gill1109 wrote:What bounds?
The upper bound doesn't change.
But now we can also deduce lower bounds 4, 0.
I'm trying to get you to tell me based on your own definition of bounds what you believe the bounds of the two expressions
E(U) + E(V) + E(X) + E(Y)
E(X) + E(-X) + E(Y) + E(-Y)
are if each of the expectation values has maximum and minimum values of +1 and -1 respectively.
You've already answered that you think the first expression should have an upper bound of 4, but for the second one you answered based on the assumption that there was no minimum for the expectation values. So I clarified that the minimum value is -1 and asked you again what you believe the upper bound for the second expression would be based on your own definition of bounds. Based on my definition, it should be 0, and neither of them can ever be violated, even by experimental error.
Then I asked whether, still based on your definition of bounds, any of those bounds you just identified could ever be violated by anything, even by statistical error. You already answered that the bound for the first one could not. Please could you clarify if you believe the bounds for the second one, now clarified can be violated by anything whatsoever?
If someone shows you a proof of a bound, and then gives you an example where the bound is violated, then either
(a) he has just proved to you that his proof is wrong, or
(b) he is talking about two different situations. The situation in which the bound can be proved, doesn't apply to the second situation.
When we violate a bound, we simply prove that the assumptions which led to the bound are not applicable.
Exactly. So when your R-code above produces a value of 2.00001, it proves that the assumptions which led to the bound of 2 are not applicable to it. In other words, the CHSH does not apply to the second part of your R code experiment. As we have established, an upper bound can not be violated, not even by experimental error. A 0.000000001 violation is just as much proof as a 10000000 violation that the assumptions which led to the inequality are not applicable to the situation which has produced the violation. Kapish?
Therefore everything you said about how the upper bound of the CHSH should apply to a system which violates it sometimes (statistically) is baloney.
And Heinera's statement that
"When we are talking about an upper bound for expectations, the bound will usually be violated half of the time" is baloney too.
I believe I have successfully demonstrated in various different threads that the apparent violation of the CHSH by QM and Experiments is simply because the CHSH was derived for one situation and is being applied to a different situation, and the difference has nothing to do with realism or locality whatsover, all it has to do with is the difference between counterfactual outcomes on a single set, and actual outcomes from 4 disjoint sets. Your arguments that the CHSH bound should still apply for some statistical reason, even though your own examples purporting to prove the claim actually violate the bound sometimes, do not survive.