Results for 'quantum measurement'

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  1. The Quantum Measurement Problem - Collapse of the Wave Function Explained.Rochelle Marianne Forrester - unknown
    Quantum physicists have made many attempts to solve the quantum measurement problem, but no solution seems to have received widespread acceptance. The time has come for a new approach. In Sense Perception and Reality: A Theory of Perceptual Relativity, Quantum Mechanics and the Observer Dependent Universe I suggest the quantum measurement problem is caused by a failure to understand that each species has its own sensory world and that when we say the wave function (...)
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  2. Quantum Measurement, Complexity and Discrete Physics.Martin Leckey - 2003 - arXiv.
    This paper presents a new modified quantum mechanics, Critical Complexity Quantum Mechanics, which includes a new account of wavefunction collapse. This modified quantum mechanics is shown to arise naturally from a fully discrete physics, where all physical quantities are discrete rather than continuous. I compare this theory with the spontaneous collapse theories of Ghirardi, Rimini, Weber and Pearle and discuss some implications of these theories and CCQM for a realist view of the quantum realm.
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  3.  47
    Quantum Measure From a Philosophical Viewpoint.Vasil Penchev - 2014 - Journal of Siberian Federal University. Humanities and Social Sciences 7 (1):4-19.
    The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be (...)
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  4.  66
    Time and the Quantum Measurement Problem.Ted Dace - 2021 - International Journal of Quantum Foundations Supplement 3 (1):32-43.
    The quantum measurement problem resolves according to the twofold nature of time. Whereas the continuous evolution of the wave function reflects the fundamental nature of time as continuous presence, the collapse of the wave function indicates the subsidiary aspect of time as the projection of instantaneity from the ongoing present. Each instant irreversibly emerges from the reversible temporal continuum implicit in the smoothly propagating wave function. The basis of this emergence is periodic conflict between quantum systems, the (...)
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  5. The Dynamics of Stock Exchange Based on the Formalism of Weak Continuous Quantum Measurement.S. I. Melnyk & I. G. Tuluzov - 2010 - Journal of Physics 238 (012035):1-9.
    The problem of measurement in economic models and the possibility of their quantum-mechanical description are considered. It is revealed that the apparent paradox of such a description is associated with a priori requirement of conformity of the model to all the alternatives of free choice of the observer. The measurement of the state of a trader on a stock exchange is formally defined as his responses to the proposals of sale at a fixed price. It is shown (...)
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  6. Is the Brain Analogous to a Quantum Measuring Apparatus?Paavo Pylkkänen - 2022 - In Shyam Wuppuluri & Anthony C. Grayling (eds.), Metaphors and Analogies in Sciences and Humanities: Words and Worlds. Cham: Springer Synthese Library. pp. 215-235.
    Researchers have suggested since the early days of quantum theory that there are strong analogies between quantum phenomena and mental phenomena and these have developed into a vibrant new field of quantum cognition during recent decades. After revisiting some early analogies by Niels Bohr and David Bohm, this paper focuses upon Bohm and Hiley’s ontological interpretation of quantum theory which suggests further analogies between quantum phenomena and biological and psychological phenomena, including the proposal that the (...)
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  7.  41
    Gentzen’s “Cut Rule” and Quantum Measurement in Terms of Hilbert Arithmetic. Metaphor and Understanding Modeled Formally.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal 14 (14):1-37.
    Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by (...)
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  8. General Relativity and Quantum Gravity in Terms of Quantum Measure: A Philosophical Comment.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 12 (17):1-37.
    The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be (...)
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  9.  88
    A Model for the Solution of the Quantum Measurement Problem.Biswaranjan Dikshit - 2019 - Science and Philosophy 7 (2):59-70.
    The basic idea of quantum mechanics is that the property of any system can be in a state of superposition of various possibilities. This state of superposition is also known as wave function and it evolves linearly with time in a deterministic way in accordance with the Schrodinger equation. However, when a measurement is carried out on the system to determine the value of that property, the system instantaneously transforms to one of the eigen states and thus we (...)
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  10.  50
    A Survey on Uncertainty Relations and Quantum Measurements: Arguments for Lucrative Parsimony in Approaches of Matters.Dumitru Spiridon - 2021 - Progress in Physics 17 (1):38-70.
    This survey tries to investigate the truths and deficiencies of prevalent philosophy about Uncertainty Relations (UR) and Quantum Measurements (QMS). The respective philosophy, known as being eclipsed by unfinished controversies, is revealed to be grounded on six basic precepts. But one finds that all the respective precepts are discredited by insurmountable deficiencies. So, in regard to UR, the alluded philosophy discloses oneself to be an unjustified mythology. Then UR appear either as short-lived historical conventions or as simple and limited (...)
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  11. A Reformulation of von Neumann's Postulates on Quantum Measurement by Using.Elio Conte - forthcoming - Submitted Physical Review A.
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  12. Quantum Theory Without Measurement or State Reduction Problems.Alan Macdonald - manuscript
    There is a consistent and simple interpretation of the quantum theory of isolated systems. The interpretation suffers no measurement problem and provides a quantum explanation of state reduction, which is usually postulated. Quantum entanglement plays an essential role in the construction of the interpretation.
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  13. Quantum-Mechanical Self-Measurement.Bradley Monton - 1998 - In D. Dieks & P. Vermaas (eds.), The Modal Interpretations of Quantum Mechanics. Kluwer Academic Publishers. pp. 307-318.
    The idea of self-measurement by a quantum-mechanical automaton is presented, and the conclusions that are typically reached about what we can come to know from doing self-measurements are shown to be mistaken. Specifically, it is shown that, while we are capable of _predicting_ and _measuring_ the values of two incompatible observables, we are incapable of _knowing_ both these values simultaneously. This is an example of the interesting limitations quantum mechanics places on knowledge.
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  14. Macroscopic Quantum Superpositions Cannot Be Measured, Even in Principle.Andrew Knight - manuscript
    I show in this paper why the universality of quantum mechanics at all scales, which implies the possibility of Schrodinger's Cat and Wigner's Friend thought experiments, cannot be experimentally confirmed, and why macroscopic superpositions in general cannot be observed or measured, even in principle. Through the relativity of quantum superposition and the transitivity of correlation, it is shown that from the perspective of an object that is in quantum superposition relative to a macroscopic measuring device and observer, (...)
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  15. Quantum Analog of the Black- Scholes Formula(Market of Financial Derivatives as a Continuous Weak Measurement).S. I. Melnyk & I. G. Tuluzov - 2008 - Electronic Journal of Theoretical Physics (EJTP) 5 (18):95–104.
    We analyze the properties of optimum portfolios, the price of which is considered a new quantum variable and derive a quantum analog of the Black-Scholes formula for the price of financial variables in assumption that the market dynamics can by considered as its continuous weak measurement at no-arbitrage condition.
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  16. Fundamental Measurements in Economics and in the Theory of Consciousness (Manifestation of Quantum-Mechanical Properties of Economic Objects in Slit Measurements).I. G. Tuluzov & S. I. Melnyk - manuscript
    A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement. We were also able to obtain the classical interpretation of the quantum-mechanical law of addition of probabilities by introducing a number of new notions. The principle of “local equity” assumes the transaction (...)
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  17. Measurement and Quantum Dynamics in the Minimal Modal Interpretation of Quantum Theory.Jacob A. Barandes & David Kagan - 2020 - Foundations of Physics 50 (10):1189-1218.
    Any realist interpretation of quantum theory must grapple with the measurement problem and the status of state-vector collapse. In a no-collapse approach, measurement is typically modeled as a dynamical process involving decoherence. We describe how the minimal modal interpretation closes a gap in this dynamical description, leading to a complete and consistent resolution to the measurement problem and an effective form of state collapse. Our interpretation also provides insight into the indivisible nature of measurement—the fact (...)
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  18.  47
    Manifestation of Quantum Mechanical Properties of a Proprietor’s Consciousness in Slit Measurements of Economic Systems.Sergiy Melnyk & Igor Tuluzov - 2014 - Neuroquantology 12 (3).
    The present paper discusses the problem of quantum-mechanical properties of a subject’s consciousness. The model of generalized economic measurements is used for the analysis. Two types of such measurements are analyzed – transactions and technologies. Algebraic ratios between the technology-type measurements allow making their analogy with slit experiments in physics. It has been shown that the description of results of such measurements is possible both in classical and in quantum formalism of calculation of probabilities. Thus, the quantum-mechanical (...)
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  19.  21
    Sensitivity of Entanglement Measures in Bipartite Pure Quantum States.Danko D. Georgiev & Stanley P. Gudder - 2022 - Modern Physics Letters B 36 (22):2250101.
    Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two entanglement measures for all quantum states, however, allows for meaningful conceptualization of sensitivity to entanglement, which will be greater for the entanglement measure that produces the larger numerical values. Here, we have investigated the partial order between the normalized versions of four entanglement measures (...)
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  20. Feyerabend on the Quantum Theory of Measurement: A Reassessment.Daniel Kuby & Patrick Fraser - manuscript
    In 1957, Feyerabend delivered a paper titled “On the quantum‐theory of measurement” at the Colston Research Symposium in Bristol to sketch a completion of von Neumann’s measurement scheme without collapse, using only unitary quantum dynamics and well‐motivated statistical assumptions about macroscopic quantum systems. Feyerabend’s paper has been recognized as an early contribution to quantum measurement, anticipating certain aspects of decoherence. Our paper reassesses the physical and philosophical content of Feyerabend’s contribution, detailing the technical (...)
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  21. A Conjecture Concerning Determinism, Reduction, and Measurement in Quantum Mechanics.Arthur Jabs - 2016 - Quantum Studies: Mathematics and Foundations 3 (4):279-292.
    Determinism is established in quantum mechanics by tracing the probabilities in the Born rules back to the absolute (overall) phase constants of the wave functions and recognizing these phase constants as pseudorandom numbers. The reduction process (collapse) is independent of measurement. It occurs when two wavepackets overlap in ordinary space and satisfy a certain criterion, which depends on the phase constants of both wavepackets. Reduction means contraction of the wavepackets to the place of overlap. The measurement apparatus (...)
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  22. Zeno Goes to Copenhagen: A Dilemma for Measurement-Collapse Interpretations of Quantum Mechanics.David J. Chalmers & Kelvin J. McQueen - forthcoming - In M. C. Kafatos, D. Banerji & D. C. Struppa (eds.), Quantum and Consciousness Revisited. DK Publisher.
    A familiar interpretation of quantum mechanics (one of a number of views sometimes labeled the "Copenhagen interpretation'"), takes its empirical apparatus at face value, holding that the quantum wave function evolves by the Schrödinger equation except on certain occasions of measurement, when it collapses into a new state according to the Born rule. This interpretation is widely rejected, primarily because it faces the measurement problem: "measurement" is too imprecise for use in a fundamental physical theory. (...)
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  23. A New Look at the Quantum Mechanical Problem of Measurement.Nicholas Maxwell - 1972 - American Journal of Physics 40:1431-5..
    According to orthodox quantum mechanics, state vectors change in two incompatible ways: "deterministically" in accordance with Schroedinger's time-dependent equation, and probabilistically if and only if a measurement is made. It is argued here that the problem of measurement arises because the precise mutually exclusive conditions for these two types of transitions to occur are not specified within orthodox quantum mechanics. Fundamentally, this is due to an inevitable ambiguity in the notion of "meawurement" itself. Hence, if the (...)
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  24.  65
    The Ontic Probability Interpretation of Quantum Theory - Part III: Schrödinger’s Cat and the ‘Basis’ and ‘Measurement’ Pseudo-Problems.Felix Alba-Juez - manuscript
    Most of us are either philosophically naïve scientists or scientifically naïve philosophers, so we misjudged Schrödinger’s “very burlesque” portrait of Quantum Theory (QT) as a profound conundrum. The clear signs of a strawman argument were ignored. The Ontic Probability Interpretation (TOPI) is a metatheory: a theory about the meaning of QT. Ironically, equating Reality with Actuality cannot explain actual data, justifying the century-long philosophical struggle. The actual is real but not everything real is actual. The ontic character of the (...)
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  25. On a Simple Derivation of the Effect of Repeated Measurements on Quantum Unstable Systems by Using the Regularized Incomplete Beta-Function.Elio Conte - 2012 - Advanced Studies in Theoretical Physics 6 (25):1207-1213.
    a simple derivation of the effect induced from repeated measurements on quantum unstable systems is obtained by using the regularized incomplete beta - function .
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  26. Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum Theory.Masanao Ozawa - 2016 - New Generation Computing 34 (1):125-152.
    The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of equality between two arbitrary observables, since the Born formula gives the probability distribution only for a commuting family of observables. In this paper, quantum set theory developed by Takeuti and the present author is used to systematically extend the standard probabilistic interpretation of quantum (...)
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  27. Addressing the Conflict Between Relativity and Quantum Theory: Models, Measurement and the Markov Property.Gareth Ernest Boardman - 2013 - Cosmos and History 9 (2):86-115.
    Twenty-first century science faces a dilemma. Two of its well-verified foundation stones - relativity and quantum theory - have proven inconsistent. Resolution of the conflict has resisted improvements in experimental precision leaving some to believe that some fundamental understanding in our world-view may need modification or even radical reform. Employment of the wave-front model of electrodynamics, as a propagation process with a Markov property, may offer just such a clarification.
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  28. The Quantum Logic of Direct-Sum Decompositions: The Dual to the Quantum Logic of Subspaces.David Ellerman - 2017
    Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The notion of a partition (or quotient set or equivalence relation) is dual (in a category-theoretic (...)
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  29.  5
    Possible Perspective for Quantum Mechanics Interpretation: An Essay-Suggestion.Spiridon Dumitru - 2022 - European Journal of Applied Physics, ISSN: 2684-4451 4 (5):55-62.
    The idea of new-type articles, named “Perspectives”, announced recently by some leading journals, is suggested to be approached for the controversial question of quantum mechanics interpretation. Firstly, it is revealed briefly the unsatisfactory situation of the nowadays predominant doctrine about that question. Then some basic elements of the proposed approach are presented. Those elements refer to (i) uncertainty relations, (ii) distinction between own tasks of quantum mechanics and description of quantum measurements, (iii) defects of collapse scenarios for (...)
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  30. Quantum Propensities in the Brain Cortex and Free Will.Danko D. Georgiev - 2021 - Biosystems 208:104474.
    Capacity of conscious agents to perform genuine choices among future alternatives is a prerequisite for moral responsibility. Determinism that pervades classical physics, however, forbids free will, undermines the foundations of ethics, and precludes meaningful quantification of personal biases. To resolve that impasse, we utilize the characteristic indeterminism of quantum physics and derive a quantitative measure for the amount of free will manifested by the brain cortical network. The interaction between the central nervous system and the surrounding environment is shown (...)
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  31.  92
    Quantum Information Theoretic Approach to the Mind–Brain Problem.Danko D. Georgiev - 2020 - Progress in Biophysics and Molecular Biology 158:16-32.
    The brain is composed of electrically excitable neuronal networks regulated by the activity of voltage-gated ion channels. Further portraying the molecular composition of the brain, however, will not reveal anything remotely reminiscent of a feeling, a sensation or a conscious experience. In classical physics, addressing the mind–brain problem is a formidable task because no physical mechanism is able to explain how the brain generates the unobservable, inner psychological world of conscious experiences and how in turn those conscious experiences steer the (...)
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  32. Entanglement, Joint Measurement, and State Reduction.Alan Macdonald - 2003 - International Journal of Theoretical Physics 42:943-953.
    Entanglement has been called the most important new feature of the quantum world. It is expressed in the quantum formalism by the joint measurement formula. We prove the formula for projection valued observables from a plausible assumption, which for spacelike separated measurements is an expression of relativistic causality. The state reduction formula is simply a way to express the joint measurement formula after one measurement has been made, and its result known.
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  33. The Problem of Measurement - Real or Imaginary?Nicholas Maxwell - 1973 - American Journal of Physics 41:1022-5.
    It is argued that criticisms of Willian Band and James Park concerning the quantum mechanics measurement problem do not succeed.
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  34.  61
    Quantum Invariance.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (22):1-6.
    Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. (...)
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  35. Quantum Leaps in Philosophy of Mind.David Bourget - 2004 - Journal of Consciousness Studies 11 (12):17--42.
    I discuss the quantum mechanical theory of consciousness and freewill offered by Stapp (1993, 1995, 2000, 2004). First I show that decoherence-based arguments do not work against this theory. Then discuss a number of problems with the theory: Stapp's separate accounts of consciousness and freewill are incompatible, the interpretations of QM they are tied to are questionable, the Zeno effect could not enable freewill as he suggests because weakness of will would then be ubiquitous, and the holism of (...) in QM is not a good explanation of the unity of consciousness for essentially the same reason that local interactions may seem incapable of accounting for it. (shrink)
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  36.  56
    A Quantum-Theoretic Argument Against Naturalism.Bruce L. Gordon - 2011 - In Bruce L. Gordon & William A. Dembski (eds.), The Nature of Nature: Examining the Role of Naturalism in Science. Wilmington, DE: ISI Books. pp. 179-214.
    Quantum theory offers mathematical descriptions of measurable phenomena with great facility and accuracy, but it provides absolutely no understanding of why any particular quantum outcome is observed. It is the province of genuine explanations to tell us how things actually work—that is, why such descriptions hold and why such predictions are true. Quantum theory is long on the what, both mathematically and observationally, but almost completely silent on the how and the why. What is even more interesting (...)
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  37.  92
    Consciousness and Matter. Information-Measuring Approach. Generalized Principle of Complementarity.Sergiy Melnyk & Igor Tuluzov - manuscript
    A wide range of problems of the relationship between consciousness and matter are discussed. Particular attention is paid to the analysis of the structure and properties of consciousness in the framework of information evolution. The role of specific (non-computational) properties of consciousness in the procedure of classical and quantum measurements is analyzed. In particular, the issue of "cloning" of consciousness (the possibility of copying its properties onto a new material carrier) is discussed in detail. We hope that the generalized (...)
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  38. Quantum Mechanics as a Deterministic Theory of a Continuum of Worlds.Kim Joris Boström - 2015 - Quantum Studies: Mathematics and Foundations 2 (3):315-347.
    A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both “time” and “world” are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and (...)
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  39. Quantum Mechanics Reality and Separability.Franco Selleri & G. Tarozzi - 1981 - la Rivista Del Nuovo Cimento 4 (2):1-53.
    TABLE OF CONTENTS: Introduction; de Broglie's paradox.; Quantum theory of distant particles; The EPR paradox; Einstein locality and Bell's inequality; Recent research on Bell's inequality; General consequences of Einstein locality; Nonloeality and relativity; Time-symmetric theories; The Bohm-Aharonov hypothesis; Experiments on Einstein locality; Reduction of the wave packet; Measurements, reality and consciousness; Conclusions.
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  40. Quantum Mechanics May Need Consciousness.Andrew Knight - manuscript
    The assertion by Yu and Nikolic that the delayed choice quantum eraser experiment of Kim et al. empirically falsifies the consciousness-causes-collapse hypothesis of quantum mechanics is based on the unfounded and false assumption that the failure of a quantum wave function to collapse implies the appearance of a visible interference pattern.
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  41. Quantum Mechanics in Terms of Realism.Arthur Jabs - 2017 - arXiv.Org.
    We expound an alternative to the Copenhagen interpretation of the formalism of nonrelativistic quantum mechanics. The basic difference is that the new interpretation is formulated in the language of epistemological realism. It involves a change in some basic physical concepts. The ψ function is no longer interpreted as a probability amplitude of the observed behaviour of elementary particles but as an objective physical field representing the particles themselves. The particles are thus extended objects whose extension varies in time according (...)
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  42.  54
    Quantum Information as the Information of Infinite Collections or Series.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (14):1-8.
    The quantum information introduced by quantum mechanics is equivalent to a certain generalization of classical information: from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The “qubit”, can be interpreted as that generalization of “bit”, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results (...)
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  43.  22
    Quantum Theories of Consciousness.Paavo Pylkkänen - 2018 - In Rocco J. Gennaro (ed.), The Routledge Handbook of Consciousness. New York, NY, USA: pp. 216-231.
    This paper provides a brief introduction to quantum theory and the proceeds to discuss the different ways in which the relationship between quantum theory and mind/consciousness is seen in some of the main alternative interpretations of quantum theory namely by Bohr; von Neumann; Penrose: Everett; and Bohm and Hiley. It briefly considers how qualia might be explained in a quantum framework, and makes a connection to research on quantum biology, quantum cognition and quantum (...)
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  44.  64
    Quantum Behavior of the Systems with a Single Degree of Freedom and the Derivation of Quantum Theory.Mehran Shaghaghi - manuscript
    The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems that have only one adjustable property cannot carry more than a single message at a time. We demonstrate this is the case for the single photons in the double-slit experiment, and the root of the fundamental limit on measuring the complementary aspect of the photons. Next, we analyze the other ‘quantal’ behavior of the systems with a single adjustable (...)
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  45. Quantum Theory Beyond the Physical: Information in Context.Kirsty Kitto, Brentyn Ramm, Laurianne Sitbon & Peter Bruza - 2011 - Axiomathes 21 (2):331-345.
    Measures and theories of information abound, but there are few formalised methods for treating the contextuality that can manifest in different information systems. Quantum theory provides one possible formalism for treating information in context. This paper introduces a quantum inspired model of the human mental lexicon. This model is currently being experimentally investigated and we present a preliminary set of pilot data suggesting that concept combinations can indeed behave non-separably.
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  46. On Classical and Quantum Logical Entropy.David Ellerman - manuscript
    The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements of (...)
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  47.  75
    Addendum to Quantum Wave Function Collapse of a System Having Three Anti Commuting Elements.Elio Conte - unknown
    We indicate a new way in the solution of the problem of the quantum measurement . In past papers we used the well-known formalism of the density matrix using an algebraic approach in a two states quantum spin system S, considering the particular case of three anticommuting elements. We demonstrated that, during the wave collapse, we have a transition from the standard Clifford algebra, structured in its space and metrics, to the new spatial structure of the Clifford (...)
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  48.  70
    A Quantum-Bayesian Route to Quantum-State Space.Christopher A. Fuchs & Rüdiger Schack - 2011 - Foundations of Physics 41 (3):345-356.
    In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent’s personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. (...)
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  49.  16
    مبانی فلسفی مکانیک کوانتوم / Philosophical Foundations of Quantum Mechanics.Alireza Mansouri - 2016 - Tehran: Nashre Ney.
    With the advent of quantum mechanics in the early 20th century, a great revolution took place in science. The philosophical foundations of classical physics collapsed, and controversial conceptual issues arose: can the quantum mechanical description of physical reality be considered complete? Are the objects of nature inseparable? Do objects not have a specific location before measurement, and are there non-causal quantum jumps? As time passed, not only did the controversies not diminish, but with the decline of (...)
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  50. An Investigation on the Basic Conceptual Foundations of Quantum Mechanics by Using the Clifford Algebra.Elio Conte - 2011 - Advanced Studies in Theoretical Physics 5 (11):485-544.
    We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the A(Si) and i,±1 N Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of (...) mechanics. In detail we realize a bare bone skeleton of quantum mechanics recovering all the basic foundations of this theory on an algebraic framework. We give proof of the quantum like Heisenberg uncertainty relations using only the basic support of the Clifford algebra. In addition we demonstrate the well known phenomenon of quantum Mach Zender interference using the same algebraic framework, as well as we give algebraic proof of quantum collapse in some cases of physical interest by direct application of the theorem that we derive to elaborate the i,±1 N algebra. We also discuss the problem of time evolution of quantum systems as well as the changes in space location, in momentum and the linked invariance principles. We are also able to re-derive the basic wave function of standard quantum mechanics by using only the Clifford algebraic approach. In this manner we obtain a full exposition of standard quantum mechanics using only the basic axioms of Clifford algebra. We also discuss more advanced features of quantum mechanics. In detail, we give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR paradox only using the Clifford algebra. By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that, as it is well known, are interpreted as logical statements, following the basic von Neumann results. Von Neumann realized a matrix logic on the basis of quantum mechanics. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic. Therefore, it seems that we may conclude that quantum mechanics, as it appears when investigated by the Clifford algebra, is a two-faced theory in the sense that it looks from one side to “matter per se”, thus to objects but simultaneously also to conceptual entities. We advance the basic conclusion of the paper: There are stages of our reality in which we no more can separate the logic ( and thus cognition and thus conceptual entity) from the features of “matter per se”. In quantum mechanics the logic, and thus the cognition and thus the conceptual entity-cognitive performance, assume the same importance as the features of what is being described. We are at levels of reality in which the truths of logical statements about dynamic variables become dynamic variables themselves so that a profound link is established from its starting in this theory between physics and conceptual entities. Finally, in this approach there is not an absolute definition of logical truths. Transformations , and thus … “redefinitions”…. of truth values are permitted in such scheme as well as the well established invariance principles, clearly indicate . (shrink)
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