Back Home Q: How is it that Bell’s Theorem proves that there are no “hidden variables” in quantum mechanics? How do we know that God really does play dice with the universe?
Just for the hell of it, take a look at: L = A 0 B 22.5 + A 45 B 22.5 + A 45 B 67.5 – A 0 B 67.5 = (A 0 + A 45 )B 22.5 + (A 45 – A 0 )B 67.5L = (A 0 + A 45 )B 22.5 + (A 45 – A 0 )B 67.5 = ±2, since either (A 0 + A 45 ) = ±2 and (A 45 – A 0 ) = 0, or (A 0 + A 45 ) = 0 and (A 45 – A 0 ) = ±2. So if you could fill out each of these values (A 0 , A 45 , B 22.5 , B 67.5 ), then L = A 0 B 22.5 + A 45 B 22.5 + A 45 B 67.5 – A 0 B 67.5 = ±2 which, notably, is less than or equal to 2. E[A 0 B 22.5 ] + E[A 45 B 22.5 ] + E[A 45 B 67.5 ] – E[A 0 B 67.5 ] = E[A 0 B 22.5 + A 45 B 22.5 + A 45 B 67.5 – A 0 B 67.5 ] ≤E[|A 0 B 22.5 + A 45 B 22.5 + A 45 B 67.5 – A 0 B 67.5 |] = E = 2. So E[A 0 B 22.5 ] + E[A 45 B 22.5 ] + E[A 45 B 67.5 ] – E[A 0 B 67.5 ] ≤ 2. This is one version of “Bell’s Inequality”, and it holds if each term (A 0 , A 45 , B 22.5 , B 67.5 ) has a value.
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