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Bell's theorem - for or against Hidden Variables?
(07-27-2016, 01:52 PM)secur Wrote:
(07-27-2016, 08:14 AM)gill1109 Wrote:
(07-26-2016, 06:47 PM)secur Wrote: To me the phrase "QM is non-local" means the following in this context. When we analyze and predict mathematically the results of the experiment, those two non-local variables must appear together in the same equation. In fact, we must use the cosine of the sum of the angles (or, the dot product of vectors representing the detector settings) to predict the correlations of Alice and Bob's two detections (or a series thereof). This happens nowhere else in physics! To analyze any other experiment, and predict its results - or a function of the results, like correlation coefficients, or moments - it's always sufficient to use only the information available in the past light cone. Except in this one case. Here we must use two variables that no possible single observer could have known, at the time of the measurement. This very peculiar and unique situation can reasonably be called "non-local".
It is more subtle than this, I think. There is a local realistic model which predicts that the correlation is half the cosine of the difference between the angles. There is no local realistic model which predicts that the correlation is the full cosine.

To predict the correlation between both observer's measurements we need to know both observer's settings, in either case. No mystery about that.

For one thing, a correlation of half the cosine is no good because it doesn't give the right results. At an angle of pi, for instance, the true correlation is -1, but this would give 0.

But one can easily imagine semi-correct correlation functions that can be produced under local realism. The key necessity is that correlations of smaller angles, less than pi/2, are not so strong as in real QM. For instance, a correlation of (1 - theta * 2/pi) would do it. (Substituting theta = 2*pi - theta when theta is between pi and 2*pi.) Something like this will give roughly the right correlations. At least for theta=pi it is, correctly, -1. And it works fine without any knowledge of the other detector's setting. But for small angles, near 0, the correlation is too weak. So sure, a wrong correlation can be achieved easily in a local-realism model. But so what? It doesn't match experiments.

Perhaps it's harder than I thought to nail down the definition of "Property X". Let me try it as follows. Consider the QRC. One way to beat it would be to communicate detector settings between the two programs simulating the two stations. This "cheating" would be equivalent to an FTL signal between Alice and Bob's detectors.

If a real-time simulation of an experiment requires incorporating an FTL signal like that, to correctly mimic Nature: then the experiment possesses "Property X".

Can you see any problem with that definition? It's meant to be equivalent to the one I gave before, but less ambiguous.
I think that's an excellent definition of "Property X".
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RE: Bell's theorem - for or against Hidden Variables? - by gill1109 - 07-28-2016, 08:21 AM

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