Correct me if I'm wrong, but this is my understanding: - Bell's inequality (one version of it) states: for all independent A, B, W, P(A & B) <= P(A & W) + P(B

Correct me if I'm wrong, but this is my understanding: - Bell's inequality (one version of it) states: for all independent A, B, W, P(A & B) <= P(A & W) + P(B & ~W). Since W can allegedly either be true or false, Bell's inequality holds: P(A & W) + P(B & W) = P(A) or P(B) (if W is true or false), and both P(A) >= P(A & B) and P(B) >= P(A & B) (since A & B = true requires A = true and B = true) - However, Bell's inequality does not hold in quantum theory. There is a way to get seemingly-independent A, B, and W (from measuring entangled electrons' spin), where P(A & B) > P(A & W) + P(B & ~W). This suggests either: - W is not either true or false, it can exist in some in-between state, meaning we can't simplify P(A & W) + P(B & ~W) into P(A) or P(B). This sounds a lot like quantum superposition. - Or, even though P(A & W) + P(B & W) might simplify into P(A) or P(B), since we don't actually know, P(A) >= P(A & B) or P(B) >= P(A & B) does not prove that P(A & W) + P(B & ~W) >= P(A & B). This sounds a lot like the electron slit experiment. - Or, the condition "A, B, W is independent" is impossible because there are no such thing as independent variables. This basically throws Bell's inequality out: if W influences A and B and A and B influence each other, and you can't prove how they influence each other, you can't prove that P(A & B) = P(A & W) + P(B & ~W) (for example, maybe in one particular scenario which experiments can never isolate, P(A & B) is almost as likely as P(A), but P(A & W) is much less likely than P(A) and P(B & ~W) is much less likely than P(B)). This is superdeterminism