06-05-2016, 09:26 PM

Depends on what you consider. If you consider a local-realistic theory which fulfills the conditions of the theorem, and talk about the sum

\[ S=E(a,b)-E(a,b^{\prime })+E(a^{\prime },b)+E(a^{\prime },b^{\prime }),\]

then S=4 is not possible. If you talk about the sum +1 -(-1) + 1 + 1, then it is not only possible, but holds always. If you talk not about computing the sum for the same \(\lambda\), but for four different particular values, without any averaging, then it is possible. If you average enough so that you have

\[E(a,b) = \int A(a,\lambda)B(b,\lambda) \rho(\lambda) d\lambda\]

with sufficient accuracy and the same functions \(A, B, \rho\) for all four expressions, then not.

So, a typical trick question, you do not give enough specification for a unique answer and hope nonetheless for an answer.

\[ S=E(a,b)-E(a,b^{\prime })+E(a^{\prime },b)+E(a^{\prime },b^{\prime }),\]

then S=4 is not possible. If you talk about the sum +1 -(-1) + 1 + 1, then it is not only possible, but holds always. If you talk not about computing the sum for the same \(\lambda\), but for four different particular values, without any averaging, then it is possible. If you average enough so that you have

\[E(a,b) = \int A(a,\lambda)B(b,\lambda) \rho(\lambda) d\lambda\]

with sufficient accuracy and the same functions \(A, B, \rho\) for all four expressions, then not.

So, a typical trick question, you do not give enough specification for a unique answer and hope nonetheless for an answer.