Probabilistic And Statistical Aspects Of Quantum Theory
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Probabilistic And Statistical Aspects Of Quantum Theory
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Author : Alexander S. Holevo
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-05
Probabilistic And Statistical Aspects Of Quantum Theory written by Alexander S. Holevo 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 2011-05-05 with Mathematics categories.
This book is devoted to aspects of the foundations of quantum mechanics in which probabilistic and statistical concepts play an essential role. The main part of the book concerns the quantitative statistical theory of quantum measurement, based on the notion of positive operator-valued measures. During the past years there has been substantial progress in this direction, stimulated to a great extent by new applications such as Quantum Optics, Quantum Communication and high-precision experiments. The questions of statistical interpretation, quantum symmetries, theory of canonical commutation relations and Gaussian states, uncertainty relations as well as new fundamental bounds concerning the accuracy of quantum measurements, are discussed in this book in an accessible yet rigorous way. Compared to the first edition, there is a new Supplement devoted to the hidden variable issue. Comments and the bibliography have also been extended and updated.
Probabilistic And Statistical Aspects Of Quantum Theory
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Author : Aleksandr Semenovich Kholevo
language : en
Publisher: North Holland
Release Date : 1982
Probabilistic And Statistical Aspects Of Quantum Theory written by Aleksandr Semenovich Kholevo and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Science categories.
Statistical Structure Of Quantum Theory
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Author : Alexander S. Holevo
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-01
Statistical Structure Of Quantum Theory written by Alexander S. Holevo 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 2003-07-01 with Science categories.
New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.
Contextual Approach To Quantum Formalism
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Author : Andrei Y. Khrennikov
language : en
Publisher: Springer
Release Date : 2009-05-19
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 2009-05-19 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.
Perspectives In Mathematical Science I Probability And Statistics
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Author : N S Narasimha Sastry
language : en
Publisher: World Scientific
Release Date : 2009-07-06
Perspectives In Mathematical Science I Probability And Statistics written by N S Narasimha Sastry and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-06 with Mathematics categories.
This book presents a collection of invited articles by distinguished probabilists and statisticians on the occasion of the Platinum Jubilee Celebrations of the Indian Statistical Institute — a notable institute with significant achievement in research areas of statistics, probability and mathematics — in 2007.With a wide coverage of topics in probability and statistics, the articles provide a current perspective of different areas of research, emphasizing the major challenging issues. The book also proves its reference and utility value for practitioners as the articles in Statistics contain applications of the methodology that will be of use to practitioners. To professional statisticians and mathematicians, this is a unique volume for its illuminating perspectives on several important aspects of probability and statistics.
State Of The Art In Probability And Statistics
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Author : Mathisca de Gunst
language : en
Publisher: IMS
Release Date : 2001
State Of The Art In Probability And Statistics written by Mathisca de Gunst and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
History Of Western Philosophy From A Perspective Of Quantum Theory
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Author : Shiro ISHIKAWA
language : en
Publisher: Shiho-Shuppan Publisher
Release Date : 2023-05-22
History Of Western Philosophy From A Perspective Of Quantum Theory written by Shiro ISHIKAWA and has been published by Shiho-Shuppan Publisher this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-22 with Philosophy categories.
Recently I proposed Quantum Language (QL) as a language of (dualistic and idealistic) science, which is also characterized as a linguistic turn of quantum mechanics. QL has two subclasses, non-commutative QL and commutative QL. They are applicable to quantum systems and to classical systems, respectively. QL is composed of Axiom 1 (measurement), Axiom 2 (causality), and the linguistic Copenhagen interpretation. This theory has a stronger descriptive power than (quantum) mechanics and statistics. Axioms 1 and 2 are usual since they are operator algebraic generalizations of quantum mechanics. On the other hand, the part of “linguistic Copenhagen interpretation” is not usual. This is defined by “a rule for drawing a line between science and pseudoscience”. For example, the Popper's falsifiability is one of the rules of the linguistic Copenhagen interpretation. Other examples are: 1) “There exists only `one', and not `many'.” (due to Parmenides) -> “Measurement can only be done once”, “A state does not move.” 2)“There is no motion.”(due to Parmenides) -> “A state does not move.” 3) “There is only the present.” ( due to Augustinus) -> “There is no tense.” 4) “To be is to be perceived.” (due to Berkely) -> “Nothing can be said without measurement.” ... It is surprising that philosophers who did not know quantum mechanics approached the Copenhagen interpretation as described above. Thus, I consider that the Copenhagen Interpretation is not attached to quantum mechanics, but to quantum language. I will show that QL is a scientific perfection of dualistic idealism in Western philosophy. In fact, the following unsolved problems in Western philosophy can be solved only by QL, not by statistics. * Zeno paradoxes, the problem of universals, Descartes problem (=mind-body problem + subjectivity problem), the Leibniz-Clarke space-time correspondence, Hume's problem of induction, the Grue paradox, From Kantian synthesis to QL-synthesis, the brain in a vat, Hempel's flagpole problem, the black raven problem, Wittgenstein's problem “ Why does logic work in our world?”, etc. The most fundamental theories in modern science are commonly said to be the three: theory of relativity, quantum mechanics, and statistics. However, as this book will show, commutative QL is more powerful and beautiful than statistics. Therefore, I would replace the above three by “ theory of relativity, quantum mechanics, and commutative QL”.
Epistemic Processes
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Author : Inge S. Helland
language : en
Publisher: Springer
Release Date : 2018-09-21
Epistemic Processes written by Inge S. Helland and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-21 with Mathematics categories.
This book discusses a link between statistical theory and quantum theory based on the concept of epistemic processes – which can be e.g. statistical investigations or quantum mechanical measurements, and refer to processes that are used to gain knowledge about something. The book addresses a range of topics, including a derivation of the Born formula from reasonable assumptions, a derivation of the Schrödinger equation in the one-dimensional case, and a discussion of the Bell inequality from an epistemic perspective. The book describes a possible epistemic foundation of quantum theory. Lastly, it presents a general philosophical discussion of the approach, which, principally speaking, is not restricted to the micro-world. Hence the book can also be seen as a motivation for further research into quantum decision theory and quantum models for cognition. The book will benefit a broad readership, including physicists and statisticians interested in the foundation of their disciplines, philosophers of science and graduate students, and anyone with a reasonably good background in mathematics and an open mind.
The Nature Of Quantum Paradoxes
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Author : G. Tarozzi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Nature Of Quantum Paradoxes written by G. Tarozzi 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 2012-12-06 with Science categories.
For three days in April of 1985, Cesena (Italy) was the scene of a national conference which was convened, by the Assessorato alia Cultura of this town under the auspices of the Societa Italiana di Logica e Filosofia delle Scienze (SILFS), in order to celebrate two historical milestones: the centenary of the birth of Niels Bohr, who was to become the leader of the orthodox, or Copenhagen, interpretation of quantum theory, and the fiftieth anniversary of the publication of the most influential challenge to this interpretation which was contained in the well-known paper coauthored by Einstein, Podolsky, and Rosen. The proceedings of the Cesena meeting, which are collected in the present volume, are intended to provide an exhaustive and panoramic view of the most recent investigations carried out by Italian scientists and philo sophers engaged in research on the foundations of quantum physics. What emerges is a critical review of, and alternative approaches to, the orthodox interpretation of the Copenhagen school.
Probability In Physics
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Author : Yemima Ben-Menahem
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-10
Probability In Physics written by Yemima Ben-Menahem 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 2012-01-10 with Science categories.
What is the role and meaning of probability in physical theory, in particular in two of the most successful theories of our age, quantum physics and statistical mechanics? Laws once conceived as universal and deterministic, such as Newton‘s laws of motion, or the second law of thermodynamics, are replaced in these theories by inherently probabilistic laws. This collection of essays by some of the world‘s foremost experts presents an in-depth analysis of the meaning of probability in contemporary physics. Among the questions addressed are: How are probabilities defined? Are they objective or subjective? What is their explanatory value? What are the differences between quantum and classical probabilities? The result is an informative and thought-provoking book for the scientifically inquisitive.