New simulations of detection and coincidence loophole models

[gill1109]

Apparently there was a problem naming two topics on this forum after simulation models created by one of the participants, and the topics are now closed. I hope that independently of where the ideas for the new simulations came from, we might still be able to discuss them on their own merits. So this new topic is devoted to the "new models" created by R. D. Gill which may or may not be a caricature of some models created by M. Fodje. But certainly, they were inspired by his beautiful programming and creative mathematics and theoretical insight.

So here I would like us to discuss Gill's R travesty of epr-simple, and Gill's R travesty of epr-clocked.

Here are the relevant starting points.

Inspired by https://github.com/minkwe/epr-simple I wrote the R script http://rpubs.com/gill1109/epr-simple
Some first comments and discussion can be found at the now locked topic
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=59

Inspired by https://github.com/minkwe/epr-clocked I wrote the R script http://rpubs.com/gill1109/epr-clocked
Some first comments and discussion can be found at the now locked topic
http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=60

The question I'd like to discuss here, is the following: can mathematics provide useful results concerning the performance limits of event-based local hidden variables simulation models of epr-b experiments?

One could consider this a topic in computer science or mathematical modelling, not in physics...

[gill1109]

I should mention two first striking findings of those simulations:

(1) up to statistical error, both simulation models did not violate appropriate (modified) CHSH bounds

(2) the statistical error in the Larsson modified CHSH and the Larsson-Gill modified CHSH (modified for detection and coincidence loophole respectively) is rather large.

One may wonder if it is the best inequality to use for those two situations. It certainly isn't (in either case) the only *appropriate* inequality and there are good reasons that the others could well be statistically better behaved.

[gill1109]

## Michel Fodje's "epr-clocked" coincidence loophole model
## Stripped down to essential core
##
## https://github.com/minkwe/epr-clocked

set.seed(-1) ## it took me a long time to find a seed
## which gave a violation of CHSH in one of these tests!

N <- 10^4

alpha <- c(0, 90) * pi / 180 # Alice's possible two settings
beta <- c(45, 135) * pi / 180 # Bob's possible two settings
a <- sample(c(1, 2), N, replace = TRUE) # Alice setting names (1, 2)
b <- sample(c(1, 2), N, replace = TRUE) # Bob setting names (1, 2)

coincWindow <- 0.0004
ts <- pi * 0.03
asym <- 0.98
spin <- 0.5
n <- 2 * spin
phase <- pi * n

el <- runif(N, 0, 2 * pi)
er <- el + phase
p <- 0.5 * sin(runif(N, 0, pi / 6))^2
ml <- runif(N, asym, 1)
mr <- runif(N, asym, 1)
Cl <- (0.5/pi) * (-1)^n * cos(n * (el - alpha[a]))
Cr <- (0.5/pi) * (-1)^n * cos(n * (er - beta[b]))
tdl <- ts * pmax(ml * p - abs(Cl), 0)
tdr <- ts * pmax(mr * p - abs(Cr), 0)
A <- sign(Cl)
B <- sign(Cr)

AB <- A * B

mean(AB[a == 1 & b == 1 & abs(tdl-tdr) < coincWindow])
mean(AB[a == 1 & b == 2 & abs(tdl-tdr) < coincWindow])
mean(AB[a == 2 & b == 1 & abs(tdl-tdr) < coincWindow])
mean(AB[a == 2 & b == 2 & abs(tdl-tdr) < coincWindow])

S <- - mean(AB[a == 1 & b == 1 & abs(tdl-tdr) < coincWindow]) +
mean(AB[a == 1 & b == 2 & abs(tdl-tdr) < coincWindow]) -
mean(AB[a == 2 & b == 1 & abs(tdl-tdr) < coincWindow]) -
mean(AB[a == 2 & b == 2 & abs(tdl-tdr) < coincWindow])

S ## CHSH

[gill1109]

The R script http://rpubs.com/gill1109/epr-clocked continues from there (the code in the last post) with experiments computing various *appropriate* CHSH inequalities, ie inequalities adapted to the actual design of the experiment. CHSH was invented for an experiment with delayed-choice settings, event-ready-detectors, no non-detections. Applying it in situations it wasn't designed for is a waste of time.

The results showed "compliance" (non-violation) every time (up to statistical error of course!), and confirmed that the adapted CHSH inequalities correctly tell us the performance limits of such a simulation model. What can you make it do, what can't you make it do.

Still to be done, is to add to the core R code the further features of Fodje's model which in first instance, for simplicity, I left out.

These are:

(1) the arrival time process (renewal process with beta distributed increments)
(2) random deletion of some particles
(3) procedure to pair events on both sides, which can no longer be paired simply by taking them in order.

These features add a small amount of local realistic noise to model so far and thereby cause a deterioration of the performance. Correlations will be slightly degraded, the detection rate (as defined appropriately for such an experiment) goes down slightly.

Thus I claim that the Larsson-Gill modified CHSH bound will apply also to the Fodje epr-clocked model. I shall test my claim in subsequent simulation experiments. By "apply" I mean that the bound will hold for sure in the limit of large N, and for finite N deviations will be "merely statistical" (not statistically significant). Deviation of the order of one or two standard errors is possible and can be common. Deviations of the order of many standard errors are perhaps possible, but highly unlikely.

Fodje considers the three just mentioned components of his model to be absolutely essential features. An experimentalist might consider them as bugs, ie they are imperfections which one would love to be able to get rid of (better apparatus? more delicate experimental tuning and control?). Obviously, in the real world one can never avoid them entirely.

We have to remember that all models are wrong, but some are useful. They're not called "models" for nothing. I claim that my simplified epr-clocked is a simplified model of Fodje's model; of course Fodje's model too can at best also only be a simplification of physical reality. The important question is: is my model fit for purpose? Well then we have to know what is the purpose. My purpose is to calculate performance limits of Fodje's model and to illustrate that it is possible by mathematical analysis of simulation models to say useful things about what they can do, and what they can't do. I think I have offered "proof of principle". And I have argued that the performance bounds which are evidently valid for the simplified model will also hold for the original model. The claim is easy to check.

[gill1109]

I have now completed the R coding of Michel Fodje's epr-clocked simulation model.

On Rpubs you can now find two forks of my original R script.

http://rpubs.com/gill1109/epr-clocked-core is just a copy of http://rpubs.com/gill1109/epr-clocked but the name is now better: this was only the heart of Fodje's simulation model.

http://rpubs.com/gill1109/epr-clocked-full is, I believe, a true R implementation of Fodje's complete model. ie with all bells and whistles added. Which might from some points of view be considered features, but from other points of views bugs, or more precisely: shortcomings or deficiencies. The experimenter would prefer these features not to be there, or only to be there to a smaller extent. He would certainly in principle be able to continually improve his experiment by reducing the imact of these features by improving experimental materials and procedures. In the real world they would never entirely go away but they might in principle eventually become negligable.

[gill1109]

Something worth noticing in the new "epr-clocked-full" R simulation: the results of the core-model (the simplified version) and the full-model were *identical*. This wouldn't always be the case. At very large N one would notice very small systematic differences. At small N one mostly sees 0 difference, but occasionally by chance one will see a difference caused by one particle pair being evaluated differently in the two situations.

[gill1109]

Here by the way is a summary of the findings with "epr-simple"

Just calculating CHSH in the usual way (we observe S = 2.77344) is actually not really appropriate, though to be sure it is what all the experimenters do. We performed a post-selection of particle pairs and did not take account of the fact that whether or not a particle gets detected might depend on the measurement setting as well as on the hidden variable carried in the particle. Thus our correlations were based on a biased sample.

Many modified Bell inequalities have been proposed ... cf Caroline Thompson's work.

Procedure 1: include non-detections as outcomes with value "0"
Result: 1.915096

Procedure 2, Clauser-Horne: compare outcomes "+1" to outcomes "-1" or "no detection"
Result: 1.888524

Procedure 3: the Larsson modifed CHSH bound.
We need to calculate the observed experimental efficiency -
the minimal probability Alice has an outcome given Bob does and vice versa

It turns out to be gamma = 0.8193422

Knowing gamma, we calculate the modified CHSH upper-bound

We find 2 + delta = 2.881965, larger than our previously observed value of S = 2.77344

We could go on from here and look at all the other generalized Bell inequalities (yet more versions of CHSH got by reducing the number of outcomes from 3 to 2 possibly depending on the settings and the party; and the CGLMP inequality, which just like CHSH is actually a family of inequalities got by considering all permutations of outcomes and parties). Nothing much is going to change. That's a theorem!

Actually the Larsson inequality would be redundant, and the inequality got by coding non-detections as 0 in CHSH, since (it is a theorem) a complete and minimal set of bounding facets of the local realist polytope is given, in the 2x2x3 situation, by all the various versions of CHSH (after grouping) and CGLMP.

For this particular data-set, none of the correct inequalities which we tested were violated, though some came close. If we repeat this experiment many, many times, our values of S and modified S will tend to fluctuate by amount of +/- 0.01 so once in a while we will probably observe a small violation of the inequality belonging to the large N limit. Very, very, very rarely we might of course observe a huge violation. Try it and see. Remember to save your random seed before each new experiment so that you can reproduce any amazing results which we otherwise might find hard to believe!

Three different valid modified Bell inequalities all invented to take account of non-detections give "non-violation" results. Is this just chance, or could it be that some people's mathematical theorems actually make true predictions about the behaviour of simulation models like this one?

Of course we must allow for statistical error. The theorems I mentioned say something about the large N limit of the estimated correlations. Here the sample size is 10 000 so there can be statistical error in the correlations of size around 0.01

The three theorems are:

Bell-CHSH allowing for measurement outcomes in the interval [-1, +1] instead of in the two point set {-1, +1};
Clauser-Horne allowing non-detections to be merged with one of the two detection events, or in effect, replacement of a two channel detector by a single channel detector;
Larsson modified CHSH (modified upper bound to take account of detection inefficiency)

***

Seems that most "opponents" of Bell didn't read much beyond Bell's 1964 paper, apart from picking up some of the objections which were raised and successfully countered in the years 64 - 70 of the last century. Since Pearle (1970) there really is no excuse not to understand the detection loophole and its many remedies. Caroline Thompson wrote lucidly about these things for years.

Even the experimentalists know now that they have to do something about this, and they know what they have to do with it. Now they just have to increase their detection efficiency a tiny bit, increase the distances a tiny bit, increase the speed of random measurement setting generation just a tiny bit ... and they'll be home and dry.

****

The scripts I have written illustrate that

(1) the CHSH inequality with "no detection" coded as the outcome "0",

(2) the CH inequality, and

(3) the Larsson modified CHSH inequality (CHSH adapted to take account of detection inefficiency)

all appear to hold, to well within the limits of experimental accuracy (i.e. statistical error), for Michel Fodje's simulation model.

In other words, it appears that it is possible to prove true and informative and non-trivial results about the limits of simulation models of EPR-B experiments. People interested in programming simulations of new experiments, and especially in keeping up with improvements in detection efficiency etc, could perhaps benefit from knowing just what can be done, and just what can't be done.

Forget for the moment about the applications of mathematics and probability and statistics to physics ... that is a long and difficult bridge to cross. A swaying suspension bridge in the mist ... Let's look at the applications of mathematics and probability and statistics to computer science. What tasks can you make a computer do? What tasks can't you make a computer do?

If you build some new machine, it is interesting to know its parameters, its operating limits. How high can you get the detection efficiency while still violating the (inappropriate) CHSH? Already, de Raedt and Hess and others made good use of Larsson and Gill's proof that the coincidence loophole allows more room for imitating quantum correlations than the old-fashioned (so 70's!) detection loophole! Already, the experimenters have woken up to the existence of this even bigger loophole than the one they already knew they had to overcome.

[minkwe]

Richard,
You seem to have forgotten our previous discussion from viewtopic.php?f=6&t=21&start=20#p515
Nothing you are saying here is interesting given I had explained these points to you months ago but you were not interested then.
viewtopic.php?f=6&t=21&start=30#p529
viewtopic.php?f=6&t=21&start=30#p538

Maybe you are better informed now to be able to understand what I was telling you back then. Please review those threads, it may save you a lot of time.

[gill1109]

Richard,
You seem to have forgotten our previous discussion from viewtopic.php?f=6&t=21&start=20#p515
Nothing you are saying here is interesting given I had explained these points to you months ago but you were not interested then.
viewtopic.php?f=6&t=21&start=30#p529
viewtopic.php?f=6&t=21&start=30#p538

Maybe you are better informed now to be able to understand what I was telling you back then. Please review those threads, it may save you a lot of time.

I understand what you are said and I have tried many times to explain why I believe you are wrong. I think you are making some category errors. In computer science terms: you are confusing the name of a variable, the content of a variable, and the algorithm which was actually used to assign that content to that variable. Those are three different "levels" or categories. Talking about EPR-B experiments, and at the algorithm level, there are at least *three* different things which we might mean by E(a, b). Three different ways to give it a value. The value is called "the correlation". The three ways to give it a value are also called "the correlation". Altogether that is six different things. I believe you are mixing them up. I believe that many people who are certain that Bell got something badly wrong are actually having the same trouble.

I also think that if you study my simulation program and the results I found with it, you might learn something new which might be of use to you. Think of it as a learning opportunity in mathematics and computer science: studying the performance limits of computer algorithms. Forget about physics for the moment.

Of course it would save you a lot of time not to do that, and it would save me a lot of time not to try again to explain these same things yet again.

But thanks for responding here, anyway. Did you check if I have correctly implemented your formulas and parameters? I am going to talk about your simulations at Växjö next week, I'll be meeting Adenier and de Raedt and Larsson and Khrennikov and others. I would not like to misrepresent your work because I admire it very much. And it has already provoked some interesting new discoveries.

[minkwe]

I'm happy for you that you finally found something to talk about. I hope you will be wise to mention that you not only changed the simulations in ways which I did not permit but produced something in the end which is absolutely irrelevant for physics. I do not agree with your implementation of my simulations. My code is free and available. Study it study the results analyze the results. You do not need to rewrite my code to study and analyze the results. The fact that you chose to rewrite it and modify it tells me you want to study something else than my simulations. Whatever results you get are therefore your own so don't deceive yourself that you are criticizing my simulations. You are simply criticizing your results.

[gill1109]

I study your model, not your implementation thereof. I have some wonderful new things to tell the world. Thanks for making your programs "open source" so anyone can study the model.

I have derived interesting performance bounds on your model. I changed nothing. The results are interesting for anyone who wants to create this kind of simulation program. You can call it computer science or computational physics if you don't want to call it physics. However there are also implications for experimenters. Which are the appropriate bounds to look at, what are the most effective ways to analyse the data from such experiments?

[minkwe]

I study your model, not your implementation thereof.

Your implementation is not my model. If you want to study my model, study my model. You have the code why did you choose to redo it your way unless it is something else you want to study. My code produces all the results as readable files, you didn't just analyze the results. You rewrote the code leaving out important bits.

I have some wonderful new things to tell the world. Thanks for making your programs "open source" so anyone can study the model.

Good for you that you learned something you did not know before.

I have derived interesting performance bounds on your model. I changed nothing.

Again, unless you are analyzing the data produced by my programs, without modifying them in any way, it is not my model that you are studying. Again I ask. Why did you have to rewrite it in order to study it, when you have the code and all the data files it produces?

However there are also implications for experimenters. Which are the appropriate bounds to look at, what are the most effective ways to analyse the data from such experiments?

You probably forgot what I've been telling you right from the beginning, that NOTHING WHATSOEVER can violate the APPROPRIATE BOUND, not even my simulations. That apparent violations by QM and Experiments are only because the wrong inequality is being used for comparison. That the reason my simulation appears to violate the bounds is the same reason Experiments appear to violate the bounds, and the same reason QM appears to violate the bounds -- The bounds are inappropriate for the experiment. That is why I have insisted to you many times that data from my experiments be analyzed in exactly the same way as data from actual experiments. Do you remember this? Check your e-mail, the very first communication I had with you before joining this forum even. Is this what you have now discovered and ready to tell the world in your talk?

[gill1109]

Please take a look at http://rpubs.com/gill1109/epr-clocked-full and http://rpubs.com/gill1109/epr-simple and please tell me if I left out any "important bits".

My simulations of the mathematical models which are implicitly described in https://github.com/minkwe/epr-clocked and https://github.com/minkwe/epr-simple do indeed not violate the appropriate bounds. Which are rather different bounds from what Michel Fodje calls "the appropriate bound".

The "usual bound" is not appropriate to models with a detection loophole or a coincidence loophole. We know this since Pearle (1970).

There are further interesting results in http://rpubs.com/gill1109/epr-clocked-core. Here, I left out some of the bits of Michel's model which he calls essential, keeping just the core (generation of outcomes and delay times). It turned out that the results of http://rpubs.com/gill1109/epr-clocked-core and of http://rpubs.com/gill1109/epr-clocked-full are identical.

[minkwe]

Please take a look at http://rpubs.com/gill1109/epr-clocked-full and http://rpubs.com/gill1109/epr-simple and please tell me if I left out any "important bits".

Your implementation is not my model. If you want to study my model, study my model. You have the code why did you choose to redo it your way unless it is something else you want to study. My code produces all the results as readable files, you can simply analyze the results if you really want to study my model. If you want me to be interested in your code, and if you want to say anything meaningful about my simulation, write your own analysis code which uses the data produced from MY programs (not yours). And post your analysis code and results. Then you will have my interest. Then I will run your analysis code against Weih's data, and other datasets from other experiments and we will compare the results with each other and with QM.

I am going to talk about your simulations at Växjö next week, I'll be meeting Adenier and de Raedt and Larsson and Khrennikov and others.

No mention of it in your talks. Had a change of mind?

[gill1109]

Your implementation is not my model. If you want to study my model, study my model. You have the code why did you choose to redo it your way unless it is something else you want to study.
...
No mention of it in your talks. Had a change of mind?

I can't code in Python, you refused to help me. So I read your code, "extracted" the mathematical components, and coded them in R. Now I could do the experiments myself, which I would have liked to have done with you. Too bad. Now you have a fine excuse to take no notice of them.

Why I decided not to talk about my simulations of my interpretation of your model: there were a number of fantastic talks by others about the coincidence loophole, both theoretical and with respect to experiment. I only had 30 minutes. However actually a number of the slides of the talk do actually apply to your simulation models, but that is no longer explicit.

[minkwe]

I can't code in Python, you refused to help me.

You don't need to know how to code in python to be able to analyze the files produced by my simulation. Again, if you want to analyze my model, you have the data files it produces and you can analyze them using any language of your choice. What you can not do is rewrite what you claim is my model and claim to be testing it. You do not need to rewrite anything. Simply analyze the data produced by my code, not yours.

/Michel.

[gill1109]

I can't code in Python, you refused to help me.

You don't need to know how to code in python to be able to analyze the files produced by my simulation. Again, if you want to analyze my model, you have the data files it produces and you can analyze them using any language of your choice. What you can not do is rewrite what you claim is my model and claim to be testing it. You do not need to rewrite anything. Simply analyze the data produced by my code, not yours.

I can claim that I am analysing your model, and you can claim that I am mistaken. Anyone can study my code and your code and decide for themselves whether or not "my model" is the same as "your model". You can't forbid me from doing what I did, and you can't forbid me from saying that I think I have done what I think I have done. You refused again and again to help me adapt your code to the experimental protocol I wanted to run (namely a standard CHSH experiment). You forced me to rewrite in R, and I'm glad of it. I learnt some cool stuff, discovered some cool stuff, and I'm not dependent on anyone else. I can easily do any crazy experiment I like. If you're not interested in "my models" then don't contribute to this topic.

[minkwe]

I can claim that I am analysing your model, and you can claim that I am mistaken. ...

You refused again and again to help me adapt your code to the experimental protocol I wanted to run (namely a standard CHSH experiment).

Bingo, I refused to help you change my model to what you want so you changed it yourself and yet you continue to claim that what you now have is my model. I can't make you stop doing that, but I'm free to call it dishonest. If you wanted to analyse my model you would have simply analyzed the output files which the model produced, but that is not what you want, you wanted to analyze something else which does not make physical sense, I refuse to change my code into something meaningless. You are free to do what you want but any one reading this thread now knows from your admission above that you have "adapted it to the experimental protocol you want to run".

If you continue to claim that you are analyzing my model, then you have an honesty issue and that is your problem not mine.

You forced me to rewrite in R, and I'm glad of it.

Not true, I have forced you to do nothing. You chose to do what you wanted to do, you are a free agent. I can't force you to tell the truth about what you are actually doing, let alone force you to write a program in R.

If you're not interested in "my models" then don't contribute to this topic.

I will continue to contribute as long as you keep mentioning falsely that you are analyzing my models, you are not.

[gill1109]

You wanted to analyze something else which does not make physical sense, I refuse to change my code into something meaningless.

You had better look at my simulations. I do not do anything "meaningless". I did not change anything. I just translated (more precisely: I tried to translate as truthfully as possible). I selected settings at random - Alice from {0, 90} and Bob from {45, 135}. I left out all the plots. I did different things with the experimental data. If you're not interested, you're not interested. Too bad. Anyone can check that "my model" and "your model" are mathematically the same. One is implemented in Python and one in R.

[minkwe]

You had better look at my simulations.

I will do no such thing. My simulation is open-source, you can download it and run it as many times as you like. It saves output files, you can analyze them as you like. You don't need to rewrite it in order to test MY simulation. If you rewrite it, I'm not going to give you my blessing that what you have is my model. Sorry it is not. Besides you have stated many times what your intentions were and I can quote you:

I fixed this defect myself.

.

Actually first I improved the detectors in his model

You do not like my model so you pretended it was an error or a defect and you changed it. Even though I told you everything in my model was part of the model and no defect. You simply ignored me and continued your tricks:

One person's feature is another person's bug! And vice versa.

So you have now explained that when you say 100% detection, you mean that all particles which you intended to be emitted are indeed detected too. But you have told us that 0.01% of the particles do not come in pairs. So your source is imperfect.

I made it perfect

No you did not. My source is already perfect. It behaves the way it is meant to behave. You don't have to like it, but that is the model. You changed the model. You are free to have your own standards of how a source should behave but results you compute according to those assumptions will not tell you anything about my simulation , or the real world experiments it attempts to model.

Anyone following this can review our prior discussion about your escapades here: viewtopic.php?f=6&t=23&start=23

Nobody should trust your claims that you are testing my model. You are not. Had you intended to test my model, you would simply have analyzed the output from my programs. But no, you rewrote everything to fulfill your wishes contrary to my warnings and now you want me to bless your work so that you may use it to discredit my work. Sorry, If you want to say anything about my model with a straight-face, you will simply analyze the data from my model not your caricatures of it.

You have admitted already in this thread that your intentions were to "ADAPT" my model to suit what you wanted to do. Those were your words. I've told you already such "ADAPTATIONS" changes the model. Anyone can read the README file included in the model as well as our discussion about it from several months ago in which you kept trying to change my model and I resisted it.

Let me remind you of a section of the License for my programs:

Also, for each author's protection and ours, we want to make certain
that everyone understands that there is no warranty for this free
software. If the software is modified by someone else and passed on, we
want its recipients to know that what they have is not the original, so
that any problems introduced by others will not reflect on the original
authors' reputations.

It is common decency that when you modify somebody's work, you do not go around claiming that what you got was their work. Why is this so hard for you to understand?