Bell's Theorem purported refutation
Rick Padua
Theorem. Is he nuts?"
I attached a couple of URLs. Since then I've found the paper in a far
superior PDF format at:
http://arxiv.org/pdf/quant-ph/0006014
The only difference I've noticed between this version and the first of the
two previously submitted is that the title of the Conclusion has been
altered here. In the previous version the words "Quantum Physics to be
Approached With Prudence" were included.
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Patrick Van Esch
"Rick Padua" <men...@hotmail.com> wrote in message news:<F48CTuMRkdumr...@hotmail.com>...
> Yesterday I submitted a question titled: "This guy says he's refuted Bell's
> Theorem. Is he nuts?"
>
> I attached a couple of URLs. Since then I've found the paper in a far
> superior PDF format at:
>
> http://arxiv.org/pdf/quant-ph/0006014
After some further reading, I've also found a second serious flaw:
equation 36.
Indeed, although the entire argument is based upon the fact that
the sets of experiments on which the 4 different terms in the
CHSH function are averaged, are 4 different sets, the AUTHOR NEGLECTS
THE FACT THAT THESE SETS ARE STATISTICALLY EQUIVALENT.
So if I take his equation 34, and then take the limit to high numbers
I can replace each term by the ensemble average:
Integral {dl} [A(a,l)B(b,l) - A(a,l)B(b',l) + A(a',l)B(b,l)
+ A(a',l)B(b',l)]
(I can of course use the same integration variable after taking
the terms together, because integration is a linear operation).
From that point on, the expectation value is limited in the same
way as in the case of equation 10 and hence nothing is invalidated
in Bell's theorem at all...
cheers,
Patrick.
Ilja Schmelzer
"Rick Padua" <men...@hotmail.com> writes:
> http://arxiv.org/pdf/quant-ph/0006014
> Yesterday I submitted a question titled: "This guy says he's refuted
> Bell's Theorem. Is he nuts?"
Once he claims to be able to refute a proven theorem (as done already
in the introduction), I would say yes. What would be meaningful is to
argue that some of the assumptions of the theorem are unreasonable,
that the class of theories forbidden is too small to cover interesting
examples, for example by presenting such a theory which is "local
realistic" in the common sense but does not fit into the set of
assumptions made by Bell's theorem. (As has been done with Bohmian
mechanics to refute von Neumann's theorem about the impossibility of
hidden variable theories.)
Another nonsense claim: "... classical physics and common sense are
usually based on the former ..." where "former" refers to "local
realistic conceptions". Instead, classical physics (and the related
"common sense") was based on a realistic but non-local theory
(Newtonian gravity). And a realistic non-local theory which gives the
same predictions as QM is not only possible in principle, but already
well-known (as was well-known by Bell): Bohmian mechanics.
p.3: "Bell's theorem consists in showing that the quantum prediction
... violates the maximum possible value given by any local realistic
hidden-variables theory. Herein, this claim is refuted by demanding
the rules of Quantum Mechanics be consistently and meaningfully
applied."
There is an obviously nonsensical interpretation of this - that the
demand is directed against Bell's theorem. But Bell's theorem is a
theorem about classical realistic hidden variable theories, not about
quantum theories. (The less nonsensical interpretation is that until
now the predictions of quantum theorie have been applied in a false
way and the true quantum prediction (obtained by applying the rules of
Quantum Mechanics consistently and meaningfully) are different and in
agreement with Bell's inequality. But this is not what is meant, see
formula (31)).
Thus, the author accepts the QM prediction (as "weakly objective").
As well, he accepts Bell's theorem, classifying it as "established
only within the strongly objective interpretation".
Now, that this "strongly objective interpretation" gives the same
results as the "weak interpretation" and, therefore, may be compared
with observation is simply part of classical realism. An assumption
of classical realism which is well-known and named "counterfactual
existence".
Thus, old and known stuff (conterfactual existence as an assumption
which is part of EPRB-realism) sold in a nonsensical way (as a
"refutation of a theorem").
Ilja
--
I. Schmelzer, <il...@ilja-schmelzer.net>, http://ilja-schmelzer.net
Patrick Van Esch
> Yesterday I submitted a question titled: "This guy says he's refuted Bell's
> Theorem. Is he nuts?"
>
> I attached a couple of URLs. Since then I've found the paper in a far
> superior PDF format at:
>
> http://arxiv.org/pdf/quant-ph/0006014
>
Well, I haven't studied it in great detail, but I see one very big error
in equation 17.
Indeed, there is ABSOLUTELY NO REASON why the eigenvector of
A x B + C x D should be of the form |psi> x | chi >.
Of course, since AxB and CxD don't commute, you won't find such
an eigenvector, but that doesn't mean that the operator doesn't have
eigenvalues !! From there on, the argument seems to fall apart.
Everything seems to hang on the fact that we can't take the average
of the terms in the CHSH function by taking averages of the
different terms by using different sets of experiments. But if an
average has some meaning, then it shouldn't depend on the exact set
of experiments over which it has been taken.
cheers,
Patrick.
Patrick Van Esch
news:<i3gbsas...@wias-berlin.de>...
> "Rick Padua" <men...@hotmail.com> writes:
> > http://arxiv.org/pdf/quant-ph/0006014
> > Yesterday I submitted a question titled: "This guy says he's refuted
> > Bell's Theorem. Is he nuts?"
> Once he claims to be able to refute a proven theorem (as done already
> in the introduction), I would say yes.
Well, I don't even understand how this got past the slightest form
of refereeing. As I pointed out in two other messages on s.p.r.,
there are two big mathematical blunders in the paper that invalidate
everything in the conclusion.
The first one is equation 18:
Of course a general operator in a product space A x B does not have
to have its eigenvectors of a form |a> x |b>. Nevertheless, that is
what the author demands, and then concludes from the fact that he
can't find such eigenfunctions, that the operator doesn't have
any !! That's concerning a maths blunder. But he moreover misses
the physical content of the "Bell-operator": exactly finding non-
product eigenstates !
This error invalidates his conclusion that the Bell-operator would
be a non-well defined operator in the "strongly objective interpretation".
>>>>>>>> ZAP
The second maths blunder is equation 36. As I explained in another
post, the author refuses to consider that the average of a sum of terms
is equal to the sum of the averages of the different terms, if we
calculate those averages on different, but statistically equivalent
sets of events, and taking the sets large enough such that the deviation
of the set average from the ensemble average is as small as one wishes.
That error really invalidates his main claim, that the calculation
of the average of the Bell function in the "weakly objective
interpretation" can be larger than 2 (he finds 4, as a very naive
upper limit).
>>>>>>>>> ZAP again
In fact, it is up to him to give us one single counterexample:
find functions A1(l), A2(l), B1(l) and B2(l) that can take on values
+/- 1 over l, such that when taking l uniformly distributed, we
have an AVERAGE of A1(l)B1(l) - A1(l)B2(l) + A2(l)B1(l) + A2(l)B2(l)
larger than 2. In fact, the space of l is rather limited: we only
have to consider 16 possible cases !
So we have a very strong claim, namely that the proof of Bell's theorem
is wrong, based on two straightforward math errors in the refutation.
cheers,
Patrick.
John Baez
In article <c23e597b.02060...@posting.google.com>,
Patrick Van Esch <van...@ill.fr> wrote:
>Well, I don't even understand how this got past the slightest form
>of refereeing.
There are enough physics journals that if you keep submitting your
paper to journal after journal, you are bound to *eventually* get it
accepted by a lazy referee unless it looks like:
MY REVOLUTIONARY THEORY OF EVERYTHING
I. M. A. Crackpot
What this means is that before you believe the results of some
paper, you really have to read it and check to see if it's right.
The refereeing system filters out some of the crap, but not all!
Charles Francis
writes
Of course what it also means is that if anyone really were to produce an
absolutely rigorous and correct Revolutionary Theory of Everything the
lazy referee would reject it as looking like I.M.A. Crackpot's version!
Actually the paper in question was given as a talk (not refereed) and
only claims to have been submitted to a journal, not accepted by one, so
we don't have to be that disillusioned about peer review.
Regards
--
Charles Francis