...
That is why I asked the following questions:
1) Do you agree that there are two scenarios involved in this discussion:
Scenario X, involving the three correlations:
C(a,b) = correlation for what we would get if we measure (a,b)
C(b,c) = correlation for what we would get if we measure (b,c)
C(a,c) = correlation for what we would get if we measure (a,c)
Scenario Y, involving the three correlations:
C(a,b) = correlation for what we would get if we measure (a,b)
C(a,c) = correlation for what we would have gotten had we measured (a,c) instead of (a,b)
C(b,c) = correlation for what we would have gotten had we measured (b,c) instead of (a,b)
2) Do you agree that Scenario X is different from Scenario Y?
3) Do you agree that the correlations in Bell's inequalities correspond to Scenario Y NOT Scenario X?
4) Do you agree that correlations calculated from QM correspond to Scenario X not Scenario Y?
5) Do you agree that correlations measured in experiments correspond to Scenario X not Scenario Y?
While the correlations in Scenario X all commute, those in Scenario Y do not all commute.