On the Problem of Hidden Variables for Quantum Mechanical Observables with Continuous Spectra

Abstract The folklore notion of the "Non-Locality of Quantum Mechanics" is examined from the point of view of hidden-variables theories according to Belinfante's classification in his Survey of Hidden Variables Theories. It is here shown that in the case of EPR, there exist hidden variables theories that successfully reproduce quantum-mechanical predictions, but which are explicitly local. Since such theories do not fall into Belinfante's classification, we propose an expanded classification which includes similar theories, which we term as theories of the "third" kind. Causal implications of such theories are explored. -Pacs: 03.65.Bz

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Is the Devil in h?

Entropy ◽

10.3390/e23050632 ◽

2021 ◽

Vol 23 (5) ◽

pp. 632

Author(s):

Andrei Khrennikov

Keyword(s):

Quantum Mechanics ◽

Bell Inequality ◽

Hidden Variables ◽

Quantum Nonlocality ◽

Quantum Mechanical ◽

Planck Constant ◽

Einstein Podolsky Rosen ◽

Epr Argument ◽

Projection Postulate ◽

The Devil

This note is a part of my effort to rid quantum mechanics (QM) nonlocality. Quantum nonlocality is a two faced Janus: one face is a genuine quantum mechanical nonlocality (defined by the Lüders’ projection postulate). Another face is the nonlocality of the hidden variables model that was invented by Bell. This paper is devoted the deconstruction of the latter. The main casualty of Bell’s model is that it straightforwardly contradicts Heisenberg’s uncertainty and Bohr’s complementarity principles generally. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the model as such. The original Einstein-Podolsky-Rosen (EPR) argument assumed the Heisenberg’s principle without questioning its validity. Hence, the arguments of EPR and Bell differ crucially, and it is necessary to establish the physical ground of the aforementioned principles. This is the quantum postulate: the existence of an indivisible quantum of action given by the Planck constant. Bell’s approach with hidden variables implicitly implies rejection of the quantum postulate, since the latter is the basis of the reference principles.

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On Hidden Variables and Quantum Mechanical Probabilities

American Journal of Physics ◽

10.1119/1.1976526 ◽

1970 ◽

Vol 38 (8) ◽

pp. 1005-1009 ◽

Cited By ~ 274

Author(s):

Eugene P. Wigner

Keyword(s):

Hidden Variables ◽

Quantum Mechanical

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TIME AND A TEMPORALLY STATISTICAL QUANTUM GEOMETRODYNAMICS

International Journal of Modern Physics A ◽

10.1142/s0217751x13300159 ◽

2013 ◽

Vol 28 (14) ◽

pp. 1330015

Author(s):

EIJI KONISHI

Keyword(s):

Quantum Gravity ◽

Symmetry Breaking ◽

Time Reversal ◽

Hidden Variables ◽

Spontaneous Breaking ◽

Quantum Mechanical ◽

Time Reversal Symmetry ◽

Physical Origin ◽

Variable Theory ◽

Quantum Geometrodynamics

This paper is an exposition of the author's recent work on modeling M-theory vacua and quantum mechanical observers in the framework of a temporally statistical description of quantum geometrodynamics, including measurement processes based on the canonical theory of quantum gravity. In this paper, we deal with several fundamental issues of time: the timeless problem in canonical quantum gravity; the physical origin of state reductions; and time-reversal symmetry breaking. We first model the observers and consider the timeless problem by invoking the time reparametrization symmetry breaking in the quantum mechanical world as seen by the observers. We next construct the hidden time variable theory, using a model of the gauged and affinized S-duality symmetry in type IIB string theory, as the statistical theory of time and explain the physical origin of state reductions using it. Finally, by the extension of the time reparametrization symmetry to all of the temporal hidden variables, we treat the issue of time reversal symmetry breaking as the spontaneous breaking of this extended time reparametrization symmetry. The classification of unitary time-dependent processes and the geometrizations of unitary and nonunitary time evolutions using the language of the derived category are also investigated.

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Bell Model with Hidden Variables and Bohr Quantum Postulate on the Existence of Indivisible Quantum of Action Given by Planck Constant H.

10.20944/preprints202007.0413.v1 ◽

2020 ◽

Author(s):

Andrei Khrennikov

Keyword(s):

Quantum Mechanics ◽

Hidden Variables ◽

Quantum Nonlocality ◽

Quantum Mechanical ◽

Planck Constant ◽

Basic Principles ◽

Fundamental Feature ◽

Projection Postulate ◽

Bell Model

This note is a part of my efforts for getting rid of nonlocality from quantum mechanics (QM). Quantum nonlocality is two faced Janus, one face is apparent quantum mechanical nonlocality (assigned with projection postulate), another face is nonlocality of Bell's model with the hidden variables. This paper is directed against the latter. The main casualty of Bell's model is that it contradicts to the Heinsenberg's uncertainty and Bohr's complementarity principles. The aim of this note is to point to the physical seed of the aforementioned principles. This is the {\it quantum postulate}: the existence of indivisible quantum of action given by the Planck constant. Bell's model by contradicting to the basic principles of QM implies rejection of this postulate. Thus, it contradicts not only to the QM-formalism, but also to the fundamental feature of the quantum world that was initially discovered by Planck.

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LINEARITY OF QUANTUM PROBABILITY MEASURE AND HARDY'S MODEL

International Journal of Modern Physics A ◽

10.1142/s0217751x14500171 ◽

2014 ◽

Vol 29 (02) ◽

pp. 1450017 ◽

Cited By ~ 2

Author(s):

KAZUO FUJIKAWA ◽

C. H. OH ◽

CHENGJIE ZHANG

Keyword(s):

Probability Measure ◽

Hidden Variables ◽

Mathematical Expression ◽

Quantum Probability ◽

Quantum Mechanical ◽

Perfect Agreement ◽

Probability Interpretation ◽

Chsh Inequality ◽

Mechanical Probability ◽

Concrete Model

We re-examine d = 4 hidden-variables model for a system of two spin-1/2 particles in view of the concrete model of Hardy, who analyzed the criterion of entanglement without referring to inequality. The basis of our analysis is the linearity of the probability measure related to the Born probability interpretation, which excludes noncontextual hidden-variables model in d≥3. To be specific, we note the inconsistency of the noncontextual hidden-variables model in d = 4 with the linearity of the quantum mechanical probability measure in the sense 〈ψ|a⋅σ ⊗b ⋅σ|ψ〉+ 〈ψ|a ⋅σ ⊗b′ ⋅σ|ψ〉 = 〈ψ|a⋅σ⊗(b + b′)⋅σ|ψ〉 for noncollinear b and b′. It is then shown that Hardy's model in d = 4 does not lead to a unique mathematical expression in the demonstration of the discrepancy of local realism (hidden-variables model) with entanglement and thus his proof is incomplete. We identify the origin of this nonuniqueness with the nonuniqueness of translating quantum mechanical expressions into expressions in hidden-variables model, which results from the failure of the above linearity of the probability measure. In contrast, if the linearity of the probability measure is strictly imposed, which tantamounts to asking that the noncontextual hidden-variables model in d = 4 gives the Clauser–Horne–Shimony–Holt (CHSH) inequality |〈B〉|≤2 uniquely, it is shown that the hidden-variables model can describe only separable quantum mechanical states; this conclusion is in perfect agreement with the so-called Gisin's theorem which states that |〈B〉|≤2 implies separable states.

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