## New 3-Sphere 3D Vectors 2-Particle Simulation

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### New 3-Sphere 3D Vectors 2-Particle Simulation

Here is a different product calculation simulation of Joy's 3-sphere model that is in his new paper.

Code: Select all
//Adaptation of Albert Jan Wonnink's GAViewer code for the S^3 model of the singlet correlations

function getRandomLambda()
{
if( rand()>0.5) {return 1;} else {return -1;}
}
function getRandomUnitVector() //unit vectors uniformly distributed over S^2
//http://mathworld.wolfram.com/SpherePointPicking.html
{
v=randGaussStd()*e1+randGaussStd()*e2+ randGaussStd()*e3; //three-dimensional vectors
return normalize(v);
}
batch test()
{
set_window_title("Test of 3D S^3 GA Model for the 2-particle singlet correlations");
default_model(p3ga);                   //choice of the model in GAViewer
N=10000;                               //number of iterations (trials)
I=e1^e2^e3;                            //the fundamental trivector of GA
ss=0;
t=0;
u=0;
for(nn=0;nn<N;nn=nn+1)                 //perform the EPR-Bohm experiment N times
{
a=getRandomUnitVector();
Da=I a;                         //detector bivector of Alice as in Eq.(30)
b=getRandomUnitVector();
Db=I b;                         //detector bivector of Bob as in Eq.(31)
s1=getRandomUnitVector();
s2=s1;                          //conservation of zero spin as in Eq.(43)
Ls1=I s1;                       //bivector representing spin of particle 1
Ls2=I s2;                       //bivector representing spin of particle 2
lambda=getRandomLambda();       //lambda is a fair coin, giving the +1 or -1 choice
A=(-Da*lambda*Ls1);             //Alice's measurement function as in Eq.(30)
B=(lambda*Ls2*Db);              //Bob's measurement function as in Eq.(31)
//Note that the limits on A and B are not required because of the conservation of
//spin, s2=s1, is imposed which reduces the product -Ls1*Ls2 in A*B to unity.
q=0;
if(lambda==1) {q=A B;} else {q=B A;} //shuffles the alternative orientations of S^3
ss=ss+q;
phi_a=atan2(scalar(Da/(e3^e1)), scalar(Da/(e2^e3)));  //gets azimuthal angle for a
phi_b=atan2(scalar(Db/(e2^e3)), scalar(Db/(e3^e1)));  //gets -azimuthal angle for b
print(neg_adotb, "f");             //outputs -a.b event by event
if(phi_a*phi_b>0) {eta_ab=acos(a.b)*180/pi;} else {eta_ab=-acos(a.b)*180/pi+360;}
print(eta_ab, "f");                //output the angles eta_ab event by event
print(correlation=scalar(q), "f"); //output the correlations; cf. Ref.[22] & Fig. 6
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();
}

Typical output is,

Code: Select all
eta_ab = 269.385742
correlation = 0.010721
eta_ab = 234.156906
correlation = 0.585568
eta_ab = 79.837830
correlation = -0.176435
eta_ab = 137.769531
correlation = 0.740447
eta_ab = 110.500862
correlation = 0.350221
eta_ab = 198.287735
correlation = 0.949493
eta_ab = 108.287560
correlation = 0.313786
eta_ab = 64.972549
correlation = -0.423052
eta_ab = 228.615097
correlation = 0.661114
eta_ab = 257.695618
correlation = 0.213105
eta_ab = 294.933502
correlation = -0.421566
eta_ab = 85.867928
correlation = -0.072056
eta_ab = 286.139557
correlation = -0.277978
eta_ab = 104.293915
correlation = 0.246896
mean = 0.001890 + 0.013989*e2^e3 + -0.004283*e3^e1 + -0.006126*e1^e2
aveA = 0.006420 + 0.007764*e2^e3 + 0.000817*e3^e1 + -0.000506*e1^e2
aveB = -0.005920 + -0.004768*e2^e3 + 0.001920*e3^e1 + 0.010372*e1^e2

And here is the plot of the data.

The plot of the data is very simple. The x axis is $\eta_{ab}$ with the negative angles from -180 to 0 shifted to +180 to +360. The y axis is simply the correlation value at that angle.

Here is a link to the raw GAViewer data for 25K trials as a .csv file (about 500K file size). The first column is the angle and the second column is the correlation value at that angle.

EPRsims/newjoyGA3D25k2.csv
.
FrediFizzx
Independent Physics Researcher

Posts: 1741
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

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

***
Thank you, Fred.

I have revised my paper, adding a reference to this thread: https://arxiv.org/abs/1911.11578.

***
Joy Christian
Research Physicist

Posts: 2200
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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

Joy Christian wrote:***
Thank you, Fred.

I have revised my paper, adding a reference to this thread: https://arxiv.org/abs/1911.11578.

***

You're welcome. Thanks for the acknowledgement.

Some people seem to think this is supposed to be a simulation of an experiment. It is merely verification of the theoretical product calculation via the computer program GAViewer. Bell's junk physics theory is shot down by it.
.
FrediFizzx
Independent Physics Researcher

Posts: 1741
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

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

FrediFizzx wrote:
Joy Christian wrote:***
Thank you, Fred.

I have revised my paper, adding a reference to this thread: https://arxiv.org/abs/1911.11578.

***

You're welcome. Thanks for the acknowledgement.

Some people seem to think this is supposed to be a simulation of an experiment. It is merely verification of the theoretical product calculation via the computer program GAViewer. Bell's junk physics theory is shot down by it.

Yeah, even though this is explicitly stated in my paper: "Although the above analytical derivation of the singlet correlations speaks for itself, it can be further verified by an event-by-event numerical simulation."

***
Joy Christian
Research Physicist

Posts: 2200
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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

FrediFizzx wrote:
Some people seem to think this is supposed to be a simulation of an experiment. It is merely verification of the theoretical product calculation via the computer program GAViewer. Bell's junk physics theory is shot down by it.

By the way, it is important to remember that quantum mechanics does not predict individual outcomes for the EPR-Bohm experiments. Neither do we observe individual outcomes in the actual Bell-test experiments. What is observed in all such experiments are "coincident counts" between the outcomes A and B, observed by Alice and Bob at their respective remote stations. Theoretically, this amounts to measuring the product, AB, of these outcomes, not A and B individually. Let me repeat this: What is observed in the experiments, by necessity, are the products, AB, in coincident counts. And since quantum mechanics does not predict individual outcomes either, it is absolutely scandalous to demand the predictions of individual outcomes from a local-realistic counterpart of quantum mechanics. A local-realistic theory is supposed to predict only that which is predicted by quantum mechanics and observed in the experiments. Therefore, Bell-believers have no right to demand an iota more than what is predicted by quantum mechanics and observed in the experiments. To be sure, the outcomes A and B must be either +1 or -1, for that is indeed observed by Alice by herself and Bob by himself. And these outcomes must average out to zero, for that is also observed by both. And, of course, the average of the product AB must work out to be -a.b. But that is all that should be demanded from any local-realistic theory. Any other additional demand is unjustified, unphysical, irrational, and scandalous.

***
Joy Christian
Research Physicist

Posts: 2200
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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

Joy Christian wrote:
FrediFizzx wrote:
Some people seem to think this is supposed to be a simulation of an experiment. It is merely verification of the theoretical product calculation via the computer program GAViewer. Bell's junk physics theory is shot down by it.

By the way, it is important to remember that quantum mechanics does not predict individual outcomes for the EPR-Bohm experiments. Neither do we observe individual outcomes in the actual Bell-test experiments. What is observed in all such experiments are "coincident counts" between the outcomes A and B, observed by Alice and Bob at their respective remote stations. Theoretically, this amounts to measuring the product, AB, of these outcomes, not A and B individually. Let me repeat this: What is observed in the experiments, by necessity, are the products, AB, in coincident counts. And since quantum mechanics does not predict individual outcomes either, it is absolutely scandalous to demand the predictions of individual outcomes from a local-realistic counterpart of quantum mechanics. A local-realistic theory is supposed to predict only that which is predicted by quantum mechanics and observed in the experiments. Therefore, Bell-believers have no right to demand an iota more than what is predicted by quantum mechanics and observed in the experiments. To be sure, the outcomes A and B must be either +1 or -1, for that is indeed observed by Alice by herself and Bob by himself. And these outcomes must average out to zero, for that is also observed by both. And, of course, the average of the product AB must work out to be -a.b. But that is all that should be demanded from any local-realistic theory. Any other additional demand is unjustified, unphysical, irrational, and scandalous.

***

That is not entirely correct. What the experiments observe is clicks on detectors along with an accurate time stamp for each event. Depending on which detector clicks, they assign a +1 or -1 or sometimes 0 for the -1. There is no "coincident counts" until the data is all put together in post processing aligned with the time stamps. De Raedt had a big thing about the window selection for the timing a few years ago. He even did a QM simulation based on it.

Bell fans are free to demand whatever they want. But we already know that Bell's junk physics theory fails even without counter examples so any demands they make are indeed just junk physics.
.
FrediFizzx
Independent Physics Researcher

Posts: 1741
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

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

FrediFizzx wrote:
That is not entirely correct. What the experiments observe is clicks on detectors along with an accurate time stamp for each event. Depending on which detector clicks, they assign a +1 or -1 or sometimes 0 for the -1. There is no "coincident counts" until the data is all put together in post processing aligned with the time stamps. De Raedt had a big thing about the window selection for the timing a few years ago. He even did a QM simulation based on it.

Yes, I remember De Raedt and his coworkers exploiting the time window loophole to reproduce the cosine curve. So pre- or post-processing of the data depends on the time window that can never be exactly zero. But quantum mechanics does not predict individual outcomes for a given run of the experiment. It is a statistical theory.

***
Joy Christian
Research Physicist

Posts: 2200
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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

***
So local-realism is not ruled out by experiments. Only excessive and unphysical demands by Bell-believers from a local-realistic theory are ruled out by experiments.

***
Joy Christian
Research Physicist

Posts: 2200
Joined: Wed Feb 05, 2014 4:49 am
Location: Oxford, United Kingdom

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

Joy Christian wrote:***
So local-realism is not ruled out by experiments. Only excessive and unphysical demands by Bell-believers from a local-realistic theory are ruled out by experiments.

***

That is correct. All the experiments do is validate the predictions of quantum mechanics via an event by event basis. They have nothing really to do with Bell's junk physics theory even though every experimenter claims they do. Going along with the crowd I suppose.
.
FrediFizzx
Independent Physics Researcher

Posts: 1741
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA