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Gordon Watson

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https://www.physicsforums.com/showthread.php?t=589134

at the request of the OP.

gill1109 said:When I said randomness I did not refer to unpredictable (experimental) phenomena. When you toss a coin, the result depends deterministically on the initial conditions. That is familiar everyday randomness which is merely practical unpredictability.

QM on the other hand says that nature is intrinsically random. There is no hidden layer "explaining" what actually will happen. The randomness is spontaneous. Inexplicable. Without antecedent. Effects without a cause.

..

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.