If you do the experient with an entangled source and two Stern Gerlach detectors oriented the same way it's not so interesting a bit like the marbles in envelopes - either they both red of green. The interesting bit is if you rotate them a bit the correlation varies like cos(the angle) between them. So correlation 1 at 0 degrees, 0 at 90 degrees, -1 at 180 degrees and about 0.98 at 10 degrees. But how does nature or whatever know the angle between them when they are far apart? In most 'hidden variables' scenarios the correlation at 10 degrees is more like 0.89 or a linear change and that is basically the essence of Bell's theorem and experiments - you can't get the correlations without the particle at one end kind of knowing the set up at the other, or 'non locality' as Bell called it.
Your answer seems to focus on the key un-addressed subtlety.
Why is the difference in orientation of the detector necessarily linear? What is the control aspect of this experiment where classical-system shows this linear pattern? Or can the argument be made more fundamentally?
Thanks for the help. I just want to point out this [detector orientation] is likely a big area where non-physics people might get tripped up:
If you told me causally this detector which measures electrons/photons/whatever and varies by the cosine of the orientation, I don't think any (non-physics person) would bat an eye; it seems like a pretty normal thing a sensor might do.
You can think of an example where things are classical, the particles start with some definite orientation randomly determined at the start and if they are within say 45 degrees of the angle of the detector they go one way, over 45 the other and it's not so hard to figure in that case it will vary linearly. As to how to prove the general case I don't know. Try Bell's paper?
As an aside I don't think the classical 'hidden variables' situation has a prefered orientation which contradicts the premise of the featured article that you get the odd entanglement effects so as to not have a prefered orientation.
