An attempt to close the Einstein–Podolsky–Rosen debate

2004 ◽  
Vol 82 (1) ◽  
pp. 53-65 ◽  
Author(s):  
T Krüger
Keyword(s):  
Quantum Mechanics ◽  
Natural Sciences ◽  
Point Of View ◽  
Bell’S Inequality ◽  
Bell's Inequality ◽  
Gedanken Experiment ◽  
Einstein Podolsky Rosen ◽  
Separability Principle ◽  
Statistical Operator ◽  
03.65 Ud

Based on a new rigorous ensemble approach to quantum mechanics, and without stressing any idea or concept of reality, the entire Einstein–Podolsky–Rosen (EPR) problem can be boiled down to the question of whether the separability principle of the natural sciences is universally valid. To give a precise answer first of all Bell's inequality is deduced from said ensemble point of view and with minimal requirements only. (In the final discussion of the results it turns out that Bell's inequality defines the upper bound for those basic correlations that are due to a mere conservation law.) Then, by use of Wheeler's gedanken experiment with coin halves, I show that the statistical operator representing an ensemble under investigation may be either separable (in a simplified sense) or not. The conceptual consequences of nonseparability are explained, and a general EPR-type experiment is re-examined. Thereby, it is proven that, if and only if, the statistical operator is nonseparable, Bell's inequality may be violated. Experimental evidence demands nonseparable operators. So, if quantum mechanics is assumed to make statistical statements on the results of measurements on ensembles only, there is no way to avoid acceptance of its (operationally) holistic character, and the question posed at the outset must be negated. PACS Nos : 03.65.Ta, 03.65.Ud

Bell's Inequalities for Any Spin

2003 ◽  
Vol 18 (28) ◽  
pp. 1931-1949
Author(s):  
V. M. González-Robles
Keyword(s):  
Quantum Mechanics ◽  
Singlet State ◽  
Point Of View ◽  
Bell’S Inequality ◽  
Bell's Inequality ◽  
Integer Spin ◽  
Half Integer ◽  
Locality Principle ◽  
Finite Integer ◽  
The Right

John Ju Sakurai's classical book in quantum mechanics makes a very illuminative presentation that studies entangled states in a two spin s=1/2 particles system in a singlet state. A Bell's inequality emerges as a consequence. Bell's inequality is a relationship among observables that discriminates between Einstein's locality principle and the nonlocal point of view of orthodox quantum mechanics. Following Sakurai's style we propose, by making natural induction, a generalization for Bell's inequality for any two spin-s particles in a singlet state (s integer or half-integer). This inequality is expressed as a function of a θ parameter, which is a measure of the angle between two possible directions in which the spin is measured. Besides the expression for this general inequality we have found that: (a) for any finite half-integer spin Bell's inequality is violated for some interval of the θ-parameter. The right limit of this interval is fixed and equal to π/2, while the left one comes closer and closer to this value as spin number grows. A function fit shows clearly that the size of this θ-interval over which Bell's inequality is violated diminishes asymptotically to zero as 1/s1/2; (b) an analogous behavior for any finite integer spin. For large spins the disagreement between Einstein's locality principle and the nonlocal point of view in orthodox quantum mechanics disappears.

scholarly journals Wigner’s Variant of Bell’s Inequality

1998 ◽  
Vol 51 (5) ◽  
pp. 835 ◽  
Author(s):  
Johannes F. Geurdes
Keyword(s):  
Bell’S Inequality ◽  
Bell's Inequality ◽  
Hidden Variable ◽  
Einstein Podolsky Rosen ◽  
Local Hidden Variable

It is shown that Wigner’s variant of Bell’s inequality does not exclude all local hidden variable explanations of the Einstein–Podolsky–Rosen problem.

scholarly journals RELATIVISTIC EINSTEIN-PODOLSKY-ROSEN CORRELATION AND BELL'S INEQUALITY

2003 ◽  
Vol 01 (01) ◽  
pp. 93-114 ◽  
Author(s):  
HIROAKI TERASHIMA ◽  
MASAHITO UEDA
Keyword(s):  
Relativistic Effect ◽  
Relativistic Quantum ◽  
Prima Facie ◽  
Bell’S Inequality ◽  
Moving Frames ◽  
Wigner Rotation ◽  
Relativistic Quantum Theory ◽  
Bell's Inequality ◽  
Einstein Podolsky Rosen ◽  
Non Local

We formulate the Einstein-Podolsky-Rosen (EPR) gedankenexperiment within the framework of relativistic quantum theory to analyze a situation in which measurements are performed by moving observers. We point out that under certain conditions the perfect anti-correlation of an EPR pair of spins in the same direction deteriorates in the moving observers' frame due to the Wigner rotation, and show that the degree of the violation of Bell's inequality prima facie decreases with increasing velocity of the observers if the directions of the measurement are fixed. However, this does not imply a breakdown of non-local correlation since the perfect anti-correlation is maintained in appropriately chosen different directions. When considering moving frames we must take account of this relativistic effect on the EPR correlation and on the violation of Bell's inequality for quantum communication.

scholarly journals Buonomano against Bell: Nonergodicity or nonlocality?

2017 ◽  
Vol 15 (08) ◽  
pp. 1740010 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Quantum Mechanics ◽  
Dynamical Systems ◽  
Stochastic Processes ◽  
Bell Inequality ◽  
Quantum Measurements ◽  
Neutron Interferometry ◽  
Bell’S Inequality ◽  
Weak Mixing ◽  
Bell's Inequality

The aim of this note is to attract attention of the quantum foundational community to the fact that in Bell’s arguments, one cannot distinguish two hypotheses: (a) quantum mechanics is nonlocal, (b) quantum mechanics is nonergodic. Therefore, experimental violations of Bell’s inequality can be as well interpreted as supporting the hypothesis that stochastic processes induced by quantum measurements are nonergodic. The latter hypothesis was discussed actively by Buonomano since 1980. However, in contrast to Bell’s hypothesis on nonlocality, it did not attract so much attention. The only experiment testing the hypothesis on nonergodicity was performed in neutron interferometry (by Summhammer, in 1989). This experiment can be considered as rejecting this hypothesis. However, it cannot be considered as a decisive experiment. New experiments are badly needed. We point out that a nonergodic model can be realistic, i.e. the distribution of hidden (local!) variables is well-defined. We also discuss coupling of violation of the Bell inequality with violation of the condition of weak mixing for ergodic dynamical systems.

Einstein-Podolsky-Rosen Paradox and Certain Aspects of Quantum Cryptology with Some Applications

2014 ◽  
pp. 1579-1587
Author(s):  
Narayanankutty Karuppath ◽  
P. Achuthan
Keyword(s):  
Quantum Computing ◽  
Computational Complexity ◽  
Quantum Cryptography ◽  
Scientific Revolution ◽  
Bell’S Inequality ◽  
Epr Paradox ◽  
Bell's Inequality ◽  
Factorization Algorithm ◽  
Einstein Podolsky Rosen ◽  
Modern Context

The developments in quantum computing or any breakthrough in factorization algorithm would have far-reaching consequences in cryptology. For instance, Shor algorithm of factorizing in quantum computing might render the RSA type classical cryptography almost obsolete since it mainly depends on the computational complexity of factorization. Therefore, quantum cryptography is of immense importance and value in the modern context of recent scientific revolution. In this chapter, the authors discuss in brief certain fascinating aspects of Einstein-Podolsky-Rosen (EPR) paradox in the context of quantum cryptology. The EPR protocol and its connections to the famous Bell's inequality are also considered in here.

ENTANGLEMENT, LOCALITY, AND SEPARABILITY: A TREATISE ON DIFFERENT VIEWPOINTS

2007 ◽  
Vol 05 (01n02) ◽  
pp. 157-167 ◽  
Author(s):  
THOMAS KESSEMEIER ◽  
THOMAS KRÜGER
Keyword(s):  
Quantum Mechanics ◽  
The Other ◽  
Statistical Interpretation ◽  
Interpretation Of Quantum Mechanics ◽  
Bell’S Inequality ◽  
Other Hand ◽  
The Common ◽  
Statistical Operator ◽  
Definition Of ◽  
Non Locality

Within the framework of a statistical interpretation of quantum mechanics, entanglement (in a mathematical sense) manifests itself in the non-separability of the statistical operator ρ representing the ensemble in question. In experiments, on the other hand, entanglement can be detected, in the form of non-locality, by the violation of Bell's inequality Δ ≤ 2. How can these different viewpoints be reconciled? We first show that (non-)separability follows different laws to (non-)locality, and, moreover, it is much more difficult to characterize as long as the mostly employed operational rather than an ontic definition of separability is used. In consequence, (i) "entanglement" has two different meanings which may or may not be realized simultaneously on one and the same ensemble, and (ii) we have to disadvise the use of the common separability definition which is still employed by the majority of the physical community.

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