Various QRC simulations in one Mathematica file

[FrediFizzx]

This program by John Reed probably deserves its own topic so here it is.

Here is a link to a PDF file of the Mathematica notebook file after running it on my Mathematica. Probably easier to read.

download/Reed_Bell_EPR2.pdf

Thanks John for emailing me the notebook file. Let me know if anything is wrong in the PDF at the link. For those that have Mathematica, here is a link to the notebook file.

download/Reed_Bell_EPR.nb

Here is a link to the notePad.txt data file for those that might be interested in running the Physics Today section of John's Mathematica code.

download/notePad.txt

[FrediFizzx]

As in the original QRC program, E0 in the Analysis section is always equal to -1. So the CHSH part is kind of incomplete. I wonder if there is a way to improve that? However NE0 has to be 0 for the anti-correlation check at equal angles to be successful so the anti correlation check probably needs to be an independent process in order to get CHSH complete.

I am also wondering about the remove zero thing since I think the A and B values are 0 and 1?

[jreed]

As in the original QRC program, E0 in the Analysis section is always equal to -1. So the CHSH part is kind of incomplete. I wonder if there is a way to improve that? However NE0 has to be 0 for the anti-correlation check at equal angles to be successful so the anti correlation check probably needs to be an independent process in order to get CHSH complete.

I am also wondering about the remove zero thing since I think the A and B values are 0 and 1?

Sascha's method of generating observations includes only the results 0 and 1. If 1 is the observation of spin up, then 0 is the observation of spin down. There are no missing values, therefore removing these observations isn't possible.

Also, in the real experimental data, these observations aren't raw. The observations with one value missing must have been removed. Therefore it isn't possible to remove observations with one value missing or to see what the statistics would be with these in. I think that may be an important point.

I want to leave the routine that removes zero observations as it is. It's much clearer that way than the R statement:
length((A * B)[A & B]), which does the same thing. Without knowing the R language this is obscure for someone trying to understand what the program is doing. In addition, in the Mathematica version this routine can be applied as an option so the statistics with zero values present can also be calculated.

[Joy Christian]

Also, in the real experimental data, these observations aren't raw. The observations with one value missing must have been removed. Therefore it isn't possible to remove observations with one value missing or to see what the statistics would be with these in. I think that may be an important point.

It is an extremely important point as far as the experiments are concerned. A lot of post-processing of the experimental data goes on before the publication of the data, if the data is published by the authors at all. Basically they cheat. That is why I raised the issue in the other thread: viewtopic.php?f=6&t=188&start=30#p5242.

Also, how does anyone know that there was a particle but it was not detected? The so-called "event-ready detectors" do not help, because they either destroy or depolarize the particle emerging from the source before it reaches the detector. It is for these and many other experimental deficiencies that Clauser-Horne (CH) inequality was devised: viewtopic.php?f=6&t=186#p5013. As I point out in that thread, my R-code violates the CH inequality as well: http://rpubs.com/jjc/84238.

From purely theoretical point of view, there are simply no "zero outcomes" within my analytical 3-sphere model, as I have explained in the following threads:

viewtopic.php?f=6&t=188#p5129

viewtopic.php?f=6&t=188&start=20#p5238

viewtopic.php?f=6&t=188&start=20#p5240

viewtopic.php?f=6&t=181&start=80#p5230

[minkwe]

To me, the best approach is always to write the analysis code separately of a given model, and apply the same code to all the models, including experimental data. This appears to have been your intention, and is what I have done with epr-simple and epr-clocked. You can throw the experimental data as well as data from any other model at it directly without any fiddling. The same goal-post for everyone since I no longer trust experimenters to analyze their own data.

But your analysis part is overly complicated and probably wrong for some of the models because of the way you are doing the calculations.

The equation for calculating the expectation value is:


Note that there are no zero outcomes in this expression, therefore whether or not a model produces zeros, is completely irrelevant for it. If zeros are causing you problems, then you are going about it the wrong way. You should be calculating each of the paired coincidence counts and then from that calculating the Expectation value from that.

[Joy Christian]

In my notation

,

which is the same as what Michel has written above, and it produces exactly the same correlations as those with the R-function

, where .

In fact, I calculate the correlations in three different ways in this simulation to emphasize that the issue of "zero outcomes" is a non-issue.

[minkwe]

In my notation

,

which is the same as what Michel has written above, and it produces exactly the same correlations as those with the R-function

, where .

In fact, I calculate the correlations in three different ways in this simulation to emphasize that the issue of "zero outcomes" is a non-issue.

Yes Joy,
,

is the same, just different notation. However, John appears to be calculating

[Joy Christian]

However, John appears to be calculating

Interesting. I didn't catch that --- because I can't read Mathematica code well enough. What does it mean? It doesn't seem right.

[minkwe]

However, John appears to be calculating

Interesting. I didn't catch that --- because I can't read Mathematica code well enough. What does it mean? It doesn't seem right.

I think that is what he calls NU and NE mean in the mathematica code. He calls them "equal" "unequal".

[FrediFizzx]

However, John appears to be calculating

Interesting. I didn't catch that --- because I can't read Mathematica code well enough. What does it mean? It doesn't seem right.

I think that is what he calls NU and NE mean in the mathematica code. He calls them "equal" "unequal".

Yes. But it is the same as the other calculation for expectations.

[minkwe]

It is only the same for post-processed data. The previous one does not need any post-processing to calculate.

[FrediFizzx]

It is only the same for post-processed data. The previous one does not need any post-processing to calculate.

Actually QRC does (NE* - NU*)/N* when it should be (NE* - NU*)/(NE* + NU*). Doesn't seem to make any difference though. And since E0 always is equal to -1, it is kind of a lame formulation of "CHSH" anyways. This is just copied over from the original QRC. John had nothing to do with it.

[jreed]

To me, the best approach is always to write the analysis code separately of a given model, and apply the same code to all the models, including experimental data. This appears to have been your intention, and is what I have done with epr-simple and epr-clocked. You can throw the experimental data as well as data from any other model at it directly without any fiddling. The same goal-post for everyone since I no longer trust experimenters to analyze their own data.

But your analysis part is overly complicated and probably wrong for some of the models because of the way you are doing the calculations.

The equation for calculating the expectation value is:


Note that there are no zero outcomes in this expression, therefore whether or not a model produces zeros, is completely irrelevant for it. If zeros are causing you problems, then you are going about it the wrong way. You should be calculating each of the paired coincidence counts and then from that calculating the Expectation value from that.

The equation that is used in Sascha's program is E = (NE - NU)/(NE + NU).
That's equal to ((N++ + N--) - (N+- + N-+)/((N++ + N--) + (N+- + N-+)), provided that the zero events are removed. Now for those zero events, I could have called my routine removeZero detectionLoophole, because that's what it is. You can pass the data through this loophole three ways:

My way, remove them after they have been created by the event generator
Michel's way, don't allow them to be picked at all
Joy's way, use the R routine length((A*B)[A & B]) which gets rid of them by selecting products where A and B are non zero

All these will give equal results. Which is best? My method lets me see what effect removing zeros has, and therefore what effect the detection loophole has on the simulation.

[Joy Christian]

There have been a lot of noise and suspicion about the so-called "zero outcomes" in the simulations like mine discussed above and Michel's "EPR simple", so I have written up another simple version of my simulation to make it plain that there are simply no "zero outcomes" in these simulations: http://rpubs.com/jjc/105450.

The crucial point is that one can separate out the "event-ready preparation" of the initial states of the spin from the computation of the correlation, as I have done.

[Mikko]

Which is best?

Usually the best way to organize the simulation is to imitate the structure of the system to be simulated. Analysis of the results, if not part of the simulated system, should be performed separately at the end. So the key question is: what physical process does that computational operation represent? The removal or zeros in Dr. Christian's model does not by itself represent any physical process. It is a part of computation that represents creation of a pair of particles. There is no attempt to simulate the physical details of that process, for those details are irrelevant to the purpose of the simulation. What matters is the end result, the produced pairs of particles, and the removal of unphysical zeros as the last step in that computation makes that. Therefore, the best place to remove the zeros is at the end of the code fragment (block, function, paragraph, whatever) that represents the creation of the pairs.

[FrediFizzx]

The equation that is used in Sascha's program is E = (NE - NU)/(NE + NU).
That's equal to ((N++ + N--) - (N+- + N-+)/((N++ + N--) + (N+- + N-+)), provided that the zero events are removed. Now for those zero events, I could have called my routine removeZero detectionLoophole, because that's what it is. .... My method lets me see what effect removing zeros has, and therefore what effect the detection loophole has on the simulation.

Yes, for those that can't see what effects S^3 topology and geometry have on the states, you will think that removeZero is part of a detection "loophole". But if you realize that those "zeroes" are states that don't exist in the first place, it might help you understand what is going on in a S^3 Nature. It is definitely not easy to wrap your mind around it while thinking in a R^3 perspective with only a right handed basis perspective. :- )

Never the less, we have a local realistic S^3 model that does give the prediction of QM for the EPRB scenario, -a.b.
http://challengingbell.blogspot.com/201 ... f-joy.html

So which is right? A non-local model or a local model? A lot of people will jump via Occam's Razor to the non-local model since it is more simple to understand. But now you will have to explain "classical entanglement".

viewtopic.php?f=6&t=191

All of a sudden, the non-local model got way more complicated.

[Joy Christian]

"Detection loophole" can be invoked when there is a real or perceived mismatch between the initial states "e" and the measurement events A and B. But when there is exact match between the initial states "e" and the measurement events A and B (as in this simulation) then "detection loophole" type explanation is not even possible.

[Ben6993]

I did post ages ago that I would prefer the zeros in the simulation to be excluded before the data generation began so that a full set of 'good' pairs of data could be identified before the data were generated. My reason was to distance the removal of zeros from the simulation calculations so as to make it clear that the removal of zeros was not intended to be post hoc removal of unwanted real data but a prevention of unreal zeros creeping into the simulation generator. There was already a randomonasphere routine and I think (I can never find old posts using the forum search box as it usually tells me my words are too common!) that I suggested something like randomonanS3sphere for the 'good' data.

My other motive was that obtaining a good data set would enable it to be explored for its patterns. When I think of the zero data I usually have in mind the Thomson chaotic ball diagram but do not know if this pattern is borne out by the "good" data pairs which are presumably now available as a preset package. And if they are borne out, how broad are the bands on the chaotic R3 ball? Why are the bands not infinitesimal in breadth with infinitesimal numbers of zeros produced? Etc.

[minkwe]

Which is best?

Usually the best way to organize the simulation is to imitate the structure of the system to be simulated. Analysis of the results, if not part of the simulated system, should be performed separately at the end. So the key question is: what physical process does that computational operation represent? The removal or zeros in Dr. Christian's model does not by itself represent any physical process. It is a part of computation that represents creation of a pair of particles. There is no attempt to simulate the physical details of that process, for those details are irrelevant to the purpose of the simulation. What matters is the end result, the produced pairs of particles, and the removal of unphysical zeros as the last step in that computation makes that. Therefore, the best place to remove the zeros is at the end of the code fragment (block, function, paragraph, whatever) that represents the creation of the pairs.

Evidently you have never read any paper that reports empirical results of EPRB experiments, otherwise you would not make such a pronouncement. Real experimentalists face real challenges which theoreticians don't even dream about. For example how to you experimentally prepare a pair of particles in a spin 1/2 state. Just pondering this question should be humbling to those who do not have to think about experiments. In many cases post-processing is part of the preparation, and the preparation would be impossible without it. It is part of what allows them to know that the two particles they have left were indeed in the state they wanted. Another thing to keep in mind is the fact that experimentally, zero outcomes do not exist. How do you know that a particle was not detected. Detectors do not announce to you that a particle was not detected, they only tell you recorded events. So when you assume that the i-th particle at Alice belongs with the i-th particle at Bob, you are making an unphysical assumption. No experimenter can know that, at least for the experiments that have been done up to this point in time. Therefore it is quite humorous to me when people throw around the accusations of non-physical while trying to impose completely bogus unphysical requirements on simulations.

[jreed]

There have been a lot of noise and suspicion about the so-called "zero outcomes" in the simulations like mine discussed above and Michel's "EPR simple", so I have written up another simple version of my simulation to make it plain that there are simply no "zero outcomes" in these simulations: http://rpubs.com/jjc/105450.

The crucial point is that one can separate out the "event-ready preparation" of the initial states of the spin from the computation of the correlation, as I have done.

Here's what all the noise is about. When zero events are removed, the CHSH inequality must be modified. See the paper by Larsson: http://arxiv.org/abs/1407.0363. The CHSH equation is changed so that the <2 on the rhs is modified to something greater, for example <2.798796 for EPR Simple. This means that with the modified CHSH equation, your simulation and EPR simple no longer violate it.

I'm adding code into my simulation program to keep track of removed events so the CHSH inequality can be modified and applied correctly.