-
169The Principle of Supplementarity: A Contextual Probabilistic Viewpoint to Complementarity, the Interference of Probabilities and Incompatibility of Variables in Quantum MechanicsFoundations of Physics 35 (10): 1655-1693. 2005.We presented a contextual statistical model of the probabilistic description of physical reality. Here contexts (complexes of physical conditions) are considered as basic elements of reality. There is discussed the relation with QM. We propose a realistic analogue of Bohr’s principle of complementarity. In the opposite to the Bohr’s principle, our principle has no direct relation with mutual exclusivity for observables. To distinguish our principle from the Bohr’s principle and to give better ch…Read more
-
159Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability LawFoundations of Physics 43 (7): 895-911. 2013.There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit…Read more
-
159CHSH Inequality: Quantum Probabilities as Classical Conditional ProbabilitiesFoundations of Physics 45 (7): 711-725. 2015.In this note we demonstrate that the results of observations in the EPR–Bohm–Bell experiment can be described within the classical probabilistic framework. However, the “quantum probabilities” have to be interpreted as conditional probabilities, where conditioning is with respect to fixed experimental settings. Our approach is based on the complete account of randomness involved in the experiment. The crucial point is that randomness of selections of experimental settings has to be taken into ac…Read more
-
111Frequency Analysis of the EPR-Bell ArgumentationFoundations of Physics 32 (7): 1159-1174. 2002.We perform a frequency analysis of the EPR-Bell argumentation. One of the main consequences of our investigation is that the existence of probability distributions of the Kolmogorov-type which was supposed by some authors is a mathematical assumption which may not be supported by actual physical quantum processes. In fact, frequencies for hidden variables for quantum particles and measurement devices may fluctuate from run to run of an experiment. These fluctuations of frequencies for micro-para…Read more
-
89Quantum Information Biology: From Information Interpretation of Quantum Mechanics to Applications in Molecular Biology and Cognitive PsychologyFoundations of Physics 45 (10): 1362-1378. 2015.We discuss foundational issues of quantum information biology —one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from “traditional quantum biophysics”. The latter is about quantum bio-physical processes, e.g., in cells or brains. QIB models the dynamics of information states of bio-system…Read more
-
85Quantum-Like Model for Decision Making Process in Two Players Game: A Non-Kolmogorovian ModelFoundations of Physics 41 (3): 538-548. 2011.In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected …Read more
-
77Reality Without Realism: On the Ontological and Epistemological Architecture of Quantum MechanicsFoundations of Physics 45 (10): 1269-1300. 2015.First, this article considers the nature of quantum reality and the concept of realism in quantum theory, in conjunction with the roles of locality, causality, and probability and statistics there. Second, it offers two interpretations of quantum mechanics, developed by the authors of this article, the second of which is also a different theory of quantum phenomena. Both of these interpretations are statistical. The first interpretation, by A. Plotnitsky, “the statistical Copenhagen interpretati…Read more
-
64Formal Foundations for the Origins of Human ConsciousnessP-Adic Numbers, Ultrametric Analysis, and Applications 8 (4): 249-279. 2016.In the framework of p-adic analysis (the simplest version of analysis on trees in which hierarchic structures are presented through ultrametric distance) applied to formalize psychic phenomena, we would like to propose some possible first hypotheses about the origins of human consciousness centered on the basic notion of time symmetry breaking as meant according to quantum field theory of infinite systems. Starting with Freud's psychophysical (hydraulic) model of unconscious and conscious flows …Read more
-
61Detection Model Based on Representation of Quantum Particles by Classical Random Fields: Born’s Rule and Beyond (review)Foundations of Physics 39 (9): 997-1022. 2009.Recently a new attempt to go beyond quantum mechanics (QM) was presented in the form of so called prequantum classical statistical field theory (PCSFT). Its main experimental prediction is violation of Born’s rule which provides only an approximative description of real probabilities. We expect that it will be possible to design numerous experiments demonstrating violation of Born’s rule. Moreover, recently the first experimental evidence of violation was found in the triple slit interference ex…Read more
-
58Complementarity of Mental ObservablesTopics in Cognitive Science 6 (1): 74-78. 2014.The aim of this note is to complete the discussion on the possibility of creation of quantum-like (QL) representation for the question order effect which was presented by Wang and Busemeyer (2013). We analyze the role of a fundamental feature of mental operators (given, e.g., by questions), namely, their complementarity
-
56On Relations Between Probabilities Under Quantum and Classical MeasurementsFoundations of Physics 34 (4): 689-704. 2004.We show that the so-called quantum probabilistic rule, usually introduced in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is commonly accepted, in contrast to the rule for the addition of probabilities of mutually exclusive events. The latter is valid under all experimental situations upon classical and quantum systems. We discuss also the quantum measurement situation that is similar…Read more
-
54Reflections on Zeilinger–Brukner Information Interpretation of Quantum MechanicsFoundations of Physics 46 (7): 836-844. 2016.In this short review I present my personal reflections on Zeilinger–Brukner information interpretation of quantum mechanics.In general, this interpretation is very attractive for me. However, its rigid coupling to the notion of irreducible quantum randomness is a very complicated issue which I plan to address in more detail. This note may be useful for general public interested in quantum foundations, especially because I try to analyze essentials of the information interpretation critically. Th…Read more
-
50Decision Theory and Choices: A Complexity Approach (edited book)Springer Verlag Italia. 2010.The New Economic Windows Series, derived from Massimo Salzano's ideas and work, incorporates material from textbooks, monographs and conference proceedings that deals with both the theoretical and applied aspects of various sub-disciplines ...
-
49Towards Better Understanding QBismFoundations of Science 23 (1): 181-195. 2018.Recently I posted a paper entitled “External observer reflections on QBism”. As any external observer, I was not able to reflect all features of QBism properly. The comments I received from one of QBism’s creators, C. A. Fuchs, were very valuable to me in better understanding the views of QBists. Some of QBism’s features are very delicate and extracting them from articles of QBists is not a simple task. Therefore, I hope that the second portion of my reflections on QBism might be interesting and…Read more
-
49What are the appropriate axioms of rationality for reasoning under uncertainty with resource-constrained systems?Behavioral and Brain Sciences 43. 2020.When constrained by limited resources, how do we choose axioms of rationality? The target article relies on Bayesian reasoning that encounter serioustractabilityproblems. We propose another axiomatic foundation: quantum probability theory, which provides for less complex and more comprehensive descriptions. More generally, defining rationality in terms of axiomatic systems misses a key issue: rationality must be defined by humans facing vague information.
-
49Prequantum Classical Statistical Field Theory: Schrödinger Dynamics of Entangled Systems as a Classical Stochastic Process (review)Foundations of Physics 41 (3): 317-329. 2011.The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a “quantum system” is just a label for (so to say “prequantum”) class…Read more
-
48The quantum-like brain on the cognitive and subcognitive time scalesJournal of Consciousness Studies 15 (7): 39-77. 2008.This article takes as its point of departure the view that the discovery of the mathematical formalism of quantum mechanics (QM) was not merely a discovery of a new mathematical way of dealing with physical, and specifically quantum, processes in nature. It was also a discovery of a general mathematical formalism (in part discovered in mathematics itself earlier), which, supplemented by certain additional rules, consistently described the processing of incomplete information about certain events…Read more
-
47On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum MeasurementsFoundations of Physics 45 (10): 1379-1393. 2015.In this paper we study the problem of a possibility to use quantum observables to describe a possible combination of the order effect with sequential reproducibility for quantum measurements. By the order effect we mean a dependence of probability distributions on the order of measurements. We consider two types of the sequential reproducibility: adjacent reproducibility ) and separated reproducibility). The first one is reproducibility with probability 1 of a result of measurement of some obser…Read more
-
41Preface of the Special Issue Probing the Limits of Quantum Mechanics: Theory and Experiment, Volume 2Foundations of Physics 50 (11): 1735-1738. 2015.
-
41Unconditional Quantum Correlations do not Violate Bell’s InequalityFoundations of Physics 45 (10): 1179-1189. 2015.In this paper I demonstrate that the quantum correlations of polarization observables used in Bell’s argument against local realism have to be interpreted as conditional quantum correlations. By taking into account additional sources of randomness in Bell’s type experiments, i.e., supplementary to source randomness, I calculate the complete quantum correlations. The main message of the quantum theory of measurement is that complete correlations can be essentially smaller than the conditional one…Read more
-
40Description of Composite Quantum Systems by Means of Classical Random FieldsFoundations of Physics 40 (8): 1051-1064. 2010.Recently a new attempt to go beyond QM was performed in the form of so-called prequantum classical statistical field theory (PCSFT). In this approach quantum systems are described by classical random fields, e.g., the electron field or the neutron field. Averages of quantum observables arise as approximations of averages of classical variables (functionals of “prequantum fields”) with respect to fluctuations of fields. For classical variables given by quadratic functionals of fields, quantum and…Read more
-
40Photon Flux and Distance from the Source: Consequences for Quantum CommunicationFoundations of Physics 44 (4): 389-405. 2014.The paper explores the fundamental physical principles of quantum mechanics (in fact, quantum field theory) that limit the bit rate for long distances and examines the assumption used in this exploration that losses can be ignored. Propagation of photons in optical fibers is modelled using methods of quantum electrodynamics. We define the “photon duration” as the standard deviation of the photon arrival time; we find its asymptotics for long distances and then obtain the main result of the paper…Read more
-
40Preface of the Special Issue Quantum Foundations: Theory and Experiment (review)Foundations of Physics 42 (6): 721-724. 2012.
-
34Entanglement of Observables: Quantum Conditional Probability ApproachFoundations of Physics 53 (5): 1-22. 2023.This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable _A_ and _B_. In our framework, it is meaningless to speak about entanglement without pointing to the fixed observables _A_ and _B_, so this is _AB_-entanglement. Dependence of quantum observables is formalized as non-coincidence of conditional probabilities. Starting with this probabilisti…Read more
-
33Aims and Scope of the Special Issue, “Quantum Foundations: Informational Perspective”Foundations of Physics 47 (8): 1003-1008. 2017.
-
33The Present Situation in Quantum Theory and its Merging with General RelativityFoundations of Physics 47 (8): 1077-1099. 2017.We discuss the problems of quantum theory complicating its merging with general relativity. QT is treated as a general theory of micro-phenomena—a bunch of models. Quantum mechanics and quantum field theory are the most widely known. The basic problems of QM and QFT are considered in interrelation. For QM, we stress its nonrelativistic character and the presence of spooky action at a distance. For QFT, we highlight the old problem of infinities. And this is the main point of the paper: it is mea…Read more
-
33Quantum Markov model for data from Shafir-Tversky experiments in cognitive psychologyIn Krzysztof Stefanski (ed.), Open Systems and Information Dynamics, World Scientific Publishing Company. pp. 16--04. 2009.