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 in such the experiments have “quantum-like” properties, which can not (...) be explained in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33–59, 1999). (shrink)

Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities—this is the conjunction fallacy. One of the most discussed accounts of this fallacy is currently the quantum-like explanation, which relies on models exploiting the mathematics of quantum mechanics. The aim of this paper is to investigate the empirical adequacy of major quantum-like models which represent beliefs with (...) quantum states. We first argue that they can be tested in three different ways, in a question order effect configuration which is different from the traditional conjunction fallacy experiment. We then carry out our proposed experiment, with varied methodologies from experimental economics. The experimental results we get are at odds with the predictions of the quantum-like models. This strongly suggests that this quantum-like account of the conjunction fallacy fails. Future possible research paths are discussed. (shrink)

The quantum-like approach of psychosomatic phenomena suggests an explanation of the correlations between mind and body in terms of quantum-like entanglement, that is, without appealing to any concept of psychophysical, efficient causality. This approach is developed within the Hilbert space formalism and its general consequences are drawn. It is first illustrated by a simple, qualitative model of the placebo effect which shows that representing psychosomatic states by entangled states can explain that purely psychological factors can produce (...) a-causal changes of physiological parameters. Then, a dynamical, quantitative and predictive model of bipolar disorder which makes use of the unitarity of the temporal evolution of psychosomatic states due to biological and psychological rhythms is worked out. This model can explain some current observations, like for example the severe fluctuations in mood between depression and mania, and it can forecast the moment of shifting. In addition, it justifies the efficiency of chronotherapy on theoretical basis. (shrink)

Consider the concept combination ‘pet human’. In word association experiments, human subjects produce the associate ‘slave’ in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of ‘pet’, or ‘human’ in isolation. In other words, the associate ‘slave’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this (...) article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified. (shrink)

The Titius–Bode law for planetary distances is reviewed. A model describing the basic features of this rule in the “quantum-like” language of a wave equation is proposed. Some considerations about the ’t Hooft idea on the quantum behavior of deterministic systems with dissipation are discussed.

Psychological empirical research has shown that human choice behavior often violates the assumptions of classical rational choice models. In the last few decades a new research field has emerged which aims to account for the observed choice behavior by resorting to the concepts and mathematical techniques developed in the realm of quantum physics, such as the “mental state vector” defined in a Hilbert space and the interference of quantum probability. This article is a short introduction to the (...) quantum-like approach to the description of cognitive processes. I argue that the mathematical apparatus of quantum physics can account for the observed violations of classical logic and can help develop effective models of psychological and cognitive phenomena. This is illustrated through the so-called conjunction and disjunction fallacies by providing an alternative interpretation of the results of Linda test and Hawaii test. No-fallacy configurations are made possible in the quantum-like approach by sequential modeling of mental states transitions. (shrink)

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 and contexts in which these (...) events occur. This article proposes a quantum-like (QL) model of the functioning of the brain based on the (Hilbert-space) formalism of quantum mechanics, but now used as part of a QL mathematical model of neural processes in the brain, rather than for describing quantum physical processes. This model is, thus, fundamentally different from the (reductionist) quantum model of the brain and consciousness, according to which cognition arises by virtue of physical quantum processes in the brain. In the present view, the brain is an advanced biological system that developed the ability to create a QL representation of contexts, which, thus, allows one to describe a significant part of its functioning by the QM mathematical formalism. The possibility of such a description has nothing to do with the constitution and workings of the brain as a quantum system (composed of photons, electrons, protons, and so forth). The QL model offered here is based instead on conventional neurophysiological model of the functioning of the brain, even though the brain, the article suggests, does use the QL rule (given by von Neumann trace formula, used in QM) for the calculation of approximate averages for mental functions. The QL model developed in this article has a temporal basis, based on a (hypothetical) argument that cognitive processes are based on at least two time scales: a (very fine) subcognitive one and a (much coarser) cognitive one. (shrink)

Consider the concept combination ‘pet human’. In word association experiments, human subjects produce the associate ‘slave’ in relation to this combination. The striking aspect of this associate is that it is not produced as an associate of ‘pet’, or ‘human’ in isolation. In other words, the associate ‘slave’ seems to be emergent. Such emergent associations sometimes have a creative character and cognitive science is largely silent about how we produce them. Departing from a dimensional model of human conceptual space, this (...) article will explore concept combinations, and will argue that emergent associations are a result of abductive reasoning within conceptual space, that is, below the symbolic level of cognition. A tensor-based approach is used to model concept combinations allowing such combinations to be formalized as interacting quantum systems. Free association norm data is used to motivate the underlying basis of the conceptual space. It is shown by analogy how some concept combinations may behave like quantum-entangled particles. Two methods of analysis were presented for empirically validating the presence of non-separable concept combinations in human cognition. One method is based on quantum theory and another based on comparing a joint probability distribution with another distribution based on a separability assumption using a chi-square goodness-of-fit test. Although these methods were inconclusive in relation to an empirical study of bi-ambiguous concept combinations, avenues for further refinement of these methods are identified. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability (...) calculus. The previous attempts all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability (...) calculus. The previous attempts all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

The present book takes the discovery that quantum-like behaviour is not solely reserved to atomic particles one step further. If electrons are modelled as vibrating droplets instead of the usually assumed point objects, and if the classical laws of nature are applied, then exactly the same behaviour as in quantum theory is found, quantitatively correct! The world of atoms is strange and quantum mechanics, the theory of this world, is almost magic. Or is it? Tiny droplets (...) of oil bouncing round on a fluid surface can also mimic the world of quantum mechanics. For the layman - for whom the main part of this book is written - this is good news. If the everyday laws of nature can conspire to show up quantum-like phenomena, there is hope to form mental pictures how the atomic world works. The book is almost formula-free, and explains everything by using many sketches and diagrams. The mathematical derivations underlying the main text are kept separate in a -peer reviewed - appendix. The author, a retired professor of Flight Mechanics and Propulsion at the Delft University of Technology, chose to publish his findings in this mixed popular and scientific form, because he found that interested laymen more often than professional physicists feel the need to form visualisations of quantum phenomena. (shrink)

The quantum corrections related to the ideal gas model often considered are those associated to the bosonic or fermionic nature of particles. However, in this work, other kinds of corrections related to the quantum nature of phase space are highlighted. These corrections are introduced as improvements in the expression of the partition function of an ideal gas. Then corrected thermodynamics properties of the ideal gas are deduced. Both the non-relativistic quantum and relativistic quantum cases are considered. (...) It is shown that the corrections in the non-relativistic quantum case may be particularly useful to describe the deviation from the Maxwell–Boltzmann model at low temperature and/or in confined space. These corrections can be considered as including the description of quantum size and shape effects. For the relativistic quantum case, the corrections could be relevant for confined space and when the thermal energy of each particle is comparable to their rest energy. The corrections appear mainly as modifications in the thermodynamic equation of state and in the expressions of the partition function and thermodynamic functions like entropy, internal energy and free energy. Expressions corresponding to the Maxwell–Boltzmann model are shown to be asymptotic limits of the corrected expressions. (shrink)

It is proposed that a human conscious experience of the sort we report to each other reflects a direct causal interaction between a pattern of information about the world, encoded in a field of postsynaptic potentials, and a quantized mode of excitation occupying dendritic cytoskeleton. The requirement for a quantized account is seen simply as the need for an event of experience to be a single indivisible, but richly patterned, causal relation between information and an 'informee'. It is argued that (...) the informee is likely to be a higher-order quantized collective mode (much as proposed by Craddock and colleagues, 2017) with the biologically relevant dynamics likely also to be describable in classical terms. No specific interpretation of quantum theory is needed. In this scenario, anaesthetics would abrogate reportable experience by detuning parameters underpinning cytoskeletal informee modes, perhaps critically increasing associated impedence. It is also proposed that tuning and detuning of informee modes in individual dendritic trees by binding of accessory proteins to cytoskeleton plays a physiological role in short-term memory and truth evaluation through ascertainment of sequential signal pattern consonance. Components of this model may be involved in cellular adaptive responses in many types of organism. (shrink)

This paper attempts an interpretation of Everett's relative state formulation of quantum mechanics that avoids the commitment to new metaphysical entities like ‘worlds’ or ‘minds’. Starting from Everett's quantum mechanical model of an observer, it is argued that an observer's belief to be in an eigenstate of the measurement (corresponding to the observation of a well-defined measurement outcome) is consistent with the fact that she objectively is in a superposition of such states. Subjective states corresponding to such (...) beliefs are constructed. From an analysis of these subjective states and their dynamics it is argued that Everett's pure wave mechanics is subjectively consistent with von Neumann's classical formulation of quantum mechanics. It follows from the argument that the objective state of a system is in principle unobservable. Nevertheless, an adequate concept of empirical reality can be constructed. (shrink)

This contribution is concerned with a particular model theoretic semantics of the object language of quantum physics. The object language considered here comprises logically connected propositions, sequentially connected propositions and modal propositions. The model theoretic semantics arises from the already established dialogic semantics, if the pragmatic concept of the dialog-game is replaced by a "metaphysical" concept of the game. The game is determined by a game tree, the branches of which constitute a set, the set of "possible worlds" of (...) an individual quantum physical system. The semantic concepts like truth, falsity and valuation are defined with respect to this set. (shrink)

A model for the structure of point-like fermions as tightly bound composite states is described. The model is based upon the premise that electromagnetism is the only fundamental interaction. The fundamental entity of the model is an object called the vorton. Vortons are semiclassical monopole configurations of electromagnetic charge and field, constructed to satisfy Maxwell's equations. Vortons carry topological charge and one unit each of two different kinds of angular momenta, and are placed in magnetically bound pair states having (...) angular momentum l=1/2. The topological charge prevents the mutual annihilation of the vorton pair. The helicity eigenstates of the vortons' intrinsic angular momenta form the basis for a set of internal quantum numbers for the pair which distinguish the different (point-like) pair states. Sixteen fourcomponent spinor states, eight leptonic and eight hadronic, are obtained. Eleven of these are identified with the quantum numbers of the experimentally known particles: e, ve, μ, vμ, τ, vτ; p, n, Λ, Λc, and b. Thus one new heavy lepton with its neutrino and three new quark states are predicted. Some possibilities for the extension of this model are discussed. (shrink)

Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wave function "self-collapse"(objective reduction: OR -Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of (...) microtubules suitable for quantum effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 milliseconds) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent mass-energy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum classical reduction occurs. Unlike the random, "subjective reduction"( SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. (shrink)

In physics, one is often misled in thinking that the mathematical model of a system is part of or is that system itself. Think of expressions commonly used in physics like “point” particle, motion “on the line”, “smooth” observables, wave function, and even “going to infinity”, without forgetting perplexing phrases like “classical world” versus “quantum world”.... On the other hand, when a mathematical model becomes really inoperative in regard with correct predictions, one is forced to replace it (...) with a new one. It is precisely what happened with the emergence of quantum physics. Classical models were superseded by quantum ones through quantization prescriptions. These procedures appear often as ad hoc recipes. In the present paper, well defined quantizations, based on integral calculus and Weyl–Heisenberg symmetry, are described in simple terms through one of the most basic examples of mechanics. Starting from probability distribution on the Euclidean plane viewed as the phase space for the motion of a point particle on the line, i.e., its classical model, we will show how to build corresponding quantum model and associated probabilities or quasi-probabilities distributions. We highlight the regularizing rôle of such procedures with the familiar example of the motion of a particle with a variable mass and submitted to a step potential. (shrink)

In another essay, I’ve argued by means of a formal analogy between (i) the incompleteness of Principia Mathematica-style systems of mathematical logic (logico-mathematical incompleteness) and (ii) the incompleteness of the Standard Models in contemporary physics (physico-mechanical incompleteness), that (iii) just as the fact of logico-mathematical incompleteness entails the existence of mathematical creativity, so too the fact of physico-mechanical incompleteness entails the existence of natural creativity. Building on that line of thought, in this essay I present a new and empirically-testable (...) strategy for completing quantum mechanics. More precisely, I argue that if we assume that the Standard Models in contemporary physics are incomplete, and if we also assume that all rational human animals are primitive sources of natural creativity via their free agency, then, by means of an appeal to Bohmian mechanics, together with the thesis that all rational human animals are primitive sources of natural creativity via their free agency, we can complete quantum mechanics. (shrink)

Aristotle is oftentimes viewed through a strictly philosophical lens as heir to Plato and has having introduced logical rigor where an emphasis on the theory of Forms formerly prevailed. It must be appreciated that Aristotle was the son of a physician, and that his inculcation of the thought of other Greek philosophers addressing health and the natural elements led to an extremely broad set of biologically- and medically-related writings. As this article proposes, Aristotle deepened the fourfold theory of the elements (...) with anatomic and physiologic observations. In books like History of Animals, Parts of Animals, and the lost Anatomai, he actively dissected organisms and recorded his findings. The corpus of medically-related literature Aristotle developed had a direct influence on subsequent Greek thinkers, including Galen, and on Medieval Islamic and modern Western practitioners such as William Harvey. Aristotle's ideas continue to influence modern medical thinkers in Europe and America through both his interpretation by European philosophers gaining the attention of medical humanists, and his writings' enduring impact on medical researchers balancing scientific with more personalistic approaches to medicine. (shrink)

Recently there has been a great deal of interest in tabletop experiments intended to exhibit the quantum nature of gravity by demonstrating that it can induce entanglement. In order to evaluate these experiments, we must determine if there is any interesting class of possibilities that will be convincingly ruled out if it turns out that gravity can indeed induce entanglement. In particular, since one argument for the significance of these experiments rests on the claim that they demonstrate the existence (...) of superpositions of spacetimes, it is important to keep in mind that different interpretations of quantum mechanics may make different predictions about superpositions of spacetimes. ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-complete interpretations of quantum mechanics, like the Everett interpretation, almost universally predict the existence of superpositions of spacetimes, whereas in ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete, ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-nonphysical interpretations it seems more natural to predict that spacetime superpositions are not possible. Meanwhile ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete, ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-supplemented interpretations present us with a more complex picture where we may or may not end up predicting that spacetime superpositions are possible, depending on the particular way in which the coupling between spacetime and matter is constructed. This line of reasoning suggests that what would be ruled out by a successful result to these tabletop experiments is a class of quantum gravity models that we refer to as ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete quantum gravity —i.e. models of the interaction between quantum mechanics and gravity in which gravity is coupled to non-quantum beables rather than quantum beables. It follows that the results of tabletop experiments can also be regarded as giving us new evidence about the interpretation of quantum mechanics: roughly speaking, a positive result to these experiments should increase our confidence in ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-complete interpretations, whilst a negative result should instead increase our confidence in ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete interpretations. We introduce these ideas in Sect. 1, and then in Sect. 2 we make the reasoning more precise by presenting a set of inferences that may be made about the ontology of quantum mechanics based on the results of tabletop experiments. In Sect. 3 we discuss some existing PIQG models and consider what more needs to be done to make these sorts of approaches more appealing. There are two competing paradigms for the interpretation of these experiments, which have been dubbed the ‘Newtonian’ paradigm and the ‘tripartite’ paradigm: here we largely work within the tripartite paradigm, because the tripartite view is specifically concerned with ontological aspects of the mediating gravitational interaction and that makes it a suitable setting for enquiries about the ontology of quantum mechanics, but in Sect. 4 we consider what conclusions can be drawn if one does not presuppose the tripartite view. Finally in Sect. 5 we discuss a cosmological phenomenon which could be regarded as providing evidence for PIQG models. (shrink)

Social norms can be understood as the grammar of social interaction. Like grammar in speech, they specify what is acceptable in a given context. But what are the specific rules that direct human compliance with the norm? This paper presents a quantitative model of self- and the other-perspective interaction based on a ‘quantum model of decision-making’, which can explain some of the ‘fallacies’ of the classical model of strategic choice. By connecting two fields of social science research—norms compliance, (...) and strategic decision-making—we aim to show how the novel quantum approach to the later can advance our understanding of the former. From the cacophony of different quantum models, we distill the minimal structure necessary to account for the known dynamics between the expectations and decisions of an actor. This model was designed for the strategic interaction of two players and successfully tested in the case of the one-shot Prisoners’ Dilemma game. Quantum models offer a new conceptual framework for examining the interaction between self- and other-perspective in the process of social interaction which enables us to specify how social norms influence individual behavior. (shrink)

Following a bi-cylindrical model of geometrical dynamics, our study shows that a 6D-gravitational equation leads to geodesic description in an extended symmetrical time–space, which fits Hubble-like expansion on a microscopic scale. As a duality, the geodesic solution is mathematically equivalent to the basic Klein–Gordon–Fock equations of free massive elementary particles, in particular, the squared Dirac equations of leptons. The quantum indeterminism is proved to have originated from space–time curvatures. Interpretation of some important issues of quantum mechanical reality (...) is carried out in comparison with the 5D space–time–matter theory. A solution of lepton mass hierarchy is proposed by extending to higher dimensional curvatures of time-like hyper-spherical surfaces than one of the cylindrical dynamical geometry. In a result, the reasonable charged lepton mass ratios have been calculated, which would be tested experimentally. (shrink)

We analyze the interrelation of quantum and classical entanglement. The latter notion is widely used in classical optic simulation of some quantum-like features of light. We criticize the common interpretation that “quantum nonlocality” is the basic factor differing quantum and classical realizations of entanglement. Instead, we point to the breakthrough Grangier et al. experiment on coincidence detection which was done in 1986 and played the crucial role in rejection of classical field models in favor (...) of quantum mechanics. Classical entanglement sources produce light beams with the coefficient of second order coherence \} \ge 1.\) This feature of classical entanglement is obscured by using intensities of signals in different channels, instead of counting clicks of photo-detectors. The interplay between intensity and clicks counting is not just a technicality. We elevate this issue to the high foundational level. (shrink)

We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it. The construction proceeds in the following steps: (a) Axioms for the algebra of events are introduced following Birkhoff and von Neumann. All axioms, except the one that expresses the uncertainty principle, are shared with the classical event space. The only (...) models for the set of axioms are lattices of subspaces of inner product spaces over a field K. (b) Another axiom due to Soler forces K to be the field of real, or complex numbers, or the quaternions. We suggest a probabilistic reading of Soler's axiom. (c) Gleason's theorem fully characterizes the probability measures on the algebra of events, so that Born's rule is derived. (d) Gleason's theorem is equivalent to the existence of a certain finite set of rays, with a particular orthogonality graph (Wondergraph). Consequently, all aspects of quantum probability can be derived from rational probability assignments to finite "quantum gambles". (e) All experimental aspects of entanglement- the violation of Bell's inequality in particular- are explained as natural outcomes of the probabilistic structure. (f) We hypothesize that even in the absence of decoherence macroscopic entanglement can very rarely be observed, and provide a precise conjecture to that effect .We also discuss the relation of the present approach to quantum logic, realism and truth, and the measurement problem. (shrink)

We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences. Theories carry with them their own ontology while the metaphysics may remain the same in the background. We follow a broadly Kantian tradition, distinguishing between the noumenal and phenomenal realities where the former is independent of our perception while the latter is assembled from the former by means of fragmentary bits of interpretation. Theories do not tell us how the noumenal (...) world is constituted but are conceptual constructs applying to models generated in the phenomenal world within limited contexts. -/- The ontology of quantum theory principally rests on the view that entities in the world are pervasively correlated with one another not by means of probabilities as in the case of the classical theory, but by means of probability amplitudes involving finely tuned phases characterising the oscillatory behaviour of quantum mechanical states. -/- The amplitude-dependent correlations (quantum entanglement) exist over and above the classical ones expressed in terms of probabilities. While the classical correlations are essentially local in nature, quantum correlations are shared globally in the process of environment-induced decoherence. The decoherence is an effectively random process that removes local correlations in the course of global sharing of entanglement—the removal being especially manifest in the case of systems that appear as classical ones. It is this aspect of the decoherence process that makes the so-called measurement postulate (one relating to wave function collapse) cohere with the rest of the principles of quantum theory where the latter implies a Schrodinger type time evolution of quantum mechanical systems. -/- The mathematical basis of the quantum correlations consists of the description of pure states of a system in terms of vectors in a linear vector space (a mixed state appears as an admixture of pure states with some probability distribution associated with it) and, in addition, the description of (pure) states of composite systems as vectors in the product space arising from the component sub-systems. -/- The crucial aspect of the decoherence process, of significance in the context of the apparent incompatibility of the measurement postulate with the unitary Schrodinger evolution, relates to the fact that it is almost instantaneous in the case of a classical object (one that is nevertheless amenable to a quantum description). Indeed, the decoherence time is, in all likelihood, of the order of the Planck scale, being driven by field fluctuations in the Planck regime. This points to factors of an unknown nature determining the finest details of the decoherence process since Planck scale physics remains an obscure terrain. -/- In other words, quantum theory is, to all intents and purposes, in the need of a radical revision, in keeping with the fact that all theories are defeasible and need revision as our domains of experience expand and get realigned in a complex manner. The context within which quantum theory (and quantum field theory too) is defined is set precisely by the Planck scale, across which a novel theoretical framework is likely to emerge. However, as in the case of theory revisions in general, that emerging theory will stand in an asymmetric relation of incommensurability with the present-day quantum theory, where the concepts of the latter will be comprehensible in terms of those of the former, but the converse will not hold. (shrink)

The monistic worldview aims at a uniform description of nature based on scientific models. Quantum physical systems are mutually part of the other quantum physical systems. An aperture distributes the subsystems and the wave front in all possible ways. The system only takes one of the possible paths, as measurements show. Conclusion from Bell's theorem: Before the quantum physical measurement, there is no point-like location in the universe where all the information that explains the measurement (...) is available. Distributed information is possible. Movement of the particle and measuring process are deterministic. The oscillation between location uncertainty and momentum uncertainty leads photons to determine their own location at short intervals. The uncertainty principle focuses the systems. The fields of the surrounding matter influence the location of the new formation. The effect of all fields is based on a common mechanism. (shrink)

The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable models; models that allow a realist interpretation. In this thesis some of these proofs are discussed, like von Neumann’s Theorem, the Kochen-Specker Theorem and the Bell-inequalities. Some more recent developments are also investigated, like Meyer’s nullification of the Kochen-Specker Theorem, (...) the MKC-models and Conway and Kochen’s Free Will Theorem. This last one is taken to suggest that the problems that arise for certain interpretations of quantum mechanics are not limited to realist interpretations only, but also affect certain instrumentalist interpretations. It is argued that one may arrive at a more satisfying interpretation of quantum mechanics if one adopts a logic that seems more compatible with the instrumentalist viewpoint namely, intuitionistic logic. The motivations for adopting this form of logic rather than classical logic or quantum logic are linked to some of the philosophical ideas of Bohr. In particular a new interpretation of Bohr’s notion of complementarity is proposed. Finally some possibilities are explored for linking the intuitionistic interpretation of quantum mechanics to the mathematical formalism of the theory. (shrink)

Decoherence and entanglement : new concepts and perspectives -- Quantum-like models in cognitive science and economics -- Invited presentations -- Contributed presentations -- Post-conference papers.

We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle–wave characteristics of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources. The final world model treated here contains only gravonons and a scalar matter field. The gravonons (...) are localized in the environment of the massive particles which generate them. The solution of the Schrödinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: There is a chooser mechanism for the selection of the localization site. The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which at present cannot be controlled experimentally and therefore let the choice appear statistical. The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. The times at which telegraph like jumps occur depend on subtleties of the gravonon structure which at present cannot be controlled experimentally and therefore let the telegraph-like jumps appear statistical. The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of CQM is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave function in configuration space according to Schrödinger’s equation without the need of introducing a probabilistic interpretation. (shrink)

We present a novel spontaneous collapse model where size is no longer the property of a physical system which determines its rate of collapse. Instead, we argue that the rate of spontaneous localization should depend on a system’s quantum Integrated Information, a novel physical property which describes a system’s capacity to act like a quantum observer. We introduce quantum Integrated Information, present our QII collapse model and briefly explain how it may be experimentally tested against (...) class='Hi'>quantum theory. (shrink)

The conceptual incompatibility between General Relativity and Quantum Mechanics is generally seen as a sufficient motivation for the development of a theory of Quantum Gravity. If - so a typical argumentation - Quantum Mechanics gives a universally valid basis for the description of the dynamical behavior of all natural systems, then the gravitational field should have quantum properties, like all other fundamental interaction fields. And, if General Relativity can be seen as an adequate description of (...) the classical aspects of gravity and spacetime - and their mutual relation -, this leads, together with the rather convincing arguments against semi-classical theories of gravity, to a strategy which takes a quantization of General Relativity as the natural avenue to a theory of Quantum Gravity. And, because in General Relativity the gravitational field is represented by the spacetime metric, a quantization of the gravitational field would in some sense correspond to a quantization of geometry. Spacetime would have quantum properties. But, this direct quantization strategy to Quantum Gravity will only be successful, if gravity is indeed a fundamental interaction. Only if it is a fundamental interaction, the given argumentation is valid, and the gravitational field, as well as spacetime, should have quantum properties. - What, if gravity is instead an intrinsically classical phenomenon? Then, if Quantum Mechanics is nevertheless fundamentally valid, gravity can not be a fundamental interaction; a classical and at the same time fundamental gravity is excluded by the arguments against semi-classical theories of gravity. An intrinsically classical gravity in a quantum world would have to be an emergent, induced or residual, macroscopic effect, caused by a quantum substrate dominated by other interactions, not by gravity. Then, the gravitational field (as well as spacetime) would not have any quantum properties. And then, a quantization of gravity (i.e. of General Relativity) would lead to artifacts without any relation to nature. The serious problems of all approaches to Quantum Gravity that start from a direct quantization of General Relativity (e.g. non-perturbative canonical quantization approaches like Loop Quantum Gravity) or try to capture the quantum properties of gravity in form of a 'graviton' dynamics (e.g. Covariant Quantization, String Theory) - together with the, meanwhile, rich spectrum of (more or less advanced) theoretical approaches to an emergent gravity and/or spacetime - make this latter option more and more interesting for the development of a theory of Quantum Gravity. The most advanced emergent gravity (and spacetime) scenarios are of an information-theoretical, quantum-computational type. A paradigmatic model for the emergence of gravity and spacetime comes from the Pregeometric Quantum Causal Histories approach. (shrink)

By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by ’t Hooft. We view these ontological states as the ones embedded with realism and compare them to the quantum states that represent superpositions, viewing the latter as mere information of the system they describe. Such a deterministic model puts forward conditions for the applicability of Bell’s (...) inequality: the usual inequality cannot be applied to the usual experiments. We build a Bell-like inequality that can be applied to the EPR scenario and show that this inequality is always satisfied by QM. In this way we show that QM can indeed have a local interpretation, and thus meet with the causal structure imposed by the Theory of Special Relativity in a satisfying way. (shrink)

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 observable A measured twice, one (...) A measurement after the other. The second one, \, is reproducibility with probability 1 of a result of A measurement when another quantum observable B is measured between two A’s. Heuristically, it is clear that the second type of reproducibility is complementary to the order effect. We show that, surprisingly, this may not be the case. The order effect can coexist with a separated reproducibility as well as adjacent reproducibility for both observables A and B. However, the additional constraint in the form of separated reproducibility of the \ type makes this coexistence impossible. The problem under consideration was motivated by attempts to apply the quantum formalism outside of physics, especially, in cognitive psychology and psychophysics. However, it is also important for foundations of quantum physics as a part of the problem about the structure of sequential quantum measurements. (shrink)

The well-known proposal to consider the Lüders-von Neumann measurement as a non-classical extension of probability conditionalization is further developed. The major results include some new concepts like the different grades of compatibility, the objective conditional probabilities which are independent of the underlying state and stem from a certain purely algebraic relation between the events, and an axiomatic approach to quantum mechanics. The main axioms are certain postulates concerning the conditional probabilities and own intrinsic probabilistic interpretations from the very (...) beginning. A Jordan product is derived for the observables, and the consideration of composite systems leads to operator algebras on the Hilbert space over the complex numbers, which is the standard model of quantum mechanics. The paper gives an expository overview of the results presented in a series of recent papers by the author. For the first time, the complete approach is presented as a whole in a single paper. Moreover, since the mathematical proofs are already available in the original papers, the present paper can dispense with the mathematical details and maximum generality, thus addressing a wider audience of physicists, philosophers or quantum computer scientists. (shrink)

There are strong indications that ancient Egyptian mythology contains knowledge of the nature of space up to higher dimensions and provides ontologic answers to the question about the creation of matter. This article examines the pentagonal interpretation of the myth of Isis and Osiris by comparing the iconographic details with recent findings from the art research project Quantum Cinema, where an interdisciplinary group of digital artists and scientists established a virtual space model for visualizing the usually non-perceivable processes in (...) the microcosm on a Planck scale. At this scale, quantum mechanics applied to space itself leads to a discrete amount of quantum states. For this research, a new geometrical tool proved invaluable: the epitahedron. The double heptahedron named epitahedron (E±), a 3D Penrose kites and darts representation, confines the dodecahedron in many ways and seems to be Plato’s fifth element. It is a 5D space cell, decorated with fragments of circles, which allows to visualize the permutations of symmetry elements within a discrete lattice (Z5). This higher-dimensional configuration is also the appropriate space to create a quantum-mechanical depiction of particles with inherent wave-like character by means of 3D animated geometry. Disguised in a mythological language the same subscendent space structure with the same golden polytope (E±) can be revealed: is this the origin of the concept of aether, the quintessence model which was a basic scientific task for the last 2500 years? (shrink)

The semantically ambiguous nature of the sign and aspects of non-classicality of elementary matter as described by quantum theory show remarkable coherent analogy. We focus on how the ambiguous nature of the image, text and art work bears functional resemblance to the dynamics of contextuality, entanglement, superposition, collapse and decoherence as these phenomena are known in quantum theory. These quantumlike properties in linguistic signs have previously been identified in formal descritions of e.g. concept combinations and mental lexicon representations (...) and have been reported on in the literature. In this approach the informationalized, communicated, mediatized conceptual configuration—of e.g. the art work—in the personal reflected mind behaves like a quantum state function in a higher dimensional complex space, in which it is time and again contextually collapsed and further cognitively entangled. The observer–consumer of signs becomes the empowered ‘produmer’ creating the cognitive outcome of the interaction, while loosing most of any ‘classical givenness’ of the sign. These quantum-like descriptions are now developed here in four example aesthetic signs; the installation Mist room by Ann Veronica Janssens, the installation Sections of a happy moment by David Claerbout, the photograph The Falling Man by Richard Drew and the documentary Huicholes. The Last Peyote Guardians by Vilchez and Stefani. Our present work develops further the use of a previously developed quantum model for concept representation in natural language. In our present approach of the aesthetic sign, we extend to individual—idiosyncratic—observer contexts instead of socially shared group contexts, and as such also include multiple idiosyncratic creation of meaning and experience. This irreducible superposition emerges as the core feature of the aesthetic sign and is most critically embedded in the ‘no-interpretation’ interpretation of the documentary signal. (shrink)

The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as central singularities. On the other hand, if they are extended (...) systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal geometries seem disfavoured. (shrink)

Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin–Löf. We extend this result and demonstrate that QM is algorithmic $$\omega$$ -random and generic, precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo–Fraenkel Solovay random (...) on infinite-dimensional Hilbert spaces. Moreover, it is more likely that there exists a standard transitive ZFC model M, where QM is expressed in reality, than in the universe V of sets. Then every generic quantum measurement adds to M the infinite sequence, i.e. random real $$r\in 2^{\omega }$$, and the model undergoes random forcing extensions M[r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit, therefore showing the structural resemblance of both in this limit. We discuss several questions regarding measurability and possible practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC; however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself, the issues considered here remain hidden to a great extent. (shrink)

An expression of the Lindbladian form is proposed that ensures an unambiguous time-continuous reduction of the initial system-pointer wave-packet to one in which the readings and the observable’s values are aligned, formalized as the transition from an outer product to an inner product of the system’s and apparatus’ density matrices. The jump operators are in the basis of the observables, with uniquely determined parameters derived from the measurement set-up (thereby differing from S. Weinberg’s Lindbladian resolution of wave-packet formalism) and conforming (...) to Born’s probability rules. The novelty lies in formalising the adaptability of the surroundings (including the measuring device) to the mode of observation. Accordingly, the transition is of finite duration (in contrast to its instantaneousness in the von Neumann’s formulation). This duration is estimated for a simple half-spin-like model. (shrink)

I propose a new class of interpretations, real world interpretations, of the quantum theory of closed systems. These interpretations postulate a preferred factorization of Hilbert space and preferred projective measurements on one factor. They give a mathematical characterisation of the different possible worlds arising in an evolving closed quantum system, in which each possible world corresponds to a (generally mixed) evolving quantum state. In a realistic model, the states corresponding to different worlds should be expected to tend (...) towards orthogonality as different possible quasiclassical structures emerge or as measurement-like interactions produce different classical outcomes. However, as the worlds have a precise mathematical definition, real world interpretations need no definition of quasiclassicality, measurement, or other concepts whose imprecision is problematic in other interpretational approaches. It is natural to postulate that precisely one world is chosen randomly, using the natural probability distribution, as the world realised in Nature, and that this world’s mathematical characterisation is a complete description of reality. (shrink)

This edited volume examines aspects of the mind/consciousness that are relevant to the interpretations of quantum mechanics. In it, an international group of contributors focus on the possible connections between quantum mechanics and consciousness. They look at how consciousness can help us with quantum mechanics as well as how quantum mechanics can contribute to our understanding of consciousness. For example, what do different interpretations aimed at solving the measurement problem in quantum mechanics tell us about (...) the nature of consciousness, such as von Neumann's interpretation? Each interpretation has, associated to it, a corresponding metaphysical framework that helps us think about possible “models” of consciousness. Alternatively, what does the nature of consciousness tell us about the role of the observer and time reversibility in the measurement process? The book features 20 papers on contemporary approaches to quanta and mind. It brings together the work of scholars from different disciplines with diverse views on the connections between quanta and mind, ranging from those who are supportive of a link between consciousness and quantum physics to those who are very skeptical of such link. Coverage includes such topics as free will in a quantum world, contextuality and causality, mind and matter interaction, quantum panpsychism, the quantum and quantum-like brain, and the role of time in brain-mind dynamics. (shrink)

An Interdisciplinary Approach to Cognitive Modelling presents a new approach to cognition that challenges long-held views. It systematically develops a broad-based framework to model cognition, which is mathematically equivalent to the emerging 'quantum-like modelling' of the human mind. The book argues that a satisfactory physical and philosophical basis of such an approach is missing, a particular issue being the application of quantization to the mind for which there is no empirical evidence as yet. In response to this issue, (...) the book adopts a COM (classical optical modelling) approach, broad-based but mathematically equivalent to quantum-like modelling while avoiding its problematic features. It presents a philosophically informed and empirically motivated mathematical model of cognition, mainly concerning decision making processes. It also deals with applications to different areas of the social sciences. It will be of interest to scholars and research students interested in the mathematical modelling of cognition and decision making, and also interdisciplinary researchers interested in broader issues of cognition. (shrink)

Manifestly covariant quantum theory with invariant evolution parameter is a parametrized relativistic dynamical theory. The study of parameterized relativistic dynamics (PRD) helps us understand the consequences of changing key assumptions of quantum field theory (QFT). QFT has been very successful at explaining physical observations and is the basis of the conventional paradigm, which includes the Standard Model of electroweak and strong interactions. Despite its record of success, some phenomena are anomalies that may require a modification of the Standard (...) Model. The anomalies include neutrino oscillations, non-locality, and gravity.The two key QFT assumptions that are altered in PRD are the following: fields depend on space and time; and interactions between fields are local. Locality and non-locality refer to the correlation of particles with space-like separation. A local theory does not allow the existence of greater than light speed correlations, while a non-local theory does. PRD is a non-local theory that allows fields to depend on space, time and an invariant evolution parameter. A formulation of PRD is presented together with applications that can be directly compared to results from the conventional paradigm. (shrink)

There has been an intense discussion, albeit largely an implicit one, concerning the inference of causal hypotheses from statistical correlations in quantum mechanics ever since John Bell’s first statement of his notorious theorem in 1966. As is well known, its focus has mainly been the so-called Einstein-Podolsky-Rosen (“EPR”) thought experiment, and the ensuing observed correlations in real EPR like experiments. But although implicitly the discussion goes as far back as Bell’s work, it is only in the last two (...) decades that it has become recognizably and explicitly a debate about causal inference in the quantum realm. The bulk of this paper is devoted to a review of three influential arguments in the philosophical literature that aim to show that causal models for the EPR correlations are impossible, due to Bas Van Fraassen, Daniel Hausman and Huw Price. I contend that all these arguments are inconclusive since they contain premises or presuppositions that are false, unwarranted, or at least controversial. Five different common cause models are outlined that seem perfectly viable for the EPR correlations. These models are then employed to illustrate various difficulties with the premises and presuppositions underlying Van Fraassen’s, Hausman’s and Price’s arguments. In all these cases it is argued that the difficulties cut deep against these authors’ own theories of causation and causal inference. My conclusions are that causal models for the EPR correlations remain viable, that philosophical work is still required to assess their relative virtues, and that in any case the mere theoretical conceivability and empirical possibility of these models sheds doubts over Van Fraassen’s, Hausman’s and (important elements in) Price’s theories of causation and causal inference. (shrink)

A number of writers have been attracted to the idea that some of the peculiarities of quantum theory might be manifestations of 'backward' or 'retro' causality, underlying the quantum description. This idea has been explored in the literature in two main ways: firstly in a variety of explicit models of quantum systems, and secondly at a conceptual level. This note introduces a third approach, intended to complement the other two. It describes a simple toy model, which, (...) under a natural interpretation, shows how retrocausality can emerge from simple global constraints. The model is also useful in permitting a clear distinction between the kind of retrocausality likely to be of interest in QM, and a different kind of reverse causality, with which it is liable to be confused. The model is proposed in the hope that future elaborations might throw light on the potential of retrocausality to account for quantum phenomena. (shrink)

This paper attempts an interpretation of Everett''s relative state formulation of quantum mechanics that avoids the commitment to new metaphysical entities like worlds or minds. Starting from Everett''s quantum mechanical model of an observer, it is argued that an observer''s belief to be in an eigenstate of the measurement (corresponding to the observation of a well-defined measurement outcome) is consistent with the fact that she objectively is in a superposition of such states. Subjective states corresponding to such (...) beliefs are constructed. From an analysis of these subjective states and their dynamics it is argued that Everett''s pure wave mechanics is subjectively consistent with von Neumann''s classical formulation of quantum mechanics. It follows from the argument that the objective state of a system is in principle unobservable. Nevertheless, an adequate concept of empirical reality can be constructed. (shrink)

This book is about how to understand quantum mechanics by means of a modal interpretation. Modal interpretations provide a general framework within which quantum mechanics can be considered as a theory that describes reality in terms of physical systems possessing definite properties. Quantum mechanics is standardly understood to be a theory about probabilities with which measurements have outcomes. Modal interpretations are relatively new attempts to present quantum mechanics as a theory which, like other physical theories, (...) describes an observer-independent reality. In this book, Pieter Vermaas summarises the results of this work. The book will be of great value to undergraduates, graduate students and researchers in philosophy of science, and physics departments with an interest in learning about modal interpretations of quantum mechanics. (shrink)

The emerging field of quantum mereology considers part-whole relations in quantum systems. Entangled quantum systems pose a peculiar problem in the field, since their total states are not reducible to that of their parts. While there exist several established proposals for modelling entangled systems, like monistic holism or relational holism, there is considerable unclarity, which further positions are available. Using the lambda operator and plural logic as formal tools, we review and develop conceivable models and (...) evaluate their consistency and distinctness. The main result is an exhaustive taxonomy of six distinct and precise models that both provide information about the mereological features as well as about the entangled property. The taxonomy is well-suited to serve as the basis for future systematic investigations. (shrink)