# Bell’s Theorem: Two Neglected Solutions

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## Abstract

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.

## Keywords

Bell’s theorem Superdeterminism Supercorrelation Measurement independence Correlated spin systems Ising lattices## Notes

### Acknowledgements

I would like to thank, for many stimulating discussions, Gilles Brassard, Mario Bunge, Emmanuel M. Dissakè, Henry E. Fischer, Yvon Gauthier, Gerhard Grössing, Andrei Khrennikov, Marian Kupczynski, Jean-Pierre Marquis and Eduardo Nahmad.

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