Classical Spheres, Division Algebras, and the Illusion of Quantum Non-locality:

Fred Diether

Here is the graph for the John Reed Mathematica version of Michel's simulation. For 10 million trials. You can see some slight deviations from the curve but that is just due to limitations imposed in the code such as rounding to 1 degree increments, etc.

Fred Diether

The graph can also be found here along with much discussion.

Fred Diether

Here is a link to an improved Mathematica version of Michel Fodje's simulation by John Reed. Click here

Here is a PDF file link for those that don't have Mathematica.

Click here

Here is a PDF File of the graph for output of 10 million trials.

Click here

Here is a link to Joy's proof that Michel's simulation works because of 3-sphere topology.

Click here

Looks like Joy's parallelized 3-sphere model works as advertised and explains quantum correlations.

Best,

Fred

James Putnam

Hi Fred,

This one doesn't work for me:

"Here is a PDF File of the graph for output of 10 million trials.

Click here"

James Putnam

[deleted]

Thanks very much, Fred, for these links.

I think one of your links is broken: this one.

Also worth mentioning here is that I have now been able to improve on Richard Gill's single S^2 version of Michel Fodje's simulation of my analytical model. Gill's simulation is off by 0.001 because Alice and Bob are not careful enough in his simulation to not end up detecting each other's particles in addition to their own. This has now been corrected and the simulation now matches with the (negative) cosine curve exactly. I will report on this latest version as soon as it is ready to be published.

Joy Christian

That was me above. I thought I was logged-in.

Fred Diether

Oops! Here is the link to the PDF file graph of the 10 million runs.

Click here

Best,

Fred

Richard Gill

The graph clearly shows the systematic deviation from the cosine curve!

Here is another illustration of the same.

http://rpubs.com/gill1109/JCS

No need to pay Wolfram Inc. for Mathematica.

R is free (both as in free beer, and as in free speech) and highly suited for this purpose.

http://www.r-project.org

Richard Gill

And another illustration of the systematic deviation from cosine

http://rpubs.com/gill1109/EPRB3opt

This is a simulation following the approach of Michel Fodje (who used Python). The other one I just mentioned

http://rpubs.com/gill1109/JCS

follows Chantal Roth (Java, later converted to Javascript for Joy's webside by Daniel Sabsay).

Richard Gill

Two images illustrating the systematic departure from cosine.Attachment #1: JCS.png Attachment #2: EPRB3opt2.png

Fred Diether

Those deviations are no big deal. Just due to limitations in the code from rounding to 1 degree increments, etc. Joy has already proven that the result of his local realistic parallelized 3-sphere model for the EPR-Bohm scenario is -a.b.

Richard Gill

The deviations are not due to rounding errors. Anyone who likes can check the code and decide for themselves. Joy himself has agreed that the simulation models are a bit off and need fixing.

Fred Diether

Yes, the deviations are due to rounding errors because we are only doing 1 degree increments. You can see what is going on in the attached jpegs for 1 million trials on the Mathematica output. When theta is small, we get the Bell straight line behavior. When theta is 0.3pi we see the output going to the cosine curve. Because of the rounding errors and some other limitations in the code, we can't quite make it all the way to the perfect cosine curve when theta is pi/2 or greater. See the previous linked graph for theta = pi/2.

With the proper sophistication in the computer program, we certainly could obtain the perfect cosine curve. And given that Joy has proven that Michel's program works due to 3-sphere geometry, we are pretty much done. Joy's local realistic parallelized 3-sphere model is in fact an explanation of quantum correlations.Attachment #1: Minkwe_Reed_EPRsim_theta_small.jpg Attachment #2: Minkwe_Reed_EPRsim_theta_medium.jpg

Richard Gill

This is not about rounding errors. The curves are computed to exquisite precision at a list of particular angles (difference between two measurement settings).

Fred Diether

Oh, and I forgot the web based JavaScript simulation that has just been improved.

Click here

Have fun!

Best,

Fred

Richard Gill

Yes, this is funny. The correlation computed in this script at exactly equal settings and exactly opposite settings is actually +/- 0.98, not +/- 1.0000000. However the graph is rescaled to have a maximum of +1 and a minimum of -1.

For an honest simulation see

http://rpubs.com/gill1109/JCS

Fred Diether

Where do you see that scaling? Daniel said it was fixed.

Richard Gill

The rescaling was plain to see in the javascript code of the last version. Chantal Roth has moreover confirmed that my R port of her JCS and JCS2 Java packages is completely correct. She disapproves of Daniel's cosmetic fix, which is not part of her code nor part of Joy's model.

Richard Gill

The current version simply does not show us the vertical scale! That's a another way to deceive the reader.

http://libertesphilosophica.info/eprsim/EPR_3-sphere_simulation5M.html

http://libertesphilosophica.info/eprsim/eprsim.txt

It's a discredit to Joy Christian that these items are on his webpage. Aside from the incredibly unprofessional simulation technique (is the sum of six uniform [0,1]'s exactly Gaussian? And what an incredible waste of time ... to pick a uniform random point on the sphere you only need to sample two uniforms.

Thomas Ray

" ... to pick a uniform random point on the sphere you only need to sample two uniforms."

On S^2. S^3 includes a simple pole at infinity that compactifies R^3, so those two points of S^2 have to swap signs randomly, because the real line has two poles at infinity (- oo, oo).

Richard, I think your arguments amount to accepting that it is impossible to get Bell's classical expectation - a.b. Because Joy has shown that the expectation works in the physical space of parallelized S^3, you have to deal honestly with the argument in the space in which it is formulated, and not with your own expectations for failure.

Tom

Thomas Ray

And by the way, unless I can be convinced otherwise, I think the vertical scaling issue is a red herring, since the framework promises coordinate free and scale independent measures. It shouldn't have to be rejiggerd to suit a particular requirement of scale, which would amount to a special case with artificial parameters. I think the demand for code corrections only reflects a prior bias toward a probabilisitic feature which Joy's model does not have.

Richard Gill

Tom, you are wildly off topic as usual.

If you want to show the world that you have reproduced the negative cosine prediction of the singlet state, but you leave off the vertical axis of the plot in order to hide the fact that you did not get perfect anti-correlation at equal settings but only correlation -0.98, you are a cheat.

Take a look at

http://rpubs.com/gill1109/JCS2

All the formulas in that code are taken from Joy's own description of how to simulate his model.

We are not talking about Christian's original S^3 model (whatever that is) but a derived version of it (Joy's derivation, not mine!) which can be expressed in S^2 terms. Implemented in Java code written by Chantal Roth, authorized by Joy; and another Javascript version written by Daniel Sabsay, authorized by Joy, proudly exhibited on his web page. My version is a port of Chantal's to R, and it has her blessing, at least.

The formulas in all these simulation experiments are taken from Joy's paper "Whither..." http://arxiv.org/abs/1301.1653 (appendix on simulation models). Cab is defined in formula (A27), Na and Nb are given by the expressions just after (A28) and (A29). The procedure generating an outcome +/-1 for the product of Alice and Bob's measurement, or 0 for "no state", with the help of an auxiliary randomization, is taken from Roth and Sabsay's code, but appears to me also to be a true reflection of Joy's own description. The numerical values of the "phase shifts" are taken from Joy's paper. Joy agrees that these are not quite spot on, yet.

Please note: I am not saying that the ommission of the vertical axis was done deliberately and with the purpose to deceive. I am not accusing any particular person of cheating.

Thomas Ray

"Tom, you are wildly off topic as usual."

Off your desired wildly inaccurate topic. Not off the true issues.

" ... you leave off the vertical axis of the plot in order to hide the fact that you did not get perfect anti-correlation at equal settings but only correlation -0.98, you are a cheat."

You still don't understand why the random variables must swap signs in the measurement space, which gives us perfect anti-correlation at every scale of measurement. A 2-dimension plot compromises the continuous function, but we have to live with until we have better methods.

"We are not talking about Christian's original S^3 model (whatever that is) but a derived version of it (Joy's derivation, not mine!) which can be expressed in S^2 terms."

Exactly.

"I am not accusing any particular person of cheating."

Understood.

Richard Gill

By the way, just to show that it is not necessary to fake or fudge, here is a simulation of a very similar model, which hits perfection.

http://rpubs.com/gill1109/Gisin2opt

Thomas Ray

Similar model, different measure space. Christian's framework in fact predicts that it should be trivial to correlate fixed and random values in the measure space of Bell's result -- Bell's error (choice of topology) is the whole point of Joy's program.

Try doing it with entirely random values; i.e., where the choice of direction is not fixed by dependence on the random variable, but the pair are independent, and let the continuous function make the choice. Then you should see why the result - a.b is the inevitable outcome of the topological structure.

Richard Gill

And here is a version of Chantal Roth's simulation (high numerical precision, large sample size)

http://rpubs.com/gill1109/JCS2opt

Richard Gill

Tom, if you think that Joy has got it all wrong, tell him. I am just programming his own instructions. I am doing it better than Chantal did, or Michel, or Daniel Sabsay. Higher numerical precision, higher statistical precision. Better tools.

Joy Christian

Neither Tom, nor anyone else, need to tell me anything. I can see what your are doing right, and I can see what you are doing wrong. It is my analytical model after all, so I can see the deficiencies in your attempts to simulate it far batter than you can.

Thomas Ray

Richard, before you injure your arm patting yourself on the back, please consider the dfference between a numerical simulation and the continuous function.

Richard Gill

"I can see what you are doing right, and I can see what you are doing wrong. It is my analytical model after all, so I can see the deficiencies in your attempts to simulate it far better than you can."

Splendid. I was just following instructions, Joy. Your completely unambiguous instructions, taken out of (a preview of?) the second edition of your book.

It is clear that the instructions need rewriting, you have said so yourself. I'm looking forward to seeing (and testing) the result.

Richard Gill

Fred, the deviation is not due to rounding. It is systematic. Joy can adjust phase shifts to get the curve closer to the cosine at some points, but then it will be off target at others.

Richard Gill

So far, the most accurate implementation of the Michel Fodje type simulation algorithm is http://rpubs.com/gill1109/EPRB3opt

Joy has agreed that phase shifts need to be introduced into the algorithm.

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