We have discovered an oversight in John S. Bell's hidden variable formulation of his inequality.

Everyone assumes Bell's result holds for all possible hidden variable theories but that assumption is false. Nonrecurrent hidden variables do not abide by Bell's inequality. The probability that two instances of a nonrecurrent variable are the same is zero, exactly zero (see W Feller Vol II page 4). Each instance of a nonreccurrent hidden variable is unique. All sequences are unique. All samples are unique. All contexts are unique. It is assumed that the source of the hidden variables is not a function of the parameters of any measurement device. However, the uniqueness of nonreccurrent hidden variables says when a measurement parameter changes the hidden variables change (because they are recorded at a different time). That induces a form of context sensitivity to measurements. That sensitivity means that Bell's formulation can not hold for nonrecurrent hidden variables, for when the parameters for Alice and Bob are (a,b) the hidden variables are different from those when the parameters are (a, b').. Bell assumed that in situation 1 (a,b) the hidden variables can be made common with situation 2 (a,b') but that is false for nonrecurrent hidden variables. If the variables are discrete it would be possible to satisfy Bell's contraint. Here is the difference between recurrent and nonrecurrent variables

Recurrent <A_{1}A_{2}> = <1> = 1

Nonrecurrent <A_{1}A_{2}> = <A_{1}><A_{2}> = 0

The latter follows from the fact that different samples are independent for nonrecurrent hidden variables.

Using independence and following Bell's steps of his derivation we arrive at a different inequality. We show that inequality places no constraints on correlations.

The same argument holds for the CHSH inequality and the GHZ expression.

Nonrecurrent hidden variables are a powerful lever that pries open quantum issues.

Everyone assumes Bell's result holds for all possible hidden variable theories but that assumption is false. Nonrecurrent hidden variables do not abide by Bell's inequality. The probability that two instances of a nonrecurrent variable are the same is zero, exactly zero (see W Feller Vol II page 4). Each instance of a nonreccurrent hidden variable is unique. All sequences are unique. All samples are unique. All contexts are unique. It is assumed that the source of the hidden variables is not a function of the parameters of any measurement device. However, the uniqueness of nonreccurrent hidden variables says when a measurement parameter changes the hidden variables change (because they are recorded at a different time). That induces a form of context sensitivity to measurements. That sensitivity means that Bell's formulation can not hold for nonrecurrent hidden variables, for when the parameters for Alice and Bob are (a,b) the hidden variables are different from those when the parameters are (a, b').. Bell assumed that in situation 1 (a,b) the hidden variables can be made common with situation 2 (a,b') but that is false for nonrecurrent hidden variables. If the variables are discrete it would be possible to satisfy Bell's contraint. Here is the difference between recurrent and nonrecurrent variables

Recurrent <A

Nonrecurrent <A

The latter follows from the fact that different samples are independent for nonrecurrent hidden variables.

Using independence and following Bell's steps of his derivation we arrive at a different inequality. We show that inequality places no constraints on correlations.

The same argument holds for the CHSH inequality and the GHZ expression.

Nonrecurrent hidden variables are a powerful lever that pries open quantum issues.

It IS possible to build a local model [1] that duplicates the quantum cosine correlation BUT the model is inefficient (detection efficiency loophole). 81.8% of the particles incident on the detectors of

the model are detected (singles efficiency) and 63.7% of the particle pairs are detected (doubles efficiency). It possible to increase those efficiencies slightly when only the 4 angles of the CHSH inequality are used. We will present the current status of this nonlocal debate in the pages that will follow (under construction).

Critique of the Rowe 2001 Detector Efficiency Experiment No Return to Classical Reality

[1] Classical entanglement

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