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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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#52
The point is not if the experiment is "unphysical", but that a theory which fulfills some properties (like EPR realism and Einstein causality) has to predict that the Ak(a)Bk(b) do not depend on the question if a measurement is actually done or not. So we can evaluation them using an experiment where Ak(a)Bk(b) is measured, and extend the result to cases where it is not measured.
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#53
(07-09-2016, 12:04 PM)Schmelzer Wrote: The point is not if the experiment is "unphysical", but that a theory which fulfills some properties (like EPR realism and Einstein causality) has to predict that the Ak(a)Bk(b) do not depend on the question if a measurement is actually done or not.  So we can evaluation them using an experiment where Ak(a)Bk(b) is measured, and extend the result to cases where it is not measured.

It is preposterous to propose a hypothesis that is impossible to test.  [...]  All the "Bell" experiments do is confirm that the predictions of QM are correct and nothing more.  They do not test locality or realism.
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#54
(07-10-2016, 06:08 PM)FrediFizzx Wrote: It is preposterous to propose a hypothesis that is impossible to test.  Are we doing science or voodoo?
We are doing normal science. We have some hypotheses, and combined together they lead to testable predictions, like Bell's inequalities.

If you don't know elementary scientific methodology, this is your problem. Testable predictions are the result of application of the whole theory, in fact even several different theories (like theories about how all the measurement devices work). Simple principles, taken alone, are typically untestable.
(07-10-2016, 06:08 PM)FrediFizzx Wrote: All the "Bell" experiments do is confirm that the predictions of QM are correct and nothing more.  They do not test locality or realism.
Once one can derive, starting from Einstein causality and realism, that the QM prediction has to be wrong, these experiments reject the combination of Einstein causality and realism. Live with this.
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#55
(07-10-2016, 09:43 PM)Schmelzer Wrote:
(07-10-2016, 06:08 PM)FrediFizzx Wrote: It is preposterous to propose a hypothesis that is impossible to test.  Are we doing science or voodoo?
We are doing normal science.  We have some hypotheses, and combined together they lead to testable predictions, like Bell's inequalities.  

If you don't know elementary scientific methodology, this is your problem.  Testable predictions are the result of application of the whole theory,  in fact even several different theories (like theories about how all the measurement devices work).   Simple principles, taken alone, are typically untestable.
(07-10-2016, 06:08 PM)FrediFizzx Wrote: All the "Bell" experiments do is confirm that the predictions of QM are correct and nothing more.  They do not test locality or realism.
Once one can derive, starting from Einstein causality and realism, that the QM prediction has to be wrong, these experiments reject the combination of Einstein causality and realism.  Live with this.

Keep doing your wrong rationalizations; it is your problem.  The bottom line is that it is impossible to test Bell's inequalities since it is mathematically impossible for anything to violate them.  [...] Look at the simple mathematics.  It is just not possible for even QM to "violate" the inequalities.  [...]
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#56
Your renaming of the phrase "Bell inequalities" is irrelevant and therefore ignored.
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#57
(07-11-2016, 05:08 AM)Schmelzer Wrote: Your renaming of the phrase "Bell inequalities" is irrelevant and therefore ignored.

???  What up doc?  How did I rename? [...]  Look at it this way.  Bell formed some inequalities thinking that it would test local realism.  But he didn't seem to realize that nothing could mathematically violate such inequalities.  He even proves it unknowingly. [...]
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#58
(07-11-2016, 05:58 AM)FrediFizzx Wrote:
(07-11-2016, 05:08 AM)Schmelzer Wrote: Your renaming of the phrase "Bell inequalities" is irrelevant and therefore ignored.
???  What up doc?  How did I rename?
A reference to your #17 where you refer to some inequality with a <4 which you have invented and refer to it (with a Wiki link) as if it would be Bell's inequality.
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#59
(07-11-2016, 05:46 PM)Schmelzer Wrote:
(07-11-2016, 05:58 AM)FrediFizzx Wrote:
(07-11-2016, 05:08 AM)Schmelzer Wrote: Your renaming of the phrase "Bell inequalities" is irrelevant and therefore ignored.
???  What up doc?  How did I rename?
A reference to your #17  where you refer to some inequality with a <4 which you have invented and refer to it (with a Wiki link) as if it would be Bell's inequality.

Now you are just being dishonest.  I never ever said it was a Bell inequality.  I have always said that the inequality with a bound of 4 is a different inequality from Bell-CHSH.  And of course I didn't invent it.  It is a natural consequence of having independent expectation terms.  Which is easy to show by simple inspection.

1 - (-1) +1 +1 = 4
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#60
Suppose we can randomly sample quadruples (A, A', B, B') with each component = +/-1
Do this n times and compute 4 averages <AB>, <AB'>, <A'B>, <A'B'>
They will certainly satisfy the CHSH inequality <AB> + <AB'> + <A'B> - <A'B'> is less than or equal to 2 (by some simple algebra)

Now suppose that I only use a random sub-sample of size about n/4 to compute <AB>
Suppose I use a disjoint random sub-sample of size about n/4 to compute <AB'> and so on.
The averages taken over four disjoint but completely random sub-samples will be close to the averages based on the whole sample, if n is large (by some elementary probability theory). So when based on four disjoint random subsamples, <AB> + <AB'> + <A'B> - <A'B'> is very unlikely to be much larger than 2.

In real Bell-CHSH experiments, we can't observe quadruples (A, A', B, B'). It is only the hypothesis of local realism that says that they do exist. We only observe one of the four pairs (A,B), (A,B'), etc. We calculate <AB> + <AB'> + <A'B> - <A'B'> using a different set of runs for each of the four averages. Of course, in principle it is possible that the observed value of <AB> + <AB'> + <A'B> - <A'B'> is exactly equal to 4 (the algebraic bound which FrediFizzx likes to remind us of). However, as anyone can easily verify by doing their own computer experiments, the result won't often be outside of the interval [-2, +2] by more than a few times 1 / sqrt n

Real experiments report error bars as well as correlations. There is more to Bell-CHSH than just algebra. There is also a little bit of statistics. It is however very commonly overlooked.
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