3-Sphere 3D Vectors 2-Particle Simulation

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3-Sphere 3D Vectors 2-Particle Simulation

Postby FrediFizzx » Sat Jul 06, 2019 12:32 am

At long last here is the code for mapping QM to GA for validation of the product calculation with 3D vectors for a and b.

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 a mapping of the quantum mechanics project to GA.

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+ randGaussStd()*e3; //3D Vectors
   return normalize(v);
}

   batch test()
{
   set_window_title("3D Test of QM mapped to GA S^3 Model for the 2-particle correlation");
   default_model(p3ga);
   N=50000;                               //number of iterations (trials)
   I=e1^e2^e3;
   s=0;
   t=0;
   u=0;
   for(nn=0;nn<N;nn=nn+1)                  //perform the experiment N times
   {
          a=getRandomUnitVector();
          Da=I a;
          b=getRandomUnitVector();
          Db=I b;
          lambda=getRandomLambda();        //lambda is a fair coin, giving the +1 or -1 choice
          Sa=Da;                           //polarizer takes Sa to Da
          Sb=Db;                           //polarizer takes Sb to Db
          A=(Da)*(lambda*(-Sa));           //Measurement function
          B=(lambda*Sb)*(Db);              //Measurement function
          LA=A/(-Sa);
          LB=B/(Sb);                       //implements the twist in the Hopf bundle of S^3
          q=0;
          if(lambda==1) {q=(LA LB);} else {q=(LB LA);}
          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/(e3^e1)), scalar(Db/(e2^e3)));  //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");                 //Output the angles
          print(correlation=scalar(q), "f"); //Output the correlations
          t=t+A;
          u=u+B;
      }
      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
      prompt();
}


And here is a plot of the data with 50K trials.

Image

And here is a sample output of the data,

Code: Select all
neg_adotb = 0.388081
theta = 112.835121
correlation = 0.388081
neg_adotb = 0.069717
theta = 266.002289
correlation = 0.069717
neg_adotb = 0.803799
theta = 216.505585
correlation = 0.803799
neg_adotb = 0.969949
theta = 194.081985
correlation = 0.969949
neg_adotb = -0.412260
theta = 65.653091
correlation = -0.412260
neg_adotb = 0.050439
theta = 92.891159
correlation = 0.050439
neg_adotb = 0.333078
theta = 109.455727
correlation = 0.333078
neg_adotb = -0.491393
theta = 299.432190
correlation = -0.491393
neg_adotb = -0.769292
theta = 39.709625
correlation = -0.769292
neg_adotb = -0.930731
theta = 21.451025
correlation = -0.930731
neg_adotb = 0.627474
theta = 128.864014
correlation = 0.627474
neg_adotb = 0.486190
theta = 240.909500
correlation = 0.486190
neg_adotb = 0.034357
theta = 91.968903
correlation = 0.034357
neg_adotb = -0.756540
theta = 40.839890
correlation = -0.756540
neg_adotb = -0.027154
theta = 88.444000
correlation = -0.027154
neg_adotb = -0.446383
theta = 296.511871
correlation = -0.446383
neg_adotb = -0.580410
theta = 54.520596
correlation = -0.580410
neg_adotb = 0.988030
theta = 171.125839
correlation = 0.988030
neg_adotb = 0.380612
theta = 112.371574
correlation = 0.380612
neg_adotb = -0.116122
theta = 83.331673
correlation = -0.116122
neg_adotb = -0.161629
theta = 80.698555
correlation = -0.161629
neg_adotb = 0.428098
theta = 244.653061
correlation = 0.428098
neg_adotb = -0.824326
theta = 325.520172
correlation = -0.824326
neg_adotb = -0.276965
theta = 286.079132
correlation = -0.276965
neg_adotb = 0.835168
theta = 146.633301
correlation = 0.835168
neg_adotb = 0.064757
theta = 266.287109
correlation = 0.064757
neg_adotb = 0.822519
theta = 214.662277
correlation = 0.822519
neg_adotb = -0.390839
theta = 293.006744
correlation = -0.390839
neg_adotb = -0.688184
theta = 46.513485
correlation = -0.688184
neg_adotb = 0.412694
theta = 114.374191
correlation = 0.412694
neg_adotb = 0.588540
theta = 233.946533
correlation = 0.588540
mean = -0.004767 + 0.004202*e2^e3 + -0.012679*e3^e1 + 0.000449*e1^e2
aveA = 0.011200
aveB = -0.011200


One can see that the correlations match -a.b exactly to 6 decimal places event by event. Scroll to the end and you will see the mean values and A and B averages.
.
FrediFizzx
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Posts: 1559
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Location: N. California, USA

Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby gill1109 » Sat Jul 06, 2019 6:20 am

FrediFizzx wrote:At long last here is the code for mapping QM to GA for validation of the product calculation with 3D vectors for a and b.

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 a mapping of the quantum mechanics project to GA.

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+ randGaussStd()*e3; //3D Vectors
   return normalize(v);
}

   batch test()
{
   set_window_title("3D Test of QM mapped to GA S^3 Model for the 2-particle correlation");
   default_model(p3ga);
   N=50000;                               //number of iterations (trials)
   I=e1^e2^e3;
   s=0;
   t=0;
   u=0;
   for(nn=0;nn<N;nn=nn+1)                  //perform the experiment N times
   {
          a=getRandomUnitVector();
          Da=I a;
          b=getRandomUnitVector();
          Db=I b;
          lambda=getRandomLambda();        //lambda is a fair coin, giving the +1 or -1 choice
          Sa=Da;                           //polarizer takes Sa to Da
          Sb=Db;                           //polarizer takes Sb to Db
          A=(Da)*(lambda*(-Sa));           //Measurement function
          B=(lambda*Sb)*(Db);              //Measurement function
          LA=A/(-Sa);
          LB=B/(Sb);                       //implements the twist in the Hopf bundle of S^3
          q=0;
          if(lambda==1) {q=(LA LB);} else {q=(LB LA);}
          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/(e3^e1)), scalar(Db/(e2^e3)));  //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");                 //Output the angles
          print(correlation=scalar(q), "f"); //Output the correlations
          t=t+A;
          u=u+B;
      }
      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
      prompt();
}


Thanks Fred! Many, many thanks.

Yes, this will reproduce the singlet correlations perfectly, as the number of trials goes to infinity, as is easy to check if you know just a little elementary GA and if you know the law of large numbers. It helps if you also trust your computers pseudo random number generator, and have studied the GAviewer manual for half a day, and have played with GAviewer on your own computer for a few hours.

In my humble opinion, your computer programme deviates from Joy's published mathematical formulas in two important respects:

1) It does not explicitly implement the *definitions* of the measurement functions (which involve taking some limits) but jumps ahead, and instead adopts Joy's own evaluation of those limits. So anyone who finds those evaluations troubling gets no solace or illumination from the code. But we knew that in advance. You and Joy find those evaluations just routine physics and definition. OK.

2) It includes an extra step, the very revealing line
Code: Select all
 if(lambda==1) {q=(LA LB);} else {q=(LB LA);}
which you will not find in Joy's written mathematical formulas. If I recall correctly, this brilliant innovation (or "fix") was discovered by Albert Jan Wonninck.

But it is the bump under the carpet, not so "hidden" this time. As I see it, Joy needs to switch a sign somewhere, and this is where you are doing it for him in your code. At least, that's how I see it. But then I don't see any errors in Bell's theorem, so I "know" that any contradiction with Bell's theorem must be due to a mistake of some kind. (I'm not one of those people who think that Bell's theorem is both true and untrue and that we have to rewrite logic and/or the ZFC axioms. But of course, that is a logical possibility).
gill1109
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby Joy Christian » Sat Jul 06, 2019 7:23 am

gill1109 wrote:
In my humble opinion, your computer programme deviates from Joy's published mathematical formulas in two important respects:

No, it doesn't. The following two papers contain all the relevant formulas used by Fred in his code: (1) https://arxiv.org/abs/1103.1879, and (2) https://arxiv.org/abs/1405.2355.

gill1109 wrote:
1) It does not explicitly implement the *definitions* of the measurement functions (which involve taking some limits) but jumps ahead, and instead adopts Joy's own evaluation of those limits. So anyone who finds those evaluations troubling gets no solace or illumination from the code. But we knew that in advance. You and Joy find those evaluations just routine physics and definition. OK.

Anyone who understands GA knows that the limit operations are equivalent to the divisions by the bivectors used by Fred. Again, for details, consult the formulas in the above two papers.

gill1109 wrote:
2) It includes an extra step, the very revealing line
Code: Select all
 if(lambda==1) {q=(LA LB);} else {q=(LB LA);}
which you will not find in Joy's written mathematical formulas.

There is no "extra step." That step simply encodes my hidden variable λ. But you, Richard D. Gill, have never understood the meaning of my hidden variable λ in all these eight years. Fred understands the physical and mathematical meanings of my hidden variable well, and now Jay also understands them very well. Only you are left behind for the past so many years. :)

gill1109 wrote:
But it is the bump under the carpet, not so "hidden" this time. As I see it, Joy needs to switch a sign somewhere, and this is where you are doing it for him in your code. At least, that's how I see it. But then I don't see any errors in Bell's theorem, so I "know" that any contradiction with Bell's theorem must be due to a mistake of some kind.

As already noted, there is no "bump under the carpet." The alternative sign is just the hidden variable λ, and that is precisely what Fred has used in his code. You will never understand this.

Bell's theorem is quite wrong. Therefore your opinion based on it is also wrong. Let me link one of my papers to make sure people here understand what I mean by "Bell's theorem is wrong."

***
Last edited by Joy Christian on Sat Jul 06, 2019 8:40 am, edited 1 time in total.
Joy Christian
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby gill1109 » Sat Jul 06, 2019 7:44 am

No, I have never understood your work, Joy.

Please find an expert on GA to comment on your claims. For our symposium, I was thinking of asking the GA specialists in Amsterdam, namely the computer scientists who actually wrote GAviewer. And I’ll certainly invite John Baez too, though I doubt he would come. Do you have any other suggestions?

It would also be good if we could get hold of Sabine Hossenfelder. She’s an eloquent critic of the physics establishment, and a very strong theoretical physicist herself.

Unfortunately Jay’s enterprise has no bearing on the technical math issues of Joy’s GA approach, since his starting point is the standard QM derivation of the singlet correlations, to which he hopes to add an interpretation, or come up with new definitions, such that they themselves can be given the “certificate” local realist. Which, by the way, was already done by Brassard and Raymond-Robichaud. They gave careful, new, metaphysical definitions of “local” and “real”, and came to your desired conclusion. I believe their paper is at least 80 pages long and very, very technical.
Last edited by gill1109 on Sat Jul 06, 2019 8:01 am, edited 2 times in total.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby Joy Christian » Sat Jul 06, 2019 7:54 am

gill1109 wrote:No, I have never understood your work, Joy.

Please find an expert on GA to comment on your claims. For our symposium, I was thinking of asking the GA specialists in Amsterdam, namely the computer scientists who actually wrote GAviewer. And I’ll certainly invite John Baez too, though I doubt he would come. Do you have any other suggestions?

You can invite whoever you like. I am unconcerned about anyone's opinion, no matter how reputable, because my mathematics and physics, as well as Fred's code, speak for themselves.

***
Joy Christian
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Location: Oxford, United Kingdom

Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby gill1109 » Sat Jul 06, 2019 8:08 am

Joy Christian wrote:
gill1109 wrote:No, I have never understood your work, Joy.

Please find an expert on GA to comment on your claims. For our symposium, I was thinking of asking the GA specialists in Amsterdam, namely the computer scientists who actually wrote GAviewer. And I’ll certainly invite John Baez too, though I doubt he would come. Do you have any other suggestions?

You can invite whoever you like. I am unconcerned about anyone's opinion, no matter how reputable, because my mathematics and physics, as well as Fred's code, speak for themselves.

I always admired your style, Joy! A real dude. Of course your work has to speak for itself. That’s the way it goes.

We’ll invite whoever you approve of, it’s a joint enterprise and you’ll be at least consulted, every step of the way. Jay coordinates. I provide the venue. And I hope sufficient funding. The symposium won’t be stopped by the RSOS. It can only be stopped by you, since you’re its raison d’etre. The workshop in which the symposium is to be embedded can of course go ahead without you. We can have a workshop excursion (canal and lake boat trip / visit to Escher museum / visit to Mauritshuis / visit to Scheveningen harbour fish restaurant) instead.
gill1109
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Location: Leiden

Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby FrediFizzx » Sat Jul 06, 2019 12:12 pm

gill1109 wrote: … Thanks Fred! Many, many thanks.

You're welcome. This is the simplified version of the mapping from QM to GA for validation of the product calculation event by event. Had to get that working first. I'm working on the more complete QM to GA mapping version now with the sgn(n.s)n function in it.
.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby FrediFizzx » Mon Jul 08, 2019 3:26 pm

Here is the GAViewer code that implements the limit functions sgn(n.s)n for validation of the product calculation. Eq. (16) is here.

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
//correlation.  This is a mapping of the quantum mechanics project to GA.

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+ randGaussStd()*e3; //3D Vectors
   return normalize(v);
}
function sgn(y)
{
     if(y < 0) {return(-1);} else {return(1);}
}
   batch test()
{
   set_window_title("3D Test of QM mapped to GA S^3 Model for the 2-particle correlation");
   default_model(p3ga);
   N=5000;                               //number of iterations (trials)
   I=e1^e2^e3;
   ss=0;
   t=0;
   u=0;
   for(nn=0;nn<N;nn=nn+1)                  //perform the experiment N times
   {
          a=getRandomUnitVector();
          Da=I a;
          b=getRandomUnitVector();
          Db=I b;
          s=getRandomUnitVector();
          //S1=I s;               //bivector for particle spins
          //S2=S1;               //-S1 + S2 = 0 for singlet zero spin
          if(sgn(a.s)==1) {S1=Da;} else {S1=-Da;}  //polarizer takes S1 to +/-Da
          if(sgn(b.s)==1) {S2=Db;} else {S2=-Db;}  //polarizer takes S2 to +/-Db
          lambda=getRandomLambda();   //lambda is a fair coin, giving the +1 or -1 choice
          A=(Da*lambda*(-S1));      //Measurement function limit is function above
          B=(lambda*S2*Db);      //Measurement function limit is function above
          q=0;
          //if(lambda==1) {q=A B;} else {q=B A;}
          //Above is the usual form of the product calculation but we will expand it.
          //if(lambda==1) {q=(Da*lambda*(-S1)) (lambda*S2*Db);} else {q=(lambda*S2*Db) (Da*lambda*(-S1));}
          //Next we will use the fact that S2 = S1 and make some replacements to conform to eq.(16)
          //and it is easy to see that lambda cancels out.  We are now ready to perform the correlations.
          if(lambda==1) {q=(Da (-S2))(S2 Db);} else {q=(Db S1)((-S1) Da);}
          ss=ss+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/(e3^e1)), scalar(Db/(e2^e3)));  //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");                 //Output the angles event by event
          print(correlation=scalar(q), "f"); //Output the correlations event by event
          t=t+A;
          u=u+B;
      }
      mean=ss/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
      prompt();
}


Here is a sample of the output data. Scroll to the end to see the mean and A and B averages.

Code: Select all
neg_adotb = 0.769051
theta = 219.731262
correlation = 0.769051
neg_adotb = 0.980398
theta = 191.363083
correlation = 0.980398
neg_adotb = -0.939377
theta = 20.052734
correlation = -0.939377
neg_adotb = -0.184919
theta = 280.656403
correlation = -0.184919
neg_adotb = 0.940939
theta = 199.790146
correlation = 0.940939
neg_adotb = -0.027878
theta = 271.597473
correlation = -0.027878
neg_adotb = 0.144887
theta = 98.330711
correlation = 0.144887
neg_adotb = 0.248063
theta = 255.637054
correlation = 0.248063
neg_adotb = -0.620178
theta = 51.670876
correlation = -0.620178
neg_adotb = 0.116364
theta = 263.317719
correlation = 0.116364
neg_adotb = 0.862768
theta = 210.371216
correlation = 0.862768
neg_adotb = -0.891815
theta = 26.897833
correlation = -0.891815
neg_adotb = 0.398351
theta = 246.524857
correlation = 0.398351
neg_adotb = -0.438543
theta = 296.010925
correlation = -0.438543
neg_adotb = -0.421157
theta = 65.092339
correlation = -0.421157
neg_adotb = -0.612455
theta = 307.767212
correlation = -0.612455
neg_adotb = 0.873530
theta = 150.871521
correlation = 0.873530
neg_adotb = 0.541121
theta = 237.240051
correlation = 0.541121
neg_adotb = 0.570693
theta = 235.201431
correlation = 0.570693
neg_adotb = 0.508569
theta = 239.431442
correlation = 0.508569
neg_adotb = -0.923558
theta = 22.548048
correlation = -0.923558
neg_adotb = 0.956183
theta = 197.023895
correlation = 0.956183
neg_adotb = 0.073493
theta = 265.785339
correlation = 0.073493
neg_adotb = -0.546572
theta = 56.867832
correlation = -0.546572
neg_adotb = 0.027456
theta = 268.426697
correlation = 0.027456
neg_adotb = -0.929541
theta = 21.636635
correlation = -0.929541
neg_adotb = -0.271182
theta = 74.265366
correlation = -0.271182
neg_adotb = 0.717043
theta = 224.189148
correlation = 0.717043
neg_adotb = -0.272586
theta = 285.818207
correlation = -0.272586
neg_adotb = -0.218020
theta = 282.592743
correlation = -0.218020
neg_adotb = -0.310607
theta = 71.904175
correlation = -0.310607
neg_adotb = 0.752469
theta = 221.195328
correlation = 0.752469
neg_adotb = 0.744046
theta = 138.077209
correlation = 0.744046
neg_adotb = -0.277602
theta = 286.117126
correlation = -0.277602
neg_adotb = -0.154770
theta = 81.096542
correlation = -0.154770
neg_adotb = 0.273201
theta = 254.145157
correlation = 0.273201
neg_adotb = 0.773508
theta = 219.330078
correlation = 0.773508
neg_adotb = 0.983223
theta = 190.509918
correlation = 0.983223
neg_adotb = -0.223568
theta = 282.918701
correlation = -0.223568
neg_adotb = 0.498953
theta = 240.069229
correlation = 0.498953
neg_adotb = 0.412289
theta = 245.651306
correlation = 0.412289
neg_adotb = 0.159591
theta = 99.183144
correlation = 0.159591
neg_adotb = -0.052631
theta = 86.983070
correlation = -0.052631
neg_adotb = 0.545646
theta = 236.931152
correlation = 0.545646
neg_adotb = 0.856315
theta = 211.094681
correlation = 0.856315
neg_adotb = -0.403730
theta = 293.811584
correlation = -0.403730
neg_adotb = 0.146485
theta = 98.423294
correlation = 0.146485
neg_adotb = -0.973713
theta = 13.166204
correlation = -0.973713
neg_adotb = -0.488209
theta = 299.222931
correlation = -0.488209
neg_adotb = 0.557705
theta = 123.897202
correlation = 0.557705
neg_adotb = 0.387777
theta = 247.183746
correlation = 0.387777
mean = -0.006428 + -0.003079*e2^e3 + 0.005229*e3^e1 + -0.009692*e1^e2
aveA = 0.014000
aveB = 0.003600


Of course the plot will be the same as in the first post of this thread.
.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby FrediFizzx » Tue Jul 09, 2019 12:34 am

Well, let's see who is paying attention here. An hour ago I discovered a mistake in the code just presented but it doesn't affect the results. I wonder who will find it first?
.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby Heinera » Tue Jul 09, 2019 1:18 am

But this is not a simulation of the draft "Quantum Mechanical Prediction of the Singlet State with a Hidden Variable."

In that draft, there are no bivectors. There is no GA. Please make a simulation that faithfully implements the formulas in the draft as they are written there.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby gill1109 » Tue Jul 09, 2019 2:30 am

FrediFizzx wrote:Well, let's see who is paying attention here. An hour ago I discovered a mistake in the code just presented but it doesn't affect the results. I wonder who will find it first?
.

I'm interested in your GA version, Fred! But I've been rather busy with other things for a couple of days. (And will be, for a couple of days to come).

But I will come back to you on this, probably next weekend...

If you want to replace the GA code by better GA code, please just go ahead. When I come back to you - I'll just take the then, latest version.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby FrediFizzx » Tue Jul 09, 2019 6:28 am

Heinera wrote:But this is not a simulation of the draft "Quantum Mechanical Prediction of the Singlet State with a Hidden Variable."

In that draft, there are no bivectors. There is no GA. Please make a simulation that faithfully implements the formulas in the draft as they are written there.

Well, Heine is not paying attention I guess. This is a pretty faithful mapping of QM to GA for EPR-Bohm. I'm not interested in doing anything else. If you want to do something else or use some other code, go ahead.

Or... if you have questions or need further explanations, go ahead with that also.
.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby FrediFizzx » Tue Jul 09, 2019 2:06 pm

gill1109 wrote:
FrediFizzx wrote:Well, let's see who is paying attention here. An hour ago I discovered a mistake in the code just presented but it doesn't affect the results. I wonder who will find it first?
.

I'm interested in your GA version, Fred! But I've been rather busy with other things for a couple of days. (And will be, for a couple of days to come).

But I will come back to you on this, probably next weekend...

If you want to replace the GA code by better GA code, please just go ahead. When I come back to you - I'll just take the then, latest version.

The code is fixed now. Enjoy!
.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby jreed » Tue Jul 09, 2019 2:49 pm

Fred:

I'm interested in working with the code. I have GAViewer and have tried using it, but I don't know how to load your program in it. Can you give me some hints about this? The console in GAViewer isn't very user friendly.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby FrediFizzx » Tue Jul 09, 2019 3:04 pm

jreed wrote:Fred:

I'm interested in working with the code. I have GAViewer and have tried using it, but I don't know how to load your program in it. Can you give me some hints about this? The console in GAViewer isn't very user friendly.

HI John,

Copy the code and save it as a text file with a .g extension. Then File/Open/Open g file. Then type test() at the prompt after the file is parsed.

Perhaps you can translate this code to a Mathematica file? That would be very good as GAViewer doesn't have much in the way of array or table support. I have to copy the data then process in Word then import into Excel.
.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby jreed » Tue Jul 09, 2019 4:13 pm

FrediFizzx wrote:
jreed wrote:Fred:

I'm interested in working with the code. I have GAViewer and have tried using it, but I don't know how to load your program in it. Can you give me some hints about this? The console in GAViewer isn't very user friendly.

HI John,

Copy the code and save it as a text file with a .g extension. Then File/Open/Open g file. Then type test() at the prompt after the file is parsed.

Perhaps you can translate this code to a Mathematica file? That would be very good as GAViewer doesn't have much in the way of array or table support. I have to copy the data then process in Word then import into Excel.
.


Thanks Fred. Yes, that's what I had in mind. I need to make sure that I can come up with the same answers in Mathematica as GAViewer gets.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby FrediFizzx » Tue Jul 09, 2019 5:07 pm

jreed wrote:
FrediFizzx wrote:
jreed wrote:Fred:

I'm interested in working with the code. I have GAViewer and have tried using it, but I don't know how to load your program in it. Can you give me some hints about this? The console in GAViewer isn't very user friendly.

HI John,

Copy the code and save it as a text file with a .g extension. Then File/Open/Open g file. Then type test() at the prompt after the file is parsed.

Perhaps you can translate this code to a Mathematica file? That would be very good as GAViewer doesn't have much in the way of array or table support. I have to copy the data then process in Word then import into Excel.
.


Thanks Fred. Yes, that's what I had in mind. I need to make sure that I can come up with the same answers in Mathematica as GAViewer gets.

You're welcome. You will probably need some kind of GA package or Clifford algebra package for Mathematica. I tried a few but didn't have the patience to get them to work. GAViewer code seems really simple compared to them and I'm pretty lazy in my old age. :D

But GAViewer is a really fun and cool way to learn geometric algebra. There is a lot of things it will do that I haven't even tried yet. And I do think it will export data to files. I remember doing that.
.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby FrediFizzx » Tue Jul 09, 2019 10:50 pm

FrediFizzx wrote:
jreed wrote:
Thanks Fred. Yes, that's what I had in mind. I need to make sure that I can come up with the same answers in Mathematica as GAViewer gets.

You're welcome. You will probably need some kind of GA package or Clifford algebra package for Mathematica. I tried a few but didn't have the patience to get them to work. GAViewer code seems really simple compared to them and I'm pretty lazy in my old age. :D

But GAViewer is a really fun and cool way to learn geometric algebra. There is a lot of things it will do that I haven't even tried yet. And I do think it will export data to files. I remember doing that.
.

It might actually be easier in Mathematica to just do the QM math with Pauli algebra. There is bound to be some good QM packages for Mathematica. Maybe I will look that up as I hadn't thought of it before.
.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby jreed » Wed Jul 10, 2019 6:12 am

FrediFizzx wrote:
FrediFizzx wrote:
jreed wrote:
Thanks Fred. Yes, that's what I had in mind. I need to make sure that I can come up with the same answers in Mathematica as GAViewer gets.

You're welcome. You will probably need some kind of GA package or Clifford algebra package for Mathematica. I tried a few but didn't have the patience to get them to work. GAViewer code seems really simple compared to them and I'm pretty lazy in my old age. :D

But GAViewer is a really fun and cool way to learn geometric algebra. There is a lot of things it will do that I haven't even tried yet. And I do think it will export data to files. I remember doing that.
.

It might actually be easier in Mathematica to just do the QM math with Pauli algebra. There is bound to be some good QM packages for Mathematica. Maybe I will look that up as I hadn't thought of it before.
.


I'm using Pauli matrices to represent the vectors in geometric algebra. The other components can be constructed from these. The Pauli matrices are already in Mathematica.
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Re: 3-Sphere 3D Vectors 2-Particle Simulation

Postby FrediFizzx » Wed Jul 10, 2019 8:01 am

jreed wrote:
FrediFizzx wrote:It might actually be easier in Mathematica to just do the QM math with Pauli algebra. There is bound to be some good QM packages for Mathematica. Maybe I will look that up as I hadn't thought of it before.
.


I'm using Pauli matrices to represent the vectors in geometric algebra. The other components can be constructed from these. The Pauli matrices are already in Mathematica.

Oh, that is right. Looking forward to seeing this calculation in Mathematica.
.
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