On the Fatal Mistake Made by John S. Bell in his theorem

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Two suggestions to settle the "Bell" debate

Postby guest1202 » Wed Jun 08, 2016 6:02 pm

Before leaving, I'd like to throw out a couple of suggestions.
The background has already been given in previous posts, but
for convenience will be summarized below. But first I'll present
the suggestions in the hope that readers may remember or guess enough
to follow the discussion.

1) In a previous post I wrote down four hypothetical "marginals"
which are derived from a quantum state (|1>|1> + |-1>|-1>)/\sqrt{2} :







(In case you've forgotten what "hypothetical marginal" means in this context,
I'll summarize later.)

Previous posts have noted that showing that there is a "local realistic"
theory that can reproduce quantum mechanics just for this state is
equivalent to showing that these hypothetical marginals are true marginals
for some probability distribution on the set of 16 outcomes (i,j,k,m)
where the entries i,j,k,m take on the values +1 or -1.

Some people claim to be able to prove that the desired distribution
p(i,j,k,m) does exist. The claimed proof is written in different notation
which makes it difficult for me to extract its claimed p in explicit form.
But for such simple hypothetical marginals, one would expect that if such
a p exists, it ought to be possible to find it explicitly.

An explicit presentation would only require specifying 16 probabilities
from which one could easily check by hand that they do indeed yield the
hypothetical marginals as true marginals. Taking into account the Alice-Bob
symmetry of the underlying quantum state and the fact that all the probabilities
must sum to 1, actually only 7 probabilities need be specified.

Someone who is more familiar with the proof than I (assuming for the sake of
discussion that the proof is correct) may be able to immediately write down p .
Or, if not, then the problem of finding p explicitly
looks like an interesting new line of research. In general, one would hope
for an algorithm for p which would apply to any quantum state, not just
the particular one given above.

If the proponents of the proof could explicitly produce p ,
that would instantly demolish any suspicions that the proof must be wrong
because it contradicts the conclusion of Bell's theorem.
(It would not prove that the proof is correct for general states,
but then at least people would take it seriously.)
That p reproduces the hypothetical marginals as true marginals
would be indisputable because it could be checked by simple arithmetic
which could be done by hand in a few minutes. Few will argue with
arithmetic!

Production of p would also show beyond any doubt that traditional
proofs of Bell's theorems are wrong. This would be huge news that
would rock the scientific world, given that many consider Bell's Theorem,
simple as it is, one of the major scientific advances in centuries.

In short, my first suggestion is that those who believe that local realistic
theories can reproduce quantum mechanics should demonstrate the truth of
a small part of their belief by explicitly exhibiting p for the above
simple marginals. Those marginals do not satisfy the hypotheses of
several forms of Bell's theorem, so that p would be an indisputable
counterexample to Bell's theorem.

2) This suggestion will describe a simple experiment that anyone with
a computer algebra system (such as Mathematica, Maple, or one of the free
systems like MacSyma) can do to try to find a p which reproduces the
hypothetical marginals.

As noted above, to find p it is enough to find seven probabilities
which satisfy some inhomogeneous linear equations. There are four
marginals, each with four entries, so there are 4x4=16 equations in all
for the 7 unknowns. Generically, we wouldn't expect a solution to 16 linear
equations in only 7 unknowns, but the way the equations were obtained
and the symmetries of the hypothetical marginals gives hope
that a solution might be possible.
Looking at it another way, we could go back to our original 16 probabilities
as unknowns, adjoin one equation specifying that the probabilities
sum to 1, and obtain 16+1=17 equations in 16 unknowns, which looks not
so overdetermined.

It would probably take less than an hour to type the linear system into
a computer algebra system. Because the entries of the hypothetical
marginals are rational numbers, an exact solution will be obtained if
the system is consistent.

If the system of equations is inconsistent (i.e., has no solution),
the computer algebra program will report that. That will show that
there is no local realistic theory (according to all definitions
that I have seen) which can reproduce the predictions of quantum mechanics
for the above state. This is the conclusion of Bell's theorems whose
usual proofs I believe to be correct, so this is what I think will happen.
(I have not invested the time to actually do the experiment because
I am so sure of the outcome!)

If the system proves consistent, the algebra program will give it explicitly,
but there will be more to be done because we need a solution for which
all probabilities are non-negative. This converts the problem into one
of so-called "linear programming", about which I know little, but I wouldn't
be surprised if computer algebra programs could do that, too. (The manual
for mine just says that it will "try" to find a solution!)
Even if not, the problem is so small that given the explicit solution,
one might be able to find a non-negative solution by hand.

If so, that would settle by explicit arithmetic that Bell's theorem is incorrect.
It would suggest, but not prove, that perhaps local realistic theories might reproduce
the predictions of quantum mechanics, thus shattering a belief almost universally
held among professional physicists. The effort involved seems small enough that it seems
worth a try by the "anti-Bellians" given that debate within this forum seems to have reached an impasse.

I chose the above marginals because of their numerical simplicity,
to produce a concrete context within which the Bell's theorem debate
in this forum might be settled without controversy.
Of course, explicitly exhibiting p for those particular marginals
would not prove that one could find p for all marginals
predicted by quantum mechanics for all quantum states.
But it would suggest hope for that possibility.



______________________________________________________________________

The rest of this post summarizes previus posts.


Consider a probability distribution p = p(i,j,k,m) defined on the
set of all 4-tuples (i,j,k,m) with each entry
i,j,k,m equal to either +1 or -1.

For example, a typical outcome is (+1, -1, -1, +1).
Its first entry +1 may be regarded as the result of measuring a quantity
which we denote A, the second as the result of measuring a quantity A',
the third of measuring B, and the fourth of measuring B'.

From p we can derive various "marginal" probability distributions,
"marginals" for short, an example of which is



where the sum ranges over all possible j and m (each being +1 or -1).
Marginals pAB', pA'B , and PA'B' are defined similarly. (There
are other marginals as well, but we will not be concerned with them.)

Consider the following purely mathematical question:
Given four probability distributions pAB , pAB' , pA'B , and pA'B'
on the probability space consisting of all ordered pairs (u,v) with
entries +1 or -1,
does there exist a p = p(i,j,k,m) for which these are the corresponding
marginals?

Of course, the answer will depend on the given (hypothetical) marginals;
for some marginals it might be possible and for others impossible.
There is a mathematical theorem giving necessary and sufficient conditions
for the existence of p , but to make my question as concrete
as possible, consider a numerical special case.

Consider the following "hypothetical marginals" pAB and pA'B,
presented as 2x2 matrices:


'
This presentation is to be interpreted according to the usual matrix
convention that pAB(1,1) = 3/8 = pAB(-1,-1) , pAB(1,-1) = 1/8 = pAB(-1,1) ,
etc. I call them "hypothetical marginals" because we cannot assume,
a priori, that they can be derived from some p = p(i,j,k,m) .
They are just four 2x2 matrices that we can write down.

Continuing, define




The following is a purely mathematical theorem with a simple proof
which has surely been checked by thousands of mathematicians.
I, myself, have checked it and consider the possibility of an error
in its proof as similar to the probability of an error in the Binomial
Theorem. It has nothing to do with physical measurements, though
it can be interpreted in that context.

Theorem: There is no probability distribution p(i,j,k,m) which
yields the above hypothetical marginals pAB , pA'B , pAB' , pA'B'
as true marginals.

The theorem is a special case of Bell's theorem.
Despite the simplicity of its statement and proof,
it is considered one of the most important scientific
advances of the past centuries. If it is false or even if there is
any mistake in any of its accepted proofs, that will be huge news,
shaking the scientific establishment to its roots.

Some theorems have proofs so complicated that their status
(true or unproved or false) remains in doubt for years.
To show that a theorem is false, it is sufficient to produce a counterexample.
This is often easier than arguing about a complicated proof which few
understand.

Some members of this forum believe that accepted proofs
of the above theorem are false,
and others vigorously dispute that claim.
Somebody who wants the fame of rocking the scientific establishment
would probably be well-advised to look for a counterexample when arguments
about established proofs have proved inconclusive.
guest1202
 

Re: Two suggestions to settle the "Bell" debate

Postby FrediFizzx » Wed Jun 08, 2016 7:46 pm

guest1202 wrote:Theorem: There is no probability distribution p(i,j,k,m) which
yields the above hypothetical marginals pAB , pA'B , pAB' , pA'B'
as true marginals.

The theorem is a special case of Bell's theorem.
Despite the simplicity of its statement and proof,
it is considered one of the most important scientific
advances of the past centuries. If it is false or even if there is
any mistake in any of its accepted proofs, that will be huge news,
shaking the scientific establishment to its roots.

.
An exercise in futility. To understand why, just try to demonstrate that anything can truly violate any of Bell's inequalities. It is mathematically impossible. Bell was right that LHV models can't violate the inequalities but he was wrong in assuming that anything else could either.
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Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Wed Jun 08, 2016 9:55 pm

guest1202 wrote:Theorem: There is no probability distribution p(i,j,k,m) which
yields the above hypothetical marginals pAB , pA'B , pAB' , pA'B'
as true marginals.

The theorem is a special case of Bell's theorem.
Despite the simplicity of its statement and proof,
it is considered one of the most important scientific
advances of the past centuries. If it is false or even if there is
any mistake in any of its accepted proofs, that will be huge news,
shaking the scientific establishment to its roots.


"guest1202" is living in his or her own fantasy world (and my bias is for "his", because I cannot imagine a woman being so incredibly stupid).

I agree with Fred's comments above. I have already posted the evidence against the laughable and audacious claims by "guest1202", which

can be found here: viewtopic.php?f=6&t=267#p6479

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Corrections to "Two suggestions" post

Postby guest1202 » Wed Jun 08, 2016 11:11 pm

guest1202 wrote:An explicit presentation would only require specifying 16 probabilities
from which one could easily check by hand that they do indeed yield the
hypothetical marginals as true marginals. Taking into account the Alice-Bob
symmetry of the underlying quantum state and the fact that all the probabilities
must sum to 1, actually only 7 probabilities need be specified.


The reduction to 7 probabilities isn't correct. Although the underlying quantum
state is Alice-Bob symmetric, encoded into the hypothetical marginals
are measurement angles (as given in Peres' book) which are not, and the marginals
themselves are not. So, one needs to specify all 16 probabilities p(i,j,k,m), or only
15 taking into account that they must sum to 1.

Also, I misspoke when I said that I expected the linear system for the probabilities to
be inconsistent. The linear system might be consistent, with no solutions for which all
the probabilities are non-negative. I meant that the linear system augmented with the
condition that all probabilities be non-negative must be inconsistent. (Unless, of course,
Bell's theorem is wrong ! )

I wonder if the moderators would tolerate me calling other posters "stupid".
The insults don't particularly bother me, but the inconsistency in enforcing
decorum does seem telling. In one of my initial posts back in December, a moderator
chastised me just for saying that I found papers of one of the posters "hard to read".
He characterized that as a "flame".
guest1202
 

Re: Corrections to "Two suggestions" post

Postby FrediFizzx » Thu Jun 09, 2016 12:11 am

guest1202 wrote:
guest1202 wrote:An explicit presentation would only require specifying 16 probabilities
from which one could easily check by hand that they do indeed yield the
hypothetical marginals as true marginals. Taking into account the Alice-Bob
symmetry of the underlying quantum state and the fact that all the probabilities
must sum to 1, actually only 7 probabilities need be specified.


The reduction to 7 probabilities isn't correct. Although the underlying quantum
state is Alice-Bob symmetric, encoded into the hypothetical marginals
are measurement angles (as given in Peres' book) which are not, and the marginals
themselves are not. So, one needs to specify all 16 probabilities p(i,j,k,m), or only
15 taking into account that they must sum to 1.

Also, I misspoke when I said that I expected the linear system for the probabilities to
be inconsistent. The linear system might be consistent, with no solutions for which all
the probabilities are non-negative. I meant that the linear system augmented with the
condition that all probabilities be non-negative must be inconsistent. (Unless, of course,
Bell's theorem is wrong ! )

I wonder if the moderators would tolerate me calling other posters "stupid".
The insults don't particularly bother me, but the inconsistency in enforcing
decorum does seem telling. In one of my initial posts back in December, a moderator
chastised me just for saying that I found papers of one of the posters "hard to read".
He characterized that as a "flame".

.
Quite frankly I don't know either what else to call what you are presenting as stupidity or something else as I don't think it is a case of ignorance. But perhaps it is. What you are presenting doesn't matter at all. That is not the problem. You are asking for someone to do something that is impossible. Violation of any of the Bell inequalities by anything is mathematically impossible! Do you get it now? It is really quite simple.

BTW, the Bell debate has been "settled" for quite some time now. We are sorry that you are having such a hard time seeing the truth about it. You probably need to try real hard to get rid of the prejudices you have formed about it before you will see how really simple it is.
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Re: Corrections to "Two suggestions" post

Postby Joy Christian » Thu Jun 09, 2016 12:19 am

guest1202 wrote:I wonder if the moderators would tolerate me calling other posters "stupid".

In my opinion anyone who repeatedly makes manifestly stupid statements and ignores the stark evidence presented contradicting his statements, and does so incessantly and repeatedly, should at least be called stupid.

Such ad hominem is sometimes necessary --- as I often point out that Richard D. Gill is algebraically challenged and mathematically incompetent --- to draw attention of the readers to the lack of credibility of the person who incessantly makes manifestly false claims.
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Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Dirkman » Thu Jun 09, 2016 10:16 am

guest1202 wrote:
I've seen some regulars make puzzling statements on the order of
"a mathematical inequality can NEVER be violated,

Mathematical inequalities generally make some assumptions which
are necessary for their validity.


Well wikipedia says a math inequality is something like 1< 2, and a math inequation is something like x<2, and I dont see how the mathematical inequality 1< 2 could be violated. I dont know...just saying, I dont know much math or physics.
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Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby FrediFizzx » Thu Jun 09, 2016 10:26 am

Dirkman wrote:
guest1202 wrote:
I've seen some regulars make puzzling statements on the order of
"a mathematical inequality can NEVER be violated,

Mathematical inequalities generally make some assumptions which
are necessary for their validity.


Well wikipedia says a math inequality is something like 1< 2, and a math inequation is something like x<2, and I dont see how the mathematical inequality 1< 2 could be violated. I dont know...just saying, I dont know much math or physics.

At least you seem to "get it". Thanks. What has been going on is that with QM or experiments they shift to a different inequality with a different bound to claim that they violate the original inequality when in actuality no such thing has happened. It is quite mind boggling that this mathematical trickery has gone on for so long.
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Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby thray » Thu Jun 09, 2016 1:37 pm

The misunderstanding of the mathematical term 'inequality', it occurs to me, is very much at the root of the misunderstanding of Joy's measurement framework.

The simplest example of an inequality* is an arithmetic mean at least as big as the geometric mean. This leads probabilists to assign only arithmetic values to an inequality, and thereby discard half the meaning. (The reference gives the analytical origin of what is known as the AM-GM inequality.) Unfortunately, they also discard spacetime geometry.

Tom

* v.19 Inequalities: in The Princeton Companion to Mathematics. T. Gowers, et al. eds.
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Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby luca valeri » Thu Jun 09, 2016 2:17 pm

Hi Joy,
Did I understand you right, that you accept the first line with the C's in the Wikipedia Derivation of the CHSH inequality but not the equality with the second line below?
But if you accept the first line - and it can be questioned, whether this should be true in local realistic theories - the following lines follow from simple mathematical manipulations, that are true independent of the physical meaning. Isn't it?

Best regards
Luca
luca valeri
 

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby luca valeri » Thu Jun 09, 2016 2:37 pm

And Fred,
you said
FrediFizzx wrote: Given the CHSH string of expectation terms that can range from -1 to +1 do you think the following as a result for CHSH is possible?

+1 -(-1) + 1 +1 = 4

if A,A',B and B' can take only the values 1 or -1 (depending on the hidden variable lambda).
Do you think AB + AB' + A'B - A'B' <= 2 is wrong?

Luca
luca valeri
 

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Thu Jun 09, 2016 3:32 pm

luca valeri wrote:Hi Joy,
Did I understand you right, that you accept the first line with the C's in the Wikipedia Derivation of the CHSH inequality but not the equality with the second line below?
But if you accept the first line - and it can be questioned, whether this should be true in local realistic theories - the following lines follow from simple mathematical manipulations, that are true independent of the physical meaning. Isn't it?

Best regards
Luca

Physics is not just mathematical manipulations.

The first line, with the four C's, has an obvious and clear-cut physical meaning. But the upper bound on the first line is clearly 4, not 2.

The second line, on the other hand, is completely meaningless. It has no physical meaning whatsoever, as I have explained in my paper.

One cannot replace correct physics with Mickey Mouse, even if it follows from "simple mathematical manipulations", and hope to get a physically sensible answer.

Bell and his followers replace sensible physics (i.e., the first line) with Micky Mouse (i.e., the second line) and obtain a physically meaningless upper bound of 2.

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Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby FrediFizzx » Thu Jun 09, 2016 4:39 pm

luca valeri wrote:And Fred,
you said
FrediFizzx wrote: Given the CHSH string of expectation terms that can range from -1 to +1 do you think the following as a result for CHSH is possible?

+1 -(-1) + 1 +1 = 4

if A,A',B and B' can take only the values 1 or -1 (depending on the hidden variable lambda).
Do you think AB + AB' + A'B - A'B' <= 2 is wrong?

When you formulate CHSH like that then the inequality is correct. Easy to see that the A in AB' depends on the A from AB, etc. so the expectation terms are dependent on each other. And that formulation is a very easy way to see what is going on. However, when they do the QM prediction or the experiments, those expectation terms are independent so the bound is actually 4 like I demonstrated with the simple mathematical inspection in the quote. So they are doing something like,

<A1B1> + <A2B2> + <A3B3> - <A4B4> <= 4

And then claiming that they have violated AB + AB' + A'B - A'B' <= 2. LOL!
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Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Thu Jun 09, 2016 10:37 pm

luca valeri wrote:if A,A',B and B' can take only the values 1 or -1 (depending on the hidden variable lambda).
Do you think AB + AB' + A'B - A'B' <= 2 is wrong?

If anyone can describe a physical experiment that can measure each quantity

AB + AB' + A'B - A'B'

within the standard EPR-Bohm setup, and then evaluate the average

< AB + AB' + A'B - A'B' >

without cheating (and without statistical obfuscations designed to cheat),

then I will withdraw my claim that Bell and his followers have been cheating the physics community for the past fifty years.

So here is my challenge to the followers of Bell:

Describe an experiment that can measure each quantity

AB + AB' + A'B - A'B'

within the standard EPR-Bohm setup, and convince us that it can actually be done (at least by the deterministic God of Spinoza).

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Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby FrediFizzx » Fri Jun 10, 2016 12:54 am

Joy Christian wrote:
luca valeri wrote:if A,A',B and B' can take only the values 1 or -1 (depending on the hidden variable lambda).
Do you think AB + AB' + A'B - A'B' <= 2 is wrong?

If anyone can describe a physical experiment that can measure each quantity

AB + AB' + A'B - A'B'

within the standard EPR-Bohm setup, and then evaluate the average

< AB + AB' + A'B - A'B' >

without cheating (and without statistical obfuscations designed to cheat),

then I will withdraw my claim that Bell and his followers have been cheating the physics community for the past fifty years.

So here is my challenge to the followers of Bell:

Describe an experiment that can measure each quantity

AB + AB' + A'B - A'B'

within the standard EPR-Bohm setup, and convince us that it can actually be done (at least by the deterministic God of Spinoza).


Hmmm... Did guest1202 rub off on you? Now you are proposing an impossible task. :)
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Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Fri Jun 10, 2016 1:33 am

FrediFizzx wrote:
Joy Christian wrote:
luca valeri wrote:if A,A',B and B' can take only the values 1 or -1 (depending on the hidden variable lambda).
Do you think AB + AB' + A'B - A'B' <= 2 is wrong?

If anyone can describe a physical experiment that can measure each quantity

AB + AB' + A'B - A'B'

within the standard EPR-Bohm setup, and then evaluate the average

< AB + AB' + A'B - A'B' >

without cheating (and without statistical obfuscations designed to cheat),

then I will withdraw my claim that Bell and his followers have been cheating the physics community for the past fifty years.

So here is my challenge to the followers of Bell:

Describe an experiment that can measure each quantity

AB + AB' + A'B - A'B'

within the standard EPR-Bohm setup, and convince us that it can actually be done (at least by the deterministic God of Spinoza).


Hmmm... Did guest1202 rub off on you? Now you are proposing an impossible task. :)

And you just spoiled my game! :)
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Answer to Dr. Christian's question

Postby guest1202 » Fri Jun 10, 2016 2:08 am

Joy Christian wrote:
luca valeri wrote:if A,A',B and B' can take only the values 1 or -1 (depending on the hidden variable lambda).
Do you think AB + AB' + A'B - A'B' <= 2 is wrong?

If anyone can describe a physical experiment that can measure each quantity

AB + AB' + A'B - A'B'

within the standard EPR-Bohm setup, and then evaluate the average

< AB + AB' + A'B - A'B' >

without cheating (and without statistical obfuscations designed to cheat),

then I will withdraw my claim that Bell and his followers have been cheating the physics community for the past fifty years.

So here is my challenge to the followers of Bell:

Describe an experiment that can measure each quantity

AB + AB' + A'B - A'B'

within the standard EPR-Bohm setup, and convince us that it can actually be done (at least by the deterministic God of Spinoza).

***


I don't intend to get in a figurative shouting match with people ill-mannered enough to
dismiss the substance of what I write by unsupported claims that I am "incredibly stupid".
(If that is true, then I am in good company because as Dr. Christian points out, my view of Bell's theorem
coincides with that of almost all of the "physics community".) I will only answer sincere questions phrased in
a courteous manner that show some minimal understanding of the issues involved.

I don't expect to convince Dr. Christian and his followers, but maybe they will prove me wrong.
I'm writing this for the benefit of readers not familiar with Bell's theorem.

The predictions of quantum mechanics seem impossible in terms of the classical physics of the nineteenth
century that we learned in high school. The idea of "hidden variables" was invented to attempt to explain
some quantum predictions using only classical ideas. The attempt goes as follows.

A source sends a "hidden variable" which I shall call t to widely separated Alice and Bob. Think of it as a slip
of paper with some writing on it. The writing specifies what each will measure. In Dr. Christian's notation,
if Alice will obtain result +1 when she measures a quantity "A", then the slip t says "A(t) = +1"; otherwise it
says "A(t) = -1". Besides specifying the result of measuring quantity A it also specifies what happens if she
measures a different quantity A' . Written on the slip along with the result A(t) is A'(t) = +1 or A'(t) = -1.
However, Alice cannot read both the result A(t) and A'(t) at the same time. That it how quantum mechanics
is set up, so if we want to reproduce quantum mechanics, we cannot assume the Alice can measure both.
However, we can imagine that some more informed entity Gideon (aka God) can read the entire slip, in particular the result that will occur if Alice measures A and also what will occur when she measures A'.
Similarly for Bob, of course; his possible results are written on the slip an called B(t) and B' (t).
(Think of Alice and Bob as receiving identical slips, but Alice doesn't have resources to read what Bob's result will be,
and vice versa.)

The question of whether quantum mechanics can be reproduced by this classical theory comes down to whether
it is possible to specify the statistics of the contents (slips) of the urn so that classical probability theory
predicts exactly what quantum mechanics predicts. What quantum mechanics predicts are the
four "hypothetical marginals" denoted , and of my previous posts. The "statistics of the urn" are defined by the probability function denoted p = p(i,j,k,m) in those posts.

I included the above for the benefit of those not used to thinking about Bell's theorem. Now comes
the simple answer to Dr. Christian's question: A CLASSICAL REPRODUCTION OF QUANTUM MECHANICS
CAN ASSUME THAT A(t), A'(t), B(t), B'(t) CAN BE SIMULTANEOUSLY READ FROM THE SLIP t .
Alice and Bob can't do it, but Gideon can.

The usual proof of Bell's theorem(s) start with the ASSUMPTION that A , A' , B, B' can be simultaneously
read from the slip by some classical observer, though not necessarily by Alice and Bob. No proof that I have seen
assumes that Alice or Bob, or both together, can do it. Thus the error that Dr. Christian thinks he sees is
just a misunderstanding of the proofs' assumptions. (Proofs of Bell's theorem are frequently obscurely written,
so such misunderstandings are perhaps to be expected.)


I phrased it that way to make contact with my previous posts. But there is another way to think about it
which I prefer. We don't have to introduce Gideon at all. The classical results are entirely determined
by classical probability theory applied to the probability distribution p of slips in the urn. The slip (hidden variable)
actually drawn determines what Alice will obtain if she measures A, and what she will obtain if she measures A'. etc.

That's all there is to it. If there exists a probability distribution p = p(i,j,k,m) such that the hypothetical marginals are the true marginals of p . then quantum mechanics (for this experiment) can be obtained from the classical "urn"
model. If there is no such p , then the classical urn model cannot reproduce the quantum predictions.

I anticipate that Dr. Christian and his followers may claim that the above urn setup is not what is meant by
a "locally realistic" model. That's their privilege. But I hope that some readers will recognize that the "urn" model is a
reasonable way to try to explain quantum mechanics classically. Bell's theorem implies that it fails.
That is all that the "Bellian"s claim ! That is all that the "physics community" believes in.
If you are unconvinced that this is the "standard" formulation of Bell's theorem,
then just ask almost any professional physicist.

That discussion leaves open the possibility that some model other than the "urn" model might reproduce quantum
mechanics. I have no opinion on that. But any model that starts with the "hidden variable" idea seems likely
to be equivalent to the urn model. That's because the "hidden variable" determines all results and is obtained
as an outcome of a probabilistic experiment. I know of no probabilistic experiment with a finite number of outcomes which is not equivalent to an urn model.
guest1202
 

Re: Answer to Dr. Christian's question

Postby FrediFizzx » Fri Jun 10, 2016 10:24 am

guest1202 wrote: I don't expect to convince Dr. Christian and his followers, but maybe they will prove me wrong.
I'm writing this for the benefit of readers not familiar with Bell's theorem.


Since you don't seem to understand that nothing can violate any of the Bell inequalities, I doubt that you will ever accept that you have been proven wrong. However, what you are presenting now is very easily debunked.

guest1202 wrote:A source sends a "hidden variable" which I shall call t to widely separated Alice and Bob. Think of it as a slip
of paper with some writing on it. The writing specifies what each will measure. In Dr. Christian's notation,
if Alice will obtain result +1 when she measures a quantity "A", then the slip t says "A(t) = +1"; otherwise it
says "A(t) = -1". Besides specifying the result of measuring quantity A it also specifies what happens if she
measures a different quantity A' . Written on the slip along with the result A(t) is A'(t) = +1 or A'(t) = -1.
However, Alice cannot read both the result A(t) and A'(t) at the same time. That it how quantum mechanics
is set up, so if we want to reproduce quantum mechanics, we cannot assume the Alice can measure both.
However, we can imagine that some more informed entity Gideon (aka God) can read the entire slip, in particular the result that will occur if Alice measures A and also what will occur when she measures A'.
Similarly for Bob, of course; his possible results are written on the slip an called B(t) and B' (t).
(Think of Alice and Bob as receiving identical slips, but Alice doesn't have resources to read what Bob's result will be,
and vice versa.)

The question of whether quantum mechanics can be reproduced by this classical theory comes down to whether
it is possible to specify the statistics of the contents (slips) of the urn so that classical probability theory
predicts exactly what quantum mechanics predicts. What quantum mechanics predicts are the
four "hypothetical marginals" denoted , and of my previous posts. The "statistics of the urn" are defined by the probability function denoted p = p(i,j,k,m) in those posts.


Guess what? Quantum mechanics can't do what you are asking classical probability theory to do either! If you think it can, then let's see you get the prediction of QM for the EPR-Bohm scenario using only +/- 1 outcomes. You can't do it; it is impossible. The reason being that it is impossible for anything to violate Bell's inequality. If you are going to truly be fair, then apples need to be compared to apples. The Bell believers always want to compare apples with oranges. It is just plain mathematical trickery.
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Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby Joy Christian » Fri Jun 10, 2016 11:27 am

***
So far no one has been able to defeat my challenge above. This proves that Bell and his followers have been cheating the physics community for the past fifty years.

I leave my challenge here once again, in case anyone else wants to convince the world that Bell and his followers have not been cheating us for the past fifty years:

Joy Christian wrote:
If anyone can describe a physical experiment that can measure each quantity

AB + AB' + A'B - A'B'

within the standard EPR-Bohm setup, and then evaluate the average

< AB + AB' + A'B - A'B' >

without cheating (and without statistical obfuscations designed to cheat),

then I will withdraw my claim that Bell and his followers have been cheating the physics community for the past fifty years.

So here is my challenge to the followers of Bell:

Describe an experiment that can measure each quantity

AB + AB' + A'B - A'B'

within the standard EPR-Bohm setup, and convince us that it can actually be done (at least by the deterministic God of Spinoza).

***

For anyone who may have lost the context of the above challenge, I leave here the standard derivation of the Bell-CHSH inequality from Wikipedia:

Image

***
Joy Christian
Research Physicist
 
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Location: Oxford, United Kingdom

Re: On the Fatal Mistake Made by John S. Bell in his theorem

Postby parnassos2001 » Fri Jun 10, 2016 12:06 pm

Re: Impossibility of Bell Violations

Couldn't gedanken experiments employing macroscopic isomorphisms count as violations? I'm thinking specifically of Diederik Aerts' series of those ... e.g., the twin vessels connected by a tube on pp 4-5, which might be seen as obviating the orthodox quantum-classical distinction:

https://arxiv.org/abs/quant-ph/0007044 ("The Violation of Bell Inequalities in the Macroworld")
parnassos2001
 

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