Bell & CHSH type inequalities and experiments

[Mikko]

1. The CHSH inequality is a statement about the upper bound of a relationship between 4 mutually dependent expectation values.
2. It does not apply to independent terms.

Does it say anyting about independent estimations of dependent expectations values?

[gill1109]

Michel Fodje says no. It seems that according to Michel, all experiment is meaningless since we know in advance the result will lie between -4 and 4; and that's all we can say. Fred Diether has the same opinion.

Aspect, Weihs and all the others needn't have bothered. They should have stayed at home. Their result was a forgone conclusion.

Michel can get anything between -4 and +4 in his simulations. So can Hans de Raedt, though Hans only publishes the results which fit to quantum mechanics (which says the result lies between -2.828... and +2.828...), not the ones which violate quantum mechanics, is Hans scared to upset the physics community?

I can get anything between -4 and +4, I published that many years ago, no one was interested.

Strange world. What is science coming too?

[minkwe]

Does it say anyting about independent estimations of dependent expectations values?

Mikko,
Are the results from tossing two coins independent estimations of the counterfactual results of tossing just one. This is the question, for Mikko only.

[Mikko]

Does it say anyting about independent estimations of dependent expectations values?

Mikko,
Are the results from tossing two coins independent estimations of the counterfactual results of tossing just one. This is the question, for Mikko only.

Your question is again as vague as usually. Anyway, some of the results are, others are not.

[minkwe]

So your original statement which I quoted is vague? Make up your mind. You haven't answered any of the questions in this thread. I guess they are all too vague for you. Let me rephrase the central question, then maybe you will answer it this time:

1. For a single coin toss where H = +1 and T = -1, where A is the outcome you get, and B is the other outcome you didn't get but could have gotten, A + B has a maximum value of 0. If you generate a spreadsheet with columns A and B for the single coin and toss that coin 1 million times (call it experiment I), <A> + <B> still has a maximum value of 0. You will never violate this bound, even by experimental error. Agree or disagree?

2. Now take two separate coins each of identical type as in the first case. Now A is the actual result from the first coin, and B is the actual result from the second coin. The linear combination of A + B for the two coins has a maximum value of 2, not 0. Throw the pair of coins 1 million times and record the *actual* results on two columns of a spreadsheet A and B (call this experiment II). The maximum value of <A> + <B> will still be 2 not zero. Agree or disagree?

3. Now somebody takes two special coins, tosses them 1 million times (like in experiment II), and obtains a result of <A> + <B> = 0.5. Can they now claim that since they violated the maximum of 0, it means coins do not have 2 sides, or unmeasured sides of coins do not exist? It makes no sense for them to say, their coin has violated the maximum of 0. Agree or disagree?

4. Just because their special coins produce <A> + <B> = 0.5 for actual results from pairs in experiment II does not mean performing the experiment I with each of those coins will violate the maximum of 0. Each of the special coins still will NEVER violate the maximum of 0. Agree or disagree?

5. Just because <A> from experiment II is an estimate of <A> from experiment I and <B> from experiment II is an estimate of <B> from experiment I does not mean that the maximum value from experiment I applies to experiment II. Agree or disagree?

6. Just because those particular special coins always produce <A> + <B> = 0.5 for experiment II, does not mean it is impossible for a different type of coin to produce say 0.9. Agree or disagree?

7. Yet no matter the type of special coin anyone can concoct, experiment I will still always produce a maximum of 0 and never more. Not even by 0.000000001. Just as experiment II will never produce any value above 2, not even by experimental error. Agree or disagree?

[gill1109]

1. Agree. In fact, in Experiment 1, | <A> + <B> | = 0 with probability 1 (here <A> denotes the average of the experimental outcomes, etc.)

2. In Experiment 2, the maximal value of <A> + <B> is 2 but I would happily bet heavily on | <A> + <B> | < 0.1

3. If the third experiment, Experiment 3, resulted in <A> + <B> = 0.5, I would be inclined to reject the hypothesis that the coins were normal coins and that they were tossed either in the way described in Experiment 1, or in the way described in Experiment 2. One might say colloquially that the experiment exhibited a violation of the theory that E(A) + E(B) = 0. Here, E(A) stands for the expectation value of A in a mathematical model of a fair coin toss. Not to be confused with <A>, an average of finitely many observed values. Both for Experiment 1, and for Experiment 2, theory says E(A) + E(B) = 0. Theory says <A> + <B> = 0 for Experiment 1. Theory does not say <A> + <B> = 0 for Experiment 2.

I don't see the point of trying to answer the subsequent questions because you are mixing up experimental averages, which are subject to statistical error, with theoretical mean values. You confuse the maximal value which an experimental average might possibly take, with the maximal value which a theoretical mean value might have according to some theory.

Please now take a break, and do that silly R experiment of mine. Then we might be able to get back on track, preparing Joy's experiment, and finalizing the conditions of the bet on its outcome. But till then ... no experiment, no bet.

[minkwe]

2. In Experiment 2, the maximal value of <A> + <B> is 2 but I would happily bet heavily on | <A> + <B> | < 0.1

And you would lose that bet because you assumed erroneously I was talking about a specific type of coin when I was talking about ALL local realistic coins.

3. If another experiment, Experiment 3, resulted in <A> + <B> = 0.5, I would be inclined to reject the hypothesis that the coins were normal coins

You assumed erroneously I was talking about a specific type of coin you have in your mind not realizing that my statements were about ALL locally realistic COINS, with heads and tails and only two possible outcomes. No other assumptions about the coin other than that it is a coin, with two sides.

and that they were tossed either in the way described in Experiment 1, or in the way described in Experiment 2. One might say colloquially that the experiment exhibited a violation of the theory that E(A)+E(B)= 0

.
Now let me show you that my "special coins" are local realistic and do not violate anything in Experiment 1. Ready:

My coins are biased to show heads 62.5% of the time and tails 37.5% of the time, ie a P(H) of 0.625 and P(T) of 0.375. Note that the coins are still local realistic and if you throw just one of them each time and write down the results in a spreadsheet (experiment 1), A + B will still never be different from 0, and neither will <A> + <B>. Yet, if you do experiment 2, <A> + <B> will NEVER violate the upper bound of 2 even though it will exceed 0 with a very high probability. No bounds are violated. Hopefully, now you understand what you've been missing.

I don't see the point of trying to answer the subsequent questions because you are mixing up experimental averages, which are subject to statistical error, with theoretical mean values.You confuse the maximal value which an experimental average might possibly take, with the maximal value which a theoretical mean value might have according to some theory.

The remaining questions are important too. You keep talking about statistical error but you are unable to produce the data of experiment 1, which violates <A> + <B> = 0. I've asked you many times, introduce as much error as you like all I ask is that you produce experiment 1 data which violates <A> + <B> = 0, by 0.0000000001.

Now for the last time, your R-code is not interesting because it is a simulation of a specific type of fair coin and it's results are irrelevant to discussions about ALL local-realistic coins. Again, providing a simulation which proves that throwing two fair coins will produce a result of <A> + <B> close to 0 with high probability does not prove that ALL local realistic coins will produce a result close to 0 as you erroneously think. So your R-code is pointless indeed.

Please now take a break, and do that silly R experiment of mine. [...] But till then ... no experiment, no bet.

Did you really threaten to quit your bet with Joy, unless *I* translated your pointless R-code to python? Or did I misunderstand your statement?

[gill1109]

I quit the bet unless I get some help with the technical preparations. I need a Python translation, and a Mathematica translation, of the code which determines who has won. It needs to be tested and verified by independent and critical people. By people who believe I lie and cheat and/or am completely incompetent.

The little bit of code I asked you to test is not pointless. It is part of the bet evaluation code.

It moreover illustrates an important point which so far you appear to be totally unaware of, making rational discussion rather difficult. We keep going round in circles, right? Maybe *you* are missing something? Maybe Adenier, de Raedt, and whatsisname from South Africa who publishes on viXra (ah, Elmer Rosinger?), are missing the same thing? Maybe, so are Joy Christian and Fred Diether? Look: lots of smart people, so it's unlikely. But it is possible, I would think, since lots of other smart people are pretty sure that those smart people all overlooked the one and the same thing. In the history of science, lots of smart people have overlooked little key facts, for hundreds of years, even though other smart people saw them, all that time.

I only said "maybe".

I only ask for 30 minutes of your time.

Why this refusal to take a look at 20 lines of code? Afraid of what you'll see? Surely not...

And indeed, why this obsession with bounds and inequalities?

Regarding the experiment, the question is, is E(45) = -0.707 and is E(135) = +0.707 ?

Or is E(45) = -0.5 and is E(135) = +0.5 ?

E(theta) stands for the theoretical expectation value (mean, ensemble average, population average) of A times B when the settings differ by 45 degrees.

In an experiment we observe the average of perhaps only 10 000 realizations of A times B, for each of four pairs of settings.

In an experiment there is always experimental error. 10 000 is large but finite so there's always statistical error. There's a chance we'll see -1.0 at 45 degrees, and +1.0 at 135 degrees, right? There's a chance we'll see 0.00 at both, right?

When people say "we observed a violation of CHSH" they mean that they observed correlations much closer to +/- 0.7 than +/- 0.5, and that the statistical error is much smaller than 0.1, so that one can have confidence that this was not just due to chance.

Get it?

[Mikko]

You haven't answered any of the questions in this thread.

I have. But I don't see any need to answer all questions. I'm a little slow so often someone else answers before me. Some questions are too far from the topic of the thread. Or perhaps otherwise uninteresting.

[gill1109]

Mikko: about translation to Python: it is important that *independent* persons verify my code and one way to do that is by making translations to other languages. Nobody should trust me.

Sure I could learn Python and actually I already did use it many times. Seems we should use Python 2, and not the more modern Python 3. It would be nice, however, if the code were Python 3 compatible. It should be clean, short, transparent. Use only easily available packages. As platform independent as possible.

[minkwe]

I quit the bet unless I get some help with the technical preparations. I need a Python translation, and a Mathematica translation, of the code which determines who has won.

That your bet with Joy is *dependent* on third parties who are not on your adjudicating committee is very strange indeed. I suspect you now see that you cannot win it given the revelations in this thread and would rather get out of the bet while you still can. That is a wise decision. But to suggest that you are quitting because I won't translate your code to Python makes no sense. Besides, you do not *need* Python or Mathematica translations. In fact you do not need a single line of code of any language. It should be up to the adjudicating committee to decide if the results of the experiment favor Joy or you. They will request any code they see as appropriate.

The little bit of code I asked you to test is not pointless. It is part of the bet evaluation code. It moreover illustrates an important point which so far you appear to be totally unaware of, making rational discussion rather difficult.

I've explained clearly why it is pointless. You haven't provided a single explanation why you think it isn't. In a rational discussion, you would present your code, present the results, and discuss why the results are relevant to the issue being discussed (in the appropriate thread). You won't just put out a piece of code and say "run it or I quit, translate it to python or I quit".

In the history of science, lots of smart people have overlooked little key facts, for hundreds of years, even though other smart people saw them, all that time.

Agree! And I've just demonstrated to you one example, as clear as a crystal, using local realistic coins, which you and many other smart people including Bell, have missed for half a century.

Why this refusal to take a look at 20 lines of code? Afraid of what you'll see? Surely not...

Because I know exactly what the code is all about, and I know in great detail and precisely the point you're missing which is carried over to the code. Because I know that if you really understood the issue, you will not suggest such irrelevant code as a counter argument. Because I have explained to you clearly, what the issue is and you did not listen. Because I have explained it again using a very clear example, but you will not listen:

Now for the last time, your R-code is not interesting because it is a simulation of a specific type of fair coin and it's results are irrelevant to discussions about ALL local-realistic coins. Again, providing a simulation which proves that throwing two fair coins will produce a result of <A> + <B> close to 0 with high probability does not prove that ALL local realistic coins will produce a result close to 0 as you erroneously think.

And indeed, why this obsession with bounds and inequalities?

You must be joking right? For the past 50 years, the quantum foundations community has been obsessed with inequalities! Claiming that QM violates them, experiments violate them, using those to claim that the moon does not exist when nobody is looking at it, claiming that particles instantaneously influence others at a distance. You have been an integral part of that, having published many papers about bounds, variations of inequalities, modifications of inequalities under different types of loopholes etc, and made a few claims yourself about realism being untenable because certain inequalities are violated. It clearly has been a profitable "business" for you.

And now you are asking me why the obsession with inequalities? After I've just demonstrated to you that the whole obsession was due to one big and silly mistake?

[gill1109]

Michel, I am not talking about inequalities and bounds with you any more.

Joy and I are going to do his experiment and compute

- E(0, 45) + E(0, 135) - E(90, 45) - E(90, 135)

on the basis of the data which is made available by his experiment. Then we will determine who has won depending on whether the result is closer to his prediction (2.8) or mine (2.0).

There will be no bet unless someone independently does some code translation for us. This is not the job of the adjudication committee. Joy and I negotiate with the adjudication committee, not you. If you want to tell them how to do their job you can b****y well talk to them yourself, privately.

Do you want to be part of the solution or are you going to remain part of the problem?

If there is no bet there will probably be no experiment. You want to sabotage the experiment, right?

[minkwe]

If there is no bet there will probably be no experiment. You want to sabotage the experiment, right?

Amusing. I didn't know I was that powerful and can sabotage a bet between two other people by refusing to translate a piece of code.

On the other hand, if I have now successfully convinced one of the parties in the bet that they have been missing a very trivial point (although they will never admit it), and they've now changed their minds about the bet, that is a wise decision and I'll be happy for them.

[gill1109]

If there is no bet there will probably be no experiment. You want to sabotage the experiment, right?

Amusing. I didn't know I was that powerful and can sabotage a bet between two other people by refusing to translate a piece of code.

On the other hand, if I have now successfully convinced one of the parties in the bet that they have been missing a very trivial point (although they will never admit it), and they've now changed their minds about the bet, that is a wise decision and I'll be happy for them.

I have not changed my mind about the bet. I want the experiment to happen, so that I can win my bet.

But it is not just about winning. It is about convincing everyone else (esp. everyone participating in the forum here), that I honestly, fairly and squarely, won. No cheating. Everything completely open. Everything checked and double-checked by many different people with different backgrounds and different opinions. No cheating. Nothing rigged. (This is not the job of the adjudicators. The adjudicators merely have to pronounce on the outcome. If we do the pre-experiment stuff right, the adjudicators hardly have to do anything. Just read the computer print-out and announce the winner).

To make the experiment happen, we have to have all kinds of practical details set up in advance, and agreed. One of those details is how exactly the data will be analyzed. It's important that *everyone* agrees what is going to happen, in advance. If we rely on a piece of R code written by me, not checked by anyone, then after the experiment, when Joy loses, he'll say it was because I cheated.

[minkwe]

To make the experiment happen, we have to have all kinds of practical details set up in advance, and agreed. One of those details is how exactly the data will be analyzed. It's important that *everyone* agrees what is going to happen, in advance.

I have just explained in this thread and the other, why the manner in which the analysis is done is relevant to the bet. I have shown that using data from a single set of particles will never violate anything, while using data from different sets can. I have explained that experiments are using data from different sets and QM predicts results for different sets and that is why they can appear to violate the CHSH. I have explained why it will be cheating to use data from a single set of particles to compare with QM and experiments. If you believe it doesn't matter whether we use a single set of particles, or two different sets of particles, then you should agree to do the experiment on distinct sets of particles just like QM predicts and experiments currently measure, and analyze the data in the same way. Joy has agreed to that but you are equivocating. Why? Unless you believe it does matter.

[gill1109]

To make the experiment happen, we have to have all kinds of practical details set up in advance, and agreed. One of those details is how exactly the data will be analyzed. It's important that *everyone* agrees what is going to happen, in advance.

I have just explained in this thread and the other, why the manner in which the analysis is done is relevant to the bet. I have shown that using data from a single set of particles will never violate anything, while using data from different sets can. I have explained that experiments are using data from different sets and QM predicts results for different sets and that is why they can appear to violate the CHSH. I have explained why it will be cheating to use data from a single set of particles to compare with QM and experiments. If you believe it doesn't matter whether we use a single set of particles, or two different sets of particles, then you should agree to do the experiment on distinct sets of particles just like QM predicts and experiments currently measure, and analyze the data in the same way. Joy has agreed to that but you are equivocating. Why? Unless you believe it does matter.

When you have done *my* experiment http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=40, you'll see the difference. Do I certainly win? Or do I only win with very large probability? (Note: the bet is decided by CHSH > 2.4, yes or no.)

[Heinera]

I have explained why it will be cheating to use data from a single set of particles to compare with QM and experiments. If you believe it doesn't matter whether we use a single set of particles, or two different sets of particles, then you should agree to do the experiment on distinct sets of particles just like QM predicts and experiments currently measure, and analyze the data in the same way. Joy has agreed to that but you are equivocating. Why? Unless you believe it does matter.

Why do you keep repeating this blatantly false BS? It is Joy that insists on leaving "nothing to chance." From earlier in the thread:

Richard believes Apples are really Oranges due to some kind of statistical tricks. If he has confidence in his work, he shouldn't mind if you guys bet to do an Orange experiment. But he appears to mind because he keeps insisting on calculating everything on the same set.

Uuuuhh...? Keeps insisting? I guess the situation is exactly the opposite: When Richard explained he was perfectly happy with calculating the correlations on four different, random subsets (provided N was sufficiently large), he got this reply:

We leave nothing to chance. We follow the first procedure. All the other variants with the data will be tried later by many people if the strong correlations are seen.

But obviously you are correct that when everything is measured on the same set of vectors, Joy can't win the bet. Since you agree, I guess that means you understand the simple proof of why that must be the case.

Obviously, Joy does not understand the proof, or he would not have insisted that measuring everything on the same set is the way it should be done (also clear from his papers).

So, since he clearly doesn't understand an elementary proof that only uses high school math, why in heaven's name do you trust him to be correct in his own proof where he has to handle geometric algebra, Riemann-surfaces, Hopf fibrations and 4D spheres? (To name just a few)

[minkwe]

Sorry Heinera, Richard already lost the bet:

2. In Experiment 2, the maximal value of <A> + <B> is 2 but I would happily bet heavily on | <A> + <B> | < 0.1

My coins have p(H,T) = (0.625,0.375), ie a P(H) of 0.625 and P(T) of 0.375. In experiment 2, <A> + <B> = 0.50 with a very high probability.

Heinera, if you and Richard understood the proof, you will not believe as you both do that there is anything unuasual about QM correlations. Richard will not be writing papers claiming non-realism. You will not be making claims that LHV is impossible.

[minkwe]

I have explained why it will be cheating to use data from a single set of particles to compare with QM and experiments. If you believe it doesn't matter whether we use a single set of particles, or two different sets of particles, then you should agree to do the experiment on distinct sets of particles just like QM predicts and experiments currently measure, and analyze the data in the same way. Joy has agreed to that but you are equivocating. Why? Unless you believe it does matter.

Why do you keep repeating this blatantly false BS? It is Joy that insists on leaving "nothing to chance."

It is you that is talking BS.

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.

For the record, let me repeat that equation (16) of my attached
experimental paper describes exactly how the expectation values
E(a, b), E(a', b), E(a, b'), and E(a', b') are to be computed in my
proposed experiment. Four separate sums are to be calculated as
follows

E(a, b) = 1/N Sum_j A_j B_j ,

E(a, b') = 1/N Sum_j A_j B'_j ,

E(a', b) = 1/N Sum_j A'_j B_j ,

and

E(a', b') = 1/N Sum_j A'_j B'_j .

It is a matter of indifference whether N here is chosen to be the same
or different for each of the four alternatives.

The experimental procedure described in my paper is unambiguous.

[FrediFizzx]

Ok, so you and Joy only want the list of vectors to reproduce all quantum correlations for any choice of a and b. Forget CHSH. Should these correlations all be computed on the same set of vectors, or a different set for each choice of (a,b)? Because if the latter is the case, and since there is an infinite number of (a,b), the experiment would have to go on for forever.