From: naturman@uctvax.uct.ac.za
Newsgroups: sci.physics
Subject: Bell Inequality consistent with LOCALITY
Date: 8 Oct 92 14:53:44 +0200
Keywords: Bell Inequality
Organization: University of Cape Town

Its me and Fluffy again.

Last night was the first time that I actually bothered to look up a rigorous
proof of the Bell Inequality. I did this to check out how Value Rule failure
affects it. As I pointed out in a previous posting, it doesn't.

However I made the following observations:

1) BI is a condition about certain mean values of products of spin values.
2) The calculation of the means involves not only measured values but "hidden
   values" which are required by realist hidden variable approaches.
3) A lot of arguing goes into show that if we take this realist approach
   then these hidden values are well-defined and independent of settings
   on remote apparati etc., if we assume LOCALITY.

Then

4) The QM expectation values of these products are calculated and compared
   with BI and they different.
5) Experiments are done to test the means and the QM expectation values
   correspond to the experimental results not the BI.

Then

5) It is assumed that LOCALITY fails.

BUT from what I can see, LOCALITY is not the issue. What is wrong is the
BLIND ASSUMPTION THAT THE BI MEANS SHOULD BE EQUAL TO THE QM EXPECTATION
VALUES. Surely this is unjustified.

The BI means ARE CORRECT. BUT they are means of measurements together with
hidden values which are inferred. On the other hand the QM expec. values are
means which implicitly edit out any hidden values regardless of whether they
exist or not. THERE IS NO REASON TO ASSUME THEY ARE EQUAL.

(I think that this is what Douglas Danforth basically said in a previous 
posting.)

The experiments are not really testing BI they are only testing QM expec.
values. In order to really test BI we would have to simitaneously measure
noncommuting observables.

In junior school terminology:  BI deals with averages of apples and oranges.
QM expec values deal only with averages of apples.

We can only experimentally test apples (QM) not oranges. Oranges are only there
to avoid non-realism paradoxes, not to measure. When you average apples with
oranges they conspire to produce the BI. QM calculations don't allow this
conspiracy. 

CONCLUSION: THE WHOLE BELL INEQUALITY ISSUE IS A NON-ISSUE. LOCALITY IS NOT
VIOLATED. BI DISAGREES WITH QM BECAUSE THEY TALK ABOUT DIFFERENT MEANS.

Now as I pointed out in previous posting VR should be denied and this prevents 
Kochen-Specker, functionality can then be kept without ontological or
environmental nonlocilty spoiling everything.

Thus if we take a realist, deterministic interpretation of QM which denies VR
but keeps functionality, we don't have any paradoxes. (Although some people
might have religious problems with determinism.)

-- 
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* Baby Doc Naturman                                                         *
* USS Enterprise                           "It's life Jim,                  *
* Final Frontier                                  but not as we know it."   *
* naturman@uctvax.uct.ac.za                                                 *
*                                                       Spock of Vulcan     *
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