Computer Simulation of EPR Scenarios

[gill1109]

Joy Christian hits the nail on the head by remarking that any proof of Bell's theorem uses the assumption of "realism" (counterfactual definiteness). Bell's theorem says that quantum mechanics is in conflict with locality + realism + freedom. To prove the theorem you assume the latter three, derive CHSH, and remark that QM violates CHSH.

Whether or not local realism is a property of the real world is of course the whole issue. But let's be more modest. The realism assumption certainly does apply to any purported event-by-event local realistic computer simulation of a CHSH type experiment.

For instance, to "minkwe" (Michel Fodje's) simulation
https://github.com/minkwe/epr-simple/

So how does Michel violate the CHSH inequality? Answer: through massive use of the detection loophole. The outcomes are not +/-1, but +/-1 or 0. From all the data generated he post-selects those pairs for which neither outcome is 0. This is a famous trick going back to Pearle (1970) and also used by Caroline Thompson (chaotic ball), Luigi Accardi (chameleon statistics), Hess and Phillip (non-local hidden variable micro-time) and so on.

What about Chantal Roth's simulation?
http://libertesphilosophica.info/eprsim/eprsim.txt

Answer: some complicated function of the detector angles equals cosine squared theta (the difference of the two angles). Chantal's program repeatedly computes that function, draws a random number between zero and one, and counts it as equality of two outcomes if the number is below cosine squared theta. In other words, she simulates Bernoulli trials with the right probability, counts the number of "successes", and outputs their relative frequency. Result: a beautiful cosine curve (up to statistical error). This is not a local realistic event-by-event simulation of a rigorously performed CHSH experiment. It is a computer simulation of the binomial distribution, illustrating the law of large numbers. The code also verifies Joy's claim that that complicated thing equals cosine squared theta, is correct. Which can also be done by some simple algebra, trigonometry.

By the way, Chantal has confirmed this analysis. She moreover told me that she could not possibly implement Joy's model in a rigorous simulation experiment.

=========================================================================================

Minkwe's experiment:

I am not a wizard with Python but I managed to dive into minkwe's Python code and save the data generated by the simulation as plain text files, instead of as numpy binary files. I reduced the number of runs from 10 million (or whatever it was) down to 1 million, just to keep things manageable and fast.

I then read the output data into R and ran the script reproduced below, which converts the measurement angles from radians to degrees, rounds to multiples of 7.5 degrees, and then selects from the whole experiment just those runs corresponding to a CHSH experiment: Alice's angles are 0 or 45 degrees, Bob's are 22.5 or 67.5 degrees.

This is exactly what minkwe does before calculating CHSH; also he does this same rounding before drawing his beautiful plots (cosine curves).

I convert the settings to the numbers 1 and 2, and then print out tables of the joint outcome statistics for Alice and Bob under each pair of settings. Recall that Alice's outcome can be -1, 0 or 1; Bob's outcome can be -1, 0, or 1. The zero stands of course for no detection.

Here they are

Setting combination 1, 1

Code: Select all

     -1   0   1
 -1   5  20 169
 0   26  24  24
 1  148  11   6


Setting combination 1, 2

Code: Select all

    -1   0   1
 -1  46  36 103
 0   36   0  35
 1  106  41  42


Setting combination 2, 1

Code: Select all

     -1   0   1
 -1   4  20 173
 0   24  24  27
 1  167  15   8


Setting combination 2, 2

Code: Select all

     -1   0   1
 -1   5  19 137
 0   15  52  25
 1  137  22   5


================================================================

Modifications to minkwe's Python code:

In order to have access to the function "savetxt", add, near the top:

Code: Select all

 
numpy import *


Reduce number of iterations, just for convenience:

Code: Select all

NUM_ITERATIONS = 1000000


Further down, in the code, add two "savetxt" lines:

Code: Select all

# save results in separate files each is a list of angles and +/- outcomes
self.alice.save()
self.bob.save()
savetxt("alice.txt", self.alice.results)
savetxt("bob.txt", self.bob.results)


===============================================================

Then here is my R script which analyses the data-files produced by epr.py:

Code: Select all

alice <- read.table("alice.txt")
bob <- read.table("bob.txt")

AliceAngle <- (alice$V1)*180/pi
BobAngle <- (bob$V1)*180/pi

AliceRoundAngle <- round(AliceAngle/7.5)*7.5
BobRoundAngle <- round(BobAngle/7.5)*7.5

AliceOutcome <- alice$V2
BobOutcome <- bob$V2

CHSHruns <- which( (AliceRoundAngle %in% c(0, 45) ) & (BobRoundAngle %in% c(22.5, 67.5) ) )

CHSH <- data.frame(SettingAlice = AliceRoundAngle[CHSHruns],
   OutcomeAlice = AliceOutcome[CHSHruns],
   SettingBob = BobRoundAngle[CHSHruns],
   OutcomeBob = BobOutcome[CHSHruns])

CHSH$SettingAlice <- CHSH$SettingAlice/45 + 1
CHSH$SettingBob <- (CHSH$SettingBob-22.5)/45 + 1

attach(CHSH)

table(OutcomeAlice[SettingAlice == 1 & SettingBob == 1], OutcomeBob[SettingAlice == 1 & SettingBob == 1])
table(OutcomeAlice[SettingAlice == 1 & SettingBob == 2], OutcomeBob[SettingAlice == 1 & SettingBob == 2])
table(OutcomeAlice[SettingAlice == 2 & SettingBob == 1], OutcomeBob[SettingAlice == 2 & SettingBob == 1])
table(OutcomeAlice[SettingAlice == 2 & SettingBob == 2], OutcomeBob[SettingAlice == 2 & SettingBob == 2])


[Joy Christian]

Whether or not local realism is a property of the real world is of course the whole issue. But let's be more modest. The realism assumption certainly does apply to any purported event-by-event local realistic computer simulation of a CHSH type experiment.

For instance, to "minkwe" (Michel Fodje's) simulation
https://github.com/minkwe/epr-simple/

So how does Michel violate the CHSH inequality? Answer: through massive use of the detection loophole.

The last sentence is completely incorrect. There is no loophole of any kind in Michel's simulation. There are no 0 outcomes, because there are no states that correspond to 0 outcomes. If there are no clouds in the sky, then there can be no rain no matter where one goes. What Gill has failed to understand is that the state of the system in Michel's simulation is given by a pair (e, t), and not just by e. This makes all the difference. It says that there are no clouds in the sky, so there can be no rain. No clouds, no rain. No states, no outcomes. It is that simple.

To understand this fact properly, however, requires some understanding of the geometry and topology of the 3-spehre, which Gill has failed to do. Consequently, everything Gill says about both Michel's simulation and about Chantal's simulation below is incorrect. To properly understand both my model as well as its simulations one must make some effort to understand the whole body of my work, with scientific integrity. A comprehensive discussion about the simulations can be found in this paper: http://libertesphilosophica.info/blog/w ... hapter.pdf. Further details can also be found on my blog: http://libertesphilosophica.info/blog/.

What about Chantal Roth's simulation?
http://libertesphilosophica.info/eprsim/eprsim.txt

Answer: ... The code also verifies Joy's claim that that complicated thing equals cosine squared theta, is correct. Which can also be done by some simple algebra, trigonometry.

Indeed. Any simulation is an implementation of an already existing analytical model. The analytical model is impeccably local, realistic, and deterministic. The simulations of this model has been kindly produced by various authors because they saw that my analytical model was unfairly attacked by various detractors with
dares such as "if your model is indeed local, realistic, and deterministic, then you should be able to simulate it on a computer so that the whole world can see that you are right." The model *has* been simulated independently by at least five different authors, and the world can now indeed see that I have been right all along.

[gill1109]

Dear Joy

Please look at the data which is generated by Michel's simulation. Many, many times, there is a measurement of one particle (i.e. outcome +/- 1) but not of the other (i.e. outcome 0). Sometimes there is no measurement of either (outcomes 0, 0).

It is not a question of sometimes there being a state, sometimes not. No: the experiment generates a mixture of "good states" and noise in such a way that there is a simple local realistic explanation for the overall "polluted" data statistics. You need to reduce the noise level to below the critical threshhold. You can find out what that is from the extensive literature on the detection loophole. I'm afraid that his simulation will not be able to reduce the noise level below the threshhold.

Right now, we cannot use CHSH on his data because his measurement outcomes are ternary, not binary. If we reduce the data to binary (merging the 0's and the -1's, for instance) then his data will *not* violate CHSH. (This merging trick leads us to what is known as the Eberhard or the Clauser-Horne inequality).

As you know, the quantum optics experimenters are still about five years away from a definitive (loophole free) Bell-CHSH experiment. Only last year did they succeed in surmounting the detection loophole. Just as the experimental community is working towards the definitive experiment, anyone who writes computer programs which do a local realistic event-based simulation of Bell-CHSH experiments, should be trying to write programs which will pass the ultimate test. The same test which, in principle, quantum mechanics can pass. The simulation of the experiment of *this* century (still five years in the future).

For the computer programmer, that test is called the quantum Randi challenge. See "Exploring inequality violations by classical hidden variables numerically" by Sascha Vongehr, http://www.sciencedirect.com/science/ar ... 1613001863
arXiv version http://arxiv.org/abs/1308.6752
The framework is set out at
http://fmoldove.blogspot.nl/2013/09/is- ... al-or.html

Good luck!

Richard

[Joy Christian]

No clouds, no rain. No states, no outcomes. That is the analytical model, and that is what is being simulated: http://libertesphilosophica.info/blog/w ... 1/EPRB.pdf

My model is model X. I am not interested in models Y1, Y2, Y3, etc., and their deficiencies.

[Heinera]

I have pointed out in other forums that Michel's simulation is an obvious and trivial exploitation of the detection loophole. And he was not the first to do this.
Richard is entirely correct here (as he is in general, by the way). Non-scientific mantras like "No cloud, no rain" will not change that fact. In this paper,

http://arxiv.org/pdf/quant-ph/9905018

a model based on the same priciples is presented. The authors never intended that this should be taken seriously as an actual theory of reality, but rather as an example of how simple a local-realistic QM-conforming model can be if you allow detection inefficiency. The paper was published in 1999 in Physic Letters A.

[FrediFizzx]

There is no detection loophole in Michel's simulation. The states never exist in the first place.

[Joy Christian]

I have pointed out in other forums that Michel's simulation is an obvious and trivial exploitation of the detection loophole.

And I pointed out to you several times in other forums that you are entirely mistaken. The state in Michel's simulation is the pair (e, t), not just e. You cannot save Bell by changing my model or denying the blatantly obvious facts. You cannot deny obvious facts simply because they do not fit into your outdated belief system.

Richard is entirely correct here (as he is in general, by the way).

Gill is entirely mistaken here (as he is in general, by the way). In fact, he is entirely clueless about what my model actually is. He thinks it is Y, but in fact it is X.

"No clouds, no rain" is not a "mantra." It is an attempt to explain to the uninformed and clueless that the initial or complete state of the physical system in my model is (e, t), not just e. This can be seen at once from the succinct description of my model presented here: http://libertesphilosophica.info/blog/w ... 1/EPRB.pdf

In what follows, let me reproduce a private email I received today from someone which illustrates well what is going on here:

"I just read the exchange between Gill and Joy/Fred.

From a non-physicist’s perspective, the reason Gill perpetuates his arguments (maybe somewhat altered, reflecting current conversations) from the past is that he BOTH does not understand Joy’s theory/math AND also refuses to learn it. He simply views everything in terms of his preconceived understanding, and you may as well be talking different languages.

If you were to imagine Einstein going back in time to meet with Newton, you can be sure that it would intrigue Newton that Einstein is able to derive his results equally well while using unfamiliar concepts and math. It is easy to be wrong in judging Newton’s likely response, but my view is that he would like to learn about it because to him a lack of understanding would simply be intolerable (“and who is this person with unkempt hair and speaking with a funny accent anyway, he must be related to that obnoxious Leibniz fellow”).

I just cannot see Newton blindly insisting that Einstein is wrong, and to support that assertion by repeatedly proceeding to prove Einstein wrong from within his own (Newton’s) established theories. I can even see Newton wanting to supersede Einstein, because he might surmise that there could be an even grander (deeper) theory. I think Newton was that good.

But we don’t see that today with too many scientists. They “all” just want to make everything fit their already made-up minds. Of course it cannot (fit)..."

[gill1109]

That's amusing, I just received the following in a private communication from a friend: "From a non-physicist’s perspective, the reason Christian perpetuates his arguments (maybe somewhat altered, reflecting current conversations) from the past is that he BOTH does not understand Gill’s theory/math AND also refuses to learn it. He simply views everything in terms of his preconceived understanding, and you may as well be talking different languages."

Yes it's so bad that so many scientists "all" just want to make everything fit their already made-up minds. Of course it cannot (fit)...

Joking aside: I think the rules of this forum are clear, that comments like these have no place here.

[gill1109]

There is no detection loophole in Michel's simulation. The states never exist in the first place.

What are the rows and columns labelled with "0"? The "states" existed in the simulation. And many times, only one of the two particles gets measured. This directly contradicts claims by Joy about his model (see his two page EPRB.pdf manuscript).

The conclusion is obvious: either Joy's claims are wrong, or Michel does not simulate Joy's model.

[Joy Christian]

How about these comments of mine? Are they acceptable?

Gill's error lies in this innocent-looking statement: "The point is that although Alice only gets to make one choice in each run, we can perfectly well define both outcomes which she would have observed, had she hit either button 1 or 2." This is the assumption of "counterfactual definiteness." Had Alice hit button 2 instead of 1, she would have observed outcome A' instead of A." This is a highly nontrivial assumption, both philosophically and mathematically. And physically of course it is *impossible* for Alice to observe both A and A' at the same time. Therefore Gill's treatment of this assumption is extraordinarily naïve, to say the least.

Let us first think about this philosophically. Do we sometimes wonder in real life like: "Had I taken a left turn instead of a right turn on the Baker street, I would have been enjoying doughnuts instead of getting mugged"? Yes we do. But it is getting mugged is what is actually happening to you, and enjoying doughnuts is just your fantasy. Thus one has to be extremely careful in using the assumption of counterfactual definiteness, especially in the EPR-Bohm type experiments. For what is involved in such experiments are events occurring in space and time, or at least in space at a given time. Therefore some knowledge and understanding of the actual physics of the general relativistic notions of space and time is absolutely essential. Any argument without this understanding is pure fantasy, like enjoying doughnuts.

So what, then, is the correct mathematical treatment of using counterfactual definiteness in analysing such experiments? Well, we must first ask: In which solution of Einstein's field equation the events A and A' which could have been observed by Alice could be actually occurring? Now there are compelling physical reasons to believe that they are in fact occurring in a parallelized 3-sphere [or in the topological space of the group SU(2)]. They are most certainly NOT occurring in an Nx4 spreadsheet. Nx4 spreadsheet is a fantasy, whereas parallelized 3-sphere is the reality. But once we recognize this, then it is clear that the counterfactually occurring outcomes like A and A' cannot be represented in a flat spreadsheet. That would be simply an incorrect representation of the actual events A, A' etc. In other words, what Gill is doing is simply incorrect. The only correct way to represent counterfactually occurring events is by representing them on the space of a unit parallelized 3-sphere. But once this is done, all quantum mechanical predictions for the experiment are easily reproduced, in a strictly local, realistic, and deterministic fashion.

The conclusion is obvious: Gill has no understanding of either my model or of its various simulations. One does not have to be Einstein to recognize the difference between the initial or complete state e and the initial or complete state (e, t). The first belongs to R^3 (i.e., flatland) and the second belongs to S^3 (a 3-sphere).

Given an initial state (e, t) and a freely chosen measurement setting a, there is a unique measurement outcome A(a; e, t) = +1 or -1. Similarly, given the same initial state (e, t) and another freely chosen measurement setting b, there is a unique measurement outcome B(b; e, t) = +1 or -1. This is exactly the prescriptions defined
by Bell, for the common cause (or hidden variable) L := (e, t). Note that there is one-to-one correspondence between the complete state (e, t) and a measurement outcome (say) A = +1 or -1. Thus no states are without an outcome, and all such outcomes are counted. Does anyone apart from Gill and his friends see a detection loophole here? Detection loophole is exploited when some outcomes go uncounted, or some states do not trigger a detector. That is clear NOT the case in my model.

[gill1109]

Dear Joy

Please take a look at the evidence I submitted: output from "minkwe" 's alleged simulation of your model.

You say: "Detection loophole is exploited when some outcomes go uncounted, or some states do not trigger a detector".

OK, so you are telling me that minkwe's simulation has got nothing whatever to do with your model. Yet you offer its existence as support for your position.

The point is that an event-based local realistic computer simulation of a rigorously performed CHSH type experiment can be thought of as generating a "flat" Nx4 spreadsheet. Please take a look at the last section (the section on quantum Randi challenges) of my "Statistics, Causality and Bell's Theorem" (http://arxiv.org/abs/1207.5103).

You used to be quite clear about this: a computer simulation could *not* be given of your model. Precisely because of the flatness.

Richard

[Joy Christian]

Please don't put words in my mouth. Instead, please read this paper in full: http://libertesphilosophica.info/blog/w ... hapter.pdf

In addition, this short derivation of the complete state (e, t) may also help: http://libertesphilosophica.info/blog/w ... mplete.pdf

The bottom line is this: We live in two different worlds --- you and other Bell-believers live in the flatland of R^3, but I live in the real world of S^3 (which,
as I have pointed out many times before, is one of the cosmological solutions of Einstein's field equations (a Friedmann-Robertson-Walker solution).

As for Michel's simulation: It is an implementation of S^3 using an algorithm based in R^3. But he is quite explicit in stating that the complete state is (e, t).

[gill1109]

Michel doesn't "say" anything. He computes. The results of his computation are there for everyone to see. Of course, they would have to take the trouble to glance at at the evidence I submitted: the output from Michel's simulation. Words are one thing, facts are another. If Michel's code implements your model, then the results from his simulation prove that the formulas in your EPRB.pdf are wrong. You are missing a very essential "conditional on both outputs being unequal to zero" in the formulas for the probabilities of ++, +-, -+, --.

Also it is interesting to compare the two page EPRB.pdf with your earlier one-page paper - the one with the novel definition of correlation. You have now abandoned the unorthodox correlation but instead, effectively, resorted to the detection loophole.

[Joy Christian]

Michel doesn't "say" anything.

Michel explicitly states that the state of the system is the pair (e, t). It is not just e. Anyone can see that: https://github.com/minkwe/epr-simple/

You are missing a very essential "conditional on both outputs being unequal to zero" in the formulas for the probabilities of ++, +-, -+, --.

I am missing nothing, and you are getting nothing. Either you don't want to get it, or getting it is extremely inconvenient for you. As I explained to you many times, there are no "zero outputs", period. Don't make things up to confuse people. Stick to my model. [comment deleted by moderator]

Also it is interesting to compare the two page EPRB.pdf with your earlier one-page paper - the one with the novel definition of correlation. You have now abandoned the unorthodox correlation but instead, effectively, resorted to the detection loophole.

I have not abandoned any part of my work. You simply do not have sufficient knowledge of physics and mathematics to understand it. This is quite clear from your comments. A 3-sphere is a topological space. One can represent this space in Riemannian geometry by either a non-vanishing curvature or a non-vanishing torsion. The latter is equivalent to representing the 3-sphere as a set of unit quaternions. My one-page paper uses such a quaternionic representation, which has been too difficult for you to fathom. My EPRB.pdf paper uses a slightly different representation of the same 3-sphere to calculate the same correlation. Any competent mathematician can see that the two papers simply calculate correlation among the points of the same space---a parallelized 3-sphere---in two different representations. [comments removed by moderator]

[gill1109]

Michel explicitly states that the state of the system is the pair (e, t). It is not just e. Anyone can see that: https://github.com/minkwe/epr-simple/

Indeed, anyone can see exactly what minkwe says and does. He explicitly states how he selects e and t and how he determines the outcomes of the measurement on each particle separately - including whether or not there is a particle. He does not implement the restriction to pairs (e,t) satisfying (A.9.1). Only later does he reject the pair of particles if the outcome A or the outcome B is zero; and for this purpose, only the directions a and b have been checked (one on each particle), not all directions x.

His simulations go on to show that, given measurement directions a and b,

Prob(A=+1, B=+1 | A != 0, B != 0) = 1/2 sin^2(eta_ab) , etc.

His e0 and theta0 were previously chosen at random independently of one another, he did not restrict (e,t) to the set Lambda defined in (A.9.1).

[Joy Christian]

...he did not restrict (e,t) to the set Lambda defined in (A.9.1).

Oh..., but he did. The state is (e, t). If you insist on replacing the sate (e, t) by a state e, then you can interpret the straw-man thereby constructed the way you wish.

[gill1109]

According to your paper, the state is (e,t) should be in Lambda. However according to Michel's simulation, it often is outside of Lambda.

Since Michel's simulation does reproduce the singlet correlations correctly, I conclude that the description of the model in EPRB.pdf must be incorrect.

Please do not use the expression "straw-man". This forum is was set up so that civilized people could discuss scientific matters. By using the word "straw-man" you are making insinuations about my motives which are unfounded. Discuss the content. Don't discuss the discussant.

[Joy Christian]

According to your paper, the state is (e,t) should be in Lambda. However according to Michel's simulation, it often is outside of Lambda.

Incorrect. There is no inside or outside of Lambda in Michel's simulation. There is only an algorithm to implement Lambda, which is successfully constructed by Michel.

Since Michel's simulation does reproduce the singlet correlations correctly, I conclude that the description of the model in EPRB.pdf must be incorrect.

You may conclude whatever you wish. That does not change the correctness of my model. The model is summarized in eight elementary equations, which can be verified by any precocious high-school student, knowing only basic trigonometry and probability theory: http://libertesphilosophica.info/blog/w ... 1/EPRB.pdf

Please do not use the expression "straw-man".

Please do not conjure up straw-men.

[gill1109]

Dear Joy

Please do not imagine straw-men.

Please imagine that your "opponent" is acting in good faith, he is not trying to discredit you with cheap debating trips.

Michel's algorithm does not succesfully construct Lambda as you defined it. In your definition there is a "for all x" requirement. Michel only chucks out (e,t) after two particular values of x have been tested: x=a, and x=b. The two values are different in every run. His "population" of hidden variables is effectively dependent on both the settings. The model which he is effectively simulating violates the "no-conspiracy" requirement.

I haven't got around to simulating your EPRB.pdf model yet or checking your algebra but I am afraid that things are looking bad since if Michel's simulation does reproduce the singlet correlations and the only difference between his implicit model and yours is the definition of Lambda, then a simulation of your model as described in EPRB.pdf would certainly not reproduce the singlet correlations.

It's as simple as that.

Richard

[Joy Christian]

Please do not imagine straw-men.

I recognize a straw-man when I see one. It is one of the logical fallacies I was taught to be vigilant about by Professor Abner Shimony when I was his doctoral student.

Michel's algorithm does not successfully construct Lambda as you defined it. In your definition there is a "for all x" requirement. Michel only chucks out (e,t) after two particular values of x have been tested: x=a, and x=b. The two values are different in every run. His "population" of hidden variables is effectively dependent on both the settings. The model which he is effectively simulating violates the "no-conspiracy" requirement.

(1) Since you have asked nicely, I will try not to see this as a straw-man. Nevertheless, your statements are quite misleading and incorrect. The requirement in my Lambda is "for any x". It is a universal quantifier, as normally used in logic and mathematics. Whether x happens to be a, or b, or c, or d, is of no consequence, either in my model or in Michel's simulation. The population of the hidden variables is thus completely independent of x. Whatever x is, the set Lambda remains the same.

(2) As Michel has pointed out elsewhere, his simulation can be written without the so-called "zero outcomes." It is only a matter of semantics.

(3) No simulation of the model described in my EPRB.pdf is necessary. The analytical model descried in the two pages stands on its own, analytically. The model is summarized in eight elementary equations, which can be verified by any precocious high-school student, knowing only basic trigonometry and probability theory.