Local realistic representation for correlations in the original EPR-model for position and momentum

It is currently widely accepted, as a result of Bell's theorem and related experiments, that quantum mechanics is inconsistent with local realism and there is the so called quantum non-locality. We show that such a claim can be justified only in a simplified approach to quantum mechanics when one neglects the fundamental fact that there exist space and time. Mathematical definitions of local realism in the sense of Bell and in the sense of Einstein are given. We demonstrate that if we include into the quantum mechanical formalism the space–time structure in the standard way then quantum mechanics might be consistent with Einstein's local realism. It shows that loopholes are unavoidable in experiments aimed to establish a violation of Bell's inequalities. We show how the space–time structure can be considered from the contextual point of view. A mathematical framework for the contextual approach is outlined.

[1]  Andrei Khrennikov,et al.  Interpretations of Probability , 1999 .

[2]  Igor Volovich,et al.  QUANTUM CRYPTOGRAPHY IN SPACE AND BELL'S THEOREM , 2001 .

[3]  William J. Munro,et al.  Erratum: Bell’s inequality test with entangled atoms [Phys. Rev. A62, 052102 (2000)] , 2001 .

[4]  Lars M. Johansen.  EPR correlations and EPW distributions revisited , 1997 .

[5]  Andrei Khrennikov.  Quantum theory: Reconsideration of foundations , 2003 .

[6]  Jian-Wei Pan,et al.  Maximal violation of Bell's inequalities for continuous variable systems. , 2002, Physical review letters.

[7]  Igor V. Volovich.  Towards Quantum Information Theory in Space and Time , 2002 .

[8]  Walmsley,et al.  Violation of Bell's inequality by a generalized einstein-podolsky-rosen state using homodyne detection , 2000, Physical review letters.

[9]  Guillaume Adenier,et al.  Quantum theory : reconsideration of foundations - 3, Växjö, Sweden, 6-11 June 2005 , 2006 .

[10]  S. Massar,et al.  Bell inequalities for arbitrarily high-dimensional systems. , 2001, Physical review letters.

[11]  A. Kolmogoroff.  Grundbegriffe der Wahrscheinlichkeitsrechnung , 1933 .

[12]  Andrei Khrennikov.  Frequency Analysis of the EPR-Bell Argumentation , 2002 .

[13]  Sylvia Pulmannová,et al.  New trends in quantum structures , 2000 .

[14]  N. Macrae.  John Von Neumann , 1992 .

[15]  Konrad Banaszek,et al.  Nonlocality of the Einstein-Podolsky-Rosen state in the Wigner representation , 1998 .

[16]  Olga Nánásiová.  Conditional probability on a quantum logic , 1986 .

[17]  H. Weinfurter,et al.  Violation of Bell's Inequality under Strict Einstein Locality Conditions , 1998, quant-ph/9810080.

[18]  Oľga Nánásiová,et al.  Ordering of observables and characterization of conditional expectation , 1987 .

[19]  Karl Hess,et al.  Einstein-separability, time related hidden parameters for correlated spins, and the theorem of Bell , 2001 .

[20]  Abner Shimony,et al.  The logic of quantum mechanics , 1981 .

[21]  Reid.  Incompatibility of macroscopic local realism with quantum mechanics in measurements with macroscopic uncertainties , 2000, Physical review letters.

[22]  Karl Svozil,et al.  Quantum Logic , 1998, Discrete mathematics and theoretical computer science.

[23]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .

[24]  P. Dirac.  Principles of Quantum Mechanics , 1982 .

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

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

[27]  Andrei Khrennikov,et al.  Foundations of Probability and Physics , 2002 .

[28]  Andrei Khrennikov.  Linear representations of probabilistic transformations induced by context transitions , 2001 .

[29]  L. Ballentine,et al.  Quantum Theory: Concepts and Methods , 1994 .

[30]  Asher Peres,et al.  Quantum Theory: Concepts and Methods , 1994 .

[31]  Michael Danos,et al.  The Mathematical Foundations of Quantum Mechanics , 1964 .

[32]  W. Philipp,et al.  Comment on "Exclusion of time in the theorem of Bell , 2002 .

[33]  Jan-Ake Larsson.  Modeling the singlet state with local variables , 1999 .

[34]  J. Bell,et al.  Speakable and Unspeakable in Quatum Mechanics , 1988 .

[35]  P. Busch,et al.  The quantum theory of measurement , 1991 .

[36]  Karl Hess,et al.  A possible loophole in the theorem of Bell , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[37]  J. Neumann.  Mathematical Foundations of Quantum Mechanics , 1955 .

[38]  William J. Munro,et al.  Bell's inequality test with entangled atoms , 2000 .

[39]  Mann,et al.  Maximal violation of Bell inequalities for mixed states. , 1992, Physical review letters.

[40]  Emilio Santos,et al.  Unreliability of performed tests of Bell's inequality using parametric down-converted photons , 1996 .