GAViewer Simulation No Hidden Variable

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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Sat Oct 31, 2020 4:52 pm

jreed wrote:
FrediFizzx wrote:
jreed wrote: ...
Just go into Mathematica, define the function f=(1+Cos[theta[)/4 then enter FourierSeries[f,theta,omega]. You'll see the three components expressed as dirac delta functions in omega. If you had some experience with Fourier series, you would see that just looking at the expression for f.

Whoa! Gull never said anything about Fourier Series. Plus Mathematica gives for what you said,

Image

Looks like nonsense to me. If you are getting Dirac Deltas, you are not doing something right. Show your math or you are just talking more nonsense.
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Sorry, my mistake. That should have FourierTransform.

That is what I figured. You are using the generic transform for that function. It's wrong. Probably the same mistake Gull made. Since the angle theta is involved, the integration only needs to be over 1 cycle. So you have your choice. 0 to 2pi or -pi to pi. It is pretty easy to just do the FT integration manually for that function. See what I posted earlier above.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Sat Oct 31, 2020 9:29 pm

FrediFizzx wrote:
jreed wrote: ...
Just go into Mathematica, define the function f=(1+Cos[theta[)/4 then enter FourierSeries[f,theta,omega]. You'll see the three components expressed as dirac delta functions in omega. If you had some experience with Fourier series, you would see that just looking at the expression for f.

Whoa! Gull never said anything about Fourier Series. Plus Mathematica gives for what you said,
Image
Looks like nonsense to me. If you are getting Dirac Deltas, you are not doing something right. Show your math or you are just talking more nonsense.

Gull indeed never said “Fourier series”. He said Fourier transform, because, from a higher math point of view familiar to Oxbridge graduates, the Fourier series *is* the Fourier transform taking the locally compact Abelian L^2[0, 2 pi] to its bidual L^2(Z). You never heard of the Pontryagin principle?

If not, please take a look at https://en.wikipedia.org/wiki/Pontryagin_duality

Sorry, it’s the arrogant way of talking which everyone speaks in Cambridge and in that other place, what’s it called? Oh yes, Oxford.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Sun Nov 01, 2020 12:27 am

I guess here is what John was talking about in Mathematica,

Image

Which uses the generic transform integrating from -infinity to +infinity. Which is silly for a cyclical function. However, as you can see, when I plot that result it looks like it is zero for all values of omega. But I'm not sure that is correct with the Dirac Deltas involved.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Sun Nov 01, 2020 9:05 am

FrediFizzx wrote:I guess here is what John was talking about in Mathematica,

Image

Which uses the generic transform integrating from -infinity to +infinity. Which is silly for a cyclical function. However, as you can see, when I plot that result it looks like it is zero for all values of omega. But I'm not sure that is correct with the Dirac Deltas involved.
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You all are slow on the uptake. :D It is zero for all omega except for -1, 0, and +1 where the result is an infinite spike. Mathematica doesn't evaluate DiracDelta[0].
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Sun Nov 01, 2020 11:01 am

Forget the Fourier Transform. What you guys need is the Fourier series. The transform from function defined (e.g.) on [0, 2pi) to sequence indexed by n in Z. And the inverse transform from sequence indexed by n in Z (the integers), to function on [0, 2 pi). And the convolution theorem for Fourier series.

Both transforms are called "Fourier transforms" by fancy-pants folk from Oxford and Cambridge. It's a secret language for elite scientists. Not for ordinary folk.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Sun Nov 01, 2020 11:29 am

gill1109 wrote:Forget the Fourier Transform. What you guys need is the Fourier series. The transform from function defined (e.g.) on [0, 2pi) to sequence indexed by n in Z. And the inverse transform from sequence indexed by n in Z (the integers), to function on [0, 2 pi). And the convolution theorem for Fourier series.

Both transforms are called "Fourier transforms" by fancy-pants folk from Oxford and Cambridge. It's a secret language for elite scientists. Not for ordinary folk.

LOL! I solve what Gull is talking about in his number (4) and you want to do something different. Typical. :mrgreen:
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Sun Nov 01, 2020 9:24 pm

FrediFizzx wrote:
gill1109 wrote:Forget the Fourier Transform. What you guys need is the Fourier series. The transform from function defined (e.g.) on [0, 2pi) to sequence indexed by n in Z. And the inverse transform from sequence indexed by n in Z (the integers), to function on [0, 2 pi). And the convolution theorem for Fourier series.

Both transforms are called "Fourier transforms" by fancy-pants folk from Oxford and Cambridge. It's a secret language for elite scientists. Not for ordinary folk.

LOL! I solve what Gull is talking about in his number (4) and you want to do something different. Typical. :mrgreen:
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Take a look at Wolfram world’s article on Fourier series. https://mathworld.wolfram.com/FourierSeries.html. Notice the passage including equations (20) to (29). The series (A_n: n in Z) defined for a given function f by formula (26) is what Gull would call the Fourier transform of the function (f(z): z in [-pi, pi]). The function f defined for a given series A_n by (20) is what Gull would call the Fourier transform of the series. It’s not difficult. We teach Fourier series very early in the bachelor curriculum. Every scientist has to know about them.

A space of functions. A space of series. Mappings between them, which are one another’s inverses. Convolution of functions maps to product of series.
Last edited by FrediFizzx on Mon Nov 02, 2020 12:35 am, edited 1 time in total.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Mon Nov 02, 2020 12:52 am

Of course Gull's number (4) is only half the story. It is only the function for 11 and 00. What about for 10 and 01 outcomes? You get Dirac Deltas with the imaginary "i" on them. What is an imaginary Dirac Delta?
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Mon Nov 02, 2020 6:08 am

FrediFizzx wrote:Of course Gull's number (4) is only half the story. It is only the function for 11 and 00. What about for 10 and 01 outcomes? You get Dirac Deltas with the imaginary "i" on them. What is an imaginary Dirac Delta?
.

Gull's number (4) is wrong, and it's only a quarter of the story! Gull says correlation when he just means "mean of the product" (he's a Cambridge astrophysicist, and he wrote this several decades ago). And at this stage in his slides he's talking about measurement functions which take values 0 and 1 only (see the picture of "p" which he draws). So his formula (4) should be the formula for the probability of ++, when the difference between the settings is Delta theta. So I think it should be 1/4 x (1 - cos(Delta theta)), since the probabilities of ++ and -- should be the same; and the marginal probabilities of + and - are one half. The probabilities of +- and of -+ should be 1/4 x (1 + cos(Delta theta)). That way we have four probabilities adding to 1. And the correlation = probability of equal minus probability of unequal = 1/2 x (1 - cos(Delta theta)) - 1/2 x (1 + cos(Delta theta)) = - cos(Delta theta), the negative cosine.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Mon Nov 02, 2020 8:30 am

Gull's number (4) is correct but he neglected to mention that those 3 non-zero FT components are Dirac Delta infinite spikes.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Mon Nov 02, 2020 10:08 am

FrediFizzx wrote:Gull's number (4) is correct but he neglected to mention that those 3 non-zero FT components are Dirac Delta infinite spikes.
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Yes, you can say it that way.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Mon Nov 02, 2020 1:32 pm

FrediFizzx wrote:Gull's number (4) is correct but he neglected to mention that those 3 non-zero FT components are Dirac Delta infinite spikes.
.

According to what he had to use for number (3) to make it correct, one of the two is wrong. If you integrate a cyclical function from -infinity to +infinity of course you will get infinity. It is silly to do that transform for a cyclical function. We are typically only interested in what happens over one cycle.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Mon Nov 02, 2020 8:13 pm

FrediFizzx wrote:
FrediFizzx wrote:Gull's number (4) is correct but he neglected to mention that those 3 non-zero FT components are Dirac Delta infinite spikes.
.

According to what he had to use for number (3) to make it correct, one of the two is wrong. If you integrate a cyclical function from -infinity to +infinity of course you will get infinity. It is silly to do that transform for a cyclical function. We are typically only interested in what happens over one cycle.
.

Exactly. You need the Fourier series, not the Fourier transform.

Gull is in fact using the Fourier series. He just calls it “FT”. He also says “FT” when he means the inverse of the transform from cyclical function to series. He says “correlation” when he means mean value of product. He switches from +/-1 valued function to 0/1 valued function. He writes “1/2” but he means “1/4”.

We are rewriting the proof, should have a preprint ready in a week. My student is slow.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Mon Nov 02, 2020 8:38 pm

gill1109 wrote:
FrediFizzx wrote:
FrediFizzx wrote:Gull's number (4) is correct but he neglected to mention that those 3 non-zero FT components are Dirac Delta infinite spikes.
.

According to what he had to use for number (3) to make it correct, one of the two is wrong. If you integrate a cyclical function from -infinity to +infinity of course you will get infinity. It is silly to do that transform for a cyclical function. We are typically only interested in what happens over one cycle.
.

Exactly. You need the Fourier series, not the Fourier transform. ...

Nonsense.

Image

The Fourier Series of that function is just the same as converting the function to exponentials.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Tue Nov 03, 2020 10:51 am

I've split this topic off and locked this thread for now since we are getting way off topic.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Thu Dec 24, 2020 11:05 am

Thread is now unlocked.

I've updated the GAViewer code for this simulation to match the quaternion simulation 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
//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);
}
function sgn(y)
{
     if(y < 0) {return(-1);} else {return(1);}
}
   batch test()
{
   set_window_title("3D Test of GA 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;
   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;
          Db=I b;
          c=RandomUnitVector();         //singlet vector
          Ls=I c;                       //singlet bivector
          A=sgn(-Da*Ls);      //Measurement function with polarizer action
          B=sgn(Db*Ls);       //Measurement function with polarizer action
          q=0;
          Aq=-Da*Ls;
          Bq=Ls*Db;
          q=(Aq Bq);     //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;} else {pp=0;}
          if(A<0&&B<0) {nn=1;} else {nn=0;}
          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,etc.
      aveNN=nNN/N;
      print(aveNN, "f");
      avePN=nPN/N;
      print(avePN, "f");
      aveNP=nNP/N;
      print(aveNP, "f");
      prompt();
}


Here is a sample of the GAViewer output.

Code: Select all
neg_adotb = -0.281313
theta = 286.338593
correlation = -0.281313
neg_adotb = -0.690760
theta = 313.690308
correlation = -0.690760
neg_adotb = -0.408114
theta = 294.086426
correlation = -0.408114
neg_adotb = 0.104076
theta = 95.973953
correlation = 0.104076
neg_adotb = 0.177995
theta = 100.252975
correlation = 0.177995
neg_adotb = -0.837511
theta = 326.878235
correlation = -0.837511
mean = 0.002252 + 0.001483*e2^e3 + -0.000048*e3^e1 + 0.001351*e1^e2
aveA = -0.003360
aveB = 0.000120
avePP = 0.248140
aveNN = 0.249760
avePN = 0.250180
aveNP = 0.251920

Scroll to the bottom to see the averages, etc. As you can see, the product calculation correlation is exactly -a.b.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Thu Dec 24, 2020 8:31 pm

Da = I a
DB = I b
Ls = I c
I is the trivector, it squares to -1 and commutes with everything in the algebra
Hence q = Aq Bq = - Da Ls Ls Db =-I^4 a c c b = - a b = - a.b - a x b
Therefore, scalar(q) = - a.b

Your definition of correlation does not use the outcomes A, B = +/-1
It just takes the scalar part of the geometric product of the vectors a, b

Have you tried calculating the correlation like an experimenter would, ie as the average of the ordinary product of AB?

I suppose the comparison operator “<“ compares the scalar part of two elements of your geometric algebra. You effectively defined
A = sgn(a c)
B = - sgn(b c)
Your event by event measurement outcomes seem to be the simple ones mentioned by Bell which would give the triangle wave correlation function.
Last edited by gill1109 on Thu Dec 24, 2020 8:33 pm, edited 1 time in total.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Thu Dec 24, 2020 8:33 pm

Blah! Blah! Blah! It is NOT a simulation of an experiment! Doesn't need to be to shoot down Bell's junk physics theory.

And..., after all these years you still don't know how to do geometric algebra properly.
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Re: GAViewer Simulation No Hidden Variable

Postby FrediFizzx » Fri Dec 25, 2020 6:24 am

Perhaps some analytical explanation is needed for why the sign functions are not used in the product calculation. The sign function actually comes from the limit substitution process, Ls --> sign(Dn Ls)Dn for the polarizer action. However, in the product calculation, -Da Ls Ls Db = -Da (-1) Db = Da Db so there is nothing left to do the limit substitution process in the product calculation.
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Re: GAViewer Simulation No Hidden Variable

Postby gill1109 » Sat Dec 26, 2020 12:40 am

FrediFizzx wrote:Perhaps some analytical explanation is needed for why the sign functions are not used in the product calculation. The sign function actually comes from the limit substitution process, Ls --> sign(Dn Ls)Dn for the polarizer action. However, in the product calculation, -Da Ls Ls Db = -Da (-1) Db = Da Db so there is nothing left to do the limit substitution process in the product calculation.
.

Indeed. And then

Da Db = I a I b = I^2 a b = - (a dot b + a wedge b), of which the scalar part is - a dot b
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