A Completelly Local and Realistic Simulation

[FrediFizzx]

I agree with you. In the version I'm using, all events are detected. I did 1,000,000 trials, and 835,710 went into the a detector, 164,290 into the ar detector. None are missing. It's not the detection loophole. I get similar results with lambda set at a constant 0.22. You may have discovered a new loophole, or maybe a disproof of Bell's theorem. It's very interesting.

Well, Bell's theory is already disproven. You did disproved it yourself with your quaternion simulation which I later enhanced to use 3D vectors and a quaternion singlet. This is a conspiracy loophole to Gill's theory. Upon further analysis when I set ar and br to 0 so that all of the constraint events are piling up at theta = 0 and cancelling out we of course get the nice negative cosine curve for 3 million events at one degree resolution,



Then when I set a and b to 0 so that all the non-constraint events are piling up at theta = 0 and cancelling out we get,



the straight lines. A possible conclusion from this is that when straight line events are mixed with the negative cosine events, you still end up with the negative cosine curve. I think we might need a math wizard for this.
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[jreed]

The first part, ar and br = 0 works as you said. This looks like the calculation using the detection loophole where events with 0 are dropped. For the second part, I had to use a and b generated by RandomInteger[{0,360}], do the test with lambda, then set a and b to zero for calculating A and B. This gives the usual classical result, straight lines.

[jreed]

I think I have the answer. I generated the classic triangle function using a Mathematica routine I wrote. Then I added this to a cosine function in the proportions I found for the detection loophole part (0.835) and the triangle part (0.165) that I got when I generated that cosine-like curve using your program. When this result is plotted on top of the cosine, it is difficult to find a difference between these curves. Those straight lines are in there, but in the proportions found by the program, can't be distinguished. What you have here is the detection loophole, but the missing events are not discarded, but hidden in the final result.

[FrediFizzx]

I think I have the answer. I generated the classic triangle function using a Mathematica routine I wrote. Then I added this to a cosine function in the proportions I found for the detection loophole part (0.835) and the triangle part (0.165) that I got when I generated that cosine-like curve using your program. When this result is plotted on top of the cosine, it is difficult to find a difference between these curves. Those straight lines are in there, but in the proportions found by the program, can't be distinguished. What you have here is the detection loophole, but the missing events are not discarded, but hidden in the final result.

So, the straight lines are being "washed out" by the overwhelming existance of the negative cosine curve. Sounds reasonable. Goes to what I have been saying about Nature somehow tricking the experimenters. Now, to figure out how to exploit this feature to go all the way so that it is not just a loophole. Keep working and thinking about it. You just might hit the grand prize jackpot.
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[gill1109]

I think I have the answer. I generated the classic triangle function using a Mathematica routine I wrote. Then I added this to a cosine function in the proportions I found for the detection loophole part (0.835) and the triangle part (0.165) that I got when I generated that cosine-like curve using your program. When this result is plotted on top of the cosine, it is difficult to find a difference between these curves. Those straight lines are in there, but in the proportions found by the program, can't be distinguished. What you have here is the detection loophole, but the missing events are not discarded, but hidden in the final result.

So, the straight lines are being "washed out" by the overwhelming existance of the negative cosine curve. Sounds reasonable. Goes to what I have been saying about Nature somehow tricking the experimenters. Now, to figure out how to exploit this feature to go all the way so that it is not just a loophole. Keep working and thinking about it. You just might hit the grand prize jackpot.

Indeed, if you can reproduce this feature while accepting Bell's constraints of a loophole-free experiment you will win a very big jackpot. I will also publicly eat my hat, resign from the Royal Dutch Academy of Sciences, and retract 20 highly cited papers. All textbooks in quantum physics will have to be rewritten. A whole lot of mathematics and computer science will have to be rewritten too. Whoever does it, will be the toast of the town! Academia will be in turmoil, all the quantum computing start-ups will collapse. It will be possible to perform Shor's algorithm extremely fast on a *classical* computer and internet security will collapse. The stock markets will collapse. Civilisation might even break down completely.

[FrediFizzx]

@gill1109 Yada! Yada! Yada! You should already be doing some of that since Bell's theoy is shot down. All you have left is Gill's theory which remains just a theory since you have no proof. Some day you will realize you are in denial.
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[FrediFizzx]

This conspiracy loophole to Gill's theory also works with 3D vectors and quaternions. It takes a really long time to run 1 million quaternion trials but it looks good enough at one degree resolution.



Here is a PDF of the Mathematia simulation along with the notebook file for those that might be interested.

EPRsims/prod_calc_quat-forum.pdf
EPRsims/prod_calc_quat-forum.nb

Enjoy!
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[FrediFizzx]

This conspiracy loophole to Gill's theory also works without the quaternions with 3D vectors. Apparently the real part of the quaternion multiplication is the same as the vector dot product so I've simplified the simulation. I also made the hidden variable, lambda, a function of the x and y coordinates of the singlet vector again. Here is 5 million events at one degree resolution,



Here is a PDF of the Mathematica simulation along with the notebook file in case anyone is interested.

EPRsims/prod_calc_quat-forum.pdf
EPRsims/prod_calc_quat-forum.nb

Enjoy!
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[gill1109]

This conspiracy loophole to Gill's theory also works without the quaternions with 3D vectors. Apparently the real part of the quaternion multiplication is the same as the vector dot product so I've simplified the simulation. I also made the hidden variable, lambda, a function of the x and y coordinates of the singlet vector again. Here is 5 million events at one degree resolution,

...

Enjoy!
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Yes. "The real part of the quaternion multiplication is the same as the vector dot product". That's exactly all there is to Joy Christian's models! No more and no less. https://www.math.leidenuniv.nl/~gill/IEEE_Access_paper-rev2.pdf. Fred, you are approaching the state of complete enlightenment.

[FrediFizzx]

@gill1109 More complete freakin' nonsense from the master of nonsense himself. This simulation model has absolutely nothing to do with Joy's GA model.
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[gill1109]

@gill1109 More complete freakin' nonsense from the master of nonsense himself. This simulation model has absolutely nothing to do with Joy's GA model.

I know. Unlike Joy’s model, your simulation model is quite interesting. You are learning, Fred!

You are the one who said "The real part of the quaternion multiplication is the same as the vector dot product"

[FrediFizzx]

@gill1109 Everything in GA is real. There is no imaginary junk to deal with. One wonders if you are every going to learn GA properly.
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[gill1109]

@gill1109 Everything in GA is real. There is no imaginary junk to deal with. One wonders if you are every going to learn GA properly.

I know everything in GA is real. What are you talking about? Complex numbers are pairs of real numbers. Quaternions are quadruples of real numbers. Standard GA is built on real 8-dimensional vectors.

[FrediFizzx]

@gill1109 Hmmm.... i, j and k are real numbers? I could have sworn that they are imaginary components.
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[gill1109]

@gill1109 Hmmm.... i, j and k are real numbers? I could have sworn that they are imaginary components.
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"i", "j", and "k" are names of the real vectors (0, 1, 0, 0), (0, 0, 1, 0) and (0, 0, 0, 1); "1" is the name of (1, 0, 0, 0).
https://en.wikipedia.org/wiki/Quaternion

[Joy Christian]

@gill1109 Hmmm.... i, j and k are real numbers? I could have sworn that they are imaginary components.
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"i", "j", and "k" are names of the real vectors (0, 1, 0, 0), (0, 0, 1, 0) and (0, 0, 0, 1); "1" is the name of (1, 0, 0, 0).
https://en.wikipedia.org/wiki/Quaternion

[FrediFizzx]

@gill1109 Hmmm.... i, j and k are real numbers? I could have sworn that they are imaginary components.
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"i", "j", and "k" are names of the real vectors (0, 1, 0, 0), (0, 0, 1, 0) and (0, 0, 0, 1); "1" is the name of (1, 0, 0, 0).
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Well..., he got one of them right. I sure would like to see how he gets those real vectors for i, j and k to square to -1.
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[gill1109]

@gill1109 Hmmm.... i, j and k are real numbers? I could have sworn that they are imaginary components.
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"i", "j", and "k" are names of the real vectors (0, 1, 0, 0), (0, 0, 1, 0) and (0, 0, 0, 1); "1" is the name of (1, 0, 0, 0).
...

Well..., he got one of them right. I sure would like to see how he gets those real vectors for i, j and k to square to -1.

By definition!

[FrediFizzx]

@gill1109 Ahh..., Of course..., make up your own rules as you go along! Plus you have a 4D vector vs. a 3D quaternion.
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[gill1109]

@gill1109 Ahh..., Of course..., make up your own rules as you go along! Plus you have a 4D vector vs. a 3D quaternion.

Those are not my rules, but Hamilton’s rules. Moreover, I am using standard terminology. Each quaternion is determined by four real parameters. A quaternion has a real part (1 real parameter) and a purely imaginary part (3 real parameters).