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FrediFizzx wrote:

FrediFizzx wrote:

Joy Christian wrote:Well, I have said all this before. The bottom line is that what the above procedure does is calculate the correlation among the usual scalar (+/-1) points within S^3.

Yes, and since the detector bivectors "drop out" of the calculation, the way I did Joy_CHSH with GAViewer was essentially a short cut. I guess I could try it with the full A_i(a, u) = d(a) h_i(a, u) type expressions.

Ok, here it is.

Code: Select all

//Adaptation of Albert Jan Wonnink's original code
//http://challengingbell.blogspot.com/2015/03/numerical-validation-of-vanishing-of.html
function getRandomLambda()
{
     if( rand()>0.5) {return 1;} else {return -1;}
}

batch test()
{
     set_window_title("Test of Joy Christian's CHSH derivation");
     N=20000; //number of iterations (trials)
     I=e1^e2^e3;
     s=0;
     a1=sin(0)*e1 + cos(0)*e2 + 0.000*e3;
     b1=sin(pi/4)*e1 + cos(pi/4)*e2 + 0.000*e3;
     a2=sin(pi/2)*e1 + cos(pi/2)*e2 + 0.000*e3;
     b2=sin(3*pi/4)*e1 + cos(3*pi/4)*e2 + 0.000*e3;

     for(nn=0;nn<N;nn=nn+1) //perform the experiment N times
     {
          lambda=getRandomLambda(); //lambda is a fair coin
                                                 //resulting in +1 or -1
          mu=lambda * I;  //calculate the lambda dependent mu
          C1=-I.a1;  //C = {-a_j B_j}
          D1=I.b1;   //D = {b_k B_k}
          C2=-I.a2;  //C = {-a_j B_j}
          D2=I.b2;   //D = {b_k B_k}
          E1=mu.a1;  //E = {a_k B_k(L)}
          F1=mu.b1;  //F = {b_j B_j(L)}
          A1=C1 E1;  //eq. (1) of arXiv:1103.1879, A(a, L) = {-a_j B_j}{a_k B_k(L)}
          B1=F1 D1;  //eq. (2) of arXiv:1103.1879, B(b, L) = {b_j B_j(L)}{b_k B_k}
          E2=mu.a2;  //E = {a_k B_k(L)}
          F2=mu.b2;  //F = {b_j B_j(L)}
          A2=C2 E2;  //eq. (1) of arXiv:1103.1879, A(a, L) = {-a_j B_j}{a_k B_k(L)}
          B2=F2 D2;  //eq. (2) of arXiv:1103.1879, B(b, L) = {b_j B_j(L)}{b_k B_k}
          q=0;
          if(lambda==1) {q=((-C1) (A1 B1) (-D1))-((-C1) (A1 B2) (-D2))+((-C2) (A2 B1) (-D1))+((-C2) (A2 B2) (-D2));}
          else {q=((-D1) (B1 A1) (-C1))-((-D2) (B2 A1) (-C1))+((-D1) (B1 A2) (-C2))+((-D2) (B2 A2) (-C2));}
          s=s+q;
     }
     Joy_CHSH=abs(s/N);
     print(Joy_CHSH, "f");
     prompt();
}


And the result is,

Joy_CHSH = 2.828427

So it comes out the same as taking the shortcut.

Code: Select all

function getRandomLambda()
{
     if( rand()>0.5)
{
     return 1;
}
     else
{
     return -1;
}
}

function getVector1(idx)
{
     step1=0.025*2*pi; //step size is taken 1/20 of pi
     angle1=idx*step1;
     v1=sin(angle1)*e1+cos(angle1)*e2+0.00001*e3;
     return v1;
}
function getVector2(idx)
{
     step2=0.025*2*pi; //step size is taken 1/20 of pi
     angle2=idx*step2;
     v2=sin(angle2)*e1+cos(angle2)*e2+0.00001*e3;
     return v2;
}

     batch test()
{
     set_window_title("Test Joy Christian");
     N=20;
     I=e1^e2^e3;
     s[0]=0;
     s[1]=0;
     s[2]=0;
     s[3]=0;
     s[4]=0;
     s[5]=0;
     s[6]=0;
     s[7]=0;
     s[8]=0;
     s[9]=0;
     s[10]=0;
     s[11]=0;
     s[12]=0;
     s[13]=0;
     s[14]=0;
     s[15]=0;
     s[16]=0;
     s[17]=0;
     s[18]=0;
     s[19]=0;
     s[20]=0;
     s[21]=0;
     s[22]=0;
     s[23]=0;
     s[24]=0;
     s[25]=0;
     s[26]=0;
     s[27]=0;
     s[28]=0;
     s[29]=0;
     s[30]=0;
     s[31]=0;
     s[32]=0;
     s[33]=0;
     s[34]=0;
     s[35]=0;
     s[36]=0;
     s[37]=0;
     s[38]=0;
     s[39]=0;
     s[40]=0;
     
     a[0]=0;
     a[1]=0;
     a[2]=0;
     a[3]=0;
     a[4]=0;
     a[5]=0;
     a[6]=0;
     a[7]=0;
     a[8]=0;
     a[9]=0;
     a[10]=0;
     a[11]=0;
     a[12]=0;
     a[13]=0;
     a[14]=0;
     a[15]=0;
     a[16]=0;
     a[17]=0;
     a[18]=0;
     a[19]=0;
     a[20]=0;
     a[21]=0;
     a[22]=0;
     a[23]=0;
     a[24]=0;
     a[25]=0;
     a[26]=0;
     a[27]=0;
     a[28]=0;
     a[29]=0;
     a[30]=0;
     a[31]=0;
     a[32]=0;
     a[33]=0;
     a[34]=0;
     a[35]=0;
     a[36]=0;
     a[37]=0;
     a[38]=0;
     a[39]=0;
     a[40]=0;

     //Ax[0]=
     angleIx=0;
     for(oo=0;oo<41;oo=oo+1) //iteration over aa
     {
         aa=getVector1(oo);
         for(pp=0;pp<41;pp=pp+1) //iteration over bb
         {
             bb=getVector2(pp);
             angleIx=oo-pp;
             if(oo<pp)
{
     angleIx=pp-oo;
}
     //minus_cos_a_b=-1*(aa.bb);

     for(nn=0;nn<N;nn=nn+1) //perform the experiment N times
     {
         lambda=getRandomLambda(); //lambda is a fair coin, resulting in +1 or -1
         mu=lambda * I;
         C=-I.aa;  //C = {-a_j B_j}
         D=I.bb;   //D = {b_k B_k}
         E=mu.aa;  //E = {a_k B_k(L)}
         F=mu.bb;  //F = {b_j B_j(L)}
         A=C E;  //eq. (1) of arXiv:1103.1879, A(a, L) = {-a_j B_j}{a_k B_k(L)}
         B=F D;  //eq. (2) of arXiv:1103.1879, B(b, L) = {b_j B_j(L)}{b_k B_k}
         q=0;
         if(lambda==1) {q=((-C) A B (-D));} else {q=((-D) B A (-C));} //eq. (6)

         s[angleIx]=s[angleIx]+q; //

         a[angleIx]=a[angleIx]+1;

}
}
}
     for(oo=0;oo<41;oo=oo+1) //iteration over angle differences
     {
         st=s[oo];
         at=a[oo];
         //an=oo*10;
         mean_A_B=st/at;
         print(mean_A_B, "f"); //print the result
}

     prompt();

}

Code: Select all

mean_A_B = -1.000000
mean_A_B = -0.987688 + -0.000000*e2^e3 + 0.000000*e3^e1
mean_A_B = -0.951057 + 0.000000*e2^e3 + -0.000000*e3^e1 + -0.006735*e1^e2
mean_A_B = -0.891007 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.011350*e1^e2
mean_A_B = -0.809017 + 0.000000*e2^e3 + -0.000000*e3^e1 + 0.023035*e1^e2
mean_A_B = -0.707107 + 0.000000*e2^e3 + -0.000000*e3^e1 + -0.018660*e1^e2
mean_A_B = -0.587785 + 0.000000*e2^e3 + 0.000000*e3^e1 + -0.001156*e1^e2
mean_A_B = -0.453990 + -0.000000*e2^e3 + 0.000000*e3^e1 + -0.013103*e1^e2
mean_A_B = -0.309017 + 0.000000*e2^e3 + 0.000000*e3^e1 + 0.044671*e1^e2
mean_A_B = -0.156434 + 0.000000*e2^e3 + 0.000000*e3^e1 + 0.016976*e1^e2
mean_A_B = -0.000000 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.003226*e1^e2
mean_A_B = 0.156434 + 0.000000*e2^e3 + -0.000000*e3^e1 + -0.032923*e1^e2
mean_A_B = 0.309017 + 0.000000*e2^e3 + 0.000000*e3^e1
mean_A_B = 0.453990 + -0.000000*e2^e3 + -0.000000*e3^e1 + -0.004773*e1^e2
mean_A_B = 0.587785 + 0.000000*e2^e3 + -0.000000*e3^e1 + 0.017978*e1^e2
mean_A_B = 0.707107 + 0.000000*e2^e3 + 0.000001*e3^e1 + 0.027196*e1^e2
mean_A_B = 0.809017 + -0.000000*e2^e3 + 0.000000*e3^e1 + 0.010580*e1^e2
mean_A_B = 0.891007 + -0.000000*e2^e3 + -0.000000*e3^e1 + -0.008512*e1^e2
mean_A_B = 0.951057 + 0.000001*e2^e3 + 0.000000*e3^e1 + 0.008061*e1^e2
mean_A_B = 0.987688 + 0.000001*e2^e3 + -0.000000*e3^e1 + -0.003911*e1^e2
mean_A_B = 1.000000 + -0.000000*e2^e3 + -0.000000*e3^e1
mean_A_B = 0.987688 + -0.000000*e2^e3 + -0.000000*e3^e1 + -0.000391*e1^e2
mean_A_B = 0.951057 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.007319*e1^e2
mean_A_B = 0.891007 + -0.000000*e2^e3 + -0.000001*e3^e1 + 0.044138*e1^e2
mean_A_B = 0.809017 + -0.000001*e2^e3 + -0.000001*e3^e1 + 0.041491*e1^e2
mean_A_B = 0.707107 + -0.000000*e2^e3 + 0.000000*e3^e1 + -0.013258*e1^e2
mean_A_B = 0.587785 + 0.000000*e2^e3 + -0.000000*e3^e1 + 0.002697*e1^e2
mean_A_B = 0.453990 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.009546*e1^e2
mean_A_B = 0.309017 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.010974*e1^e2
mean_A_B = 0.156434 + 0.000000*e2^e3 + -0.000000*e3^e1 + 0.024692*e1^e2
mean_A_B = -0.000000 + 0.000000*e2^e3 + 0.000001*e3^e1 + -0.050000*e1^e2
mean_A_B = -0.156434 + -0.000001*e2^e3 + -0.000001*e3^e1 + 0.113584*e1^e2
mean_A_B = -0.309017 + -0.000000*e2^e3 + 0.000001*e3^e1 + -0.047553*e1^e2
mean_A_B = -0.453990 + -0.000000*e2^e3 + 0.000000*e3^e1 + -0.011138*e1^e2
mean_A_B = -0.587785 + 0.000000*e2^e3 + -0.000000*e3^e1 + 0.046230*e1^e2
mean_A_B = -0.707107 + -0.000000*e2^e3 + -0.000000*e3^e1 + 0.011785*e1^e2
mean_A_B = -0.809017 + 0.000000*e2^e3 + 0.000000*e3^e1 + -0.011756*e1^e2
mean_A_B = -0.891007 + -0.000000*e2^e3 + -0.000001*e3^e1 + 0.090798*e1^e2
mean_A_B = -0.951057 + 0.000000*e2^e3 + 0.000000*e3^e1 + -0.030902*e1^e2
mean_A_B = -0.987688 + -0.000000*e2^e3 + 0.000000*e3^e1 + -0.023465*e1^e2
mean_A_B = -1.000000

ajw wrote:But in the GAviewer code above the N is only the number of iterations in the most inner loop, and can be chosen any convenient value.

Code: Select all

for(nn=0;nn<N;nn=nn+1)
{
     Arr[nn]=....
}

Mikko wrote:

FrediFizzx wrote:

Code: Select all

...
     N=40;
...
     s[0]=0;
...
     s[40]=0;

     a[0]=0;
...
     a[40]=0;
...
     for(oo=0;oo<41;oo=oo+1) //iteration over aa
...


Why is N given the value 40 but s and a are given 41 values and the loop is repeated 41 times?

FrediFizzx wrote:

Code: Select all

...
     N=40;
...
     s[0]=0;
...
     s[40]=0;

     a[0]=0;
...
     a[40]=0;
...
     for(oo=0;oo<41;oo=oo+1) //iteration over aa
...


Joy Christian wrote:Hi Fred, Thanks for the new plot. It may be worthwhile to post the revised (or extended) code here (and also at Albert Jan's blog) ?

Code: Select all

function getRandomLambda()
{
     if( rand()>0.5)
{
     return 1;
}
     else
{
     return -1;
}
}

function getVector(idx)
{
     step=0.025*2*pi; //step size is taken 1/20 of pi
     angle=idx*step;
     v=sin(angle)*e1+cos(angle)*e2+0.0001*e3;
     return v;
}
     batch test()
{
     set_window_title("Test Joy Christian");
     N=40;
     I=e1^e2^e3;
     s[0]=0;
     s[1]=0;
     s[2]=0;
     s[3]=0;
     s[4]=0;
     s[5]=0;
     s[6]=0;
     s[7]=0;
     s[8]=0;
     s[9]=0;
     s[10]=0;
     s[11]=0;
     s[12]=0;
     s[13]=0;
     s[14]=0;
     s[15]=0;
     s[16]=0;
     s[17]=0;
     s[18]=0;
     s[19]=0;
     s[20]=0;
     s[21]=0;
     s[22]=0;
     s[23]=0;
     s[24]=0;
     s[25]=0;
     s[26]=0;
     s[27]=0;
     s[28]=0;
     s[29]=0;
     s[30]=0;
     s[31]=0;
     s[32]=0;
     s[33]=0;
     s[34]=0;
     s[35]=0;
     s[36]=0;
     s[37]=0;
     s[38]=0;
     s[39]=0;
     s[40]=0;

     a[0]=0;
     a[1]=0;
     a[2]=0;
     a[3]=0;
     a[4]=0;
     a[5]=0;
     a[6]=0;
     a[7]=0;
     a[8]=0;
     a[9]=0;
     a[10]=0;
     a[11]=0;
     a[12]=0;
     a[13]=0;
     a[14]=0;
     a[15]=0;
     a[16]=0;
     a[17]=0;
     a[18]=0;
     a[19]=0;
     a[20]=0;
     a[21]=0;
     a[22]=0;
     a[23]=0;
     a[24]=0;
     a[25]=0;
     a[26]=0;
     a[27]=0;
     a[28]=0;
     a[29]=0;
     a[30]=0;
     a[31]=0;
     a[32]=0;
     a[33]=0;
     a[34]=0;
     a[35]=0;
     a[36]=0;
     a[37]=0;
     a[38]=0;
     a[39]=0;
     a[40]=0;

     //Ax[0]=
     angleIx=0;
     for(oo=0;oo<41;oo=oo+1) //iteration over aa
     {
         aa=getVector(oo);
         for(pp=0;pp<41;pp=pp+1) //iteration over bb
         {
             bb=getVector(pp);
             angleIx=oo-pp;
             if(oo<pp)
{
     angleIx=pp-oo;
}
     //minus_cos_a_b=-1*(aa.bb);

     for(nn=0;nn<N;nn=nn+1) //perform the experiment N times
     {
         lambda=getRandomLambda(); //lambda is a fair coin, resulting in +1 or -1

         v=I.aa ;
         w=I.bb;
         q=0;
         if(lambda==1)
     {
         q=v w;
     }
         else
     {
         q=w v;
     }

     s[angleIx]=s[angleIx]+q; //

     a[angleIx]=a[angleIx]+1;

}
}
}
     for(oo=0;oo<41;oo=oo+1) //iteration over angle differences
     {
         st=s[oo];
         at=a[oo];
         //an=oo*10;
         mean_mu_a_mu_b=st/at;
         print(mean_mu_a_mu_b, "f"); //print the result
}

     prompt();

}

Code: Select all

mean_mu_a_mu_b = -1.000000
mean_mu_a_mu_b = -0.987688 + 0.000000*e2^e3 + -0.000001*e3^e1 + -0.001858*e1^e2
mean_mu_a_mu_b = -0.951057 + -0.000000*e2^e3 + -0.000000*e3^e1 + -0.001387*e1^e2
mean_mu_a_mu_b = -0.891007 + -0.000001*e2^e3 + 0.000000*e3^e1 + 0.000299*e1^e2
mean_mu_a_mu_b = -0.809017 + 0.000001*e2^e3 + 0.000000*e3^e1 + -0.016680*e1^e2
mean_mu_a_mu_b = -0.707107 + 0.000000*e2^e3 + -0.000001*e3^e1 + 0.011294*e1^e2
mean_mu_a_mu_b = -0.587785 + -0.000003*e2^e3 + -0.000000*e3^e1 + 0.016180*e1^e2
mean_mu_a_mu_b = -0.453991 + -0.000001*e2^e3 + -0.000000*e3^e1 + -0.021620*e1^e2
mean_mu_a_mu_b = -0.309017 + -0.000000*e2^e3 + -0.000000*e3^e1 + -0.011528*e1^e2
mean_mu_a_mu_b = -0.156434 + -0.000000*e2^e3 + -0.000003*e3^e1 + -0.000772*e1^e2
mean_mu_a_mu_b = -0.000000 + 0.000002*e2^e3 + -0.000001*e3^e1 + -0.019355*e1^e2
mean_mu_a_mu_b = 0.156434 + 0.000005*e2^e3 + -0.000002*e3^e1 + -0.005762*e1^e2
mean_mu_a_mu_b = 0.309017 + -0.000002*e2^e3 + -0.000000*e3^e1 + -0.003280*e1^e2
mean_mu_a_mu_b = 0.453990 + -0.000002*e2^e3 + 0.000003*e3^e1 + 0.027048*e1^e2
mean_mu_a_mu_b = 0.587785 + -0.000002*e2^e3 + 0.000002*e3^e1 + 0.001498*e1^e2
mean_mu_a_mu_b = 0.707107 + 0.000001*e2^e3 + 0.000006*e3^e1 + 0.023797*e1^e2
mean_mu_a_mu_b = 0.809017 + 0.000000*e2^e3 + 0.000001*e3^e1 + 0.015282*e1^e2
mean_mu_a_mu_b = 0.891007 + -0.000002*e2^e3 + -0.000003*e3^e1 + -0.009931*e1^e2
mean_mu_a_mu_b = 0.951056 + 0.000002*e2^e3 + 0.000006*e3^e1 + 0.014443*e1^e2
mean_mu_a_mu_b = 0.987688 + 0.000003*e2^e3 + 0.000002*e3^e1 + 0.003555*e1^e2
mean_mu_a_mu_b = 1.000000 + -0.000004*e2^e3 + -0.000002*e3^e1
mean_mu_a_mu_b = 0.987688 + 0.000002*e2^e3 + -0.000002*e3^e1 + 0.001760*e1^e2
mean_mu_a_mu_b = 0.951056 + -0.000004*e2^e3 + 0.000002*e3^e1 + -0.001220*e1^e2
mean_mu_a_mu_b = 0.891007 + -0.000005*e2^e3 + 0.000004*e3^e1 + -0.009458*e1^e2
mean_mu_a_mu_b = 0.809017 + -0.000005*e2^e3 + 0.000001*e3^e1 + -0.001729*e1^e2
mean_mu_a_mu_b = 0.707107 + 0.000000*e2^e3 + -0.000003*e3^e1 + 0.012153*e1^e2
mean_mu_a_mu_b = 0.587785 + 0.000003*e2^e3 + -0.000003*e3^e1 + 0.018877*e1^e2
mean_mu_a_mu_b = 0.453990 + 0.000003*e2^e3 + -0.000004*e3^e1 + 0.028639*e1^e2
mean_mu_a_mu_b = 0.309017 + -0.000006*e2^e3 + -0.000004*e3^e1 + 0.031092*e1^e2
mean_mu_a_mu_b = 0.156434 + -0.000000*e2^e3 + 0.000009*e3^e1 + -0.059673*e1^e2
mean_mu_a_mu_b = -0.000000 + 0.000003*e2^e3 + -0.000001*e3^e1 + 0.004545*e1^e2
mean_mu_a_mu_b = -0.156434 + 0.000001*e2^e3 + 0.000002*e3^e1 + -0.014815*e1^e2
mean_mu_a_mu_b = -0.309017 + 0.000001*e2^e3 + 0.000003*e3^e1 + -0.029060*e1^e2
mean_mu_a_mu_b = -0.453991 + 0.000001*e2^e3 + 0.000006*e3^e1 + -0.055688*e1^e2
mean_mu_a_mu_b = -0.587785 + -0.000000*e2^e3 + 0.000003*e3^e1 + -0.031783*e1^e2
mean_mu_a_mu_b = -0.707107 + -0.000002*e2^e3 + 0.000001*e3^e1 + -0.011785*e1^e2
mean_mu_a_mu_b = -0.809017 + -0.000000*e2^e3 + -0.000000*e3^e1
mean_mu_a_mu_b = -0.891007 + -0.000001*e2^e3 + 0.000002*e3^e1 + -0.017025*e1^e2
mean_mu_a_mu_b = -0.951057 + -0.000000*e2^e3 + 0.000000*e3^e1
mean_mu_a_mu_b = -0.987688 + 0.000000*e2^e3 + -0.000000*e3^e1 + 0.001955*e1^e2
mean_mu_a_mu_b = -1.000000

Gordon Watson wrote:

FrediFizzx wrote:Hi Gordon,

In a typical EPRB experiment with photons, I doubt very much that they could get the polarizers for A and B detection aligned perfectly perpendicular to the axis of propagation. Sorry, they aren't actually in the same plane so my terminology there wasn't good but hopefully most people would understand what I mean.

We have found via doing these simulations with GAViewer that the perfect correlation happens if the a and b vectors are perfectly aligned perpendicular to the propagation axis. Which is a good thing because it is definitely easier to work with them being 2D instead of 3D.

Given EPRB as per the topic heading (and with its spin-half particles or with the photonic variant), the state is spherically-symmetric.

So the detector settings a and b can be widely varied over 3-space and certainly neither need be anywhere near orthogonal to the line of flight: yet (under all variants) the Expectation remains as E(a, b) = cos 2s (π ± (a,b)) where s denotes the relevant intrinsic spin and (a,b) denotes the angle between the detector settings.

I'd welcome your comment; me now wondering about the strength of the model being used and/or the versatility of the GA Viewer?

Specifically, I'm presuming that Joy's model does not require that orthogonality?

With my thanks again; Gordon
...

FrediFizzx wrote:

Gordon Watson wrote:Fred, this sentence has me confused: "And this is like it would be in a typical experiment; they can never get those vectors to be perfectly in the same 2D plane."

Could you elaborate please: What is the niggle that arises, in the model and in practice, with respect to the two detector settings; a (set by Alice) and b (set by Bob)?

Hi Gordon,

In a typical EPRB experiment with photons, I doubt very much that they could get the polarizers for A and B detection aligned perfectly perpendicular to the axis of propagation. Sorry, they aren't actually in the same plane so my terminology there wasn't good but hopefully most people would understand what I mean.

We have found via doing these simulations with GAViewer that the perfect correlation happens if the a and b vectors are perfectly aligned perpendicular to the propagation axis. Which is a good thing because it is definitely easier to work with them being 2D instead of 3D.

Gordon Watson wrote:Fred, this sentence has me confused: "And this is like it would be in a typical experiment; they can never get those vectors to be perfectly in the same 2D plane."

Could you elaborate please: What is the niggle that arises, in the model and in practice, with respect to the two detector settings; a (set by Alice) and b (set by Bob)?

Joy Christian wrote:Here is a link to the original simulations by Albert Jan and Fred, for those who are unaware of the history: http://challengingbell.blogspot.co.uk/2 ... f-joy.html.

Sadly, the revolution actually happened way back in 2007, but the physics community has yet to catch up: http://arxiv.org/find/all/1/au:+Christi ... /0/all/0/1.

Code: Select all

mean_mu_a_mu_b = -1.000000
mean_mu_a_mu_b = -0.951057 + 0.000000*e2^e3 + 0.000000*e3^e1 + -0.012361*e1^e2
mean_mu_a_mu_b = -0.809017 + 0.000000*e2^e3 + 0.000001*e3^e1 + -0.021037*e1^e2
mean_mu_a_mu_b = -0.587785 + 0.000002*e2^e3 + 0.000001*e3^e1 + 0.005393*e1^e2
mean_mu_a_mu_b = -0.309017 + 0.000001*e2^e3 + -0.000001*e3^e1 + 0.008392*e1^e2
mean_mu_a_mu_b = -0.000000 + 0.000002*e2^e3 + 0.000004*e3^e1 + 0.023125*e1^e2
mean_mu_a_mu_b = 0.309017 + -0.000001*e2^e3 + 0.000002*e3^e1 + 0.003804*e1^e2
mean_mu_a_mu_b = 0.587785 + 0.000002*e2^e3 + -0.000003*e3^e1 + -0.013291*e1^e2
mean_mu_a_mu_b = 0.809017 + -0.000006*e2^e3 + -0.000002*e3^e1 + -0.006782*e1^e2
mean_mu_a_mu_b = 0.951056 + -0.000004*e2^e3 + 0.000001*e3^e1 + -0.002060*e1^e2
mean_mu_a_mu_b = 1.000000 + 0.000001*e2^e3 + 0.000001*e3^e1
mean_mu_a_mu_b = 0.951056 + -0.000000*e2^e3 + 0.000002*e3^e1 + -0.003399*e1^e2
mean_mu_a_mu_b = 0.809017 + 0.000001*e2^e3 + 0.000002*e3^e1 + -0.012409*e1^e2
mean_mu_a_mu_b = 0.587785 + -0.000004*e2^e3 + -0.000000*e3^e1 + 0.003034*e1^e2
mean_mu_a_mu_b = 0.309017 + -0.000003*e2^e3 + 0.000002*e3^e1 + -0.012228*e1^e2
mean_mu_a_mu_b = -0.000000 + 0.000002*e2^e3 + -0.000003*e3^e1 + 0.018333*e1^e2
mean_mu_a_mu_b = -0.309017 + 0.000001*e2^e3 + -0.000003*e3^e1 + 0.024727*e1^e2
mean_mu_a_mu_b = -0.587785 + -0.000001*e2^e3 + -0.000004*e3^e1 + 0.034383*e1^e2
mean_mu_a_mu_b = -0.809017 + -0.000001*e2^e3 + -0.000000*e3^e1 + 0.003919*e1^e2
mean_mu_a_mu_b = -0.951057 + -0.000000*e2^e3 + -0.000002*e3^e1 + 0.023176*e1^e2
mean_mu_a_mu_b = -1.000000


Code: Select all

function getRandomLambda()
{
     if( rand()>0.5)
{
     return 1;
}
     else
{
     return -1;
}
}

function getVector(idx)
{
     step=0.05*2*pi; //step size is taken 1/10 of pi
     angle=idx*step;
     v=sin(angle)*e1+cos(angle)*e2+0.01*e3;
     return v;
}
     batch test()
{
     set_window_title("Test Joy Christian");
     N=100;
     I=e1^e2^e3;
     s[0]=0;
     s[1]=0;
     s[2]=0;
     s[3]=0;
     s[4]=0;
     s[5]=0;
     s[6]=0;
     s[7]=0;
     s[8]=0;
     s[9]=0;
     s[10]=0;
     s[11]=0;
     s[12]=0;
     s[13]=0;
     s[14]=0;
     s[15]=0;
     s[16]=0;
     s[17]=0;
     s[18]=0;
     s[19]=0;
     s[20]=0;
     a[0]=0;
     a[1]=0;
     a[2]=0;
     a[3]=0;
     a[4]=0;
     a[5]=0;
     a[6]=0;
     a[7]=0;
     a[8]=0;
     a[9]=0;
     a[10]=0;
     a[11]=0;
     a[12]=0;
     a[13]=0;
     a[14]=0;
     a[15]=0;
     a[16]=0;
     a[17]=0;
     a[18]=0;
     a[19]=0;
     a[20]=0;

     //Ax[0]=
     angleIx=0;
     for(oo=0;oo<21;oo=oo+1) //iteration over aa
     {
         aa=getVector(oo);
         for(pp=0;pp<21;pp=pp+1) //iteration over bb
         {
             bb=getVector(pp);
             angleIx=oo-pp;
             if(oo<pp)
         {
         angleIx=pp-oo;
}
     minus_cos_a_b=-1*(aa.bb);

     for(nn=0;nn<N;nn=nn+1) //perform the experiment N times
     {
         lambda=getRandomLambda(); //lambda is a fair coin, resulting in +1 or -1

         v=I.aa ;
         w=I.bb;
         q=0;
         if(lambda==1)
     {
         q=v w;
     }
         else
     {
         q=w v;
     }

     s[angleIx]=s[angleIx]+q; //

     a[angleIx]=a[angleIx]+1;

}
}
}
     for(oo=0;oo<21;oo=oo+1) //iteration over angle differences
     {
         st=s[oo];
         at=a[oo];
         an=oo*10;
         mean_mu_a_mu_b=st/at;
         print(mean_mu_a_mu_b, "f"); //print the result
}

     prompt();

}

Code: Select all

mean_mu_a_mu_b = -1.000100
mean_mu_a_mu_b = -0.951156 + -0.000000*e2^e3 + 0.000033*e3^e1 + -0.001545*e1^e2
mean_mu_a_mu_b = -0.809117 + 0.000122*e2^e3 + -0.000017*e3^e1 + -0.006497*e1^e2
mean_mu_a_mu_b = -0.587885 + -0.000117*e2^e3 + -0.000030*e3^e1 + -0.000899*e1^e2
mean_mu_a_mu_b = -0.309117 + -0.000069*e2^e3 + -0.000061*e3^e1 + -0.010629*e1^e2
mean_mu_a_mu_b = -0.000100 + -0.000142*e2^e3 + -0.000047*e3^e1 + 0.004375*e1^e2
mean_mu_a_mu_b = 0.308917 + -0.000001*e2^e3 + -0.000022*e3^e1 + -0.024093*e1^e2
mean_mu_a_mu_b = 0.587685 + 0.000120*e2^e3 + 0.000035*e3^e1 + 0.023693*e1^e2
mean_mu_a_mu_b = 0.808917 + 0.000229*e2^e3 + -0.000086*e3^e1 + -0.004521*e1^e2
mean_mu_a_mu_b = 0.950957 + 0.000336*e2^e3 + 0.000095*e3^e1 + 0.002833*e1^e2
mean_mu_a_mu_b = 0.999900 + -0.000208*e2^e3 + 0.000145*e3^e1
mean_mu_a_mu_b = 0.950957 + 0.000022*e2^e3 + 0.000119*e3^e1 + -0.001236*e1^e2
mean_mu_a_mu_b = 0.808917 + 0.000221*e2^e3 + 0.000159*e3^e1 + -0.009796*e1^e2
mean_mu_a_mu_b = 0.587685 + 0.000267*e2^e3 + -0.000048*e3^e1 + -0.002023*e1^e2
mean_mu_a_mu_b = 0.308917 + 0.000447*e2^e3 + 0.000445*e3^e1 + -0.032608*e1^e2
mean_mu_a_mu_b = -0.000100 + -0.000034*e2^e3 + 0.000183*e3^e1 + -0.025000*e1^e2
mean_mu_a_mu_b = -0.309117 + 0.000211*e2^e3 + 0.000046*e3^e1 + -0.005706*e1^e2
mean_mu_a_mu_b = -0.587885 + 0.000083*e2^e3 + 0.000857*e3^e1 + -0.080902*e1^e2
mean_mu_a_mu_b = -0.809117 + 0.000045*e2^e3 + -0.000061*e3^e1 + 0.005878*e1^e2
mean_mu_a_mu_b = -0.951156 + -0.000034*e2^e3 + -0.000155*e3^e1 + 0.015451*e1^e2
mean_mu_a_mu_b = -1.000100