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AIP conference proceedings

Non Kolmogorov Probability Models Outside Quantum Mechanics

Luigi Accardi, Luigi Accardi, Guillaume Adenier, Christopher A. Fuchs, Gregg S. Jaeger, Andrei Yu. Khrennikov, Jan-Åke Larsson, Stig Stenholm

Published Jan 1, 2009• 4 citations
Publisher

Abstract

This paper is devoted to analysis of main conceptual problems in the interpretation of QM: reality, locality, determinism, physical state, Heisenberg principle, “deterministic” and “exact” theories, laws of chance, notion of event, statistical invariants, adaptive realism, EPR correlations and, finally, the EPR‐chameleon experiment.

DOI
10.1063/1.3109969

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Is quantum mechanics compatible with a deterministic universe?: two interpretations of quantum probabilities

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Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical probabilities. Our analysis will be focused, as a particular example, on the EPR experiment. It will be shown that the quantum mechanical probabilities can be consistently understood as conditional probabilities without any paradoxical consequences. Therefore, nothing implies that quantum mechanics is incompatible with a deterministic universe. ____________________________ This is a compressed postscript file. You can find an attached file, the compressed version of a computer program for DOS ("EPR.EXE").It demonstrates a deterministic, local hidden parameter model of the Aspect experiment.

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We present a detailed analysis of assumptions that J. Bell used to show that local realism contradicts QM. We find that Bell’s viewpoint on realism is nonphysical, because it implicitly assume that observed physical variables coincides with ontic variables (i.e., these variables before measurement). The real physical process of measurement is a process of dynamical interaction between a system and a measurement device. Therefore one should check the adequacy of QM not to “Bell’s realism,” but to adaptive realism (chameleon realism). Dropping Bell’s assumption we are able to construct a natural representation of the EPR‐Bohm correlations in the local (adaptive) realistic approach.

arXiv:quant-ph/0611259•AIP conference proceedings•Jan 1, 2007•6 citations

Probability and non-locality

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Review and preview In chapters 6 and 7, I described some links between locality and the treatment of probabilities in models of the EPR–Bohm experiment. From chapter 6, the main lesson was that, given the strict correlations of quantum mechanics, factorizability of the two-time probabilities is equivalent to two-time determinism. I also noted there that an adequate factorizable theory – one that avoids Bell's theorem – is possible only if λ-independence fails. In chapter 7, I argued that weak symmetry, local determination, and independent evolution together entail deterministic results and weak deterministic transitions. In chapter 8, I discussed the relationships among the locality conditions of chapter 6 and 7, Lorentz-invariance, and ‘metaphysical’ locality, especially local causality. I have by no means tried to give general answers to the questions raised there. Indeed, part of my thesis is that there is no general answer to be had. Nonetheless, one can use the results of chapters 6 and 7 to investigate the status of various interpretations. Most obviously, they can be used to evaluate whether a given theory is local: if a theory can be shown to violate one or more of the types of determinism entailed by the locality conditions of chapters 6 and 7, then that theory must be non-local in some sense.

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Microphysical reality and quantum formalism : proceedings of the Conference 'Microphysical Reality and Quantum Formalism', Urbino, Italy, September 25th - October 3rd, 1985

Microphysical Reality, Quantum Formalism, Alwyn van der Merwe +2 more

Quantum Measurements.- Quantum mechanics of macroscopic systems and measurement processes.- The haunted measurement in quantum theory.- A quantum-statistical model of quantum measurement.- Potential and real states in quantum mechanics.- Wave function collapse in the ensemble interpretation.- Nonlinear models for quantum-mechanical measurements.- Meaning and measurability of nonlocal quantum states.- New Developments of Quantum Theory.- The mathematical expression of the uncertainty principle.- Quantization of Hamiltonian theories based on a probability operator.- Classical to quantum: A generalized phase transition.- Quantum description of microscopic and microscopic systems: Old problems and recent investigations.- Towards a process formalism in quantum physics.- A generalized Schroedinger formalism from a Hamiltonian flow in a higher dimensional space.- How the nonlinear phenomena impose the reinterpretation of quantum mechanics.- On the equivalence between the superposition principle and a global gauge invariance.- Meanings of Quantum Theory.- The 2-photon elementary quantum phenomenon and spacetime structure.- Causality as indentified with conditional probability and the quantal nonseparability.- Realism versus positivism: An attempt at reconcilement in the Einstein-Bohr debate.- Four-dimensional realism and waves carrying physical data codedly as keys to understandable models.- Testing interpretations of quantum mechanics.- On the relation between the recent new statistical prediction of quantum mechanics by Albert, Aharonov, and D'Amato, the EPR reasoning, and Bell's Inequality.- Beyond quantum theory: A realist psycho-biological interpretation of physical reality.- Locality, causality, quantum events, and all that.- The Einstein-Bohr debate: I. The background.- Contingency and lawfulness: Conditions for encounter.- Epr Paradox: Critical Examinations.- Towards a realist theory of measurement.- The tacit postulate on single events and the comparison of classical and quantum spin correlation experiments.- Weak realism for pairs of correlated systems.- Comments on EPR, locality and reality.- The EPR and the proposal of action at a distance.- The discription of separated systems and quantum mechanics and a possible explanation for the probabilities of quantum mehanics.- Against dualism: An observation concerning non-locality.- Bell's theorem: A note on locality.- EPR paradox considered as a criticism of the statevector reduction in the quantum mechanical description of correlated separated systems.- EPR and the strange nature of the quantum state or why I can live with EPR.- Why the EPR paradox has been resolved in favor of Einstein.- Probability and the way out of the great quantum muddle.- Where lies the mistake in the clauser and Home proof of Bell's theorem?.

Kluwer Academic Publishers eBooks•Jan 1, 1988•3 citations

Nonlocality, Bell’s Ansatz, and probability

Aloysius F. Kracklauer

Quantum mechanics lacks an intuitive interpretation, which is the cause of a generally formalistic approach to its use. This in turn has led to a certain insensitivity to the actual meaning of many words used in its description and interpretation. Herein, we analyze carefully the possible mathematical meanings of those terms used in analysis of EPR’s contention, that Quantum Mechanics is incomplete, as well as Bell’s work descendant therefrom. As a result, many inconsistencies and errors in contemporary discussions of nonlocality, as well as in Bell’s Ansatz with respect to the laws of probability, are identified. Evading these errors precludes serious conflicts between Quantum Mechanics and both Special Relativity and Philosophy.

arXiv:quant-ph/0602080•Optics and Spectroscopy•Sep 1, 2007•8 citations

The EPR paradox, hidden variables, and Bell's theorem

Marlan O. Scully, Muhammad Suhail Zubairy

Quantum mechanics is an immensely successful theory, occupying a unique position in the history of science. It has solved mysteries ranging from macroscopic superconductivity to the microscopic theory of elementary particles and has provided deep insights into the nature of vacuum on the one hand and the description of the nucleon on the other. Whole new fields such as quantum optics and quantum electronics owe their very existence to this body of knowledge. However, despite the stunning successes of quantum mechanics, there is no general agreement on the conceptual foundations and interpretation of the subject. The theory provides unambiguous information about the outcome of a measurement of a physical object. However, many feel that it does not provide a satisfactory answer to the nature of the “reality” we should attribute to the physical objects between the acts of measurement. The conceptual difficulty comes about because the wave function |ψ〉 is usually given by a coherent superposition of various distinguishable experimental outcomes. If we denote the collection of states that represent the possible outcomes of an experiment by |ψ j 〉, then |ψ〉 = ∑ j c j |ψ j 〉 where c j = 〈ψ j |ψ〉. The probability of the outcome |ψ j 〉 is P j =|c j | 2 . In the process of measurement, the so called collapse of the wave function takes place and a single, definite state |ψ i 〉 of the physical object is chosen. The difficulty comes about in the interpretation of the mechanism by which this definite state is chosen from amongst all the possible outcomes.

Cambridge University Press eBooks•Sep 4, 1997•1 citation
This paper is devoted to analysis of main conceptual problems in the interpretation of QM: reality, locality, determinism, physical state, Heisenberg principle, “deterministic” and “exact” theories, laws of chance, notion of event, statistical invariants, adaptive realism, EPR correlations and, finally, the EPR‐chameleon experiment.
Two problems will be considered: the question of hidden parameters and the problem of Kolmogorovity of quantum probabilities. Both of them will be analyzed from the point of view of two distinct understandings of quantum mechanical probabilities. Our analysis will be focused, as a particular example, on the EPR experiment. It will be shown that the quantum mechanical probabilities can be consistently understood as conditional probabilities without any paradoxical consequences. Therefore, nothing implies that quantum mechanics is incompatible with a deterministic universe. ____________________________ This is a compressed postscript file. You can find an attached file, the compressed version of a computer program for DOS ("EPR.EXE").It demonstrates a deterministic, local hidden parameter model of the Aspect experiment.
We present a detailed analysis of assumptions that J. Bell used to show that local realism contradicts QM. We find that Bell’s viewpoint on realism is nonphysical, because it implicitly assume that observed physical variables coincides with ontic variables (i.e., these variables before measurement). The real physical process of measurement is a process of dynamical interaction between a system and a measurement device. Therefore one should check the adequacy of QM not to “Bell’s realism,” but to adaptive realism (chameleon realism). Dropping Bell’s assumption we are able to construct a natural representation of the EPR‐Bohm correlations in the local (adaptive) realistic approach.
Review and preview In chapters 6 and 7, I described some links between locality and the treatment of probabilities in models of the EPR–Bohm experiment. From chapter 6, the main lesson was that, given the strict correlations of quantum mechanics, factorizability of the two-time probabilities is equivalent to two-time determinism. I also noted there that an adequate factorizable theory – one that avoids Bell's theorem – is possible only if λ-independence fails. In chapter 7, I argued that weak symmetry, local determination, and independent evolution together entail deterministic results and weak deterministic transitions. In chapter 8, I discussed the relationships among the locality conditions of chapter 6 and 7, Lorentz-invariance, and ‘metaphysical’ locality, especially local causality. I have by no means tried to give general answers to the questions raised there. Indeed, part of my thesis is that there is no general answer to be had. Nonetheless, one can use the results of chapters 6 and 7 to investigate the status of various interpretations. Most obviously, they can be used to evaluate whether a given theory is local: if a theory can be shown to violate one or more of the types of determinism entailed by the locality conditions of chapters 6 and 7, then that theory must be non-local in some sense.
Quantum Measurements.- Quantum mechanics of macroscopic systems and measurement processes.- The haunted measurement in quantum theory.- A quantum-statistical model of quantum measurement.- Potential and real states in quantum mechanics.- Wave function collapse in the ensemble interpretation.- Nonlinear models for quantum-mechanical measurements.- Meaning and measurability of nonlocal quantum states.- New Developments of Quantum Theory.- The mathematical expression of the uncertainty principle.- Quantization of Hamiltonian theories based on a probability operator.- Classical to quantum: A generalized phase transition.- Quantum description of microscopic and microscopic systems: Old problems and recent investigations.- Towards a process formalism in quantum physics.- A generalized Schroedinger formalism from a Hamiltonian flow in a higher dimensional space.- How the nonlinear phenomena impose the reinterpretation of quantum mechanics.- On the equivalence between the superposition principle and a global gauge invariance.- Meanings of Quantum Theory.- The 2-photon elementary quantum phenomenon and spacetime structure.- Causality as indentified with conditional probability and the quantal nonseparability.- Realism versus positivism: An attempt at reconcilement in the Einstein-Bohr debate.- Four-dimensional realism and waves carrying physical data codedly as keys to understandable models.- Testing interpretations of quantum mechanics.- On the relation between the recent new statistical prediction of quantum mechanics by Albert, Aharonov, and D'Amato, the EPR reasoning, and Bell's Inequality.- Beyond quantum theory: A realist psycho-biological interpretation of physical reality.- Locality, causality, quantum events, and all that.- The Einstein-Bohr debate: I. The background.- Contingency and lawfulness: Conditions for encounter.- Epr Paradox: Critical Examinations.- Towards a realist theory of measurement.- The tacit postulate on single events and the comparison of classical and quantum spin correlation experiments.- Weak realism for pairs of correlated systems.- Comments on EPR, locality and reality.- The EPR and the proposal of action at a distance.- The discription of separated systems and quantum mechanics and a possible explanation for the probabilities of quantum mehanics.- Against dualism: An observation concerning non-locality.- Bell's theorem: A note on locality.- EPR paradox considered as a criticism of the statevector reduction in the quantum mechanical description of correlated separated systems.- EPR and the strange nature of the quantum state or why I can live with EPR.- Why the EPR paradox has been resolved in favor of Einstein.- Probability and the way out of the great quantum muddle.- Where lies the mistake in the clauser and Home proof of Bell's theorem?.
Quantum mechanics lacks an intuitive interpretation, which is the cause of a generally formalistic approach to its use. This in turn has led to a certain insensitivity to the actual meaning of many words used in its description and interpretation. Herein, we analyze carefully the possible mathematical meanings of those terms used in analysis of EPR’s contention, that Quantum Mechanics is incomplete, as well as Bell’s work descendant therefrom. As a result, many inconsistencies and errors in contemporary discussions of nonlocality, as well as in Bell’s Ansatz with respect to the laws of probability, are identified. Evading these errors precludes serious conflicts between Quantum Mechanics and both Special Relativity and Philosophy.
Quantum mechanics is an immensely successful theory, occupying a unique position in the history of science. It has solved mysteries ranging from macroscopic superconductivity to the microscopic theory of elementary particles and has provided deep insights into the nature of vacuum on the one hand and the description of the nucleon on the other. Whole new fields such as quantum optics and quantum electronics owe their very existence to this body of knowledge. However, despite the stunning successes of quantum mechanics, there is no general agreement on the conceptual foundations and interpretation of the subject. The theory provides unambiguous information about the outcome of a measurement of a physical object. However, many feel that it does not provide a satisfactory answer to the nature of the “reality” we should attribute to the physical objects between the acts of measurement. The conceptual difficulty comes about because the wave function |ψ〉 is usually given by a coherent superposition of various distinguishable experimental outcomes. If we denote the collection of states that represent the possible outcomes of an experiment by |ψ j 〉, then |ψ〉 = ∑ j c j |ψ j 〉 where c j = 〈ψ j |ψ〉. The probability of the outcome |ψ j 〉 is P j =|c j | 2 . In the process of measurement, the so called collapse of the wave function takes place and a single, definite state |ψ i 〉 of the physical object is chosen. The difficulty comes about in the interpretation of the mechanism by which this definite state is chosen from amongst all the possible outcomes.