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Bell’s stated assumptions in deriving his inequality were sufficient conditions. It is shown that a far simpler condition exists for derivation of the inequality: the mere existence of finite data sets regardless of their statistical or deterministic characteristics. When explicitly computing various quantum correlations, the non-commutation of some observables must be taken into account. The resulting variation in correlations among the observables leads to satisfaction of the Bell inequality. Bell’s mistaken assumption of the same functional form for all correlations is the principal reason for inequality violation. Upon correction of this error, it is no longer necessary to invoke non-locality or non-reality to explain violation of the Bell inequality.

The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′ s assuming merely that they exist