OK, and I think one thing that leads to misunderstanding is a terminology issue. You're using local determinism to refer to a philosophical stance, while you're using local realism to refer to a particular formal model which tries to implement this philosophical stance. I'm using both local realism and local determinism, pretty much interchangably, to refer to the philosophical stance, not to any formal model or formal constraint. So just keep that in mind when reading my posts.
OK, let me try once more to show you how the logic of Bell's theorem forces any local determinist to disagree with at least some of the predictions of quantum mechanics.
1. Pretend you are a local determinist who believes that all the experimental predictions of quantum mechanics is correct.
2. One of these experimental predictions is that entangled photons are perfectly correlated when sent through polarizers oriented at the same angle.
3. From this you conclude that both photons are consulting the same function P(θ). If P(θ)=1, then the photon goes through the polarizer, and if it equals zero the photon does not go through.
4. Another experimental prediction of quantum mechanics is that if the polarizers are set at different angles, the mismatch (i.e. the lack of correlation) between the two photons is a function R(θ) of the relative angle between the polarizers.
5. From this you conclude that the probability that P(-30)≠P(0) is R(30), the probability that P(0)≠P(30) is R(30), and the probability that P(-30)≠P(30) is R(60).
6. It is a mathematical fact that if you have two events A and B, then the probability that at least one of these events occurs (in other words the probability that A or B occurs) is less than or equal to the probability that A occurs plus the probability that B occurs.
7. From this you conclude that the probability that P(-30)≠P(30) is less than or equal to the probability that that P(-30)≠P(0) plus the probability that P(0)≠P(30), or in other words R(60)≤R(30)+R(30)=2R(30).
Which of these steps do you disagree with and why?
But you're only agreeing that some particular formal model does not agree with the predictions of QM. In my 7-step argument above, I am trying to prove that ANY believer in local determinism MUST disagree with some of the predictions of QM.
The reason that quantum mechanics is able to have both perfect correlation at identical angles and nonlinear correlations as a function of angle is that QM does not say that the decision about whether the photon goes through the polarizer or not is predetermined by a function P(θ). In particular, if one polarizer is turned to -30 degrees and the other polarizer is turned to 30 degrees, quantum mechanics doesn't believe that the photons have a definite polarization at 0 degrees, and thus QM does not believe in P(0) which is essential for the proof above.
Yes, it does. The proof above decisively shows that in any local determinist universe, we must have R(60)≤2R(30). But the way superdeterminism gets around this is by saying that it is impossible to get accurate measurements of R(30) and R(60), because the experiment is rigged: since whatever is controlling the measurement decision interacted in the past with the (ancestors of) the entangled photons, the experimenters are selecting the angles just right (because the particles controlling them know the exact details of the function P(θ) for the entangled pair of photons) so that it appears that R(60)>2R(30).
That's why I said the following to you earlier in this thread:
"So here's another way to put it: An ordinary local realist theory just assumes that particles which are considered entangled according to QM must have had local interactions in the past which is determining their EPR-type nonlocal correlations today. But a local superdeterminist theory assumes that a particle must have interacted in the past with not only those that are entangled with it according to quantum mechanics, but also other particles which quantum mechanics would say have no connection with it. This is how a local superdeterministic theory would be able to produce Bell-type nonlocal correlations."
And again, remember that when I say local realism I mean the philosophical stance you call local determinism.