This post moved from "Nick Herbert's proof?" https://www.physicsforums.com/showthread.php?t=589134 at the request of the OP. .. Effects without a cause in Herbert's experiment? I presume that you believe that some quantum events have no cause; not classical effects? So I would welcome any and all comments and calculations on the following scenario, based on a typical Bell-test set-up and the CHSH inequality. We replace the quantum-entanglement-producing source with a classical source which sends a short pulse of light to Alice and Bob each day (over many years), each pulse correlated by having the same linear-polarization; though each day the common pulse polarization-orientation is different . Let x denote any variable of your choosing. Then (as in a standard Bell-analysis) Alice's results are represented by (1) A(a, x) = ±1 where a is any analyzer orientation of her choosing; Bob's by (2) B(b, x) = ±1 where b is any analyzer orientation of his choosing; (3) 0 [itex]\leq[/itex] ρ(x); (4) ∫ρ(x) dx = 1. Please (after Bell, showing all your workings), calculate the expectation: (5) E(AB) = ∫AB ρ(x) dx. Please provide the maximum value achievable for the CHSH inequality under these conditions. With thanks in advance, GW EDIT added with move: I'd like to understand how physicists and mathematicians deal with the above wholly classical setting in the context set by Bell (1964) when arriving at his theorem. Thanks.