Coming Soon!

[FrediFizzx]

.. Yes, you get near the original number of valid events. You first of all double the original number with two detectors each getting -1, nothing, or +1, but you have arranged that half are invalid. Very cunning. (nonsense deleted)

How did I arrange that half are invalid? I did no such thing. You just need to admit you are toast. Burnt toast!

You wrote your code. Are you telling me you have no idea what it does?

"I did no such thing". Apparently you are still having reading comprehension problems. I know exactly what the code does. The only thing I arranged was for it to produce the -cosine curve or extremely close to it.
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[gill1109]

.. Yes, you get near the original number of valid events. You first of all double the original number with two detectors each getting -1, nothing, or +1, but you have arranged that half are invalid. Very cunning. (nonsense deleted)

How did I arrange that half are invalid? I did no such thing. You just need to admit you are toast. Burnt toast!

You wrote your code. Are you telling me you have no idea what it does?

"I did no such thing". Apparently you are still having reading comprehension problems. I know exactly what the code does. The only thing I arranged was for it to produce the -cosine curve or extremely close to it.

Everybody knows exactly what your code does. Yes, of course, you got pretty close to the cosine curve. That was your aim. It's not difficult to get close to the cosine.

But you did not get it exactly and there are some weird oscillations in the results.

It's hard to get the cosine exactly (in the large "M" limit), and also very hard to arrange that the particle pair generating rate doesn't depend on the setting difference. You have quite some way still to go!

I now did M = 1 million at 1 degree intervals.
https://rpubs.com/gill1109/fred

[FrediFizzx]

@gill1109 Still doing that junky strawman. One thing we learned from Gull's junk is that it is not possible to get a continuous curve using +/-1's exactly. So, there is not going to be any exactly. But anyways you are finished. Time to admit defeat, get real, get over it and move onnnnnnnnnnn!
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[FrediFizzx]

Here is another way of doing the current simulation. I'm sending the 4 output streams to 2 analysis stations then putting those 2 results together. 20 million trials one degree resolution.





The deviations got real regular doing it this way. Total Events = 19 997 638

The Cloud,

https://www.wolframcloud.com/obj/fredif ... -forum2.nb

Direct files.

EPRsims/newCS-24-2hv-simp-forum2.pdf
EPRsims/newCS-24-2hv-simp-forum2.nb

Enjoy more of the same Bell theory and Gill theory killers!
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[FrediFizzx]

Ok Folks and you Bell fanatics, here is the quaternion version. Joy will have more to say about this later. 100 percent local and 100 percent NO loopholes. First the product calculation.



Perfect match to the -cosine curve as usual. Then the main plot at 1 million trials one degree resolution.



The Cloud,

https://www.wolframcloud.com/obj/fredif ... -forum1.nb

The direct files,

EPRsims/newCS-24-S3quat-prodcalc-forum1.pdf (Large File)
EPRsims/newCS-24-S3quat-prodcalc-forum1.nb

Enjoy the ultimate awesomeness that finishes off all you Bell fanatics for good!
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[gill1109]

Please add a plot of “sum2”. Let’s see your smile!

@John Reed: can you convert the quaternions back to 4-vectors? That would make it easier to write versions in other languages.

@gill1109 Still doing that junky strawman. One thing we learned from Gull's junk is that it is not possible to get a continuous curve using +/-1's exactly. So, there is not going to be any exactly.

I’m glad my efforts led to your progress.

[FrediFizzx]

:D Please add a plot of “sum2”. Let’s see your smile!

@John Reed: can you convert the quaternions back to 4-vectors? That would make it easier to write versions in other languages. ...

Quaternions aren't 4-vectors. They are a scalar plus a 3-vector. Don't know what you mean by plot of "sum2".
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[gill1109]

:D Please add a plot of “sum2”. Let’s see your smile!

@John Reed: can you convert the quaternions back to 4-vectors? That would make it easier to write versions in other languages. ...

Quaternions aren't 4-vectors. They are a scalar plus a 3-vector. Don't know what you mean by plot of "sum2".
.

Yes, quaternions are little packages containing four real numbers. See for instance:

Code: Select all

​​β0=Quaternion[1,0,0,0];​​β1=Quaternion[0,1,0,0];​​β2=Quaternion[0,0,1,0];​​β3=Quaternion[0,0,0,1];


One can define a quaternion by giving four real numbers as coordinates. You can pull out different components. Quaternion algebra is programmed in Mathematica, it is built up from the ordinary algebra of real numbers, using the famous rules discovered or invented by Hamilton.

Here’s where you define “sum2”. Your correlations are called “mean” and they are defined as sum1/sum2.

Code: Select all

mean=ConstantArray[0,trialDeg];​​
sum1=ConstantArray[0,trialDeg];​​
sum2=ConstantArray[0,trialDeg];
​​Do[sum1[[i]]=(nPP[[i]]+nNN[[i]]-nPN[[i]]-nNP[[i]]);​​
sum2[[i]]=nPP[[i]]+nPN[[i]]+nNP[[i]]+nNN[[i]]+0.0000001;​​
mean[[i]]=sum1[[i]]/sum2[[i]],{i,trialDeg}]


Later, you plot “mean”.

Code: Select all

simulation=ListPlot[mean,PlotMarkers{Automatic,Tiny}];


Please also plot sum2.

[FrediFizzx]

:D Please add a plot of “sum2”. Let’s see your smile!

@John Reed: can you convert the quaternions back to 4-vectors? That would make it easier to write versions in other languages. ...

Quaternions aren't 4-vectors. They are a scalar plus a 3-vector. Don't know what you mean by plot of "sum2".
.

Yes, quaternions are little packages containing four real numbers. ...

No, quaternions are one real number and 3 imaginary numbers that may have real coefficients.

Code: Select all

In[767]:= c=RandomPoint[Sphere[]];
d=c.Qcoordinates;
FromQuaternion[d]
Out[769]= 0. +0.995364*I +0.0952991*J -0.0130214*K

See the I, J and K in there?
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[FrediFizzx]

Ok, here is a plot of sum2 along with a histogram of theta (a-b).



Looks like sum2 is just a function of (a - b).
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[gill1109]

Ok, here is a plot of sum2 along with a histogram of theta (a-b).
...
Looks like sum2 is just a function of (a - b).

Can you do the same with a = 0 fixed and b varying from 0 to 180 degrees, say at 1 degree intervals, with a fixed number of trials per value of b?
*Before* removal of "phantom observations", there would then be the *same* number of trials with each value of b - a, namely 2 * M trials.
I'm interested in the number of particle pairs after you have discarded virtual particle pairs, in a situation when the total number of initially created particle pairs (channel 1 and channel 2 combined), per value of b - a, is constant. It will oscillate about the value M. I showed it follows a "smile" shape, starting at about 60%, going down to about 40%, then going up to about 60% again. On average, about 50%. Thus: on average, about equal to M.

That was before you added some quaternionic stuff - which according to you yourself, hardly makes a difference.

[jreed]

:D Please add a plot of “sum2”. Let’s see your smile!

@John Reed: can you convert the quaternions back to 4-vectors? That would make it easier to write versions in other languages.

@gill1109 Still doing that junky strawman. One thing we learned from Gull's junk is that it is not possible to get a continuous curve using +/-1's exactly. So, there is not going to be any exactly.

I’m glad my efforts led to your progress.

Wonderful! We're back to quaternions again. Let me see if I can convert Fred's latest attempt to something you can use.

[FrediFizzx]

:D Please add a plot of “sum2”. Let’s see your smile!

@John Reed: can you convert the quaternions back to 4-vectors? That would make it easier to write versions in other languages.

@gill1109 Still doing that junky strawman. One thing we learned from Gull's junk is that it is not possible to get a continuous curve using +/-1's exactly. So, there is not going to be any exactly.

I’m glad my efforts led to your progress.

Wonderful! We're back to quaternions again. Let me see if I can convert Fred's latest attempt to something you can use.

Hold off. There is going to be another update COMING SOON.
.

[jreed]

@Richard
To convert quaternions to numbers, you can do the following:
If Q is a quaternion, the real part is given by Q[[1]], the i, j, k coefficients are given by Q[[2]], Q[[3]] and Q[[4]]

[FrediFizzx]

@Richard
To convert quaternions to numbers, you can do the following:
If Q is a quaternion, the real part is given by Q[[1]], the i, j, k coefficients are given by Q[[2]], Q[[3]] and Q[[4]]

Or for the real part Q[[1]] you can do Re[Q].
.

[gill1109]

@Richard
To convert quaternions to numbers, you can do the following:
If Q is a quaternion, the real part is given by Q[[1]], the i, j, k coefficients are given by Q[[2]], Q[[3]] and Q[[4]]

Or for the real part Q[[1]] you can do Re[Q].

I would like not only to see Fred's code with quaternions replaced by real 4-vectors, I'd like to see the functions from Mathematica's quaternion package which Fred uses replaced by more basic functions, so that I don't need to learn quite so much Mathematica in order to read the code and then to translate to (e.g.) R.

Oh well, it doesn't matter too much. Fred's code remains a moving target so I should wait for it to become stable. At least there has been a major improvement in readability: the code is relatively short and its structure is transparent.

[FrediFizzx]

@Richard
To convert quaternions to numbers, you can do the following:
If Q is a quaternion, the real part is given by Q[[1]], the i, j, k coefficients are given by Q[[2]], Q[[3]] and Q[[4]]

Or for the real part Q[[1]] you can do Re[Q].

I would like not only to see Fred's code with quaternions replaced by real 4-vectors, I'd like to see the functions from Mathematica's quaternion package which Fred uses replaced by more basic functions, so that I don't need to learn quite so much Mathematica in order to read the code and then to translate to (e.g.) R.

Just use the simple model. Re[Q] is the cosine. Q[[4]] is the sine when 2D. But there is a surprise coming soon that you won't be able to do in R most likely.
Doesn't really matter since your goose is cooked and cooked thoroughly done for quite some time now.
.

[jreed]

@Richard
To convert quaternions to numbers, you can do the following:
If Q is a quaternion, the real part is given by Q[[1]], the i, j, k coefficients are given by Q[[2]], Q[[3]] and Q[[4]]

Or for the real part Q[[1]] you can do Re[Q].

I would like not only to see Fred's code with quaternions replaced by real 4-vectors, I'd like to see the functions from Mathematica's quaternion package which Fred uses replaced by more basic functions, so that I don't need to learn quite so much Mathematica in order to read the code and then to translate to (e.g.) R.

Oh well, it doesn't matter too much. Fred's code remains a moving target so I should wait for it to become stable. At least there has been a major improvement in readability: the code is relatively short and its structure is transparent.

I would convert the code to one without quaternions, but as soon as I do that, Fred will have a new version. This is becoming tedious. This last version is just Fred's double detector version using the detector loophole, now made more complex with quaternions, which don't add anything except complexity. The lost detections are made less obvious since they now show up as { }, empty lists.

[FrediFizzx]

And here is the update to the latest quaternion version. It involves 3-sphere topology which will be explained in the updated paper. 2 million trials, one degree resolution.

Total Events = 1990970.



I took out the plot for the product calculation because it makes the PDF file too large with this many trials. Here is the Cloud file.

https://www.wolframcloud.com/obj/fredif ... -forum1.nb

And the direct files.

EPRsims/newCS-24-S3quat-forum1.pdf
EPRsims/newCS-24-S3quat-forum1.nb

Enjoy the super-duper ultimate Bell theory and Gill theory killer!
.

[jreed]

I will assume that this is a more-or-less final version. I should have a simpler version without quaternions for Richard ready in a few days. Fred probably won't be happy with it since it no longer has quaternions and is therefore not the 3 sphere topology model.