## 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

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

parnassos2001 wrote: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")

To answer your question; no. When they say "macroscopic violation" they mean it in the same sense that everyone says that QM "violates" the Bell inequality. When in reality, no such thing has ever happened. I will say it again; it is mathematically impossible for anything to violate any of the Bell inequalities! People like in the paper you linked just continue to propagate the myth that violation is possible when it isn't. I suspect it is just due to years of being subject to what like guest1202 keeps proposing. Totally brainwashed without truly realizing what is actually going on.
FrediFizzx
Independent Physics Researcher

Posts: 1488
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

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

FrediFizzx wrote:...I will say it again; it is mathematically impossible for anything to violate any of the Bell inequalities!

Fred,

I have no idea what you mean here!

The CHSH inequality is a Bell inequality. So, in the context of CHSH, I'd like to see the detailed basis for your repeated claim that "it is mathematically impossible for anything to violate any of the Bell inequalities!"

Thanks.

Gordon
Gordon Watson

Posts: 240
Joined: Wed Apr 30, 2014 4:39 am

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

Gordon Watson wrote:
FrediFizzx wrote:...I will say it again; it is mathematically impossible for anything to violate any of the Bell inequalities!

Fred,

I have no idea what you mean here!

The CHSH inequality is a Bell inequality. So, in the context of CHSH, I'd like to see the detailed basis for your repeated claim that "it is mathematically impossible for anything to violate any of the Bell inequalities!"

Thanks.

Gordon

It is obvious that it is mathematically impossible to violate the Bell-CHSH inequality because that is the mathematical definition of an inequality. If you think it is possible then please give a counter-example. guest1202 has been sort of trying but he has been shot down every time.
...
FrediFizzx
Independent Physics Researcher

Posts: 1488
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

### Amplification of answer to Dr. Christian's question

To start, I'd like to express my appreciation for the
courteous nature of the posts replying to my answer to Dr. Christian's question.

In rereading that post, I noticed that it repeatedly refers to
an "urn model" without explicitly saying what that means, though it
was discussed in a previous post. This addition is to correct that.

One physical model of a "hidden variable" that attempts to reproduce
quantum mechanics thinks of the "hidden variable" as a slip of paper
drawn from an urn with many such slips. identical copies of each slip
are sent to widely separated Alice and Bob. Written on each slip is
what Alice and Bob are to obtain if each performs either one of two possible
measurements, A or A' for Alice and B or B' for Bob.

The formulation of quantum mechanics forbids Alice from performing
measurements A or A' simultaneously, meaning that she cannot read the
whole slip. If she chooses to perform measurement A, she can only read
the part of the slip which specifies the result of measurement A.
But it is possible that a classical observer (Gideon, or God)
can read the whole slip. (Of course, this is just a way of speaking.
Alice's "reading" of the slip is done by measuring A, and "nature"
tells her the result.)

The classical model assumes that someone can read the slip;
i.e., that it makes sense to talk about Alice's result A and her result
A' even when she has only measured one of them. Put differently,
a so-called "realistic" model assumes that what Alice is measuring (A or A')
"really" exists whether or not it is measured. Thus in the framework
of this classical model, it makes sense to talk about a CHSH sum like

(*) A(t)B(t) + A(t)B'(t) + A'(t)B(t) - A'(t)B'(t)

even though everyone agrees that it doesn't make sense within quantum mechanics.
And it makes sense to talk about the average of such sums, which
leads to the CHSH form of Bell's inequalities, which states that
the average cannot have absolute value greater than 2, often denoted

-2 = <AB> + <AB'> + <A'B> - <A'B'> <= 2 .

Please keep in mind that that quantum mechanics does permit
experimental determination of each of the separate averages <AB>, etc.
Thus quantum mechanics allows us to test the bounds on the CHSH averages
even though the individual sums (*) whose averages lead to CHSH don't make sense
within quantum mechanics.

If the measured values of the averages in a quantum-mechanical experiment
violates this CHSH inequality, then that shows that the proposed classical model
cannot reproduce the predictions of quantum mechanics.

I'm not sure how to interpret a poster's insistence that nothing
can violate this Bell inequality, given that many experiments have been
done that do violate it. My impression is that he may think that the usual
derivations of this inequality are wrong, and that a bound 4 instead of 2
would result after the errors in the derivation are corrected. But if the
bound of 2 above is replaced by 4, then the result should not be called
a "Bell inequality" because neither Bell, nor any book or paper that I know,
has proposed it.

_____________________________________________________________________

I'd like to again suggest that "anti-Bellian" posters might
find it useful to look at the matter from another perspective.
The impossibility of the above classical "urn" model to reproduce quantum
mechanics is equivalent to the impossibiity of finding a probability function
p(i,j,k,m) (defined in previous posts) for which the hypothetical "marginals"

$p_{AB}= p_{AB}(i,j)$
$p_{AB^\prime} = p_{AB^\prime}(i,m)$
$p_{A^\prime B}= p_{AB}(j,k)$
$p_{A^\prime B^\prime} = p_{A^\prime B^\prime}(j,m)$

are true marginals. A theorem states that for some quantum marginals, p cannot exist.

If the "anti-Bellians" admit the possibility that this
theorem could be correct, making that clear would focus the discussion.
That's because this theorem is precisely what the "Bellian" view claims,
no more and no less. In that case, the "anti-Bellian"s objections would
in effect question that what I just stated is in fact the traditional
"Bellian" view. That objection would be understandable (though mistaken)
because many formulations in the older literature look somewhat different.

If the "anti-Bellians" think that the theorem's conclusion is wrong,
then they could at one stroke demolish the "Bellian" viewpoint by producing
a counterexample to the theorem. My "Two Suggestions" post pointed out
that this might not be difficult assuming that the theorem is in fact false.

__________________________________________________________________________

I expect that this will be my last post to this group.
I've spent far too much time on this already, and I regret that I started.
If I don't answer replies to this, please don't interpretit as acquiescence or discourtesy.
guest1202

### Re: Amplification of answer to Dr. Christian's question

guest1202 wrote:The formulation of quantum mechanics forbids Alice from performing
measurements A or A' simultaneously, meaning that she cannot read the
whole slip. If she chooses to perform measurement A, she can only read
the part of the slip which specifies the result of measurement A.
But it is possible that a classical observer (Gideon, or God)
can read the whole slip. (Of course, this is just a way of speaking.
Alice's "reading" of the slip is done by measuring A, and "nature"
tells her the result.)

The classical model assumes that someone can read the slip;
i.e., that it makes sense to talk about Alice's result A and her result
A' even when she has only measured one of them. Put differently,
a so-called "realistic" model assumes that what Alice is measuring (A or A')
"really" exists whether or not it is measured.

Yep, that is the "standard party line" about "realistic". Which just means that a deterministic theory in principle can predict what the result will be for measuring angle a or a'. Of course no experiment in the world could ever test for that in an EPR-Bohm type scenario. So what is the point of even considering it other than to allow Bell to derive an inequality that nothing else can violate either? It is really stupid if you ask me.

guest1202 wrote: I'm not sure how to interpret a poster's insistence that nothing
can violate this Bell inequality, given that many experiments have been
done that do violate it. My impression is that he may think that the usual
derivations of this inequality are wrong, and that a bound 4 instead of 2
would result after the errors in the derivation are corrected. But if the
bound of 2 above is replaced by 4, then the result should not be called
a "Bell inequality" because neither Bell, nor any book or paper that I know,
has proposed it.

That is right and what I have been saying all along. QM and the experiments don't use the Bell-CHSH inequality even though they lie to us and say they are using it. They shift to a different inequality that has a bound of 4. It is so easy to see that that is what they are doing and what they have to do because it is impossible for anything to violate a Bell inequality. Perhaps you are starting to "get it"?

The same applies to you as it does to Gordon. Give a counter-example of a true violation of a Bell inequality. And we don't want to see any examples that use the inequality with a bound of 4. They are real easy to debunk.
...
FrediFizzx
Independent Physics Researcher

Posts: 1488
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

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

FrediFizzx wrote:
Gordon Watson wrote:
FrediFizzx wrote:...I will say it again; it is mathematically impossible for anything to violate any of the Bell inequalities!

Fred,

I have no idea what you mean here!

The CHSH inequality is a Bell inequality. So, in the context of CHSH, I'd like to see the detailed basis for your repeated claim that "it is mathematically impossible for anything to violate any of the Bell inequalities!"

Thanks.

Gordon

It is obvious that it is mathematically impossible to violate the Bell-CHSH inequality because that is the mathematical definition of an inequality. If you think it is possible then please give a counter-example. guest1202 has been sort of trying but he has been shot down every time.
...

Fred,

Here is the Bell-CHSH inequality, designed by them (in 1969) to be experimentally tested:

|E(a, b) - E(a, b') + E(a' b) + E(a', b')| ⪯ 2. (1)

Here is the result from Aspect's experiments* - eg, see Aspect (2002); http://arxiv.org/pdf/quant-ph/0402001v1.pdf - rounded within experimental error:

E(a, b) = cos 2(a, b); etc. (2)

Substituting the relations from (2) into LHS (1) shows that the RHS (1) is breached by many combinations of the settings a, a', b, b'.

* NB: The Bell-CHSH expectations E(a, b), etc., are NOT bound by any qualifier when it comes to an experimental test or a theoretical rebuttal. (1) is refuted both theoretically and experimentally..

Gordon
Gordon Watson

Posts: 240
Joined: Wed Apr 30, 2014 4:39 am

### Re: Amplification of answer to Dr. Christian's question

guest1202 wrote:...it makes sense to talk about a CHSH sum like

(*) A(t)B(t) + A(t)B'(t) + A'(t)B(t) - A'(t)B'(t)

It also makes sense to talk about Mickey Mouse.

But unlike "guest1202", no one in their right mind would claim that Mickey Mouse has anything whatsoever to do with physics.

The above sum expressed by "guest1202" as (*) cannot be observed or measured in any experiment, ever, by anyone, even by the deterministic God of Spinoza.

"guest1202" is trying very hard to do what all Bell followers do. They cheat --- and then try to cover up their cheating in some elaborate statistical obfuscation.

Note the slight-of-hand in "guest1202"'s arguments.

He or she wants to prove the bound on the four separate averages,

CHSH = E(a, b) + E(a, b') + E(a', b) - E(a', b' ).

The bound on the above sum of averages is clearly 4. It does not take much effort to see that: https://www.academia.edu/25514662/On_th ... us_Theorem.

But this bound of 4 does not help "guest1202" much in maintaining his or her Bell ideology. Hence he or she, like all Bell followers, resorts to a blatant slight-of-hand.

He or she replaces the sum of four separate averages

E(a, b) + E(a, b') + E(a', b) - E(a', b' )

with a single average of an un-observable, and hence un-physical quantity (a Mickey Mouse)

E( a, b, a', b' ) = << A(t)B(t) + A(t)B'(t) + A'(t)B(t) - A'(t)B'(t) >>.

And, lo and behold, this single average of an un-physical quantity has a bound of 2 that "guest1202" desperately wants.

So he or she declares, without even a hint of shame, that the bound on the original sum of four separate averages is 2.

I mean even Uri Geller can learn a thing or two from "guest1202" and his cargo cult of Bell believers.

***
Joy Christian
Research Physicist

Posts: 1956
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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

Gordon Watson wrote:Fred,

Here is the Bell-CHSH inequality, designed by them (in 1969) to be experimentally tested:

|E(a, b) - E(a, b') + E(a' b) + E(a', b')| ⪯ 2. (1)

Here is the result from Aspect's experiments* - eg, see Aspect (2002); http://arxiv.org/pdf/quant-ph/0402001v1.pdf - rounded within experimental error:

E(a, b) = cos 2(a, b); etc. (2)

Substituting the relations from (2) into LHS (1) shows that the RHS (1) is breached by many combinations of the settings a, a', b, b'.

* NB: The Bell-CHSH expectations E(a, b), etc., are NOT bound by any qualifier when it comes to an experimental test or a theoretical rebuttal. (1) is refuted both theoretically and experimentally.

What you are failing to understand is that it is not mathematically legal to make the substitution in your eq. (1) with the results from any experiment or QM. Someone earlier in this thread gave the example that easily shows why. Bell-CHSH can also be shown as the following with A and B = +/-1,

<A1B1> - <A1B2> + <A2B1> + <A2B2> ⪯ 2

However the data from any experiment or QM is of the type,

<A1B1> - <A2B2> + <A3B3> + <A4B4> ⪯ 4

So you can see that the substitution for the first expectation term is valid, but the substitution for the second to the fourth terms is not valid for Bell-CHSH. It is quite amazing but you too apparently have been brainwashed by years of people claiming a violation of the Bell inequalities when in actuality no such thing has ever happened.
....
FrediFizzx
Independent Physics Researcher

Posts: 1488
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

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

FrediFizzx wrote:Bell-CHSH can also be shown as the following with A and B = +/-1,

<A1B1> - <A1B2> + <A2B1> + <A2B2> ⪯ 2

Even this claim is wrong. It is impossible to prove that the bound on the above sum is 2 without an illegal slight-of-hand, as I explained in my previous post.

But I agree with the main point Fred is making. There is absolutely nothing that can violate the bound of 2. But the bound of 2 has also nothing to do with physics.

***
Joy Christian
Research Physicist

Posts: 1956
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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

Joy Christian wrote:
FrediFizzx wrote:Bell-CHSH can also be shown as the following with A and B = +/-1,

<A1B1> - <A1B2> + <A2B1> + <A2B2> ⪯ 2

Even this claim is wrong. It is impossible to prove that the bound on the above sum is 2 without an illegal slight-of-hand, as I explained in my previous post.

But I agree with the main point Fred is making. There is absolutely nothing that can violate the bound of 2. But the bound of 2 has also nothing to do with physics.

***

Joy,

Thanks for correcting Fred here!

1. If the Bell-CHSH bound of 2 has nothing to do with physics, please show me a published classical experiment that surpasses it.*

2. Of course, in our quantum world, the bound of 2 is easily surpassed (by more than 40%) with published quantum experiments (like Aspect's, that I cited above).

Gordon

*NB: Bell-CHSH inequalities are based on Bell's assumption of classicality. So it is a valid upper bound under Bell's assumption. What CHSH offer (as they knew) is an inequality that can be tested AND EXCEEDED quantum-mechanically via experiments like Aspect's.
Gordon Watson

Posts: 240
Joined: Wed Apr 30, 2014 4:39 am

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

Gordon Watson wrote:
Joy Christian wrote:
FrediFizzx wrote:Bell-CHSH can also be shown as the following with A and B = +/-1,

<A1B1> - <A1B2> + <A2B1> + <A2B2> ⪯ 2

Even this claim is wrong. It is impossible to prove that the bound on the above sum is 2 without an illegal slight-of-hand, as I explained in my previous post.

But I agree with the main point Fred is making. There is absolutely nothing that can violate the bound of 2. But the bound of 2 has also nothing to do with physics.

***

Joy,

Thanks for correcting Fred here!

1. If the Bell-CHSH bound of 2 has nothing to do with physics, please show me a published classical experiment that surpasses it.*

2. Of course, in our quantum world, the bound of 2 is easily surpassed (by more than 40%) with published quantum experiments (like Aspect's, that I cited above).

Gordon,

Here is my published classical experiment that I predict will surpass the erroneous bound of 2 on CHSH: http://link.springer.com/article/10.100 ... 014-2412-2

When this experiment is done, the bogus bound of 2 will be duly surpassed. Anyone who knows a little bit about the geometry of the physical space should know this.

But just in case anyone has any doubt, here is an explicit simulation of my proposed model which "violates" all the bogus bounds on CHSH and CH type inequalities.

Also, have a look at this thread concerning classical "violations": viewtopic.php?f=6&t=254

***
Joy Christian
Research Physicist

Posts: 1956
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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

Joy Christian wrote:
Gordon Watson wrote:
Joy Christian wrote:
FrediFizzx wrote:Bell-CHSH can also be shown as the following with A and B = +/-1,

<A1B1> - <A1B2> + <A2B1> + <A2B2> ⪯ 2

Even this claim is wrong. It is impossible to prove that the bound on the above sum is 2 without an illegal slight-of-hand, as I explained in my previous post.

But I agree with the main point Fred is making. There is absolutely nothing that can violate the bound of 2. But the bound of 2 has also nothing to do with physics.

***

Joy,

Thanks for correcting Fred here!

1. If the Bell-CHSH bound of 2 has nothing to do with physics, please show me a published classical experiment that surpasses it.*

2. Of course, in our quantum world, the bound of 2 is easily surpassed (by more than 40%) with published quantum experiments (like Aspect's, that I cited above).

Gordon,

Here is my published classical experiment that I predict will surpass the erroneous bound of 2 on CHSH: http://link.springer.com/article/10.100 ... 014-2412-2

When this experiment is done, the bogus bound of 2 will be duly surpassed. Anyone who knows a little bit about the geometry of the physical space should know this.

But just in case anyone has any doubt, here is an explicit simulation of my proposed model which "violates" all the bogus bounds on CHSH and CH type inequalities.

Also, have a look at this thread concerning classical "violations": viewtopic.php?f=6&t=254

***

Thanks Joy,

I'm aware of your published proposal for that experiment. I was seeking a completed and published classical experiment (ie, completed and published like Aspect's) that exceeds 2. Thankfully, your reply confirms the relevance of the Bell-CHSH bound of 2 for physics.

G
Gordon Watson

Posts: 240
Joined: Wed Apr 30, 2014 4:39 am

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

Gordon Watson wrote:Thankfully, your reply confirms the relevance of the Bell-CHSH bound of 2 for physics.

Indeed, Gordon. The Bell-CHSH bound of 2 has exactly the same relevance for physics as Mickey Mouse.

***
Joy Christian
Research Physicist

Posts: 1956
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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

Gordon Watson wrote:I was seeking a completed and published classical experiment (ie, completed and published like Aspect's) that exceeds 2.

Joy Christian
Research Physicist

Posts: 1956
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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

Gordon Watson wrote:1. If the Bell-CHSH bound of 2 has nothing to do with physics, please show me a published classical experiment that surpasses it.*

https://www.osapublishing.org/optica/fu ... &id=321243
FrediFizzx
Independent Physics Researcher

Posts: 1488
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

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

FrediFizzx wrote:
Gordon Watson wrote:1. If the Bell-CHSH bound of 2 has nothing to do with physics, please show me a published classical experiment that surpasses it.*

https://www.osapublishing.org/optica/fu ... &id=321243

So here we have definitive proof that Bell was wrong. The only question that remains is can a mechanical singlet experiment also surpass the bound of 2? Joy says it should. The experiment needs to be done.
FrediFizzx
Independent Physics Researcher

Posts: 1488
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

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

FrediFizzx wrote:
The only question that remains is can a mechanical singlet experiment also surpass the bound of 2? Joy says it should. The experiment needs to be done.

A simplified version of my published experimental proposal can now be downloaded directly from my blog: http://libertesphilosophica.info/blog/w ... opExp1.pdf.

***
Joy Christian
Research Physicist

Posts: 1956
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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

Isn't there a contradiction between (1.) "it is mathematically impossible for anything to violate any of Bell's inequalities" and (2.) "it is demonstrated why Bell inequalities must be violated even in such a manifestly local, macroscopic domain, just as they are in the microscopic domain"? Isn't that eating your cake and having it too?
parnassos2001

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

parnassos2001 wrote:Isn't there a contradiction between (1.) "it is mathematically impossible for anything to violate any of Bell's inequalities" and (2.) "it is demonstrated why Bell inequalities must be violated even in such a manifestly local, macroscopic domain, just as they are in the microscopic domain"? Isn't that eating your cake and having it too?

I'm not exactly sure what you are quoting for (2) since no links. Unfortunately the language is inappropriate in (2). It is just part of the 50 years of brainwashing. Bell inequalities are never violated as shown why previously in this thread. IOW, exceeding the Bell-CHSH bound of 2 is not really a "violation" since a different inequality other than a Bell inequality is really being used. But saying it is a violation just means in the same way that say QM exceeds the 2 bound.
FrediFizzx
Independent Physics Researcher

Posts: 1488
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

parnassos2001

PreviousNext