This is the first fundamental book devoted to non-Kolmogorov probability models. It provides a mathematical theory of negative probabilities, with numerous applications to quantum physics, information theory, complexity, biology and psychology. The book also presents an interesting model of cognitive information reality with flows of information probabilities, describing the process of thinking, social, and psychological phenomena.

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 s

Endophysics, Time, Quantum and the Subjective is the first systematic cross- and trans-disciplinary appraisal of the endophysical paradigm and its possible role in our understanding of Nature. Focusing on three of the most pressing issues of contemporary science, the interpretation of quantum theory, the nature of time, and the problem of consciousness, it provides the reader with some forefront research, concepts and ideas in these areas, such as incessant Big Bang, geometrizing of “mental space-times,” and a contextual view of quantum mechanics and/or a view of the Universe as a self-evolving quantum automaton. Although primarily aimed at academics this engaging volume can be read by anyone interested in modern physics, philosophy, psychology and cognitive sciences.

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.

The recent years have been characterized by stormy social protests throughout the world. These protests have some commonalities, but at the same time, their sociopolitical, psychological, and economic contexts differ essentially. An important class of such protests is known as color revolutions. The analysis of these events in social and political literature is characterized by huge diversity of opinions. We remark that the sociopolitical perturbations under consideration are characterized by the cascade dynamics leading to the exponential amplification of coherent social actions. In quantum physics, such exponential and coherent amplification is the basic feature of laser’s functioning. (“Laser” is acronym for light amplification by stimulated emission of radiation). In this book we explore the theory of laser to model aforementioned waves of social protests, from color revolutions to Brexit and Trump’s election. We call such social processes Stimulated Amplification of Social Actions (SASA), but to keep closer to the analogy with physics we merely operate with the term “social laser.”

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.

This is the 12th conference in Växjö, Sweden, which is devoted to quantum foundations and quantum information, especially the clarification of fundamental questions. The Växjö series is the longest continuous series of conferences devoted to quantum foundations in the history of quantum mechanics. During this conference, FPP6, we were fortunate to have not only physicists (theorists as well as experimentalists), but also mathematicians and several philosophers discussing the foundations of quantum theory, especially in the light of recent developments of quantum information theory. Fundamental questions of quantum mechanics, especially information theory, quantum computing, cryptography and teleportation have continued to be central topics in this series of conferences.

This Växjö conference was devoted to the reconsideration of quantum foundations. Due to increasing research in quantum information theory, especially on quantum computing and cryptography, many questions regarding the foundations of quantum mechanics, which have long been considered to be exclusively of philosophical interest, nowadays play an important role in theoretical and experimental quantum physics.

In this essay collection, leading physicists, philosophers, and historians attempt to fill the empty theoretical ground in the foundations of information and address the related question of the limits to our knowledge of the world. Over recent decades, our practical approach to information and its exploitation has radically outpaced our theoretical understanding - to such a degree that reflection on the foundations may seem futile. But it is exactly fields such as quantum information, which are shifting the boundaries of the physically possible, that make a foundational understanding of information increasingly important. One of the recurring themes of the book is the claim by Eddington and Wheeler that information involves interaction and putting agents or observers centre stage. Thus, physical reality, in their view, is shaped by the questions we choose to put to it and is built up from the information residing at its core. This is the root of Wheeler’s famous phrase “it from bit.” After reading the stimulating essays collected in this volume, readers will be in a good position to decide whether they agree with this view.

In this book we develop various mathematical models of information dynamics, I -dynamics (including the process of thinking), based on methods of classical and quantum physics. The main aim of our investigations is to describe mathematically the phenomenon of consciousness. We would like to realize a kind of Newton-Descartes program (corrected by the lessons of statistical and quantum mechanics) for information processes. Starting from the ideas of Newton and Descartes, in physics there was developed an adequate description of the dynamics of material systems. We would like to develop an analogous mathematical formalism for information and, in particular, mental processes. At the beginning of the 21st century it is clear that it would be impossible to create a deterministic model for general information processes. A deterministic model has to be completed by a corresponding statistical model of information flows and, in particular, flows of minds. It might be that such an information statistical model should have a quantum-like structure.