GAViewer Simulation No Hidden Variable

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GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Tue Aug 18, 2020 10:21 am

Disclaimer: This is NOT a simulation for an experiment. This simulation demonstrates that a local model can match the predictions of quantum mechanics even without a hidden variable. However, one might claim in this model that the singlet vector is a hidden variable. Here is the GAViewer code script.

Code: Select all
//Adaptation of Albert Jan Wonnink's original code based on GAViewer for Joy Christian's S^3 Model of the 2-particle
//This is NOT Joy Christian's S^3 model.  It is a GA R^3 model that works.

function RandomUnitVector()    //uniform random unit vector:
                               //http://mathworld.wolfram.com/SpherePointPicking.html
{
   v=randGaussStd()*e1+randGaussStd()*e2+ randGaussStd()*e3; //3D Vectors
   return normalize(v);
}
   batch test()
{
   set_window_title("3D Test of GA Model for the 2-particle correlation");
   default_model(p3ga);
   N=10000;                               //number of iterations (trials)
   I=e1^e2^e3;
   s=0;
   t=0;
   u=0;
   nPP=0;
   nNN=0;
   nPN=0;
   nPN=0;
   for(mm=0;mm<N;mm=mm+1)                  //perform the experiment N times
   {
          a=RandomUnitVector();
          Da=I a;
          b=RandomUnitVector();
          Db=I b;
          c=RandomUnitVector();         //singlet vector
          //Sa=I c;                     //singlet bivector
          //Sa=Sb;
          if((a.c)>0) {Sa=Da;} else {Sa=-Da;}  //polarizer takes Sa to +/-Da
          if((b.c)>0) {Sb=Db;} else {Sb=-Db;}  //polarizer takes Sb to +/-Db
          A=-Da*Sa;      //Measurement function
          B=Sb*Db;       //Measurement function
          q=0;
          //Since Sa*Sb = -1 the product calculation reduces to A B = -Da Sa Sb Db = Da Db.
          q=(Da Db);     //Product calculation
          s=s+q;
          p_a=atan2(scalar(Da/(e3^e1)), scalar(Da/(e2^e3)));  //Get angle for a vector in x-y plane
          p_b=atan2(scalar(Db/(e2^e3)), scalar(Db/(e3^e1)));  //Get angle for b vector in x-y plane
          neg_adotb=-(a.b);
          print(neg_adotb, "f");             //Outputs -a.b event by event
          if(p_a*p_b>0) {theta=acos(a.b)*180/pi;} else {theta=-acos(a.b)*180/pi+360;}
          print(theta, "f");                 //Outputs the angles
          print(correlation=scalar(q), "f"); //Outputs the correlations event by event
          t=t+A;
          u=u+B;
          pp=0;
          nn=0;
          pn=0;
          np=0;
          if(A>0&&B>0) {pp=1;}
          if(A<0&&B<0) {nn=1;}
          if(A>0&&B<0) {pn=1;}
          if(A<0&&B>0) {np=1;}
          nPP=nPP+pp;
          nNN=nNN+nn;
          nPN=nPN+pn;
          nNP=nNP+np;
      }
      mean=s/N;
      print(mean, "f");    //shows the vanishing of the non-scalar part
      aveA=t/N;
      print(aveA, "f");    //verifies that individual average < A > = 0
      aveB=u/N;
      print(aveB, "f");    //verifies that individual average < B > = 0
      avePP=nPP/N;
      print(avePP, "f");   //verifies plus-plus outcome prediction
      aveNN=nNN/N;
      print(aveNN, "f");
      avePN=nPN/N;
      print(avePN, "f");
      aveNP=nNP/N;
      print(aveNP, "f");
      prompt();
}

Here is a plot of the product calculation for 100K trials.

Image

However, it is easy to see from the product calculation in the code script that it will be exactly -a.b.

Here is the overall average of the +/-1 outcomes where you can see the vanishing of the cross products. However, in this R^3 model, the cross products are mathematical artifacts and don't exist since a and b are physically separated. The program simply does not know that fact.

mean = -0.001382 + 0.002110*e2^e3 + -0.000940*e3^e1 + 0.001990*e1^e2

Here are the A and B individual averages which are also vanishing.

aveA = -0.002780
aveB = 0.003240

And finally, here are the probability results for the ++, --, +-, and -+ outcome sets.

avePP = 0.249260
aveNN = 0.249030
avePN = 0.249350
aveNP = 0.252360

We can see that they are approaching 1/4 as should be.
.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Thu Aug 27, 2020 10:51 am

OK, no objections so another very simple example about why Bell was wrong about making the junk physics theory that he did.
.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Fri Aug 28, 2020 12:20 pm

FrediFizzx wrote:OK, no objections so another very simple example about why Bell was wrong about making the junk physics theory that he did.
.

Sorry, I didn't notice. I object.

The joint wave function of the two particles can be thought of as a hidden variable. It is "non-local". Where is it? It is not located somewhere, or distributed over space in some fashion. Alice does a measurement, and the joint wave function changes (von Neumann-Lüders collapse postulate). After Alice's measurement, the wave function, the function which determines the probabilities of Bob's measurement outcomes, has changed. Nobody ever said "where" it was. Everywhere? Nowhere? In another dimension? In the mind of God, perhaps?

Bell's theorem says that there is no "local realistic non-conspiratorial" way to explain this. The theorem might be wrong, of course. People can make mistakes. If so, you should be able to give us a counter example.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Fri Aug 28, 2020 1:10 pm

gill1109 wrote:
FrediFizzx wrote:OK, no objections so another very simple example about why Bell was wrong about making the junk physics theory that he did.
.

Sorry, I didn't notice. I object.

The joint wave function of the two particles can be thought of as a hidden variable. It is "non-local". Where is it? It is not located somewhere, or distributed over space in some fashion. Alice does a measurement, and the joint wave function changes (von Neumann-Lüders collapse postulate). After Alice's measurement, the wave function, the function which determines the probabilities of Bob's measurement outcomes, has changed. Nobody ever said "where" it was. Everywhere? Nowhere? In another dimension? In the mind of God, perhaps?

Bell's theorem says that there is no "local realistic non-conspiratorial" way to explain this. The theorem might be wrong, of course. People can make mistakes. If so, you should be able to give us a counter example.

LOL! Wavefunction? What wavefunction? :mrgreen: There is no wavefunction in this model. The GAViewer simulation is a perfect counter example. You are just spewing gibberish again because you have no real argument against it.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Fri Sep 04, 2020 7:40 pm

FrediFizzx wrote:
gill1109 wrote:
FrediFizzx wrote:OK, no objections so another very simple example about why Bell was wrong about making the junk physics theory that he did.

Sorry, I didn't notice. I object.
The joint wave function of the two particles can be thought of as a hidden variable. It is "non-local". Where is it? It is not located somewhere, or distributed over space in some fashion. Alice does a measurement, and the joint wave function changes (von Neumann-Lüders collapse postulate). After Alice's measurement, the wave function, the function which determines the probabilities of Bob's measurement outcomes, has changed. Nobody ever said "where" it was. Everywhere? Nowhere? In another dimension? In the mind of God, perhaps?
Bell's theorem says that there is no "local realistic non-conspiratorial" way to explain this.
The theorem might be wrong, of course. People can make mistakes. If so, you should be able to give us a counter-example.

Wavefunction? What wave function? There is no wave function in this model. The GAViewer simulation is a perfect counter-example. You are just spewing gibberish again because you have no real argument against it.

I didn't say there was a wave function in *your* model. Your GAViewer simulation is a perfect simulation of a non-local hidden variables theory. There are very many. One of them is by taking the joint wave function to be the hidden variable. Congratulations on doing it neatly with GA and without the wave function.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Fri Sep 04, 2020 8:12 pm

gill1109 wrote:
FrediFizzx wrote:
gill1109 wrote:
FrediFizzx wrote:OK, no objections so another very simple example about why Bell was wrong about making the junk physics theory that he did.

Sorry, I didn't notice. I object.
The joint wave function of the two particles can be thought of as a hidden variable. It is "non-local". Where is it? It is not located somewhere, or distributed over space in some fashion. Alice does a measurement, and the joint wave function changes (von Neumann-Lüders collapse postulate). After Alice's measurement, the wave function, the function which determines the probabilities of Bob's measurement outcomes, has changed. Nobody ever said "where" it was. Everywhere? Nowhere? In another dimension? In the mind of God, perhaps?
Bell's theorem says that there is no "local realistic non-conspiratorial" way to explain this.
The theorem might be wrong, of course. People can make mistakes. If so, you should be able to give us a counter-example.

Wavefunction? What wave function? There is no wave function in this model. The GAViewer simulation is a perfect counter-example. You are just spewing gibberish again because you have no real argument against it.

I didn't say there was a wave function in *your* model. Your GAViewer simulation is a perfect simulation of a non-local hidden variables theory. There are very many. One of them is by taking the joint wave function to be the hidden variable. Congratulations on doing it neatly with GA and without the wave function.

Whoa! Non-local??? Where exactly do you see this non-local behavior? When you make such claims you should point out exactly where you think the claim originates from. The model is 100 percent local.
.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Sat Sep 05, 2020 5:26 am

Excellent, then you are all set to win undying fame, by adapting your program so that it can be run on a network of computers, whereby the two streams of settings are submitted sequentially by an external agent. The world is holding its breath.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Sat Sep 05, 2020 6:48 am

gill1109 wrote:Excellent, then you are all set to win undying fame, by adapting your program so that it can be run on a network of computers, whereby the two streams of settings are submitted sequentially by an external agent. The world is holding its breath.

Sorry, I wasn't doing YOUR "theorem". Only Bell's junk physics theory.
.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Mon Sep 28, 2020 1:32 am

FrediFizzx wrote:
gill1109 wrote:Excellent, then you are all set to win undying fame, by adapting your program so that it can be run on a network of computers, whereby the two streams of settings are submitted sequentially by an external agent. The world is holding its breath.

Sorry, I wasn't doing YOUR "theorem". Only Bell's junk physics theory.

It’s not “my” theorem. It’s a theorem which many physicists think is true and think is very important. Of course they could be wrong, and anyway, the theorem could be wrong too. It could all be junk. So: opportunity beckons for you ...
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Tue Sep 29, 2020 7:48 pm

gill1109 wrote:
FrediFizzx wrote:
gill1109 wrote:Excellent, then you are all set to win undying fame, by adapting your program so that it can be run on a network of computers, whereby the two streams of settings are submitted sequentially by an external agent. The world is holding its breath.

Sorry, I wasn't doing YOUR "theorem". Only Bell's junk physics theory.

It’s not “my” theorem. It’s a theorem which many physicists think is true and think is very important. Of course they could be wrong, and anyway, the theorem could be wrong too. It could all be junk. So: opportunity beckons for you ...

Yes, it is your "theorem". You are the one that put it exactly to Nature and the experiments. I don't see that anyone else ever did that exactly. But it is not coin tosses and other trinkets. It is about quantum spin of particles which is a very dynamical thing and probably follows 3-sphere if not 7-sphere topology. It actually has nothing whatsoever to do with Bell's junk physics theory. The hoax on the inequalities has been exposed more than one way. So, you actually have no proof of Gill's "theorem" at all. If Nature does it, it can be modelled.
.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Fri Oct 02, 2020 5:23 am

FrediFizzx wrote:
gill1109 wrote:
FrediFizzx wrote:
gill1109 wrote:Excellent, then you are all set to win undying fame, by adapting your program so that it can be run on a network of computers, whereby the two streams of settings are submitted sequentially by an external agent. The world is holding its breath.

Sorry, I wasn't doing YOUR "theorem". Only Bell's junk physics theory.

It’s not “my” theorem. It’s a theorem which many physicists think is true and think is very important. Of course they could be wrong, and anyway, the theorem could be wrong too. It could all be junk. So: opportunity beckons for you ...

Yes, it is your "theorem". You are the one that put it exactly to Nature and the experiments. I don't see that anyone else ever did that exactly. But it is not coin tosses and other trinkets. It is about quantum spin of particles which is a very dynamical thing and probably follows 3-sphere if not 7-sphere topology. It actually has nothing whatsoever to do with Bell's junk physics theory. The hoax on the inequalities has been exposed more than one way. So, you actually have no proof of Gill's "theorem" at all. If Nature does it, it can be modelled.
.

Nature does it; it can be modelled in a particle-by-particle way; but not locally or without conspiracy. Who says so? Just about everyone.

So maybe they are all wrong? Maybe, that can happen.

Come on, show us your computer simulation. Win the Nobel prize. Revolutionise physics. Expose the quantum computing hoax. Google and many other big players would like to know! Or ... do they already know? It *is* a conspiracy. Google, Microsoft, Apple, are out to get total control of the world. They make you believe in quantum cryptography but they can break it ... because of local realism. Wow!!!!!

No. Tchechen gangsters paid by Google will take you out the moment they think you are about to expose them... It's a bit like the number "42".
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Fri Oct 02, 2020 6:14 pm

gill1109 wrote:
FrediFizzx wrote:
gill1109 wrote: ...
It’s not “my” theorem. It’s a theorem which many physicists think is true and think is very important. Of course they could be wrong, and anyway, the theorem could be wrong too. It could all be junk. So: opportunity beckons for you ...

Yes, it is your "theorem". You are the one that put it exactly to Nature and the experiments. I don't see that anyone else ever did that exactly. But it is not coin tosses and other trinkets. It is about quantum spin of particles which is a very dynamical thing and probably follows 3-sphere if not 7-sphere topology. It actually has nothing whatsoever to do with Bell's junk physics theory. The hoax on the inequalities has been exposed more than one way. So, you actually have no proof of Gill's "theorem" at all. If Nature does it, it can be modelled.
.

Nature does it; it can be modelled in a particle-by-particle way; but not locally or without conspiracy. Who says so? Just about everyone.
...

You are clearly not paying attention. Jay Yablon demonstrated that quantum mechanics is local for the EPR-Bohm scenario. So, it is very doubtful that there is any kind of non-local behavior at play. That issue has been basically ruled out. But besides that, you made a big mistake with your "theorem". Quantum mechanics can't do it either so Bell's comparison of QM to local theories is not involved. Bell's junk physics theory is dead. About time you realize that.

The problem is that it is very difficult to model 3-sphere and certainly 7-sphere topological action by the quantum spin of the particles. It may take a super-computer to do it. Mathematica can do some very limited 3-sphere action via quaternions but it doesn't do it correctly. I've tested that.
.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Fri Oct 02, 2020 8:18 pm

FrediFizzx wrote:
gill1109 wrote:
FrediFizzx wrote:
gill1109 wrote: ...
It’s not “my” theorem. It’s a theorem which many physicists think is true and think is very important. Of course they could be wrong, and anyway, the theorem could be wrong too. It could all be junk. So: opportunity beckons for you ...

Yes, it is your "theorem". You are the one that put it exactly to Nature and the experiments. I don't see that anyone else ever did that exactly. But it is not coin tosses and other trinkets. It is about quantum spin of particles which is a very dynamical thing and probably follows 3-sphere if not 7-sphere topology. It actually has nothing whatsoever to do with Bell's junk physics theory. The hoax on the inequalities has been exposed more than one way. So, you actually have no proof of Gill's "theorem" at all. If Nature does it, it can be modelled.
.

Nature does it; it can be modelled in a particle-by-particle way; but not locally or without conspiracy. Who says so? Just about everyone.
...

You are clearly not paying attention. Jay Yablon demonstrated that quantum mechanics is local for the EPR-Bohm scenario. So, it is very doubtful that there is any kind of non-local behavior at play. That issue has been basically ruled out. But besides that, you made a big mistake with your "theorem". Quantum mechanics can't do it either so Bell's comparison of QM to local theories is not involved. Bell's junk physics theory is dead. About time you realize that.

The problem is that it is very difficult to model 3-sphere and certainly 7-sphere topological action by the quantum spin of the particles. It may take a super-computer to do it. Mathematica can do some very limited 3-sphere action via quaternions but it doesn't do it correctly. I've tested that.
.

Fred, I am paying close attention. There is a big, big scientific literature on what we should mean by “local”. In some senses, standard QM can be said to respect locality. For instance, it does not allow “action at a distance”. There is a big, big literature on the concept “realism”. Bell’s theorem is a theorem about whether or not QM could be the surface expression, a merely “emergent phenomenon”, arising from of a more classical-like underlying theory. It is not physics. It is meta-physics. It is not junk. You are free to find it uninteresting. It is great that people like you, who have not been brainwashed by contemporary physics orthodoxy, look at the whole thing with fresh eyes and an open mind. Good luck!
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Sun Oct 04, 2020 5:55 pm

gill1109 wrote:...
Fred, I am paying close attention. There is a big, big scientific literature on what we should mean by “local”. In some senses, standard QM can be said to respect locality. For instance, it does not allow “action at a distance”. There is a big, big literature on the concept “realism”. Bell’s theorem is a theorem about whether or not QM could be the surface expression, a merely “emergent phenomenon”, arising from of a more classical-like underlying theory. It is not physics. It is meta-physics. It is not junk. You are free to find it uninteresting. It is great that people like you, who have not been brainwashed by contemporary physics orthodoxy, look at the whole thing with fresh eyes and an open mind. Good luck!

Realism??? The heck with realism. That's like religion. It's crap and and very subjective. Quantum mechanics is about real probability factors for real physical events. That is real enough for me.

But you are NOT paying attention to what I am telling you. Probably because you don't want to or like to face the truth. Bell's junk physics theory is about comparing local theories to quantum mechanics. End of story!. It's just that. Junk physics. You made up some cockamamie thing about Bell applying to the simulation of experiments. It does not compute. Another end of story. You made a mistake. Have the decency to admit it.
.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Mon Oct 05, 2020 2:33 am

FrediFizzx wrote:
gill1109 wrote:...
Fred, I am paying close attention. There is a big, big scientific literature on what we should mean by “local”. In some senses, standard QM can be said to respect locality. For instance, it does not allow “action at a distance”. There is a big, big literature on the concept of “realism”. Bell’s theorem is a theorem about whether or not QM could be the surface expression, a merely “emergent phenomenon”, arising from of a more classical-like underlying theory. It is not physics. It is meta-physics. It is not junk. You are free to find it uninteresting. It is great that people like you, who have not been brainwashed by contemporary physics orthodoxy, look at the whole thing with fresh eyes and an open mind. Good luck!

Realism??? The heck with realism. That's like religion. It's crap and very subjective. Quantum mechanics is about real probability factors for real physical events. That is real enough for me.
But you are NOT paying attention to what I am telling you. Probably because you don't want to or like to face the truth. Bell's junk physics theory is about comparing local theories to quantum mechanics. End of story! It's just that. Junk physics. You made up some cockamamie thing about Bell applying to the simulation of experiments. It does not compute. Another end of story. You made a mistake. Have the decency to admit it.

Luigi Accardi, Hans de Raedt and Karl Hess, Han Geurdes, you, me (Pearle's model), and a hundred other people simulated experiments.

Nobody yet, as far as I know, successfully simulated the 2015 "loophole free" experiments under the spatial-temporal constraints freely imposed by those experimenters.

Stephen Gull, a famous astro-physicist and famous for his work on geometric algebra too, wrote "Many years ago (about 1984), I used to give a Mathematical Physics course to the Part II students. I illustrated the quantum paradox covered by Bell's theorem by showing that you can't program two independently running computers to mimic the results of spin measurements on two spin-1/2 particles in a singlet state. I believe this demonstration is actually better than Bell's original argument" https://physics.stackexchange.com/questions/547039/help-understanding-prof-steve-gulls-explanation-of-bells-theorem.

Bell wrote that Niels Bohr's reaction to his work would have been "I told you so". You are on the side of Niels Bohr. Indeed, for most "shut up and calculate" quantum physicists, Bell's theorem is irrelevant. "Realism" is crap. It's a legitimate point of view.

I'm a mathematician and of course I made many mathematical mistakes in my life but every time I become aware of one I admit it and publish a correction note, or take other similar action. That's just normal scientific practice. Nothing to be ashamed of. In fact, on the contrary, it's something to be proud of.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Fri Oct 09, 2020 1:14 pm

gill1109 wrote: ...
Stephen Gull, a famous astro-physicist and famous for his work on geometric algebra too, wrote "Many years ago (about 1984), I used to give a Mathematical Physics course to the Part II students. I illustrated the quantum paradox covered by Bell's theorem by showing that you can't program two independently running computers to mimic the results of spin measurements on two spin-1/2 particles in a singlet state. I believe this demonstration is actually better than Bell's original argument" https://physics.stackexchange.com/questions/547039/help-understanding-prof-steve-gulls-explanation-of-bells-theorem.
...

Ah, so that is where you got Gill's "theorem" from! Is the answer (proof) given at that stackexchange link correct?
.
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Re: GAViewer Simulation No Hidden Variable

Postby Joy Christian » Fri Oct 09, 2020 2:09 pm

FrediFizzx wrote:
gill1109 wrote: ...
Stephen Gull, a famous astro-physicist and famous for his work on geometric algebra too, wrote "Many years ago (about 1984), I used to give a Mathematical Physics course to the Part II students. I illustrated the quantum paradox covered by Bell's theorem by showing that you can't program two independently running computers to mimic the results of spin measurements on two spin-1/2 particles in a singlet state. I believe this demonstration is actually better than Bell's original argument" https://physics.stackexchange.com/questions/547039/help-understanding-prof-steve-gulls-explanation-of-bells-theorem.
...

Ah, so that is where you got Gill's "theorem" from! Is the answer (proof) given at that stackexchange link correct?

There is no "proof" of either Gull's "theorem" or Gill's "theorem." All they have got is some wishful thinking. Gill wouldn't recognize a proof even if he saw one.

**
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Fri Oct 09, 2020 3:14 pm

Joy Christian wrote:
FrediFizzx wrote:
gill1109 wrote: ...
Stephen Gull, a famous astro-physicist and famous for his work on geometric algebra too, wrote "Many years ago (about 1984), I used to give a Mathematical Physics course to the Part II students. I illustrated the quantum paradox covered by Bell's theorem by showing that you can't program two independently running computers to mimic the results of spin measurements on two spin-1/2 particles in a singlet state. I believe this demonstration is actually better than Bell's original argument" https://physics.stackexchange.com/questions/547039/help-understanding-prof-steve-gulls-explanation-of-bells-theorem.
...

Ah, so that is where you got Gill's "theorem" from! Is the answer (proof) given at that stackexchange link correct?

There is no "proof" of either Gull's "theorem" or Gill's "theorem." All they have got is some wishful thinking. Gill wouldn't recognize a proof even if he saw one.

**

Yeah, you and I know that but he doesn't seem to understand. I'm trying to figure out a way to get him to understand it.
.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Fri Oct 09, 2020 9:30 pm

Fred, a way to get me to understand: you could get me to understand that there is no proof, by winning my computer challenge. Or more precisely and more interestingly: you would then convince me and the world that the numerous published proofs must all be wrong.

This would bring you and Joy a Nobel prize, and stop any chance that Alain Aspect, or Anton Zeilinger, or anyone else like that, would ever get one.

The second answer at stackexchange is a carefully written out, full proof of *Gull’s theorem*, including a careful statement of his theorem, of course. What is there that you two (Joy and Fred) don’t understand about it?

https://physics.stackexchange.com/questions/547039/help-understanding-prof-steve-gulls-explanation-of-bells-theorem

Gull’s theorem is that a certain assignment from a fictitious course on “distributed computing” is impossible to fulfil. You two discovered the truth of that, yourselves, the hard way. You both tried many times and failed. Finally you moved the goalposts, and succeeded in doing imperfectly something that Philip Pearle already showed how how to do perfectly in 1970. There are other perfect solutions, such as one due to Gisin and Gisin; and a legion of imperfect ones (Caroline Thompson, Michielsen and de Raedt, Michel Fodje, ..., and Diether and Christian in IEEE Access). [IEEE is presently investigating a complaint about that paper. If you are interested, I can send you the correspondence which I’ve had in that affair so far, or post it somewhere. No idea how it will end. Probably mostly nothing will happen for a long, long, time].

See my paper on Pearle’s model: https://www.mdpi.com/1099-4300/22/1/1

Another mathematical version of Bell’s theorem can be found here:

https://arxiv.org/abs/1402.1972
Constraints on determinism: Bell versus Conway-Kochen

Eric Cator, Klaas Landsman
Bell's Theorem from 1964 and the (Strong) Free Will Theorem of Conway and Kochen from 2009 both exclude deterministic hidden variable theories (or, in modern parlance, `ontological models') that are compatible with some small fragment of quantum mechanics, admit `free' settings of the archetypal Alice & Bob experiment, and satisfy a locality condition called Parameter Independence. We clarify the relationship between these theorems by giving reformulations of both that exactly pinpoint their resemblance and their differences. Our reformulation imposes determinism in what we see as the only consistent way, in which the `ontological state' initially determines both the settings and the outcome of the experiment. The usual status of the settings as `free' parameters is subsequently recovered from independence assumptions on the pertinent (random) variables. Our reformulation also clarifies the role of the settings in Bell's later generalization of his theorem to stochastic hidden variable theories.

Appeared in Foundations of Physics. A pretty reliable, peer-reviewed, journal.

What don’t you understand in that paper?
gill1109
Mathematical Statistician
 
Posts: 2812
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Location: Leiden

Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Sun Oct 11, 2020 10:40 am

Here is a simple counter example to Gull's so-called "proof" using the same GAViewer script that started this thread when a = b. Here is a sample output from GAViewer,

Code: Select all
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
theta = 0
correlation = -1.000000
mean = -1.000000
aveA = -0.014400
aveB = 0.014400
avePP = 0
aveNN = 0
avePN = 0.492800
aveNP = 0.507200


All 10,000 correlations are exactly -1 as can be seen by the mean value. Here is the GAViewer code script,

Code: Select all
//Adaptation of Albert Jan Wonnink's original code based on GAViewer for Joy Christian's S^3 Model of the 2-particle
//This is NOT Joy Christian's S^3 model.  It is a GA R^3 model that works.
//This is a counter example to Gull's so-called "proof".

function RandomUnitVector()    //uniform random unit vector:
                               //http://mathworld.wolfram.com/SpherePointPicking.html
{
   v=randGaussStd()*e1+randGaussStd()*e2+ randGaussStd()*e3; //3D Vectors
   return normalize(v);
}
   batch test()
{
   set_window_title("3D Test of GA Model for the 2-particle correlation for Gull's proof");
   default_model(p3ga);
   N=10000;                               //number of iterations (trials)
   I=e1^e2^e3;
   s=0;
   t=0;
   u=0;
   nPP=0;
   nNN=0;
   nPN=0;
   nPN=0;
   for(mm=0;mm<N;mm=mm+1)                  //perform the experiment N times
   {
          a=RandomUnitVector();
          Da=I a;
          //b=RandomUnitVector();
          b=a;                                     //as specified in Gull's "proof"
          Db=I b;
          c=RandomUnitVector();         //singlet vector
          //Sa=I c;                     //singlet bivector
          //Sa=Sb;
          if((a.c)>0) {Sa=Da;} else {Sa=-Da;}  //polarizer takes Sa to +/-Da
          if((b.c)>0) {Sb=Db;} else {Sb=-Db;}  //polarizer takes Sb to +/-Db
          A=-Da*Sa;      //Measurement function
          B=Sb*Db;       //Measurement function
          q=0;
          //Since Sa*Sb = -1 the product calculation reduces to A B = -Da Sa Sb Db = Da Db.
          q=(Da Db);     //Product calculation
          s=s+q;
          p_a=atan2(scalar(Da/(e3^e1)), scalar(Da/(e2^e3)));  //Get angle for a vector in x-y plane
          p_b=atan2(scalar(Db/(e2^e3)), scalar(Db/(e3^e1)));  //Get angle for b vector in x-y plane
          neg_adotb=-(a.b);
          //print(neg_adotb, "f");             //Outputs -a.b event by event
          //if(p_a*p_b>0) {theta=acos(a.a)*180/pi;} else {theta=acos(a.a)*180/pi+0;}
          theta = 0;                         //obvious when a = b
          print(theta, "f");                 //Outputs the angles
          print(correlation=scalar(q), "f"); //Outputs the correlations event by event
          t=t+A;
          u=u+B;
          pp=0;
          nn=0;
          pn=0;
          np=0;
          if(A>0&&B>0) {pp=1;}
          if(A<0&&B<0) {nn=1;}
          if(A>0&&B<0) {pn=1;}
          if(A<0&&B>0) {np=1;}
          nPP=nPP+pp;
          nNN=nNN+nn;
          nPN=nPN+pn;
          nNP=nNP+np;
      }
      mean=s/N;
      print(mean, "f");    //shows the vanishing of the non-scalar part
      aveA=t/N;
      print(aveA, "f");    //verifies that individual average < A > = 0
      aveB=u/N;
      print(aveB, "f");    //verifies that individual average < B > = 0
      avePP=nPP/N;
      print(avePP, "f");   //verifies plus-plus outcome prediction
      aveNN=nNN/N;
      print(aveNN, "f");
      avePN=nPN/N;
      print(avePN, "f");
      aveNP=nNP/N;
      print(aveNP, "f");
      prompt();
}


So I REPEAT! Gill's "theorem" has no actual proof!
.
FrediFizzx
Independent Physics Researcher
 
Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

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