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Bell's theorem - for or against Hidden Variables?
#51
(06-07-2016, 12:00 AM)FrediFizzx Wrote:
(06-06-2016, 08:27 PM)Schmelzer Wrote: The linked paper shows only that Joy Christian has not understood why Bell can do this.  It is an application of the EPR argument.

Nonsense.  Please demonstrate how ⟨Ak(a)Bk(b)+Ak(a)Bk(b′)+Ak(a′)Bk(b)−Ak(a′)Bk(b′)⟩ could represent something that is actually physical.

I will do that, with pleasure.

Suppose that at each run (each value of k) we choose, completely at random, whether to observe Ak(a) or Ak(a'), and whether to observe Ak(b) or Ak(b'). For each k, we get to observe just one of the four products: Ak(a)Bk(b), Ak(a)Bk(b′), Ak(a′)Bk(b), Ak(a′)Bk(b′). Now we split the complete set of n runs into four subsets, according to the chosen pairs of measurement settings.

We observe the average of Ak(a)Bk(b) for those runs k such that the settings were a, b
We observe the average of Ak(a)Bk(b') for those runs k such that the settings were a, b'
We observe the average of Ak(a')Bk(b) for those runs k such that the settings were a', b
We observe the average of Ak(a')Bk(b') for those runs k such that the settings were a', b'

If n is large, then those four observed averages (got by averaging over four disjoint subsets of runs, each of size about n/4) will, with probability close to 1, be close to the four "unphysical" (not observed) averages got by averaging over all n runs.

We combine the four observed averages "CHSH style" (add three of them and subtract the fourth). The result will, with large probability, be close to the "unphysical" (not observed) ⟨Ak(a)Bk(b)+Ak(a)Bk(b′)+Ak(a′)Bk(b)−Ak(a′)Bk(b′)⟩. Though unphysical, we do know that it lies between -2 and 2. So the observed value of CHSH is very unlikely to be much larger than 2 or much smaller than -2.

It doesn't matter that Ak(a)Bk(b)+Ak(a)Bk(b′)+Ak(a′)Bk(b)−Ak(a′)Bk(b′) is "unphysical". The argument only assumes that it exists. It exists because of "local realism". Even if in run k you choose setting a and setting b, so only Ak(a) and Bk(b) get physically realized, still Ak(a') and Bk(b') exist too. After all, all of these quantities are merely some deterministic functions of hidden variables and detector settings. If you knew the functions and you knew the hidden variables, you could in fact have simply computed the not actually observed Ak(a') and Bk(b').
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RE: Bell's theorem - for or against Hidden Variables? - by gill1109 - 07-08-2016, 02:59 PM

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