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probability 1 and, therefore, also Y 1 ( i, i ) = − Y 2 ( i, i ) = 0, with probability 1, as mentioned earlier. 

We formalize the hypothesis of ”local hidden variables” by the hypothesis that spin mea- sured on one particle does not depend on the angle at which the other particle is measured. This can be stated as: for all angles ( x 1 , x 2 ) 

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In some of the experiments referenced above the times of the two measurements were sufficiently close and the separation of the particles sufficiently great that even a signal traveling at the speed of light could not inform one particle of the result of the other’s spin measurement. Therefore, refuting the hypothesis of ”local hidden variables” implies reality is not local and therefore we can essentially treat the hypothesis of local hidden variable and local reality as the same; we return to this point in the discussion. 

The hypothesis asserts both locality and reality. It asserts locality because the angle x 2 at which particle 2 is measured has no effect the spin Y 1 ( x 1 ) of particle 1 . It asserts reality because the spin Y$_{i}$ ( x ) of a particle measured along axis x is assumed to exist for every x, even though for each i , only one of the Y$_{i}$ ( x ) is observed; the one corresponding to the axis along which particle was actually measured. All other Y$_{i}$ ( x ) are missing data in the language of statisticians or, equivalently, hidden variables in the language of physicists. The counterfactuals Y$_{i}$ ( x ) correspond exactly to what Einstein called ”elements of reality”. In the language of counterfactual theory, the hypothesis of local reality is, by definition, the hypothesis of no interference between treatments. In the following a unit may be taken to be a pair of entangled particles. 

Theorem 1 . If for some unit, M (0 , 0) = 0, M (1 , 2) = 1, M (0 , 2) = 0, M (1 , 0) = 0 then the hypothesis of ’local hidden variables’ is false. 

Proof. By contradiction: Suppose the hypothesis holds. Now M (1 , 2) = 1 implies either 

