Showing papers in "Foundations of probability and physics in 2005"
TL;DR: In this paper, the authors show that the standard proofs of the Bell theorem are based on the Kolmogorov axioms of probability theory, and they show that these proofs contain mathematical steps that cannot be reconciled with the Vorob'ev theorem of joint distributions.
Abstract: Most of the standard proofs of the Bell theorem are based on the Kolmogorov axioms of probability theory. We show that these proofs contain mathematical steps that cannot be reconciled with the Kolmogorov axioms. Specifically we demonstrate that these proofs ignore the conclusion of a theorem of Vorob’ev on the consistency of joint distributions. As a consequence Bell’s theorem stated in its full generality remains unproven, in particular, for extended parameter spaces that are still objective local and that include instrument parameters that are correlated by both time and instrument settings. Although the Bell theorem correctly rules out certain small classes of hidden variables, for these extended parameter spaces the standard proofs come to a halt. The Greenberger‐Horne‐Zeilinger (GHZ) approach is based on similar fallacious arguments. For this case we are able to present an objective local computer experiment that simulates the experimental test of GHZ performed by Pan, Bouwmeester, Daniell, Weinfurter and Zeilinger and that directly contradicts their claim that Einstein‐local elements of reality can neither explain the results of quantum mechanical theory nor their experimental results.
94 citations
TL;DR: The EPR•chameleon experiment has closed a long standing debate between the supporters of quantum nonlocality and the thesis of quantum probability according to which the essence of the quantum pecularity is non Kolmogorovianity rather than non locality.
Abstract: The EPR‐chameleon experiment has closed a long standing debate between the supporters of quantum nonlocality and the thesis of quantum probability according to which the essence of the quantum pecularity is non Kolmogorovianity rather than non localityThe theory of adaptive systems (symbolized by the chameleon effect) provides a natural intuition for the emergence of non‐Kolmogorovian statistics from classical deterministic dynamical systems These developments are quickly reviewed and in conclusion some comments are introduced on recent attempts to “reconstruct history” on the lines described by Orwell in “1984”
66 citations
TL;DR: In this paper, a uniqueness property of states, explosion views and link observables is introduced, and a context translation principle is defined and critically evaluated with regard to its non-empirical content.
Abstract: Counterfactual reasoning and contextuality is defined and critically evaluated with regard to its nonempirical content. To this end, a uniqueness property of states, explosion views and link observables are introduced. If only a single context associated with a particular maximum set of observables can be operationalized, then a context translation principle resolves measurements of different contexts.
32 citations
TL;DR: In this article, the authors show that the main structures of quantum theory (interference of probabilities, Born's rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the classical Kolmogorov probability model.
Abstract: The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born’s rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities. In our approach it is forbidden to consider abstract context independent probabilities: “first context and then probability.” We start with the conventional formula of total probability for contextual (conditional) probabilities and then we rewrite it by eliminating combinations of incompatible contexts from consideration. In this way we obtain interference of probabilities without to appeal to the Hilbert space formalism or wave mechanics. However, we did not just reconstruct the probabilistic formalism of conventional quantum mechanics. Our contextual probabilistic model is essentially more general and, besides the projection to the complex Hilbert space, it has other projections. The most important new prediction is the possibility (at least theoretical) of appearance of hyperbolic interference. A projection of the classical contextual probabilistic model to the hyperbolic Hilbert space (a module over the commutative two dimensional Clifford algebra) has some similarities with the projection to the complex Hilbert space. However, in the hyperbolic quantum mechanics the principle of superposition is violated. Our realistic (but contextual!) approach to quantum mechanics does not contradict to various “no‐go theorems”, e.g., von Neumann, Bell, Kochen‐Specker. We emphasize that our projection of the classical probabilistic model to the complex Hilbert space is based on two incompatible observables (“reference observables”), e.g., the position and the momentum, or the position and the energy. Only these two observables can be considered as objective properties of quantum systems.
32 citations
TL;DR: In this article, it is shown that practical constraints of a fundamental nature preclude the application of Bell Inequalities to data from do-able EPR•B experiments and that the violation of these inequalities by data from such experiments is without significance for the questions posed by EPR or Bell.
Abstract: It is shown that practical constraints of a fundamental nature preclude the application of Bell Inequalities to data from do‐able EPR‐B experiments Thus, the violation of these inequalities by data from such experiments is without significance for the questions posed by EPR or Bell Further, other implicit, misguided assumptions in analysis of this issue are discussed and a counterexample to conventional opinion in the form of a local realistic model and simulation of EPR‐B experiments is displayed
23 citations
TL;DR: In this article, an exactly solvable model for a quantum measurement is discussed which is governed by hamiltonian quantum dynamics, where the z −component of a spin −12 is measured with an apparatus, which itself consists of magnet coupled to a bath.
Abstract: An exactly solvable model for a quantum measurement is discussed which is governed by hamiltonian quantum dynamics. The z‐component ŝz of a spin −12 is measured with an apparatus, which itself consists of magnet coupled to a bath. The initial state of the magnet is a metastable paramagnet, while the bath starts in a thermal, gibbsian state. Conditions are such that the act of measurement drives the magnet in the up or down ferromagnetic state according to the sign of sz of the tested spin. The quantum measurement goes in two steps. On a timescale 1/N the off‐diagonal elements of the spin’s density matrix vanish due to a unitary evolution of the tested spin and the N apparatus spins; on a larger but still short timescale this is made definite by the bath. Then the system is in a ‘classical’ state, having a diagonal density matrix. The registration of that state is a quantum process which can already be understood from classical statistical mechanics. The von Neumann collapse and the Born rule are derived r...
16 citations
TL;DR: In this article, a method for calculating the precise quantum bounds on arbitrary Bell-type inequalities by solving the eigenvalue problem for the operator associated with each Bell type inequality was proposed.
Abstract: Bell‐type inequalities and violations thereof reveal the fundamental differences between standard probability theory and its quantum counterpart. In the course of previous investigations ultimate bounds on quantum mechanical violations have been found. For example, Tsirelson’s bound constitutes a global upper limit for quantum violations of the Clauser‐Horne‐Shimony‐Holt (CHSH) and the Clauser‐Horne (CH) inequalities. Here we investigate a method for calculating the precise quantum bounds on arbitrary Bell‐type inequalities by solving the eigenvalue problem for the operator associated with each Bell‐type inequality. Thereby, we use the min‐max principle to calculate the norm of these self‐adjoint operators from the maximal eigenvalue yielding the upper bound for a particular set of measurement parameters. The eigenvectors corresponding to the maximal eigenvalues provide the quantum state for which a Bell‐type inequality is maximally violated.
14 citations
TL;DR: The existence of complete sets of MUBs is directly related to the existence of finite affine planes of order N = pk, where p is a prime number.
Abstract: A complete set of N + 1 mutually unbiased bases (MUBs) exists in Hilbert spaces of dimension N = pk, where p is a prime number. They mesh naturally with finite affine planes of order N, that exist when N = pk. The existence of MUBs for other values of N is an open question, and the same is true for finite affine planes. I explore the question whether the existence of complete sets of MUBs is directly related to the existence of finite affine planes. Both questions can be shown to be geometrical questions about a convex polytope, but not in any obvious way the same question.
13 citations
TL;DR: In this paper, games between two partners with mixed strategies, calculated by the use of the probability amplitude as some vector in Hilbert space, are given, and the games are macroscopic, no microscopic quantum agent is supposed.
Abstract: Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude as some vector in Hilbert space are given. The games are macroscopic, no microscopic quantum agent is supposed. The reason for the use of the quantum formalism is in breaking of the distributivity property for the lattice of yes‐no questions arising due to the special rules of games. The rules of the games suppose two parts: the preparation and measurement. In the first part due to use of the quantum logical orthocomplemented non‐distributive lattice the partners freely choose the wave functions as descriptions of their strategies. The second part consists of classical games described by Boolean sublattices of the initial non‐Boolean lattice with same strategies which were chosen in the first part. Examples of games for spin one half are given. New Nash equilibria are found for some cases. Heisenberg uncertainty relations without the Planck constant are written for the “spin one half game”.
9 citations
TL;DR: In this article, the authors describe an experiment in which generates single photons on demand and measures properties accounted to both particle and wave-like features of light, using data that are sampled simultaneously in a single experimental run.
Abstract: We describe an experiment in that generates single photons on demand and measures properties accounted to both particle and wave‐like features of light. The measurement is performed by exploiting data that are sampled simultaneously in a single experimental run.
7 citations
Journal Article•
TL;DR: In this article, a connection between statistics and quantum theory is established between these two areas, and a new, less formalistic way of looking upon basic quantum theory has been suggested.
Abstract: Both statistics and quantum theory deal with prediction using probability We will show that there can be established a connection between these two areas This will at the same time suggest a new, less formalistic way of looking upon basic quantum theoryA total parameter space Φ, equipped with a group G of transformations, gives the mental image of some quantum system, in such a way that only certain components, functions of the total parameter φ can be estimated Choose an experiment/question a, and get from this a parameter space Λa, perhaps after some model reduction compatible with the group structure As in statistics, it is important always to distinguish between observations and parameters, in particular between (minimal) observations ta and state variables (parameters) λa Let Ka be the L2 ‐space of functions of ta, and let Ha be the image of Ka under the expectation operator of the model The measure determining the L2‐spaces is the invariant measure under the maximal subgroup which induces a t
TL;DR: In this article, the information degree of entanglement is calculated for the entangled PPT state as an example of bound entangled state shown by Horodecki family, and the separability of quantum compound state is discussed from the operational points of view.
Abstract: We review the operational structure of quantum entanglement studied by Belavkin and Ohya. The separability of quantum compound state is discussed from the operational points of view. The information degree of entanglement is calculated for the entangled PPT state as an example of bound entangled state shown by Horodecki family.
TL;DR: In this paper, the observer is placed inside the system and special rules are required to engage and interpret the Schrodinger solutions in individual measurements, which are restricted to observer measurements, so state reduction can only occur when an observer is present.
Abstract: Quantum mechanics traditionally places the observer ‘outside’ of the system being studied and employs the Born interpretation. In this presentation and related papers the observer is placed ‘inside’ the system. To accomplish this, special rules are required to engage and interpret the Schrodinger solutions in individual measurements. The rules in this presentation (called the oRules) do not include the Born rule that connects probability with square modulus. It is required that the rules allow conscious observers to exist inside the system without empirical ambiguity — reflecting our own unambiguous experience in the universe. This requirement is satisfied by the oRules. These rules are restricted to observer measurements, so state reduction can only occur when an observer is present.
TL;DR: This paper surveys some of the recent results that have been obtained in fuzzy quantum probability theory and discusses the relationship between the law of total probability and compatibility of measurements, Probabilities, conditional probabilities and sequential products of effects.
Abstract: This paper surveys some of the recent results that have been obtained in fuzzy quantum probability theory. In this theory fuzzy events are represented by quantum effects and fuzzy random variables are represented by quantum measurements. Probabilities, conditional probabilities and sequential products of effects are discussed. The relationship between the law of total probability and compatibility of measurements is treated. Results concerning independent effects are given. Finally, properties of the sequential product, almost sharp effects and nearly sharp effects are discussed.
TL;DR: In this article, the significance of quantum waves and of Erwin Schrodinger's work was reassessed by extending Max Born's 1926 interpretation in terms of probability to the viewpoint of modern-day quantum information theory.
Abstract: The aim of this article is to reassess the significance of quantum waves and of Erwin Schrodinger’s work by extending Max Born’s 1926 interpretation of Schrodinger’s wave function in terms of probability to the viewpoint of the modern‐day quantum information theory, which, I argue, was anticipated by Schrodinger in his cat paradox paper, “Die gegenwartige Situation in der Quantenmechanik” [The Present Situation in Quantum Mechanics], published in 1935.
TL;DR: In this article, the effects of time dependence in the Bell inequality were analyzed and a generalized inequality was derived for the case when coincidence and non-coincidence is controlled by timing that depends on the detector settings.
Abstract: This paper analyzes effects of time‐dependence in the Bell inequality. A generalized inequality is derived for the case when coincidence and non‐coincidence [and hence whether or not a pair contributes to the actual data] is controlled by timing that depends on the detector settings. Needless to say, this inequality is violated by quantum mechanics and could be violated by experimental data provided that the loss of measurement pairs through failure of coincidence is small enough, but the quantitative bound is more restrictive in this case than in the previously analyzed “efficiency loophole.”
TL;DR: In this article, the role of geometry in quantum entanglement is explored, and Minkowskian geometry is seen to provide elegant representations of entenglement in multiple-qubit systems, particularly the language of twistors.
Abstract: The behavior of quantum states under local unitary transformations (LUTs) and stochastic local quantum operations and classical communication (SLOCC) has proven central to the understanding of entanglement in multipartite quantum systems. In particular, invariants under these operations have provided insight into quantum entanglement in multiple‐qubit states. Relationships between entanglement, mixedness and spin symmetry in multiple‐qubit quantum states can be found by exploiting these properties. For example, concurrence and n‐tangle are naturally expressed in terms of spin‐flip transformations. In the case of specialized entanglement measures and/or special families of states, complementarity relations involving these lengths and state transformations are derivable. Here, the role of geometry in such investigations is explored. Minkowskian geometry is seen to provide elegant representations of entanglement in multiple‐qubit systems, particularly the language of twistors.
IBM1
TL;DR: The notion of reversibility and irreversibility in the stochastic field is introduced by means of the so‐called Stochastic entropy and this function is applied in the calculus of the system reliability and reparability and four major results are illustrated.
Abstract: This paper introduces the notion of reversibility and irreversibility in the stochastic field. It quantifies this feature by means of the so‐called stochastic entropy. We apply this function in the calculus of the system reliability and reparability and illustrate four major results. The notion of entropy appears intriguing from the philosophical stance and a few remarks upon the relations existing between the stochastic entropy and the Boltzmann and Shannon functions close this work.
TL;DR: In this article, a philosophy of physics called "linguistic empiricism" is presented and applied to the interpretation problem of quantum mechanics, which is based on the works of Jacques Derrida.
Abstract: A philosophy of physics called “linguistic empiricism” is presented and applied to the interpretation problem of quantum mechanics. This philosophical position is based on the works of Jacques Derrida. The main propositions are (i) that meaning, included the meaning attached to observations, are language‐dependent and (ii) that mathematics in physics should be considered as a proper language, not necessary translatable to a more basic language of intuition and immediate experience. This has fundamental implications for quantum mechanics, which is a mathematically coherent and consistent theory; its interpretation problem is associated with its lack of physical images expressible in ordinary language.
TL;DR: In this article, a distinction between two types of models is proposed based on the articulated recognition that different models are brought to play different roles in the process of theory-building, and a distinction is made between two classes of models.
Abstract: A distinction between two types of models is proposed based on the articulated recognition that different models are brought to play different roles in the process of theory‐building.
TL;DR: In this article, the physical and philosophical principles of stochastic master equations describing the dynamics of a continuously observed quantum system are explained in terms of quantum filtering equations, and these principles constitute a consistent interpretation of quantum theory and measurement.
Abstract: Starting from an elementary level we present the theory of quantum filtering. The physical and philosophical principles of stochastic master equations describing the dynamics of a continuously observed quantum system are explained in terms of quantum filtering equations. We believe these principles constitute a consistent interpretation of quantum theory and measurement.
TL;DR: In this paper, the verification procedure of Bell inequalities consists of three parts, the first stage consists of measurements of a set of spin correlations using them one can reconstruct a density matrix of two-particle state It can be done with the help of quantum tomography technique.
Abstract: It is shown that verification procedure of Bell inequalities consists of three parts The first stage of verification procedure is consist of measurements of a set of spin correlations Using them one can reconstruct a density matrix of two‐particle state It can be done with the help of quantum tomography technique At the second stage one must construct a generalized Bell inequality corresponding to this state This inequality must be constructed in two forms: within the framework of the traditional formulation of quantum mechanics and in the frames of a local hidden variables theory Only after that the results of experimental measurements can be compared with theoretical predictions It is a third stage of verification
TL;DR: In this paper, the authors present an emulation interpretation of quantum theory based on the Copenhagen interpretation, which is a discrete theory of quantum physics, which can be computed by a generalized Turing machine.
Abstract: The emulation interpretation of quantum theory is described which may solve problems of the Copenhagen interpretation finally. According to Kolmogorov complexity theory it is conceivable that a bit string exists encoding our world which can be computed by an appropriate generalized Turing machine. In this case the computation would emulate the world, therefore this can be called an emulation theory of quantum physics, and the emulation interpretation of quantum theory. The probability of a string is dominated by the probabilities of its shortest programs which is known as the ‘coding theorem’. This leads to the suggestion that there may be a relatively short shortest program by which our world may be run. This suggestion appears to be in accordance with our world. The world exhibits a number of symmetries. It is plausible that the shortest algorithm for our special world is shorter than those for worlds where symmetries are broken more often than in our world, because each further deviation from a symmetry has to be encoded within the algorithm which would enlarge its length. Therefore, laws of physics may be identical rather globally in spacetime. Further, in the Copenhagen interpretation of quantum theory it is defined, how to compute probabilities for, e.g., measurement results when conducting measurements on variables of quantum systems. In a completely satisfactory theory of everything this would not be sufficient, but such a theory should give a reason why the values of the probabilities seem, as far as it is known, to be identical also in all different regions of the observed world. The emulation interpretation suggests that all deviations from this symmetry of the probabilities would enlarge the shortest program of the world, and, therefore, we would probably not live in a world with such deviations. A second question arises from the attempt to combine the theory of black holes, thermodynamics and quantum theory. Bekenstein derives a holography principle which would restrict the number of degrees of freedom that can be present within a bounding surface to a finite number. In case the principle holds, he suggests that the final theory may be a discrete theory. The emulation interpretation is discrete. A promising detailed discrete theory which is currently developed is loop quantum gravity. Its discreteness was derived from some mathematical principles. It is also conceivable that string theories and/or M‐theory can be unified with loop quantum gravity in future to a discrete theory. Additionally, the emulation interpretation suggests that parameters of physics may be encoded by a finite number of bits, they may be rational numbers, events in quantum physics may not be random but in principle computable, and, in a certain sense, space and time may be discrete variables. Falsifiability of the results is discussed.
TL;DR: In this paper, it has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast, which indicates a persisting coupling in p..., i.e. contextuality can be verified.
Abstract: Entanglement of two photons, or atoms is a complementary situation to a double slit situation of a single photon, neutron or atom. With neutrons single particle interference phenomena can be observed and the “entanglement of degrees of freedom”, i.e. contextuality can be verified. In this respect, neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment and they are subject to all basic interactions, and they are sensitive to topological effects, as well. Related experiments will be discussed. Deterministic and stochastic partial absorption experiments can be described by Bell‐type inequalities. Recent neutron interferometry experiments based on postselection methods renewed the discussion about quantum nonlocality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates a persisting coupling in p...
TL;DR: In this paper, two major approaches to probability, namely, frequentism and subjectivistic Bayesian theory, are discussed, together with the replacement of frequentist objectivity for Bayesian intersubjectivity, and a discussion is then expanded to Quantum Theory, as quantum states and operations can be seen as structural elements of a subjective nature.
Abstract: Two of the major approaches to probability, namely, frequentism and (subjectivistic) Bayesian theory, are discussed, together with the replacement of frequentist objectivity for Bayesian intersubjectivity. This discussion is then expanded to Quantum Theory, as quantum states and operations can be seen as structural elements of a subjective nature.
TL;DR: In this paper, a scattering problem is formulated and solved, showing that the grain angle can be determined from the polarization of the incident field minimizing the reflected orthogonal component, which is stable for changes in dielectric constants for the log.
Abstract: The scattering of electromagnetic waves by logs that have spiral grain is studied to find methods for determining the grain angle. Very little in the literature on spiral grain determination treat wave modelling and it appears to be no publication on modelling of cylindrical logs. Since the cylindrical shape of the log is expected to be fundamental, a theory for electromagnetic waves in spiral grain wood is developed. It is generally proved, from this theory, that the presence of spiral grain produces a component in the reflected electric field, orthogonal to the incident field and proportional to the grain angle at small angles. A scattering problem is formulated and solved showing that the grain angle can be determined from the polarization of the incident field minimizing the reflected orthogonal component. Arguments are put forward that this procedure is stable for changes in dielectric constants for the log, which vary with moisture content. In addition, procedures, for determining the dielectric constants from scattering measurements are also presented. While the analysis is carried out for a small grain angle and an incident plane wave with measurements in the far field, these restrictions should be possible to remove if necessary.
TL;DR: In this paper, the asymptotic behavior of the heat kernel on the cotangent bundle of a Riemannian manifold defined by a stochastically perturbed geodesic flow generalizing WKB-type methods to a diffusion corresponding to a particular regular degenerate Hamiltonian was studied.
Abstract: We consider the asymptotic behaviour for small time and small parameter of the heat kernel on the cotangent bundle of a Riemannian manifold defined by a stochastically perturbed geodesic flow generalizing WKB‐type methods to a diffusion corresponding to a particular regular degenerate Hamiltonian. For small time equivalence of the dynamics for the degenerate Hamiltonian system and for the system given by the corresponding Hamilton‐Jacobi equation is used.
TL;DR: In this paper, the authors advocate for more thorough investigations of EPR experiments with photons, and in particular of the main remaining loophole (i.e., the low detection efficiency loophole) using some recent proposals to circumvent this problem.
Abstract: The purpose of this paper is to advocate for more thorough investigations of EPR experiments with photons, and in particular of the main remaining loophole (i.e., the low detection efficiency loophole) using some recent proposals to circumvent this problem.
TL;DR: In this paper, a different approach to wave mechanics is presented in accordance with de Broglie's original hypothesis applying the case of photons to all material particles, where a monoenergetic particle transport along two directions is described by a partial differential equation and by a random walk model.
Abstract: A different approach to wave mechanics is presented in accordance with de Broglie’s original hypothesis applying the case of photons to all material particles. It derives propagating matter waves conceptually from a theory of evolution, and not by the formal setting of eigenvalue equations. The quality of explanation is at issue, and not the mere description of phenomena. A monoenergetic particle transport along two directions is described by a partial differential equation and by a random walk model. The dual description is applied to the particle picture and the wave picture; it leads with identical initial values to identical causal and timelike solutions in either picture. The partial differential equations are a Telegrapher equation in 1‐d space and its analytic continuation, a modified Klein Gordon equation; the solutions represent a density distribution and an amplitude profile, respectively. However, only the corresponding random walk models — equivalent to Feynman’s integral over all paths — derive the solutions as path‐end distributions with the additional information about the flight direction. This allows following up momentum dissipation along two directions by means of two particle beams and their profiles. Thereby the total number of particles is divided up onto the two beams according to linear or squared fractions depending on the beam configuration putting up a 1‐d or a 2‐d space. This aspect escapes conventional descriptions but serves to describe the transport in the particle or in the wave picture in dependence on the knowledge/ignorance of the particle’s flight direction.