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.
Traditional approaches to cognitive psychology correspond with a classical view of logic and probability theory. More specifically, one typically assumes that cognitive processes of human thought are founded on the Boolean structures of classical logic, while the probabilistic aspects of these processes are based on the Kolmogorovian structures of classical probability theory. However, growing experimental evidence indicates that the models founded on classical structures systematically fail when human decisions are at stake. These experimental deviations from classical behavior have been called `paradoxes’, `fallacies’, `effects’ or `contradictions’, depending on the specific situation where they appear. But, they involve a broad spectrum of cognitive and social science domains, ranging from conceptual combination to decision making under uncertainty, behavioral economics, and linguistics. This situation has constituted a serious drawback to the development of various disciplines, like cognitive science, linguistics, artificial intelligence, economic modeling and behavioral finance. A different approach to cognitive psychology, initiated two decades ago, has meanwhile matured into a new domain of research, called ‘quantum cognition’. Its main feature is the use of the mathematical formalism of quantum theory as modeling tool for these cognitive situations where traditional classically based approaches fail. Quantum cognition has recently attracted the interest of important journals and editing houses, academic and funding institutions, popular science and media. Specifically, within a quantum cognition approach, one assumes that human decisions do not necessarily obey the rules of Boolean logic and Kolmogorovian probability, and can on the contrary be modeled by the quantum-mechanical formalism. Different concrete quantum-theoretic models have meanwhile been developed that successfully represent the cognitive situations that are classically problematical, by explaining observed deviations from classicality in terms of genuine quantum effects, such as `contextuality’, `emergence’, `interference’, `superposition’, `entanglement’ and `indistinguishability’. In addition, the validity of these quantum models is convincingly confirmed by new experimental tests. We also stress that, since the use of a quantum-theoretic framework is mainly for modeling purposes, the identification of quantum structures in cognitive processes does not presuppose (without being incompatible with it) the existence of microscopic quantum processes in the human brain. In this Research Topic, we review the major achievements that have been obtained in quantum cognition, by providing an accurate picture of the state-of-the-art of this emerging discipline. Our overview does not pretend to be either complete or exhaustive. But, we aim to introduce psychologists and social scientists to this challenging new research area, encouraging them, at the same time, to consider its promising results. It is our opinion that, if continuous progress in this domain can be realized, quantum cognition can constitute an important breakthrough in cognitive psychology, and potentially open the way towards a new scientific paradigm in social science.
Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modeling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision.
Over the last ten years, elements of the formalism of quantum mechanics have been successfully applied beyond physics in areas such as psychology (especially cognition), economics and finance (especially in the formalization of so-called ‘decision making’), political science, and molecular biology. An important stream of work along these lines, commonly under the heading of quantum-like modeling, has been published in well regarded scientific journals, and major publishers have devoted entire books to the topic. This Festschrift honors a key figure in this field of research: Andrei Khrennikov, who made momentous contributions to it and to quantum foundations themselves. While honoring these contributions, and in order to do so, this Festschrift orients its reader toward the future rather than focusing on the past: it addresses future challenges and establishes the way forward in both domains, quantum-like modeling and quantum foundations. A while ago, in response to the developments of using the quantum formalism outside of quantum mechanics, the eminent quantum physicist Anton Zeilinger said, ‘Why should it be precisely the quantum mechanics formalism? Maybe its generalization would be more adequate...’ This volume responds to this statement by both showing the reasons for the continuing importance of quantum formalism and yet also considering pathways to such generalizations. Khrennikov’s work has been indispensable in establishing the great promise of quantum and quantum-like thinking in shaping the future of scientific research across the disciplines.
Introduces number operators with a focus on the relationship between quantum mechanics and social science Mathematics is increasingly applied to classical problems in finance, biology, economics, and elsewhere. Quantum Dynamics for Classical Systems describes how quantum tools—the number operator in particular—can be used to create dynamical systems in which the variables are operator-valued functions and whose results explain the presented model. The book presents mathematical results and their applications to concrete systems and discusses the methods used, results obtained, and techniques developed for the proofs of the results. The central ideas of number operators are illuminated while avoiding excessive technicalities that are unnecessary for understanding and learning the various mathematical applications. The presented dynamical systems address a variety of contexts and offer clear analyses and explanations of concluded results. Additional features in Quantum Dynamics for Classical Systems include: Applications across diverse fields including stock markets and population migration as well as a unique quantum perspective on these classes of models Illustrations of the use of creation and annihilation operators for classical problems Examples of the recent increase in research and literature on the many applications of quantum tools in applied mathematics Clarification on numerous misunderstandings and misnomers while shedding light on new approaches in the field Quantum Dynamics for Classical Systems is an ideal reference for researchers, professionals, and academics in applied mathematics, economics, physics, biology, and sociology. The book is also excellent for courses in dynamical systems, quantum mechanics, and mathematical models.
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.
It is not intuitive to accept that there exists a link between quantum physical systems and cognitive systems. However, recent research has shown that cognitive systems and collective (social) systems, including biology, exhibit uncertainty which can be successfully modelled with quantum probability. The use of such probability allows for the modelling of situations which typically violate the laws of classical probability. The Palgrave Handbook of Quantum Models in Social Science is is a unique volume that brings together contributions from leading experts on key topics in this new and emerging field. Completely self-contained, it begins with an introductory section which gathers all the fundamental notions required to be able to understand later chapters. The handbook then moves on to address some of the latest research and applications for quantum methods in social science disciplines, including economics, politics and psychology. It begins with the issue of how the quantum mechanical framework can be applied to economics. Chapters devoted to this topic range from how Fisher information can be argued to play a role in economics, to the foundations and application of quantum game theory. The handbook then progresses in considering how belief states can be updated with the theory of quantum measurements (and also with more general methods). The practical use of the Hilbert space (and Fock space) in decision theory is then introduced, and open quantum systems are also considered. The handbook also treats a model of neural oscillators that reproduces some of the features of quantum cognition. Other contributions delve into causal reasoning using quantum Bayes nets and the role of quantum probability in modelling so called affective evaluation. The handbook is rounded off with two chapters which discuss the grand challenges which lie ahead of us. How can the quantum formalism be justified in social science and is the traditional quantum formalism too restrictive? Finally, a question is posed: whether there is a necessary role for quantum mathematical models to go beyond physics. This book will bring the latest and most cutting edge research on quantum theory to social science disciplines. Students and researchers across the discipline, as well as those in the fields of physics and mathematics will welcome this important addition to the literature.
Quantum theory is perhaps our best confirmed theory for a description of the physical properties of nature. On top of demonstrating great empirical effectiveness, many technological developments in the 20th century (such as the interpretation of the periodic table of elements, CD players, holograms, and quantum state teleportation) were only made possible with Quantum theory.Despite its success in the past decades, even today it still remains without a universally accepted interpretation.This book provides an interdisciplinary perspective on the question; 'What is Quantum Mechanics talking about?', a question which continues to be one of the most fascinating and important questions in science.Using an interdisciplinary approach to foundational problems in Quantum Mechanics (QM), ranging from philosophical questions about the interpretation of QM to technical problems in quantum computation, this book explores quantum mechanics from different perspectives (physical, logical, philosophical and mathematical), by researchers from Europe, North America, and South America.
This two-volume set (LNAI 10448 and LNAI 10449) constitutes the refereed proceedings of the 9th International Conference on Collective Intelligence, ICCCI 2017, held in Nicosia, Cyprus, in September 2017. The 117 full papers presented were carefully reviewed and selected from 248 submissions. The conference focuseson the methodology and applications of computational collective intelligence, included: multi-agent systems, knowledge engineering and semantic web, social networks and recommender systems, text processing and information retrieval, data mining methods and applications, sensor networks and internet of things, decision support & control systems, and computer vision techniques.
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.
