I am approaching this from an intuitive perspective and I don't speak the language. However, I have been doing a lot of reading about Bell's Theorum and how invalidates either locality or counterfactual definiteness.
From my point of view, locality is the concept that there is no way that two particles can interact with each other "instantaneously" at a distance (i.e. faster than light.). Realism/counterfactual definitiveness is the concept that all particles have some true value for all variables at some instant regardless of whether or not that value was observed. Let's assume for the sake of this question that locality is true, which I believe is the current popular model in QM.
Assuming locality, why do Bell's Inequalities show that conterfactual definiveness must be false?
Edit to respond to below post:
This is crazy. Let me see if I am following you. I'll use your framework.
I'm not really sure what spin is but I'm seeing it as an observable phenomenon that exists as a function of a specific direction in a given particle at an instant of time, and the spin itself at any angle changes (randomly?) over time.
A and B are, we are assuming, perfectly correlated so so the spin at angle θ in A is definitely the same as the spin at angle θ in B. In any given electron (let's just take A) we can define some angle θ as the angle between two 'directions' on that electron that have an exactly 99% correlated spin. There's no way we can measure those two directions on the same particle at the same time, but since A and B are perfectly correlated, we can measure A at 0 degrees and B at θ degrees and experimentally we would see that they are the same spin This is crazy. Let me see if I am following you. A and B are, we are assuming, perfectly correlated so so the spin at angle θ in A is definitely the same as the spin at angle θ in B. In any given electron (let's just take A) we can define some angle θ as the angle between two 'directions' on that electron that have an exactly 99% correlated spin. There's no way we can measure those two directions on the same particle at the same time, but since A and B are perfectly correlated, we can measure A at 0 degrees and B at θ degrees and they will be the same spin 99% of the time.
Similarly, if we measure the spin at θ in A and at 2θ in B, we will see that these two values are the same spin 99% of the time. Assumingly, this will work for any two angles that are exactly θ apart -- with enough measurements they will be correlated exactly 99% of the time.
However, if we measure the spin at 0 in A and at 2θ in B, they are only correlated 96% of the time. If V0 is at most 1% off from V1, and V1 is at most 1% off from V2, V0 should be anywhere from 0-2% off from V2. But, we find, according to QM and experimentation, it is not! It is less heavily correlated than that.
This is where I lose you. Why does saying no to realism resolve this issue?