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Bell's theorem - for or against Hidden Variables?
(09-07-2016, 04:14 PM)secur Wrote: For an inequality to be satisfied: consider Christian's paper cited above, equation C15, which is the CHSH inequality, but with Tsirel'son's bound, 2*sqrt(2). He derived it in this appendix for SU(2), not SO(3). He says:

"... the above inequality can be reduced to the form [C15] exhibiting the upper bound on all possible correlations."

Now, for this inequality to be satisfied would mean the following. Do the computations he specifies. If the result is, in fact, less than about 2.828, the inequality has been satisfied. Otherwise, not. That's not philosophy, just math. Philosophy comes in when we ask what this implies, in the real world.

I feel I'm getting a better idea of your complaint against Bell. Consider this quote from him,

"In a theory in which parameters are added to QM to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remotely. Moreover, the signal involved must propagate instantaneously ..."

IOW if a theory violates his inequality, it must be nonlocal. It's not unreasonable to label this "philosophy". The statement's not science because it really can't be falsified. To do so you'd have to demonstrate a violation, and then prove there's no FTL signal. Apparently that's impossible. Bell can always claim there is such a signal, you just haven't detected it yet.

The typical "Bellist" conclusion is similar but not so specific about "nonlocality". If a situation violates the inequality, then it must be - nonreal, nonlocal, noncausal, nonclassical - or something like that. Again, how can that be falsified? It's too vague; there's no prediction here. If a certain result happens we will assign a philosophical label to it. So what?

Perhaps this is what you mean by saying Bell is "founded on philosophy"?

Excellent reply, secur!

Inequality is a fundamental tool of analysis.  Taking the simple example of the am-gm inequality (the arithmetic mean of two nonnegative real numbers is at least as big the geometric mean), we find that boundary conditions drive the result.  Tsirelson's bound being the most general bound on correlations (any correlations, not just quantum mechanical) at the upper limit, zero assumed at the lower, begs an initial condition within the scope of the real numbers (Lebesgue measure).

What boundary conditions satisfy Bell's inequality?

secur wrote, "I feel I'm getting a better idea of your complaint against Bell. Consider this quote from him, 

"'In a theory in which parameters are added to QM to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remotely. Moreover, the signal involved must propagate instantaneously ...'"

Yes, indeed.  Which is why I don't fault Bell, the accomplished physicist, for the shortcomings of Bell-Aspect, and the conclusions of later acolytes.  In the course of this debate, I will show a clear path pf induction from physical observation to experiment to conclusion.

See what's meant by the importance of falsification? 

secur: "prove there's no FTL signal."

Yes, you do. Smile

It follows that nonlocality is a prior assumption of Bell's theorem.
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RE: Bell's theorem - for or against Hidden Variables? - by Thomas Ray - 09-07-2016, 07:16 PM

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