LsT said:
Care to make it more clear to me why this is the case?
That's exactly what Bell proved.
The claim is this: Let P(A,B, \alpha,\beta) be the probability that Alice will get result A and Bob will get result B, given that Alice's detector has setting \alpha and Bob's detector has setting \beta. For an EPR-type experiment, A = 0 or A=1, depending on whether Alice detects a photon, or not. Similarly for B. The prediction of QM for the two-photon case is:
P(A,B,\alpha,\beta) = \frac{1}{2} cos^2(\alpha - \beta) (if A = B) and P(A,B,\alpha,\beta) = \frac{1}{2} sin^2(\alpha - \beta) (if A \neq B)
(That's assuming perfect detection, and no spurious photons. I don't know how the formula should be adjusted to allow for detector mistakes)
We can say that the correlation P(A,B,\alpha,\beta) has a "local causal explanation" if there is some property, or variable \lambda characterizing the photon creation event such that the probabilities can be written as follows:
P(A, B, \alpha, \beta) = average over all \lambda of P_A(A, \alpha, \lambda) \cdot P_B(B, \alpha, \lambda)
Your hypothesis about \theta, \kappa is exactly of this form.