EPR Paradox, Locality and Completeness of Quantum Theory

The quantum theory (QT) and new stochastic approaches have no deterministic prediction for a single measurement or for a single time‐series of events observed for a trapped ion, electron or any other individual physical system. The predictions of QT being of probabilistic character apply to the statistical distribution of the results obtained in various experiments. The Copenhagen interpretation (CI) of QT acknowledged the abstract and statistical character of the predictions of QT but at the same time claimed that a state vector Ψ provided complete description of each individual physical system. The assigning the state vector to an individual physical system together with a postulate of its instantaneous reduction in the measurements was shown by Einstein Podolski and Rosen to lead to so called EPR paradox for the experiments with the entangled pairs of the particles. EPR concluded that a state vector could not provide a complete description of the individual systems and the question arose whether the pr...

[1]  L. Accardi Topics in quantum probability , 1981 .

[2]  陳文卿 The Statistical Interpretation of Quantum Mechanics , 1971 .

[3]  Diederik Aerts,et al.  Example of a macroscopical classical situation that violates Bell inequalities , 1982 .

[4]  R. Rosenfeld Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[5]  M. Rédei,et al.  Quantum probability theory , 2006, quant-ph/0601158.

[6]  Stan Gudder Fuzzy Quantum Probability Theory , 2005 .

[7]  M. Kupczyński,et al.  Bertrand's paradox and Bell's inequalities , 1987 .

[8]  Guillaume Adenier,et al.  Is the fair sampling assumption supported by EPR experiments , 2007 .

[9]  I. Pitowsky Resolution of the Einstein-Podolsky-Rosen and Bell Paradoxes , 1982 .

[10]  Andrei Khrennikov Quantum mechanics from time scaling and random fluctuation , 2006 .

[11]  M. Kupczynski,et al.  On some important statistical tests , 1977 .

[12]  D. Brillinger Time series - data analysis and theory , 1981, Classics in applied mathematics.

[13]  L. Ballentine Quantum mechanics : a modern development , 1998 .

[14]  Luigi Accardi,et al.  Locality and Bell's inequality , 2000, quant-ph/0007005.

[15]  R. Balian,et al.  The quantum measurement process: an exactly solvable model , 2003, cond-mat/0408316.

[16]  D. Bohm A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES. II , 1952 .

[17]  Dirk Aerts,et al.  A possible explanation for the probabilities of quantum mechanics , 1986 .

[18]  J. Winkler Entanglement and Bell ’ s Inequalities , 2009 .

[19]  M. Born,et al.  Statistical Interpretation of Quantum Mechanics. , 1955, Science.

[20]  A. Zeilinger,et al.  Speakable and Unspeakable in Quantum Mechanics , 1989 .

[21]  Andrei Khrennikov,et al.  Reconstruction of quantum theory on the basis of the formula of total probability , 2003, quant-ph/0302194.

[22]  Diederik Aerts,et al.  The Violation of Bell Inequalities in the Macroworld , 2000, quant-ph/0007044.

[23]  W. M. de Muynck,et al.  Interpretations of quantum mechanics, joint measurement of incompatible observables, and counterfactual definiteness , 1994 .

[24]  M. Kupczyński,et al.  Pitovsky model and complementarity , 1987 .

[25]  A. Holevo Statistical structure of quantum theory , 2001 .

[26]  James D. Hamilton Time Series Analysis , 1994 .

[27]  A. F. Kracklauer,et al.  Bell’s inequalities and EPR‐B experiments: are they disjoint? , 2005 .

[28]  Richard Gill,et al.  Bell's inequality and the coincidence-time loophole , 2003, quant-ph/0312035.

[29]  T. Phipps On the “Completeness” of Quantum Mechanics , 1992 .

[30]  Marian Kupczynski Seventy Years of the EPR Paradox , 2006 .

[31]  Contextual Observables and Quantum Information , 2004, quant-ph/0408002.

[32]  Luigi Accardi,et al.  Some loopholes to save quantum nonlocality , 2005 .

[33]  A. Shimony,et al.  Bell's theorem. Experimental tests and implications , 1978 .

[34]  I. Pitowsky,et al.  George Boole's ‘Conditions of Possible Experience’ and the Quantum Puzzle , 1994, The British Journal for the Philosophy of Science.

[35]  G. Röpke,et al.  Operational Quantum Physics , 1997 .

[36]  B. V. Fraassen The Einstein-Podolsky-Rosen paradox , 1974, Synthese.

[37]  G. Emch Not What Models Are, But What Models Do , 2005 .

[38]  N. Mermin Hidden variables and the two theorems of John Bell , 1993, 1802.10119.

[39]  Marek Czachor,et al.  On some class of random variables leading to violations of the Bell inequality , 1988 .

[40]  J. Gajewski,et al.  Purity tests for π-d charge multiplicity distributions , 1979 .

[41]  M. KtYeCZYNSrdt Is the Hilbert space language too rich , 2005 .

[42]  M. Kupczyński,et al.  On some new tests of completeness of quantum mechanics , 1986 .

[43]  Jean-Philippe Bouchaud,et al.  Lévy Statistics and Laser Cooling , 2001 .

[44]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[45]  A. Matzkin Local hidden-variables can account for EPR quantum correlations , 2007 .

[46]  S. R. Garner,et al.  Coherent control of optical information with matter wave dynamics , 2007, Nature.

[47]  M. Kafatos Bell's theorem, quantum theory and conceptions of the universe , 1989 .

[48]  Karl Hess,et al.  Bell’s theorem: Critique of proofs with and without inequalities , 2005 .

[49]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[50]  Itamar Pitowsky,et al.  Deterministic model of spin and statistics , 1983 .

[51]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[52]  R. B. Lindsay,et al.  Essays 1958-1962 on Atomic Physics and Human Knowledge , 1987 .