Bell’s Theorem: Two Neglected Solutions

Bell’s theorem admits several interpretations or ‘solutions’, the standard interpretation being ‘indeterminism’, a next one ‘nonlocality’. In this article two further solutions are investigated, termed here ‘superdeterminism’ and ‘supercorrelation’. The former is especially interesting for philosophical reasons, if only because it is always rejected on the basis of extra-physical arguments. The latter, supercorrelation, will be studied here by investigating model systems that can mimic it, namely spin lattices. It is shown that in these systems the Bell inequality can be violated, even if they are local according to usual definitions. Violation of the Bell inequality is retraced to violation of ‘measurement independence’. These results emphasize the importance of studying the premises of the Bell inequality in realistic systems.

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

[2]  J. Rogel-Salazar,et al.  Quantum Phase Transitions, 2nd edn., by S. Sachdev , 2012 .

[3]  S. Sachdev.  Quantum Phase Transitions , 1999 .

[4]  A. Fine.  Hidden Variables, Joint Probability, and the Bell Inequalities , 1982 .

[5]  T. Nieuwenhuizen,et al.  Where Bell went wrong , 2008, 0812.3058.

[6]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[7]  A. Einstein.  QUANTEN‐MECHANIK UND WIRKLICHKEIT , 1948 .

[8]  H. Schwabl,et al.  An explanation of interference effects in the double slit experiment: Classical trajectories plus ba , 2011, 1106.5994.

[9]  C. Thompson.  The Statistical Mechanics of Phase Transitions , 1978 .

[10]  Daniel C. Cole,et al.  The quantum dice: An introduction to stochastic electrodynamics , 1996 .

[11]  R. Penrose,et al.  Quantum Concepts in Space and Time , 1986 .

[12]  S. Sachdev.  Quantum Phase Transitions: A first course , 1999 .

[13]  J. Z. Fullmer,et al.  Historical studies in the physical sciences , 1976 .

[14]  M. Hall,et al.  Relaxed Bell inequalities and Kochen-Specker theorems , 2011, 1102.4467.

[15]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[16]  Max Jammer,et al.  The philosophy of quantum mechanics : the interpretations of quantum mechanics in historical perspective , 1974 .

[17]  M. Bunge.  Chasing Reality: Strife over Realism , 2006 .

[18]  N. David Mermin,et al.  Is the Moon There When Nobody Looks? Reality and the Quantum Theory , 1985 .

[19]  Gerard 't Hooft,et al.  Entangled quantum states in a local deterministic theory , 2009, 0908.3408.

[20]  J. Uffink.  The Principle of the Common Cause Faces the Bernstein Paradox , 1999, Philosophy of Science.

[21]  P. H. Eberhard,et al.  Bell's theorem without hidden variables , 1977 .

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

[23]  James E. Jarrett,et al.  On the Physical Significance of the Locality Conditions in the Bell Arguments , 1984 .

[24]  Yves Couder,et al.  Single-particle diffraction and interference at a macroscopic scale. , 2006, Physical review letters.

[25]  Henry P. Stapp,et al.  S-MATRIX INTERPRETATION OF QUANTUM THEORY. , 1971 .

[26]  A. Aspect.  Bell's inequality test: more ideal than ever , 1999, Nature.

[27]  S. Moscovici,et al.  Changing conceptions of conspiracy , 1987 .

[28]  G. Ghirardi,et al.  A general argument against superluminal transmission through the quantum mechanical measurement process , 1980 .

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

[30]  J. Bell.  BERTLMANN'S SOCKS AND THE NATURE OF REALITY , 1981 .

[31]  L. Vervoort.  The interpretation of quantum mechanics and of probability: Identical role of the 'observer' , 2011, 1106.3584.

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

[33]  M. Horne,et al.  Experimental Consequences of Objective Local Theories , 1974 .

[34]  L. Richardson.  Mathematical Psychology of War , 1935, Nature.

[35]  A. Khrennikov.  Prequantum classical statistical field theory: background field as a source of everything? , 2011 .

[36]  J. Bell,et al.  Speakable and Unspeakable in Quantum Mechanics: Preface to the first edition , 2004 .

[37]  E. Fort,et al.  Dynamical phenomena: Walking and orbiting droplets , 2005, Nature.

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

[39]  B. D'espagnat,et al.  Nonseparability and the tentative descriptions of reality , 1984 .

[40]  M. Hall.  Local deterministic model of singlet state correlations based on relaxing measurement independence. , 2010, Physical review letters.

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

[42]  Bell's theorem and non-linear systems , 2000, quant-ph/0003057.

[43]  A. Osterloh,et al.  Scaling of entanglement close to a quantum phase transition , 2002, Nature.

[44]  Routledge,et al.  Routledge Encyclopedia of Philosophy , 1998 .

[45]  N. Bohr,et al.  Quantum Mechanics and Physical Reality , 1935, Nature.

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

[47]  Wayne C. Myrvold,et al.  Bell’s Theorem , 2011 .

[48]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

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

[50]  C. Brans.  Bell's theorem does not eliminate fully causal hidden variables , 1988 .