Quantum Bio-informatics III written by Luigi Accardi and published by World Scientific. This book was released on 2010 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this proceedings volume is to look for interdisciplinary bridges in mathematics, physics, information and life sciences, in particular, research for new paradigms for information and life sciences on the basis of quantum theory. The main areas in this volume are all related to one of the following subjects: (1) quantum information, (2) bio-informatics and (3) the interrelation between (1) and (2).
Book Synopsis Quantum Adaptivity in Biology: From Genetics to Cognition by : Masanari Asano
Download or read book Quantum Adaptivity in Biology: From Genetics to Cognition written by Masanari Asano and published by Springer. This book was released on 2015-04-14 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines information processing performed by bio-systems at all scales: from genomes, cells and proteins to cognitive and even social systems. It introduces a theoretical/conceptual principle based on quantum information and non-Kolmogorov probability theory to explain information processing phenomena in biology as a whole. The book begins with an introduction followed by two chapters devoted to fundamentals, one covering classical and quantum probability, which also contains a brief introduction to quantum formalism, and another on an information approach to molecular biology, genetics and epigenetics. It then goes on to examine adaptive dynamics, including applications to biology, and non-Kolmogorov probability theory. Next, the book discusses the possibility to apply the quantum formalism to model biological evolution, especially at the cellular level: genetic and epigenetic evolutions. It also presents a model of the epigenetic cellular evolution based on the mathematical formalism of open quantum systems. The last two chapters of the book explore foundational problems of quantum mechanics and demonstrate the power of usage of positive operator valued measures (POVMs) in biological science. This book will appeal to a diverse group of readers including experts in biology, cognitive science, decision making, sociology, psychology, and physics; mathematicians working on problems of quantum probability and information and researchers in quantum foundations.
Book Synopsis Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems by : Masanori Ohya
Download or read book Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems written by Masanori Ohya and published by Springer Science & Business Media. This book was released on 2011-01-15 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems. It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive dynamics, relativistic quantum information, and a new paradigm for quantum computation beyond the usual quantum Turing machine. Also, some important applications of information theory to genetics and life sciences, as well as recent experimental and theoretical discoveries in quantum photosynthesis are described.
Book Synopsis The Emerging Quantum by : Luis de la Peña
Download or read book The Emerging Quantum written by Luis de la Peña and published by Springer. This book was released on 2014-07-15 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the latest findings from a long-term research project intended to identify the physics behind Quantum Mechanics. A fundamental theory for quantum mechanics is constructed from first physical principles, revealing quantization as an emergent phenomenon arising from a deeper stochastic process. As such, it offers the vibrant community working on the foundations of quantum mechanics an alternative contribution open to discussion. The book starts with a critical summary of the main conceptual problems that still beset quantum mechanics. The basic consideration is then introduced that any material system is an open system in permanent contact with the random zero-point radiation field, with which it may reach a state of equilibrium. Working from this basis, a comprehensive and self-consistent theoretical framework is then developed. The pillars of the quantum-mechanical formalism are derived, as well as the radiative corrections of nonrelativistic QED, while revealing the underlying physical mechanisms. The genesis of some of the central features of quantum theory is elucidated, such as atomic stability, the spin of the electron, quantum fluctuations, quantum nonlocality and entanglement. The theory developed here reaffirms fundamental scientific principles such as realism, causality, locality and objectivity.
Book Synopsis Quantum Interaction by : Jerome R. Busemeyer
Download or read book Quantum Interaction written by Jerome R. Busemeyer and published by Springer. This book was released on 2012-11-28 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 6th International Symposium on Quantum Interaction, QI 2012, held in Paris in June 2012. The 21 revised full papers presented were carefully reviewed and selected from 32 submissions. The papers cover various topics on quantum interaction.
Book Synopsis Quantum Foundations, Probability and Information by : Andrei Khrennikov
Download or read book Quantum Foundations, Probability and Information written by Andrei Khrennikov and published by Springer. This book was released on 2018-06-13 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composed of contributions from leading experts in quantum foundations, this volume presents viewpoints on a number of complex problems through informational, probabilistic, and mathematical perspectives and features novel mathematical models of quantum and subquantum phenomena. Rich with multi-disciplinary mathematical content, this book includes applications of partial differential equations in quantum field theory, differential geometry, oscillatory processes and vibrations, and Feynman integrals for quickly growing potential functions. Due to rapid growth in the field in recent years, this volume aims to promote interdisciplinary collaboration in the areas of quantum probability, information, communication and foundation, and mathematical physics. Many papers discuss complex yet novel problems that depart from the mainstream of quantum physical studies. Others devote explanation to fundamental problems of the conventional quantum theory, including its mathematical formalism. Overall, authors cover a diverse set of topics, including quantum and classical field theory and oscillatory processing, quantum mechanics from a Darwinian evolutionary perspective, and biological applications of quantum theory. Together in one volume, these essays will be useful to experts in the corresponding areas of quantum theory. Theoreticians, experimenters, mathematicians, and even philosophers in quantum physics and quantum probability and information theory can consider this book a valuable resource.
Book Synopsis Emergent Quantum Mechanics by : Jan Walleczek
Download or read book Emergent Quantum Mechanics written by Jan Walleczek and published by MDPI. This book was released on 2019-04-02 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in "deeper-level" theories for quantum phenomena challenges the standard, textbook interpretation. The book presents expert views that critically evaluate the significance—for 21st century physics—of ontological quantum mechanics, an approach that David Bohm helped pioneer. The possibility of a deterministic quantum theory was first introduced with the original de Broglie-Bohm theory, which has also been developed as Bohmian mechanics. The wide range of perspectives that were contributed to this book on the occasion of David Bohm’s centennial celebration provide ample evidence for the physical consistency of ontological quantum mechanics. The book addresses deeper-level questions such as the following: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent? As the book demonstrates, the advancement of ‘quantum ontology’—as a scientific concept—marks a clear break with classical reality. The search for quantum reality entails unconventional causal structures and non-classical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.
