Joy Christian's colourful exploding balls experiment

[Joy Christian]

I thought of a solution to the instability of spinning hemispheres. We take two rubber balls which are quite squeezy so that when you push one against a flat surface it takes on the form of a ... squashed ball, squashed against a flat plate, ie roughly ... a hemisphere. Two are glued together but little explosive charges let them shoot away from each other, regaining their spherical shape... no wobbles!!!!

Sounds good to me.

But there would be many other issues. The "measurements"---or determinations of the actual spin directions---must be made at the same time on both sides, when the two balls are exactly at the same distance from the centre of the "explosion" (we don't want to end up comparing apples with oranges). I am talking about "time" and "coincidences", of which you are an expert. I don't think this is going to be an easy experiment to do. But---win or loose---it must be done; for the sake of physics.

There is another important issue that I should have clarified a long time ago. Suppose all four correlation functions---when calculated individually---produce the cosine correlations, but when they are "added" up they don't violate CHSH. In that case who would be the winner? I am not asking for a statistical reason why this scenario is possible or impossible. I am asking a question concerning the bet. In such an eventuality---i.e., when E(a, b) is good but CHSH is no good---who would be the winner?

[gill1109]

I thought of a solution to the instability of spinning hemispheres. We take two rubber balls which are quite squeezy so that when you push one against a flat surface it takes on the form of a ... squashed ball, squashed against a flat plate, ie roughly ... a hemisphere. Two are glued together but little explosive charges let them shoot away from each other, regaining their spherical shape... no wobbles!!!!

Sounds good to me.

But there would be many other issues. The "measurements"---or determinations of the actual spin directions---must be made at the same time on both sides, when the two balls are exactly at the same distance from the centre of the "explosion" (we don't want to end up comparing apples with oranges). I am talking about "time" and "coincidences", of which you are an expert. I don't think this is going to be an easy experiment to do. But---win or loose---it must be done; for the sake of physics.

There is another important issue that I should have clarified a long time ago. Suppose all four correlation functions---when calculated individually---produce the cosine correlations, but when they are "added" up they don't violate CHSH. In that case who would be the winner? I am not asking for a statistical reason why this scenario is possible or impossible. I am asking a question concerning the bet. In such an eventuality---i.e., when E(a, b) is good but CHSH is no good---who would be the winner?

I will be happy that Joy and the experimenter together work out any sensible procedure they like for determining the two directions of spin which come out, from each exploding ball. For instance, it is also fine by me if we get a pair of unit vectors s_k and t_k, the directions of spin of each of the two objects, where t_k is not exactly equal to -s_k. The important thing for me is that this will be done independently of which directions a and b are going to be measured.

About the bet: I want to bet on CHSH. But I don't really understand the question since if E(a, b) is good then CHSH has to be good too?

If the experiment gives us, for a particular set of pairs of correlations, E(a, b) = 0.707, E(a, b') = 0.707, E(a', b) = 0.707 and E(a', b')= -0.707, then E(a, b) + E(a, b') + E(a', b) - E(a', b') = 2.828.

A bit of statistical noise won't spoil this. A bit of bias towards zero doesn't hurt: +/- 0.65 is OK too. Too much bias does hurt: +/- 0.60 takes us below the threshhold which I proposed. Bell predicts +/- 0.50

[Joy Christian]

The important thing for me is that this will be done independently of which directions a and b are going to be measured.

This is not a problem. In the experiment the actual spin directions will be recorded, without needing to specify either a or b in advance. The four pairs of directions, say (a, b), (a, b'), (a', b), and (a', b'), can be postponed to be chosen until the next century if we like. And when we actually choose them, we can do so by whichever method we like. Thus the proposed experiment will respect, most faithfully, the EPR criterion of realism---or counterfactual definiteness. None of the experiments done to date actually respect counterfactual definiteness at all, as minkwe has been arguing. They replace counterfactually possible directions with an altogether different set of actual particles. In my proposed experiment all counterfactually possible directions will be there at our disposal to be chosen for centuries to come.

About the bet: I want to bet on CHSH. But I don't really understand the question since if E(a, b) is good then CHSH has to be good too?

If the experiment gives us, for a particular set of pairs of correlations, E(a, b) = 0.707, E(a, b') = 0.707, E(a', b) = 0.707 and E(a', b')= -0.707, then E(a, b) + E(a, b') + E(a', b) - E(a', b') = 2.828.

A bit of statistical noise won't spoil this. A bit of bias towards zero doesn't hurt: +/- 0.65 is OK too. Too much bias does hurt: +/- 0.60 takes us below the threshold which I proposed. Bell predicts +/- 0.50.

Fine. I am interested (and predict) the actual strong correlation: E(a, b) = -a.b. But I am happy to see that we agree that if E(a, b) is good then CHSH will be good too.

[minkwe]

If the experiment gives us, for a particular set of pairs of correlations, E(a, b) = 0.707, E(a, b') = 0.707, E(a', b) = 0.707 and E(a', b')= -0.707, then E(a, b) + E(a, b') + E(a', b) - E(a', b') = 2.828.

There is a subtlety being missed here. The QM and traditional experimental results for E(a,b), E(a, b'), E(a', b) E(a', b'), do not contain any counterfactual results, since they are all mutually independent of each other and since each E(.,.) is an observable on a different set of particles from any other E(.,.). However, the terms in the CHSH are all mutually interdependent, having resulted from the same set of particles, due to the algebra of the derivation of the inequality.

Therefore it is not reasonable to expect an experiment or simulation which produces mutually inter-dependent terms including counterfactual outcomes to match QM values for ALL the correlations. This does not mean, QM violates counterfactual definiteness. It just means we have to compare oranges and oranges. For Joy's suggested experiment therefore, I would say if the results are gathered in a manner such that they are mutually interdependent (all from the same set of particles), such results can not be compared with QM or other EPR-type experiment if we are being fair in the analysis.

As illustrated in this post viewtopic.php?f=6&t=21&start=20#p515 it is possible for a manifestly locally realistic model to violate the CHSH and match all the QM correlations when the correlations are all independent (calculated from different sets of particles) while at the same time not violating the CHSH and not matching all the QM correlations when the correlations inter-dependent (calculated form a single set).

[minkwe]

Let me try to explain again the point in my previous post, perhaps it will be understood this time:

If I throw a pair of fair coins {x,y} the probability of double outcomes P(Hx,Ty) = 0.25, this probability is similar to the QM prediction for E(a,b) in that it is well understood that every pair of coins I'm referring to are independent of every other pair.

But if I throw three fair coins {1,2,3}, even though I can separately say P(1,2) = 0.25 independently of P(2,3) = 0.25, independently of P(1,3) = 0.25. It is nonsense to use those values in the same mathematical expression, because the assumption of independence no longer holds. By doing that, I have assumed erroneously that outcomes (1,2), is independent of outcomes (2,3) etc. This is the same as assuming more degrees of freedom than are present for the random variables. Those terms share outcomes and therefore cannot be independent. Therefore when jointly considered, the probabilities will not all be equal to 0.25 as they were in the independent case, and there is nothing quantum or spooky about coins.

Maybe the reason why many people do not understand this is because they are trying hard to make sure the "perfect" experiment is done with absolutely no dependence between one run of the experiment and the next. Unfortunately, the CHSH and other such inequalities require mutual-interdependence between the terms for their derivation. Violation of the CHSH simply reminds us we are not using the right terms.

So in my opinion, Richard and Joy have to agree whether they want to test if the experiment matches QM (terms are independent, different sets of partices), or whether they want to test CHSH (terms are mutually inter-dependent, the same set of particles). A genuine CHSH test experiment has never been performed (loopholes are a red-herring, even if all loopholes are assumed closed, this statement will still be true). All experiments so far have been testing QM not CHSH. It is impossible to test both in the same experiment. A genuine CHSH test will never violate the CHSH, and not all the terms will match QM, though some will. If this bet is about testing the violation of the CHSH with a geniune CHSH test (including counterfactual outcomes form the same set of particles), then it is certainly rigged in Richard's favor and I will strongly advice Joy to stay clear of it. If it is about testing QM with a manifestly local realistic macroscopic system using different sets of particles to calculate independent correlations for settings freely chosen by the experimenter, then it is fair.

[FrediFizzx]

A genuine CHSH test experiment has never been performed (loopholes are a red-herring, even if all loopholes are assumed closed, this statement will still be true). All experiments so far have been testing QM not CHSH.

Hmm... I suspect you are missing something from the opposite direction of what Richard is missing. Or there is something very subtle in CHSH that I am missing. I believe CHSH was specifically designed for an Aspect or Weihs, et al, type of experiment where two angles are randomly selected for A and B per particle pair. I do believe it works for that and has been violated in those kinds of experiments sans any loopholes.

[gill1109]

A genuine CHSH test experiment has never been performed (loopholes are a red-herring, even if all loopholes are assumed closed, this statement will still be true). All experiments so far have been testing QM not CHSH.

Hmm... I suspect you are missing something from the opposite direction of what Richard is missing. Or there is something very subtle in CHSH that I am missing. I believe CHSH was specifically designed for an Aspect or Weihs, et al, type of experiment where two angles are randomly selected for A and B per particle pair. I do believe it works for that and has been violated in those kinds of experiments sans any loopholes.

We are talking about experiments designed to discriminate between QM and LR, which make different predictions concerning correlations E(a, b) between two binary outcomes, depending on two settings a and b, which are directions in space.

Clauser, Horne, Shimony and Holt proposed an experiment, generalising/improving an experiment proposed by Bell.
Aspect, Weihs and others, performed it.

The CHSH idea is to focus on just four of the correlations. We consider a clever choice of directions a1, a2, b1, b2; and look at E(a1, b1), E(a1, b2), E(a2, b1) and E(a2, b2). Under QM the four correlations can be +/-0.7, under local realism they could be maximally +/-0.5; with in both cases, the same pattern, three positive and one negative, or the other way round.

The CHSH experiment was a clever generalization of Bell's experiment which had a1 = b1 and insisted that E(a1, b1) = -1. The CHSH experiment is easier to do and easier for QM to win, than the Bell experiment. In real life experiments you won't find *perfect* anticorrelation at equal settings, so the experiment would always fail.

In all of these classical experiments, for each pair of particles, one measurement only is done on each particle.

Two important things make the experiment loophole free.

(1) For each run, the settings are chosen randomly and independently of everything else. So if there are N runs, there will be about N/4 with each of the four measurement setting pairs. Disjoint.

(2) Each run generates two binary outcomes +/- 1

Now in Joy's experimental papers Joy describes how the directions of spin of two objects will be determined by computer analysis of video movies, resulting in two directions s_k and - s_k, k=1, ..., N. *Given* these two directions, the outcomes of measurements with settings a and b are sign(a . s_k) and sign(b . - s_k) respectively. So this is a major departure from quantum optics measurements where two "black boxes" generates two binary outcomes given two settings (they are both fed information from another "black box", the source). In Joy's experiment we *measure the hidden variables* s_k and - s_k and then *compute* the two binary outcomes. There is only one huge "black box", and out of the black box comes s_k and -s_k.

So it would be perfectly feasible to calculate A(a, b) on all N runs, as well as to calculate it for a random sample of about one quarter of all N runs. Joy said he was completely indifferent to this choice and I am fairly indifferent too: if the measurement settings are chosen by tossing fair coins (altogether N x 2 times) and N is decently large (e.g. 10 000) there won't be much difference.

I am prepared to bet on the outcome of Joy's experiment, as described in Joy's experimental paper. If he wants to *change* the description of the experiment, then the bet has to be re-negotiated; maybe it has to be called off.

Note that Michel's epr-simple computer programs, and my modification of it leading to the current favourite, the Pearle model, can be considered simulations of Joy's experiment, in that the hidden variable, directions s_k and - s_k, are *generated* by some (pseudo) random procedure, and only after that, outcomes sign(a . s_k) and sign(b . - s_k) are *computed*. Michel imposes this separation of these two stages very elegantly with one program computing the s_k's and a different program computing the outputs given the settings.

In both Michel's and Pearle's programs there is however an extra ingredient: a further test is done ensuring that, depending on the settings a and b, some runs k are rejected.

[gill1109]

I do believe it works for that and has been violated in those kinds of experiments sans any loopholes.

There has as yet been no loophole-free successful CHSH-style experiment. It is still perhaps five years in the future, despite 50 years of hard work. The top four experimental groups in the world are racing to be first. I think there will be a Nobel prize in it.

Requirements for a loophole free experiment:

(1) For each run, the settings (a binary choice on each side of the experiment) are chosen randomly and independently of everything else. So if there are N runs, there will be about N/4 with each of the four measurement setting pairs. Disjoint.

(2) Each run generates two binary outcomes +/- 1

Conditions (1) and (2) can easily be imposed on Joy's experiment. I believe that Joy has agreed to them. As Joy has carefully explained, we do the N runs first and get a collection of N directions of spin of two hemispheres (or squishy balls). Store the data in a file, go home. Wait a century if you like ... then pick measurement directions and *compute* binary outcomes etc etc. Just like Michel's epr-simple except that N pairs of spin directions go in, N pairs of settings go in, and N pairs of measurement outcomes come out. Michel only finally outputs about 70% of the pairs of measurement outcomes.

He probably realises that he can't raise this to 100% and at the same time maintain the cosine correlations. People have proven theorems giving the exact limit to the detection rate at which the CHSH quantity is forced below 2.8. Such results go back about 40 years now, it is all very well understood.

[FrediFizzx]

As I said before, we don't care about any loopholes. Joy's model is beyond that since it produces the exact predictions of QM for an EPR-Bohm scenario. Loopholes are for those mis-guided souls that don't think QM actually works correctly. We think QM works correctly but is not a complete theory of nature. We agree with Einstein.

[minkwe]

Hmm... I suspect you are missing something from the opposite direction of what Richard is missing. Or there is something very subtle in CHSH that I am missing. I believe CHSH was specifically designed for an Aspect or Weihs, et al, type of experiment where two angles are randomly selected for A and B per particle pair. I do believe it works for that and has been violated in those kinds of experiments sans any loopholes.

Fred, I'm afraid you too are missing something subtle. I will start a new thread so we can talk about the CHSH. When you say "it works". You mean it is violated? Doesn't that mean it doesn't work?

[minkwe]

The CHSH idea is to focus on just four of the correlations. We consider a clever choice of directions a1, a2, b1, b2; and look at E(a1, b1), E(a1, b2), E(a2, b1) and E(a2, b2). Under QM the four correlations can be +/-0.7, under local realism they could be maximally +/-0.5;

Unfortunately, this still misses the point I've been making. You can not look at the terms E(a1, b1), E(a1, b2), E(a2, b1) and E(a2, b2) from the CHSH inequality and completely ignore how those terms are assembled. All of those terms in the CHSH originate from recombinations of ONLY 4 functions one for each of the so called cleaver choice of directions a1, a2, b1, b2. That is A(a1), B(b1), A(a2), B(b2).
A geniune CHSH test must recombine those 4 measurement functions to produce the 4 correlations, just as was done in the derivation of the inequality. Anything other than this has no relationship with the terms in the CHSH. That is, in a geniune CHSH test, you should be measuring A(a1), B(b1), A(a2), B(b2) and using those to determine E(a1, b1), E(a1, b2), E(a2, b1) and E(a2, b2). This is not done, instead, 8 functions are measured two of which are used to determine each of the correlations.

if you measure 4 functions only and recombine them to produce the correlations, they won't all match QM because the QM correlations are all independent and not generated by recombination. This is why I say all experiments performed to date are testing the QM prediction not the CHSH.

My prediction for Joy's experiment is that the results will match QM and violate the CHSH if all the correlations are independent, calculated from distinct sets of particles, but will not all match QM and will not violate the CHSH if all the correlations are inter-dependent, calculated from the same set of particles. This is clearly illustrated here: viewtopic.php?f=6&t=21&start=20#p515

If Joy agrees to a geniune CHSH test, in which all the correlations are calculated from only 4 functions, ie a single set of particles, he will surely lose the bet because it will be rigged in Richards favor. However, if the bet is about whether the results match QM for all angle pairs freely chosen, then it cannot at the same time be a geniune CHSH test. As a reminder, Bell's theorem says "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics."

I ask again, why is it not enough for Joy's experiment to reproduce all the predictions of QM for the experiment? Why must we introduce confusion in the form of the CHSH or other inequalities? In my opinion, the bet should be centered on whether Joy can disprove Bell's theorem by reproducing all the predictions of QM with a local-realistic system.

[Joy Christian]

I ask again, why is it not enough for Joy's experiment to reproduce all the predictions of QM for the experiment? Why must we introduce confusion in the form of the CHSH or other inequalities? In my opinion, the bet should be centered on whether Joy can disprove Bell's theorem by reproducing all the predictions of QM with a local-realistic system.

That is exactly what I have proposed in my papers (see, for example, here and here), and that is exactly what I have described on my blog as well.

So I too fail to see why the preoccupation with CHSH when the set up of my experiment is manifestly local and realistic. My own interest lies only in observing

E(a, b) = -a.b.

That, for me, is more than enough, since there is no possibility of mischief like remote parameter dependence or remote outcome dependence in my set up.

[minkwe]

So I too fail to see why the preoccupation with CHSH when the set up of my experiment is manifestly local and realistic. My own interest lies only in observing

E(a, b) = -a.b.

That, for me, is more than enough, since there is no possibility of mischief like remote parameter dependence or remote outcome dependence in my set up.

Joy, I thought as much, that what you've written is very clear. I guess we have to hear Richard's opinion why it is not enough for the bet that the experiment disproves Bell's theorem by reproducing all the predictions of QM without any reference to the CHSH.

[FrediFizzx]

It doesn't really matter because if the experiment does indeed show E(a, b) = -a.b then the "real" CHSH is violated automatically since it is the same result as QM.

[gill1109]

It doesn't really matter because if the experiment does indeed show E(a, b) = -a.b then the "real" CHSH is violated automatically since it is the same result as QM.

Exactly! But for a bet we need a simple unambiguous criterion for who has won. And to make the experiment feasible we should grab any opportunities for major economic savings. The budget is not going to be Higgs boson size, unfortunately. Though this experiment is arguably much, much more important.

I insist on the following: take the four standard setting pairs of CHSH. They are cleverly chosen so that E(a, b), E(a, b'), E(a', b) and E(a', b') have the same absolute value but different signs. According to QM, three are equal to +0.7 and one is equal to - 0.7. According to LHV, three can at most equal +0.5 and one -0.5. This is the biggest difference between QM and LHV which you can get. So it's the most sensible spot to focus the experiment on. We needn't measure E(a, b) for every a and every b, but just pick four points where we should most clearly be able to see who's right!

If Joy is right that E(a, b) = - a.b and N is large enough that we may ignore statistical error, Joy will win. If I am right and N is large enough I will win. N needs to be large enough that the error bars on the curve are very small, relative to the difference (0.7 versus 0.5) in the theoretical correlations under the two models.

It's a question of time and money. Why do a zillion runs to estimate E(a, b) for incredibly many different a and b, when 10,000 runs, two different a's and two different b's (four different combinations) is enough to settie the matter? We measure the correlation at four judiciously chosen points where the theories differ most in their predictions.

[gill1109]

I ask again, why is it not enough for Joy's experiment to reproduce all the predictions of QM for the experiment? Why must we introduce confusion in the form of the CHSH or other inequalities? In my opinion, the bet should be centered on whether Joy can disprove Bell's theorem by reproducing all the predictions of QM with a local-realistic system.

Of course it is enough if the experiment reproduces *all* the predictions of QM. But it is also enough for me to admit defeat, if the experiment reproduces only a few of them! Four, to be precise.

About the issue of different sets of exploding pairs of squishy balls for each different correlation, or the same set, let me remind everyone that Joy has repeatedly written that this choice is a matter of complete indifference to him. His experimental paper unambiguously describes an experiment where the same N runs provide the same directions s_k and -s_k for every single correlation E(a, b) which we want to look at.

Joy challenged me to a bet on his experiment. I accepted the bet subject to some three main basic conditions. My first condition is that we decide who has won by consideration of just four points on the curve, not the whole curve. My second condition is that I get to supply random sequences of settings a and a' for Alice, b and b' for Bob. My third condition is that each run generates two binary outcomes (there will be 100% detection rate).

Joy already accepted my three conditions, subject to some further "security measures" of his own. I also have "security requirements" e.g. how large is N?

The adjudication committee (Khrennikov, de Raedt, Weihs) will advise us drawing up a definitive protocol, and will adjudicate if any conflicts arise in the implementation.

Forum participants' advice is welcome, but Joy and I both have to be wary if goal posts get moved. The bet is a way to provoke public interest in the experiment and that leads to financial means to do it (crowd funding). I fear that if there is no bet there will be no experiment. I have put my conditions on the table.

BTW, I also accepted Khrennikov and de Raedt's invitation to Vaxjo, and I will present the bet there publicly. My revised paper with my new proof of CHSH is up on arXiv and is hopefully soon accepted by "Statistical Science" (which is published by the IMS: the Institute of Mathematical Statistics; it's one of the highest impact journals in the field) for their special issue in causality. The referees and editors (statisticians and physicists) asked only for minor editorial improvements. They rather liked Theorem 1, and they liked the material on Randi challenges.

[Joy Christian]

It doesn't really matter because if the experiment does indeed show E(a, b) = -a.b then the "real" CHSH is violated automatically since it is the same result as QM.

That is what I am counting on. To me it is clear that the experiment will inevitably show E(a, b) = -a.b, regardless of CHSH or statistics (as long as N is sufficiently large). I am convinced about this since 2007. My confidence comes, not from knowing that Bell's argument is wrong or that CHSH is baloney, but from elementary classical mechanics of rotations. All it takes is some basic understanding of how rotations work in the physical space to know that E(a, b) will be equal to -a.b in my proposed experiment. It cannot be otherwise.

Having said that, I do take Michel's concerns very seriously. After all, we are talking about a real life experiment involving a large number of trials. So statistics and statistical trickery are definitely part of the game.

[gill1109]

Having said that, I do take Michel's concerns very seriously. After all, we are talking about a real life experiment involving a large number of trials. So statistics and statistical trickery are definitely part of the game.

If the number of trials is very large, statistics are irrelevant and statistical trickery is impossible. As Rutherford said, if you need statistics, you did the wrong experiment.

However, if you indeed take Michel's concerns seriously, are you going to revise your experimental paper in order to address them, and then propose a bet with me, or are we having a bet on the basis of the original proposal in your experimental paper?

Original proposal from your experimental paper: *all of the correlations* are based on the *same* set of N direction pairs lambda and - lambda, computed once and for all from N sets of videos of N pairs of exploding balls or whatever.

Michel advises against this.

Alternative proposal (closer to usual CHSH practice): each of just four particular correlations is based on a (disjoint) sample of about N/4 of the complete set of directions.

Michel knows this would be fine.

He knows a thing or two about statistical degrees of freedom and he knows that the CHSH bound does not apply in this case. The only certain bound one can give is 4. I must say, that he's absolutely right there. That's why I made a careful study of probabilistic bounds, like: ... <= 2 + epsilon with probability at least 1 - A exp(- N B epsilon^2). But don't worry, Fred and Michel are both absolutely certain that my Theorem 1 has absolutely no relevance to real experiments, nor to real computer simulations for that matter. Since hidden variables are by definition hidden it makes no sense to randomly sample them. And counterfactual definiteness is an oxymoron. How can something exist which doesn't exist?

"Randomization" is how we in statistics make sure that experiments are valid (unbiased). We do randomization in order to *prevent* trickery (bias...).

Please make up your mind. There will be no trickery, either way. I'll submit my random choices to the adjudication team who can check them. I'll create them with R's state of the art pseudo random number generator, with intial seed (a 32 bit integer) generated by 32 real coin tosses, filmed on video in the presence of the adjudicators, saved and written down, so everyone can check there was no cheating. Everyone can reproduce the sequence of pseudo random choices (between a and a', and between b and b') in deterministic fashion from my inItial random seed. I have no way of knowing in advance what they'll be.

If the four correlations we minimally need to find are to be based on different subsets of trials, I insist on selecting them at random (as just described), CHSH-style. Otherwise: no bet.

[Joy Christian]

You have no worries! But please make up your mind.

I am not worried. The bet is on based on what I have written and proposed in my experimental paper(s): http://libertesphilosophica.info/blog/e ... taphysics/

Just to make sure that my only other condition is on the record here, I quote myself from the FQXi forum where the bet was first discussed:

OK, I propose that you first prove to the adjudicators (without letting me or the experimentalists know) that QM does predict |CHSH| > 2.414 for your chosen settings. This way I can be sure that you are not cheating. In any case, if you read the last page of the attached paper you will see that settings need not be chosen before all the runs are completed. You will also see that there cannot be any non-detections in the experiment.

[gill1109]

You have no worries! But please make up your mind.

I am not worried. The bet is on based on what I have written and proposed in my experimental paper(s): http://libertesphilosophica.info/blog/e ... taphysics/

Just to make sure that my only other condition is on the record here, I quote myself from the FQXi forum where the bet was first discussed:

OK, I propose that you first prove to the adjudicators (without letting me or the experimentalists know) that QM does predict |CHSH| > 2.414 for your chosen settings. This way I can be sure that you are not cheating. In any case, if you read the last page of the attached paper you will see that settings need not be chosen before all the runs are completed. You will also see that there cannot be any non-detections in the experiment.

Joy, *you* choose the *values* of the settings. You fix two settings for Alice and two settings for Bob. It's a matter of complete indifference to me what you take. You call Alice's two settings "setting 1" and "setting 2", similarly for Bob.

I am only going to provide sequences of coin tosses to determine which of Alice's two settings, and which of Bob's two settings, holds in each run. Heads for setting 1, tails for setting 2. OK?

If *you* are smart *you* will pick the usual CHSH choices based on cosine(45 degrees) = 1/sqrt 2 = 0.70, cosine(135 degrees) = -1/sqrt 2 = -0.7. Picking out the points where the difference between the QM cosine and the LHV saw-tooth curve is maximal. The standard CHSH settings make all the differences between Alice and Bob's angles equal to 45 degrees or 135 degrees. Hence all four correlations are equal to +/- 0.70. Three positive and one negative (or three negative and one positive). 4 times 0.7 = 2.8. You must know all this... do I have to look it up for you? I recommend you figure it out for yourself! This is *your* call; you want to pick the settings which maximally violate Bell-CHSH!

I think you can find them in my paper. I wrote there: α = 0, α′ = π/2, β = 5π/4, β′ = 3π/4. Just check cos(alpha_i - beta_j) for i = 1, 2; j = 1, 2. See Figure 2, page 7, http://arxiv.org/abs/1207.5103 (version 3 or version 4 - probably going to be the final version).