@ lugita15,
The exchange between you and I got a little off track. Which was my fault, and I apologize for not taking the time to sort it out properly. Below I'll comment in reference to an exchange between you and zonde, and hopefully any misunderstanding will be clarified.
zonde said:
Linear relationship between θ and correlation level follows directly from that assumption.
lugita15 said:
You're right, it's a fairly direct route from the assumption that there is perfect correlation at identical polarizer settings to the conclusion that the local realist must believe that the correlation is linear. But ThomasT does not agree with this fairly direct line of reasoning, so I'm trying to convince him that it works.
I think that there's some step or steps in the LR line of reasoning which then lead(s) to the logically necessary conclusion that the correlation between θ and rate of coincidental detection should be linear. But I don't think it's the prediction of perfect correlation at θ = 0°. After all, QM predicts the same thing as LR at θ = 0°, but wrt all θ the QM and LR correlations are different. So it seems that we can't attribute that difference to the prediction of perfect correlation at θ = 0°.
zonde said:
Local realistic theory can not reproduce all predictions of QM.
lugita15 said:
If I could persuade ThomasT of this, I'd be done.
I already agree with this, and have said so many times in this thread. But you're not then done. This is where the assessment of the necessity of a local superdeterministic model of quantum entanglement begins.
zonde said:
But local realistic theory can try to reproduce QM predictions in domain where they are experimentally verified. And that domain does not include (something close to) perfect correlations for matching measurement settings.
lugita15 said:
But that just has to do with practical experimental limitations. The point I'm arguing with him about is whether someone can believe that all the predictions of quantum mechanics are correct and still believe in (non-superdeterministic) local realism. I'm trying to show that the answer is no ...
I agree that the answer is no.
lugita15 said:
... because one experimental prediction of QM is perfect correlations at identical polarizer settings, from which the local realist is forced to believe in a linear correlation relationship ...
Ok, now I disagree.
This is the basis of both the QM and LR treatments, but I would argue that, given this perfect correlation (ideally) at θ = 0°, one is not then forced to believe in a linear correlation wrt all values of θ. After all, the QM treatment leads to a nonlinear correlation wrt all θ.
So, given what we do agree on, wouldn't the first step in assessing the applicability of the concept of superdeterminism wrt generating the simplest and clearest possible understanding of why BIs are violated have to do with identifying any and all points in the LR reasoning which lead to the prediction of a linear correlation between θ and rate of coincidental detection?
zonde said:
What I think ThomasT is disputing is that given Malus law it is very unreasonable conclusion that there is linear relationship between θ and correlation level.
lugita15 said:
I agree that this is the point of contention, but keep in mind that he thinks a local realist can believe in the nonlinear correlation given by Malus' law, while at the same time also believing that there is perfect correlation at identical settings.
Ok, I think I see one source of our misunderstanding. I'm not a local realist. That is, I don't think that a viable LR model of quantum entanglement is possible.
But I am a local determinist. I think that both of these assumptions, locality and determinism, are supported by ample empirical evidence. They seem to be the basis of our everyday navigations through our shared reality. And they seem to be the basis for doing physical (essentially mechanistic) science. As far as I can tell, the assumptions of nonlocality and indeterminism arise, more or less ad hoc, from our inability to make viable LR models of quantum entanglement and our inability to predict certain quantum experimental phenomena.
I'm going to stop here, but will pick up, eventually, where I left off, with a brief exposition of the local deterministic approach to understanding quantum entanglement, and then tying it into the thread question. The focus will eventually be on identifying the precise elements in the standard LR formulation (line of reasoning) which are at odds with what's presumably (according to a local deterministic view) occurring in the underlying reality, and how the encoding of certain elements contrary to that view into an LR formalism, and a Bell inequality, necessarily entails the violation of BIs.
Then the question will be: what, exactly, has been proven, and does our understanding of BI violations necessarily warrant the assumption of superdeterminism in order to maintain a local deterministic view of our universe?
Note: It's important to keep in mind that the formal requirement, local realism, is not equivalent to the philosophical orientation, local determinism. The former having to do with what's required to render a model of quantum entanglement explicitly local or explicitly realistic (without any ad hoc associated nonlocal mechanisms or assumptions), or, as with Bell's formulation, both -- and the latter having to do with assumptions about the way our world is, based on extant empirical observations.