My Challenge to All Bell-Believers --- Meet it or Beat it:

[gill1109]

***
There is no "Gull's proof." There is not even a sketch of a proof. At best, it is just wishful thinking by Gull.

One obvious problem with Gull's wishful thinking is that his argument ignores the geometry and topology of the physical space in which EPR-Bohm type experiments are performed.

As for my claim of "stealing", the fact remains that neither Bell nor the early followers of Bell ever gave any credit to Boole for his inequality. That is "stealing" in my book.

***

I do see a sketch of a proof in Gull's overhead slides. Lots more people saw it and understood that it was easy to write out a complete and formal proof. Nobody bothered to do it because it was so easy. Please do take a careful look!

I wonder most of all, what other people on the forum here think of it?

I took Gull's outline even further in my https://arxiv.org/abs/1312.6403 "The triangle wave versus the cosine (how to optimally approximate EPR-B Correlations by classical systems)"

Your accusation that J.S. Bell actually did shamelessly steal ideas from others brings various well-known sayings to my mind! Surely you knew him better (in real life, in person) than to seriously mean that. And what did Abner Shimony think of the "theft"? Tsk, tsk, tsk.

[gill1109]

***
Gull's ... argument ignores the geometry and topology of the physical space in which EPR-Bohm type experiments are performed.

This is of course the heart of the matter. Bell and his "followers" believe that "the geometry and topology of the physical space in which EPR-Bohm type experiments are performed" is totaly irrelevant. We just need one spatial dimension, we need time, and that's it. We need binary inputs and outputs at particular space-time coordinates. You can embed all that in whatever bigger space time system you like but that doesn't change the argument.

Various writers, such as David Oaknin, Karl Hess and Walter Philipp; and no doubt others,do believe that the global geometry and topology make a difference.

[FrediFizzx]

Actually it is the geometry and topology of the singlets but since they separate into two particles, that topology is extended to the space between them. And I do believe that Joy has proven that singlets have 3-sphere topology. And that means that they also have two orientations.

[Joy Christian]

Bell and his "followers" believe that "the geometry and topology of the physical space in which EPR-Bohm type experiments are performed" is totaly irrelevant.

Who are Bell and his followers that Nature should be mindful of them?

***

[gill1109]

Bell and his "followers" believe that "the geometry and topology of the physical space in which EPR-Bohm type experiments are performed" is totaly irrelevant.

Who are Bell and his followers that Nature should be mindful of them?

***

I guess that’s meant to be a rhetorical question. But seriously, whether or not Nature is mindful of any mere human seems to me a question of religion, not physics. And on the other hand we scientists had better be mindful of Nature. We had better thereby make careful use of the faculties of reasoning which Nature has given us.

I hope some other participants of the forum will let us know what they think of Gull’s very cute, very original idea of a proof. Joy’s opinion is already very well known!

[Heinera]

I think Gull's outline of a proof is great. Novel, and an interesting alternative to Bell's theorem.

Not that there is anything wrong with Bell's theorem. But why shouldn't we be allowed to use statistical theorems to prove a result about correlations, which is 100% a statistical/probabilistic concept? That's why Joy's challenge is silly.

[Joy Christian]

I think Gull's outline of a proof is great. Novel, and an interesting alternative to Bell's theorem.

Not that there is anything wrong with Bell's theorem. But why shouldn't we be allowed to use statistical theorems to prove a result about correlations, which is 100% a statistical/probabilistic concept? That's why Joy's challenge is silly.

Both of your points are absurd.

Gull's so-called "poof" is a non-starter, because it does not take into account the geometry and topology of the physical space in which we are confined to perform the Bell-test experiments.

Moreover, Gull's so-called proof is necessarily wrong because since 2011 there already exists an explicit and constructive counterexample to Bell's theorem: https://arxiv.org/abs/1103.1879

Bell-believers like yourself have not been able to meet my challenge for nearly three years because it is not possible to meet it. It is here to demonstrate how silly Bell's theorem really is.

For those readers of this forum who are unbiased observers, I recommend this short paper to appreciate how nonsensical Bell's theorem really is: https://arxiv.org/abs/1704.02876.

***

[gill1109]

Poof!

Indeed. If Christian's proof is correct, Gull's must be wrong.

And conversely.

Bell-believers like yourself have not been able to meet my challenge for nearly three years because it is not possible to meet it.

What is the point of posing a challenge which it is not possible to meet?

It is not possible to meet it, since *you* are judge and jury, and your verdict is fixed in advance.

Quite unlike the quantum Randi challenge!

[gill1109]

There is a nice proof of Bell's theorem by Steve Gull which uses Fourier analysis instead of the usual algebra.

http://www.mrao.cam.ac.uk/~steve/maxent2009/
http://www.mrao.cam.ac.uk/~steve/maxent ... s/bell.pdf

This sketch of the "proof" does not meet my challenge above.

To begin with, the "proof" violates my condition (2) right from the start. Secondly, it says, with emphasis, that "This is a mathematical project. There are no physical assumptions." I couldn't care less about a mathematical project in this context. I am talking about the physically realisable EPR-Bohm type experiment. Thirdly, I see no derivation of the bounds on the CHSH correlator at all in the "proof." Finally, there actually exists an explicit, clear-cut local-realistic model, trivially derived and verified in several independent event-by-event computer simulations: http://arxiv.org/abs/1405.2355.

Therefore the above "proof" cannot possibly have any physical significance.

***

Steve Gull’s proof sketch is the outline of a proof which master students in physics in Cambridge could easily flesh out. Maybe it would be more problematic in Oxford. It is a proof of Bell’s theorem which does not use the CHSH inequality. There is no obligation to prove that theorem via that inequality. Indeed, there exist many proofs of Bell’s theorem “without inequalities”. I recall one by Lucien Hardy. Physicists use mathematical theorems all the time and give “proofs” which perhaps are not entirely rigorous, ie not entirely complete, but perfectly adequate for all scientific purposes.

That just leaves your counterexample. You present what appears to be a mathematical counterexample to a statement which appears to look like someone’s attempt at stating a theorem. So, we have what appears to be a theorem and what appears to be a counterexample. Something has to give, otherwise mathematics as we know it is inconsistent, and then physics has a problem too, I think.

To end on a constructive note: Nicolas Gisin presently thinks that there is a big physics problem connected to our conventional use and conception of “real numbers”. https://arxiv.org/abs/1803.06824, and several other papers.

[Curiosity]

I just cannot understand how Bell-deniers here (it is ok they may call me Bell-fan, Bell believer, or whatever) cannot understand the simple proof of GHZ. I agree that the proof of the Bell theorem is obscure and I also agree with Joy Christian's criticism of the Bell theorem's proof. His derivation, which is also the ordinary orthodox derivation, is absurd.
However, GHZ is cristal clear, If you assume that outcomes of spin measurements are given by local realistic functions A(a,l), B(b,l), C(c,l), and D(d,l), where l=\lambda then it is impossible to reproduce the quantum mechanics predictions for two runs of the experiment, one with a+b-c-d=0 and the other with a+b-c-d=\pi. That's it! Incredibly simple, no statistical assumptions needed. It means that quantum mechanics or whatever other theory like Christian's models that are supposed to reproduce quantum correlations cannot be local realistic.
I may regret to have asked this, but I am just curious.

[Joy Christian]

I just cannot understand how Bell-deniers here (it is ok they may call me Bell-fan, Bell believer, or whatever) cannot understand the simple proof of GHZ. I agree that the proof of the Bell theorem is obscure and I also agree with Joy Christian's criticism of the Bell theorem's proof. His derivation, which is also the ordinary orthodox derivation, is absurd.
However, GHZ is cristal clear, If you assume that outcomes of spin measurements are given by local realistic functions A(a,l), B(b,l), C(c,l), and D(d,l), where l=\lambda then it is impossible to reproduce the quantum mechanics predictions for two runs of the experiment, one with a+b-c-d=0 and the other with a+b-c-d=\pi. That's it! Incredibly simple, no statistical assumptions needed. It means that quantum mechanics or whatever other theory like Christian's models that are supposed to reproduce quantum correlations cannot be local realistic.
I may regret to have asked this, but I am just curious.

You need not regret asking this question because it is a natural question to ask once one recognizes that all Bell-type arguments involving Boole-type inequalities are flawed.

This thread is rather old, but in the last couple of years I have refined my criticism of Bell's argument in this paper that may be worth reading: https://arxiv.org/pdf/1704.02876.pdf.

Coming to the GHZ-type arguments without involving inequalities or statistics, the answer to your question can be found in Sections 3.5 and 4.3 of the following paper:

https://royalsocietypublishing.org/doi/ ... sos.180526.

Please read the two sections of the above paper for the answer to your question. If you still have questions after reading the two sections, then I will be happy to address them here.
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[FrediFizzx]

I think we never put the S^7 4 particle 2D GHZ GAViewer product calculation validation code on the forum. Here is a partial plot of the result from -360 to +360 degrees.



The blue is the product calculation correlation and the magenta is the negative cosine curve. Of course, they are exactly the same. Here is the GAviewer code for that plot.

Code: Select all

//Adaptation of A-J. Wonnink's code in GAViewer for the S^7 Model of the 4-particle
//GHSZ Correlations [40-42]

function getRandomLambda()
{
   if( rand()>0.5) {return 1;} else {return -1;}
}
function getRandomUnitVector() //uniform random unit vector:
                               //http://mathworld.wolfram.com/SpherePointPicking.html
{
   v=randGaussStd()*e1+randGaussStd()*e2+ 0.00*e3;  //vectors are restricted to x-y plane
   return normalize(v);                             //as in Eq. (9) of the GHSZ paper [7]
}

   batch test()
{
   set_window_title("Test of the S^7 Model for the 4-particle GHSZ correlations");
   default_model(p3ga);
   m=10000;                               //number of iterations, or trials
   I=e1^e2^e3;
   s=0;
   t=0;
   u=0;
   w=0;
   x=0;
   for(nn=0;nn<m;nn=nn+1)                  //perform the experiment m times
   {
          ar=getRandomUnitVector()/(sqrt(2));
          ad=normalize(ar.(e1*e2))/(sqrt(2)); //makes ad orthogonal to ar in the x-y plane
          Da=((I ar) + (ad e0));           
          br=getRandomUnitVector()/(sqrt(2));
          bd=normalize(br.(e1*e2))/(sqrt(2));
          Db=((I br) + (bd e0));
          cr=getRandomUnitVector()/(sqrt(2));
          cd=normalize(cr.(e1*e2))/(sqrt(2));
          Dc=((I cr) + (cd e0));
          dr=getRandomUnitVector()/(sqrt(2));
          dd=normalize(dr.(e1*e2))/(sqrt(2));
          Dd=((I dr) + (dd e0));
          lambda=getRandomLambda();        //lambda is a fair coin, giving the +1 or -1 choice
          A=(-Da).(lambda*Da);             
          B=(lambda*Db).(Db);             
          LA=A/-Da;
          LB=B/Db;                         //implements the twist in the Hopf bundle of S^3
          C=(-Dc).(lambda*Dc);             
          D=(lambda*Dd).(Dd);             
          LC=C/-Dc;
          LD=D/Dd;                         //implements the twist in the Hopf bundle of S^3
          q=0;
          if(lambda==1) {q=(LA LB LC LD);} else {q=(LD LC LB LA);}
          s=s+q;
          phi_a=atan2(scalar(-Da/(e3^e1)), scalar(Da/(e2^e3)))*180/pi;
          phi_b=atan2(scalar(Db/(e3^e1)), scalar(Db/(e2^e3)))*180/pi;
          phi_c=atan2(scalar(Dc/(e3^e1)), scalar(Dc/(e2^e3)))*180/pi;
          phi_d=atan2(scalar(Dd/(e3^e1)), scalar(-Dd/(e2^e3)))*180/pi;
          angle=(phi_a + phi_b - phi_c - phi_d);
          print(angle);                    //Output the angles
          print(corrs=scalar(q), "f");     //Output the correlations
          t=t+A;
          u=u+B;
          w=w+C;
          x=x+D;
      }
      mean=s/m;
      print(mean, "f");
      aveA=t/m;
      aveB=u/m;
      aveC=w/m;
      aveD=x/m;
      print(aveA, "f");
      print(aveB, "f");
      print(aveC, "f");
      print(aveD, "f");
      prompt();
}

I did not put in the specific equation references line by line but you can get that from the paper Joy linked above. So, another so-called "proof" bites the dust.
.

[gill1109]

I just cannot understand how Bell-deniers here (it is ok they may call me Bell-fan, Bell believer, or whatever) cannot understand the simple proof of GHZ. I agree that the proof of the Bell theorem is obscure and I also agree with Joy Christian's criticism of the Bell theorem's proof. His derivation, which is also the ordinary orthodox derivation, is absurd.
However, GHZ is cristal clear, If you assume that outcomes of spin measurements are given by local realistic functions A(a,l), B(b,l), C(c,l), and D(d,l), where l=\lambda then it is impossible to reproduce the quantum mechanics predictions for two runs of the experiment, one with a+b-c-d=0 and the other with a+b-c-d=\pi. That's it! Incredibly simple, no statistical assumptions needed. It means that quantum mechanics or whatever other theory like Christian's models that are supposed to reproduce quantum correlations cannot be local realistic.
I may regret to have asked this, but I am just curious.

I agree with you, Curiosity. Except that I believe that a modern proof of Bell's theorem is not obscure at all. It helps to know and use the language of present-day probability theory. Bell was hampered by the poor state of knowledge of probability and statistics among the physicists of his time.

Here is a proof which uses standard Fourier theory, and necessarily uses some probability theory too, since the QM predictions for an EPR-B experiment are probabilistic https://arxiv.org/abs/2012.00719 . I'm presently revising it, I'm interested in comments; though you might better wait a week or so for a coming new version.

Even experimenters who do a GHZ experiment have to use probability and statistics, since one does not observe perfect correlations in the lab. Theory may say that some probability is zero, but at best, with experiment, you can only show that it seems to be very small. You'll never engineer that state, and those measurements, perfectly. "Behind" the GHZ argument "without probability" there is actually a generalized Bell inequality, which is tested in a GHZ experiment.

That was exactly the reason we moved from Bell's 1964 three correlation inequality to the 1969 CHSH four correlation inequality. Bell's 1964 argument needed an assumption of perfect anti-correlation in certain circumstances. When you experimentally test that, you will find the anti-correlation is not perfect.

Physicists, statisticians and probabilists have to work together and speak one another's languages

[Joy Christian]

.
Rats! Gill has resurfaced. I thought karma had finally caught up with him!
.

[FrediFizzx]

.
Rats! Gill has resurfaced. I thought karma had finally caught up with him!
.

Yeah, but it was nice and peaceful for a while here anyways. And..., he still doesn't understand that all the so-called Bell "proofs" are shot down.
.

[gill1109]

.
Rats! Gill has resurfaced. I thought karma had finally caught up with him!
.

Yeah, but it was nice and peaceful for a while here anyways. And..., he still doesn't understand that all the so-called Bell "proofs" are shot down.

Thanks, guys, for your delightful and insightful contributions to the ongoing discussion of Christian’s extraordinary challenge. Christian wants to ban the use of probability and statistics in physics. But if you look at it more carefully, his real problem is a problem with arithmetic. An arithmetical identity must not be used in physics.

For instance, we all know that 3 squared plus 4 squared equals 5 squared. Christian forbids you to use this identity in mathematical physics except perhaps when there really is a right-angled triangle with those sides in the physics experiment we are talking about.

The embarrassing truth is that Christian’s physics is based on elementary mathematical errors carefully disguised by dressing them in what appears to be sophisticated mathematical language. Diether has a strange idea of the notion of “proof”.

Oh well, I’ve no doubt that this is true of a lot of present day theoretical physics. In this case, Christian did start with a thought-provoking germ of an idea. It has got published, at long last, in some high visibility journals.

[FrediFizzx]

@gill1109 You're welcome. And..., as usual, more boring nonsense from you.
.

[Curiosity]

Even experimenters who do a GHZ experiment have to use probability and statistics, since one does not observe perfect correlations in the lab. Theory may say that some probability is zero, but at best, with experiment, you can only show that it seems to be very small. You'll never engineer that state, and those measurements, perfectly. "Behind" the GHZ argument "without probability" there is actually a generalized Bell inequality, which is tested in a GHZ experiment.

That was exactly the reason we moved from Bell's 1964 three correlation inequality to the 1969 CHSH four correlation inequality. Bell's 1964 argument needed an assumption of perfect anti-correlation in certain circumstances. When you experimentally test that, you will find the anti-correlation is not perfect.

Physicists, statisticians and probabilists have to work together and speak one another's languages

My point is that the purely theoretical argument of GHZ does not need statistics or probability. This is an important point because GHZ theoretical argument is so simple that an error should be easily and unambiguously detected if there is one.
Experiments are complicated and are a different issue.

Joy Christian claims to have disproved the Bell theorem. I believe that besides having disproved the theorem it is also important to point out where it went wrong. He also has done that. I am not saying that I agree with his proofs/disproofs. I am only pointing out that it is important to explain where it went wrong.

In the GHZ case, he also claims that his model reproduces the quantum predictions. In my opinion, it will be good for his claim to be taken seriously, that he explains, as he did for the Bell's theorem case, where the GHZ reasoning went wrong. If he could explain that, it would motivate people to analyze his proof.

I am just trying to make an objective and unbiased point. I don't want to be a rodent.

[Joy Christian]

In the GHZ case, he also claims that his model reproduces the quantum predictions. In my opinion, it will be good for his claim to be taken seriously, that he explains, as he did for the Bell's theorem case, where the GHZ reasoning went wrong. If he could explain that, it would motivate people to analyze his proof.

Thank you. Yes, it is important to understand where the GHZ reasoning has gone wrong. The hints of that are already there in Sections 3.5 and 4.3 of my RSOS paper:

https://royalsocietypublishing.org/doi/ ... sos.180526.

However, you are quite right that I should write a special paper on GHZ, explaining where their reasoning has gone wrong. I will attempt to do that as soon as I find some time.
.

[Curiosity]

However, you are quite right that I should write a special paper on GHZ, explaining where their reasoning has gone wrong. I will attempt to do that as soon as I find some time.

I believe that is a very good idea. Then you can open another thread like this one to discuss it.