gill1109 wrote:I think we *must* carefully separate the mathematics from the physics and from the experiment. We must separate and carefully look at all three. We next need to very carefully think about the connection between the physics and the mathematics.
Needless to say, I disagree with this approach. It is the approach that has led us to the current mess. Logic first, physics second, and math only as needed to support both at the same time with careful consideration to make sure there is direct correspondence between the physical situations and any mathematical abstractions used to describe them.
My understanding is that Bell did very carefully motivate his "local realist" picture (which is a purely mathematical model).
Einstein would definitely have agreed with Bell's motivation for the model. The motivation did come from cherished pre-existing fundamental principles of physics. So fundamental that many would consider them just "common sense" (Caroline Thompson's point of view), or perhaps "the bare minimum of assumptions that we need to make in order to make physics possible at all!" (the point of view of Alexei Nikulov, famous Russian guy, you can find him on ResearchGate).
Thus the local-realism mathematical model has fundamental physical principles or assumptions built into it.
If experiments apparently do not fit to the model, then we learn that the physical assumptions are apparently false.
As I have tried to explain many times, it is unfortunately not as easy as that. Bell proponents are too quick to eliminate their favorite assumptions which generate mystery without careful consideration of what exactly was modelled in the first place. The conclusion that certain experiments do not fit certain models and thus certain assumptions must be false, is fallacious because those experiments, properly modelled, would not be expected to fit those mathematical models anyway, even if all the assumptions are true. That is why we must go back to the drawing board and look at the mathematics together with the physics, not separately.
As I said many times before, there are now many different standpoints which can logically be taken. At least five.
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I think that Bell's theorem should be thought of as a theorem from theoretical computer science, belonging to the field of distributed (classical) computing. Boris Tsirelson agrees. There are elegant proofs of this abstract theorem (Steve Gull's proof - an old exam question in the Cambridge master programme in theoretical physics) which do not have anything to do with statistics or with real experiments. You could say that the theorem is an easy corollary of standard results from Fourier analysis. Certain functions cannot be represented in certain ways. One does, of course, need some classical calculus (ordinary Riemann integration is enough), to formulate and prove the theorem in this way. In modern terminology, one could call it a pretty elementary theorem in functional analysis or in approximation theory. It would be very interesting to look at it from a category theory point of view.
But but but, a theorem about what exactly? Is the key question. All those proofs do the same thing. They demonstrate that given a single sample space, a certain inequality must hold. You can have 10 different ways of proving it, but if you perform an experiment in which there is not a single sample space but separate sample spaces, all bets are off. The design of the experiment requires multiple sample spaces and any apparent violation is simply telling you what you should already know from the experimental design -- that the outcomes do not originate from a single sample space. The fact that you could imagine them to have originated from a single sample space in principle is irrelevant. What matters is what is actually measured. By separating the mathematics from the physics, it becomes easy to overlook this. I think perhaps your most important paper was https://arxiv.org/abs/quant-ph/0312035 because it hinted at the solution of this mess. I understand that you disagree with my reading of that paper but I believe the roots of the solution can be found in it.
But you don't have to take my word for it. If you carefully analyze all the experiments done to date you will realize separately from any considerations of locality or realism, that there is not a single sample space for the data as required by Bell's toy model. Once you realize this, you will appreciate just how embarrassingly meaningless Bell's theorem is.