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by **gill1109** » Wed Apr 23, 2014 11:44 pm

Joy Christian wrote:
gill1109 wrote:The reason I can generously go to 0.2 rather than the symmetric cut-off 0.1 is because all chance has been totally eradicated. My "spread-sheet argument" (the math core of CHSH) says that -E (0, 45) + E(0, 135) - E(90, 45) - E(90, 135) is less than or equal to 2. No probability. This is certain.

And yet Nature says -E (0, 45) + E(0, 135) - E(90, 45) - E(90, 135) = 2.828427125...

And that is what we shall observe.

And that is why we are doing the experiment: to learn from Nature!

by **Joy Christian** » Wed Apr 23, 2014 11:13 pm

gill1109 wrote:The reason I can generously go to 0.2 rather than the symmetric cut-off 0.1 is because all chance has been totally eradicated. My "spread-sheet argument" (the math core of CHSH) says that -E (0, 45) + E(0, 135) - E(90, 45) - E(90, 135) is less than or equal to 2. No probability. This is certain.

And yet Nature says -E (0, 45) + E(0, 135) - E(90, 45) - E(90, 135) = 2.828427125...

And that is what we shall observe.

by **gill1109** » Wed Apr 23, 2014 11:01 pm

The reason I can generously go to 0.2 rather than the symmetric cut-off 0.1 is because all chance has been totally eradicated. My "spread-sheet argument" (the math core of CHSH) says that -E (0, 45) + E(0, 135) - E(90, 45) - E(90, 135) is less than or equal to 2. No probability. This is certain. Just substitute the four expressions for E and merge the four sums over k = 1 to N into one sum. You don't have to actually do it, and Joy has forbidden it to be actually done, but unfortunately in a thought experiment nothing is forbidden. And pure mathematics is pure thought experiment.

If each of the four terms is within 0.2 of 0.7071, then the smallest that that thing can be is 4 * (0.7071 - 0.2) = 4 * 0. 5071 = 2 + 4 * 0.071 = 0.284 > 2. Contradiction. So at least one must be within 0.2 of 0.7071.

It's very neat. (This was Heinera's brilliant idea).

by **Ben6993** » Wed Apr 23, 2014 3:53 pm

Hi Richard

I had noticed that you had mentioned 0.2 rather than 0.1. I would have stayed with a symmetric cutoff correlation coefficient of 0.6, but never mind.

Don't feel guilty about being certain that you will win the bet. You seem to me to have been scrupulously fair at all times in this forum wrt the bet. A number of times you have suggested different versions of the bet which would have meant that you were less sure of winning and possibly that is because you do not want it to be too easy for yourself. But on the other hand you said the experiment should be done without the need for a complex probability judgement to determine the winner. And you now have that. You are sure, Joy is sure. That seems ideal.

by **gill1109** » Tue Apr 22, 2014 7:48 am

Ben6993 wrote:If I read it correctly, Joy's recent post on FQXi is a stunner. He doesn't need your, nor anybody's, computer programs. He probably doesn't even need a computer, spreadsheet or calculator. He just needs the back of an envelope to record the four numbers in categories 00, 01, 10 and 11. Just to be calculated for one pair of a and b values. He is probably correct!

Dear Ben

Yes it is a stunner. Well, we do need computer programs, but they are so simple there is no need to discuss coding issues now.

Speaking metaphorically, I need the back of four envelopes. Joy will only need one, to check my finding.

The experiment (N exploding balls, and analysis of a a lot of video footage of those explosions) generates two computer files each containing N directions of angular momentum. Spherical coordinates theta (azimuth), phi (zenith).

Let's call the directions of angular momentum in Alice's file u_k, k=1, ..., N, and in Bob's file v_k, k = 1, ..., N

In theory one would have v_k = - u_k, but in practice that might not be exactly the case.

If I pick measurement directions a and b, then according to Joy's experimental paper the outcomes left and right are

A_k = sign(a . u_k) and
B_k = sign(b . v_k),

and the estimated (observed, sample, experimental ...) correlation is

E(a, b) = 1/N sum_k A_k B_k
= ( N(++) + N(--) - N(+-) - N(-+) ) / ( N(++) + N(--) + N(+-) + N(-+) )

in the obvious notation.

Joy predicts the theoretical (population, large N limit, ensemble) correlation rho(a, b) = - a . b = - cos(angle between a and b)

Now we are going to look at two possible directions for Alice and two for Bob. They are all in the equatorial plane so they can be described just by azimuthal angles alpha = 0 and 90 for Alice and beta = 45 and 135 for Bob.

Joy predicts

E(0, 45) = - 0.7071...,

E(0, 135) = + 0.7071...,

E(90, 45) = - 0.7071...,

E(90, 135) = - 0.7071....

I will win my bet if I show him that one of these four predictions has failed, by an amount 0.2 or more.

He will give me two computer files "AliceDirections.txt" and "BobDirections.txt"
I'll claim that I'll be able to show him that one of his predictions has failed by a large amount (0.2 in either direction, or more).

I am actually certain that I will win. Notice that I even generously went to 0.2 whereas in my old proposal (when we randomly sampled subsets of the runs) I only went to 0.1

by **gill1109** » Mon Apr 21, 2014 1:40 pm

Ben6993 wrote:If I read it correctly, Joy's recent post on FQXi is a stunner. He doesn't need your, nor anybody's, computer programs. He probably doesn't even need a computer, spreadsheet or calculator. He just needs the back of an envelope to record the four numbers in categories 00, 01, 10 and 11. Just to be calculated for one pair of a and b values. He is probably correct!

Of course one can count four kinds of outcomes on the back of an envelope. But if you are making a bet with someone, you need to agree in advance who is going to count what.

If you only use one value of a and one value of b, known in advance, you prove absolutely nothing. There is nothing remarkable about a correlation of +/- 0.7. The remarkable thing is the pattern of four correlations, three - 0.7, and one + 0.7. In fact the whole mystery revolves around the joint distribution of four binary variables - Alice setting, Alice outcome, Bob setting, Bob outcome.

Which is too complicated a concept for anyone to understand intuitively.

Sounds to me that Joy's stunning post yet again exhibits his total lack of understanding what the whole thing is about.... but then I read Heinera's recent post on the forum here, with a stunningly original idea.

Brilliant!

We do the experiment.
Joy hands me over the two files of N directions of angular momentum, u_k and -u_k, k=1, ..., N.
I will then produce a pair of measurement directions a and b such that the computed correlation differs from the QM correlation by at least +/- 0.2!

by **Ben6993** » Mon Apr 21, 2014 10:32 am

I should have written: categories --, -+, +-, ++ rather than 00, 01, 10 and 11.

by **Ben6993** » Mon Apr 21, 2014 8:12 am

Hi Richard

I have read more on counterfactual reasoning and agree that my example was as you said.

Thank you very much for the link to your statistical paper on historical demography, which I will read.

I had seen the video of your TEDx talk a few days earlier than your post. A nurse was charged yesterday concerning three death at Stepping Hill hospital, Stockport, which is not much more than ten miles from me. I don't know the details of this case and whether probabilty calculations played any part in the accusation.

If I read it correctly, Joy's recent post on FQXi is a stunner. He doesn't need your, nor anybody's, computer programs. He probably doesn't even need a computer, spreadsheet or calculator. He just needs the back of an envelope to record the four numbers in categories 00, 01, 10 and 11. Just to be calculated for one pair of a and b values. He is probably correct!

by **gill1109** » Tue Apr 15, 2014 9:42 am

Ben6993 wrote: Someone will have estimated that a man in, say the 1700s, usually gets married at age 25 and so will invent a birth record dated 25 years before the marriage and place that on the IGI site. Is that fake birth record not a "wax apple"? A naive user of the site could take the supposed birth record as genuine.

This is nothing to do with counterfactual reasoning. This is to do with modelling the data generation process. There is some truth: some actual marriages, births, and so on. There is the data which we have today. There is a whole process in between. I have written one paper about historical demography which generated quite a large literature. http://www.academia.edu/6425295/Nonparametric_Estimation_under_Censoring_and_Passive_Registration

In statistics one learns that one should not only model the underlying (physical/historical/biological/...) phenomonen but also the process whereby you gain some information about it. The messenger is part of the message. See my TEDx talk https://www.youtube.com/watch?v=cbkdhD6BsoY

by **Ben6993** » Tue Apr 15, 2014 2:45 am

Richard wrote:

"A counterfactual apple does not exist in the real world. You can't eat it. But if you imagined counterfactually eating it you could imagine it would be delicious."

In haste as I am soon going out for the day. I will be spending some time looking at copies of parish registers of baptisms etc. I do not expect to find any wax apples, but there may be some multiple records of the same event. For example, there is a baptism record for a son James who was baptised in 1802 to an unmarried mother. There was a baptism in 1803 of a son James to a married woman in a different but nearby parish. I am fairly sure that the baby was the same in each case.

The IGI web site, however, does seem to me to contain 'wax apples'. Baptism data are recorded on the site often with details of parish and exact date of baptism. These are usually trustworthy. But sometimes there is a supposed birth record of a man with just the year of birth and a town. There is usually a genuine marriage record for the man 25 years later. Someone will have estimated that a man in, say the 1700s, usually gets married at age 25 and so will invent a birth record dated 25 years before the marriage and place that on the IGI site. Is that fake birth record not a "wax apple"? A naive user of the site could take the supposed birth record as genuine.

by **gill1109** » Tue Apr 15, 2014 2:00 am

Ben6993 wrote:I assumed that no one made a direct experimental measurement of a counterfactual.

In Joy's experimental paper the hidden variable lambda is measured. After that, he calculates A(a, lambda) and B(b, lambda) for some a and some b. The formula he stated is A(a, lambda) = sign(a . lambda), B(b, lambda) = sign(b . -lambda). Even if one doesn't calculate it for all a and b, one could have done so. In fact, Joy wrote that A(a, lambda) and B(b, lambda) should be calculated for a whole lot of different a's and b's. He said that this must not be done at the same time. OK. So today I calculate E(a, b). Tomorrow I calculate E(a, b'). I use the same computer file with N values of lambda, every day. That what is says in his paper and he confirms that he stands by what he said. He said it was a matter of complete indifference to him whether we redo the whole experiment for calculating a new E(a', b'), or use the same experiment. The same file of directions lambda.

Ben6993 wrote:The population and sample are different but is not the A measurement based on "the same thing" in each case.

According to a local hidden variables theory they are based on the "same thing" in some sense. But the theory does not say that they have to be measured. The mean value of all the weight of all men in the world yesterday existed even though there is no way to determine it.

Ben6993 wrote:That is a very unkind nom-de-plume to use in this thread.

It was not a nom-de-plume. It was an imaginary name of an imaginary scientist with an imaginary theory. I poke fun at everyone including myself. Next time I will call him Muhammed Ben. OK?

Ben6993 wrote:I am not too hot on the theory, but in my opinion a 2pi rotation does not change a macroscopic apple into a macroscopic pear. But a 2pi rotation does change the measured outcome of the spin in some way for an electron, as a complete cycle is 4pi. In my own model, the electron does not physically change throughout the 4pi cycle. Ie its chirality is unchanged, but its measured spin can vary throughout the cycle.

Me neither. Irrelevant. Joy has a theory which makes certain predictions. I propose an experiment which tests those predictions. The experiment allows Joy and his experimenter to use whatever scientific knowledge and experimental experience which they have, to optimize the experiment, from their point of view. I don't have to know anything at all about all that. Their theory says rho(0, 45) = rho(90, 45) = rho(90, 135) = - 0.7, rho(0, 135) = + 0.7. My theory says rho(0, 45) = rho(90, 45) = rho(90, 135) = - 0.5, rho(0, 135) = + 0.5

When we do the experiment we compute some experimental averages, which are statistical estimates of these four numbers. They might well be off by a couple of standard deviations. But if N = 10 000, say, we needn't worry.

Ben6993 wrote:Eating a counterfactual one (a wax apple?) might give you indigestion!

A counterfactual apple does not exist in the real world. You can't eat it. But if you imagined counterfactually eating it you could imagine it would be delicious.

Ben6993 wrote:I very much doubt that Michel will want secretly to add in counterfactual data via program coding. You would seem to be the most likely suspect for that! I trust you ... but no doubt the code will be well checked.

You are completely missing the point now. I did not talk about adding counterfactual data. I talked about adding an extra "print" line to code written by Michel, whose presence would not in any way alter the other calculations. Moreover I don't talk about *actually* adding this line, but about *imagining* that this line is added. A thought experiment. No one can forbid anyone from Gedankenexperimenten. They are a wonderful tool in science. I don't want to mess up Michel's beautiful code. I want him to use his imagination.

by **Ben6993** » Tue Apr 15, 2014 1:17 am

Hi Richard

Richard wrote: "
No one "uses" counterfactual data in an experiment! There is no counterfactual data observed in an experiment!"

Agreed. I assumed that no one made a direct experimental measurement of a counterfactual. I assumed that the counterfactual value was used in the analysis of the experiment based on the observed measurements. So that there was a use of one measurement as more than one outcome in the CHSH statistic calculation (using averages) of a single physical measurement. Eg an A outcome is measured in the lab and A' is estimated from the A in the calculation. I may be wrong in this of course. Your earlier post implied that this was wrong.

Richard wrote:
"The symbols "A" and "B" are names of something completely different in my expression "ave(AB)" from what I want them to refer to in my expression "E(AB)". Taking a mean value means something completely different in the two contexts. I proposed to distinguish them notationally. The operations "ave" and "E" are two completely different things."

"The interminable discussions going on here have a simple root cause: confusion about notation. "Notation" is about what symbols are supposed to denote. "A" in the statement and proof of the CHSH inequality is not "A" in an experimenter's report of a CHSH experiment. "

"I propose from now on to rigorously distinguish the operation of taking a population expectation value in theory, from the operation of taking an average of values observed in an experiment."

"One must distinguish apples from pears."

OK, but .... I do not believe that anyone here cannot already distinguish between a theoretical population rho and a sample r, or between a theoretical population sigma and a sample SD. The population and sample are different but is not the A measurement based on "the same thing" in each case. If you have a theoretical population of the heights of all the men in the world who have ever lived, then you somehow pick a sample of men and measure their heights. Heights and heights, not apples and pears. Not all men are in the sample, so the population has all men but the sample has some men.

Richard wrote: "One may *compare* the average weight of 10 apples with the average weight of 15 pears. And one may compare both samples' averages with the mean weights of apples and pears and indeed oranges too in any crazy theory."

Agreed.

Richard wrote: "According to Gill Pagan's S^11 based theory, every pear is actually an apple and we just need to do a counterfactual rotation through 2pi to convert an apple into a pear. Thus every apple actually has two weights: its weight as an apple and its weight as a pear. Moreover, because of the Hopf fibration, the pear weights of both apples and pears are sqrt 2 times their apple weights. Hence according to this theory, the population mean weight of pears is sqrt 2 times the population mean weight of apples."

That is a very unkind nom-de-plume to use in this thread.

I am not too hot on the theory, but in my opinion a 2pi rotation does not change a macroscopic apple into a macroscopic pear. But a 2pi rotation does change the measured outcome of the spin in some way for an electron, as a complete cycle is 4pi. In my own model, the electron does not physically change throughout the 4pi cycle. Ie its chirality is unchanged, but its measured spin can vary throughout the cycle.

Richard wrote:
"One could now test this theory by taking a sample of 100 apples and another sample of 100 pears (sorry, 98, I ate two of them)."

Eating a counterfactual one (a wax apple?) might give you indigestion!

Richard wrote:
"PS I said: there is no counterfactual data in an experiment. I referred here to a "real" (quantum optics lab) CHSH exoeriment. In a computer simulation, or in Joy's exploding balls experiment, it does exist, or at least, it can be made without changing the rest of the data!"

"For instance, Michel could add some statements writing counterfactual data to a separate computer file, without changing anything else. Whether or not one or two extra lines of code are actually in the program or not, one may imagine that they are there, and one may carry out some reasoning or analysis involving them. By consideration of what would have been in the extra, "secret", output file, one can deduce something about the not-hidden output of the program ... "

I very much doubt that Michel will want secretly to add in counterfactual data via program coding. You would seem to be the most likely suspect for that! I trust you ... but no doubt the code will be well checked.

There is also a potential for the experimenters to pass over files of data including multiple measurements on the same fragment. This is possible on macroscopic fragments, though impossible on electrons.

by **gill1109** » Mon Apr 14, 2014 9:54 pm

Dear Ben,

I'm very glad you came back, on track, exactly where we were, at the crux of the matter.

No one "uses" counterfactual data in an experiment! There is no counterfactual data observed in an experiment!

The symbols "A" and "B" are names of something completely different in my expression "ave(AB)" from what I want them to refer to in my expression "E(AB)". Taking a mean value means something completely different in the two contexts. I proposed to distinguish them notationally. The operations "ave" and "E" are two completely different things.

The interminable discussions going on here have a simple root cause: confusion about notation. "Notation" is about what symbols are supposed to denote. "A" in the statement and proof of the CHSH inequality is not "A" in an experimenter's report of a CHSH experiment.

I propose from now on to rigorously distinguish the operation of taking a population expectation value in theory, from the operation of taking an average of values observed in an experiment.

One must distinguish apples from pears.

One may *compare* the average weight of 10 apples with the average weight of 15 pears. And one may compare both samples' averages with the mean weights of apples and pears and indeed oranges too in any crazy theory.

According to Gill Pagan's S^11 based theory, every pear is actually an apple and we just need to do a counterfactual rotation through 2pi to convert an apple into a pear. Thus every apple actually has two weights: its weight as an apple and its weight as a pear. Moreover, because of the Hopf fibration, the pear weights of both apples and pears are sqrt 2 times their apple weights. Hence according to this theory, the population mean weight of pears is sqrt 2 times the population mean weight of apples.

One could now test this theory by taking a sample of 100 apples and another sample of 100 pears (sorry, 98, I ate two of them).

PS I said: there is no counterfactual data in an experiment. I referred here to a "real" (quantum optics lab) CHSH exoeriment. In a computer simulation, or in Joy's exploding balls experiment, it does exist, or at least, it can be made without changing the rest of the data!

For instance, Michel could add some statements writing counterfactual data to a separate computer file, without changing anything else. Whether or not one or two extra lines of code are actually in the program or not, one may imagine that they are there, and one may carry out some reasoning or analysis involving them. By consideration of what would have been in the extra, "secret", output file, one can deduce something about the not-hidden output of the program ...

It's all a question of using some imagination!

by **Ben6993** » Mon Apr 14, 2014 3:49 pm

Hi Richard. I wrote that I would reply to your detailed post. A little late maybe and the threads have moved on a lot in the meantime.

Richard wrote: "Ben you are confused. In one run (one pair of particles) of a CHSH experiment only one of A and A' is observed, only one of B and B'. The other two are counterfactual. You don't observe them. And it is only under a local hidden variables theory, that they can be said to 'exist'. "

Yes, that is what I meant by: "If A and B are measurement outcomes, and A' (90°) and B'(135°) are counterfactual estimates ...". Aren't we saying the same thing?

Richard wrote: "You said the "independence case" was that the quadruple (A, A', B and B') took on any of 16 possible combinations of values. But this is already counterfactual. Factually, only one of A and A' exists, and only one of B and B' exists."

I had at this stage moved on to a non-CHSH case [I agree that calling it an independence case was confusing] which has four measurements rather than two. I still managed to get it wrong as Michel later corrected me. He showed that you need eight measurements to have a chance of obtaining a CHSH statistic greater than 2. This is the usual CSHS calculation but applied in a different scenario where each of the eight outcomes are measurements. Ie each instance of the same symbol in the following, E(AB) - E(AB') + E(A'B) + E(A'B'), refers to a separate measurement. Eight measurements in all, based on four exploding balls. That needs to be repeated for up to N balls per correlation making 4N balls in such an experiment.

Richard wrote: "Then you talked about the "counterfactual case" and said that A would equal -A' and B would equal -B'. But we are talking about spin half particles and there is no deterministic relation between any of the pairs which you can form (under counterfactual definiteness). There is no pair of angles differing by 0 or by 180 degrees."

Yes, I agree that there is no pair of angles differing by 0 or by 180n degrees. At settings a, a′, b and b′ of 0°, 90°, 45° and 135° respectively, a and a' differ by 90° and b and b' differ by 90°.

Richard wrote: "However your observation that all 16 combinations in what you incorrectly called the "independence case" were either equal to -2 or +2. This means that if you would repeat a calculation of AB - AB' + A'B + A'B' (in the counterfactual world which only exists if we believe in local hidden variables) many many times, independently, and go to the infinite N limit, you would (in the limit) find the value of E(AB - AB' + A'B + A'B') where E stands for expectation value. So this limit has to lie between -2 and +2. Read a book about probability theory if you don't know what all this means."

I did not intend there to be any counterfactual data in this scenario. I agree that the limit for the CHSH statistic has to lie between -2 and +2 when counterfactual data are used. I do not bet on horses, since, despite possible short term wins (on small samples), my long term results would be an expectation of a lifetime loss. However, if I had seen the list of Grand national runners before the start I might have wanted to back the winner (Pineau) as we had been coincidentally talking about the word 'Pinot' the day before.

Richard wrote: "Putting everything together, we expect that ave(AB) - ave(AB') +ave(A'B) +ave(A'B') lies within +/- a few multiples of 1/sqrt N away from E(AB) - E(AB') + E(A'B) + E(A'B'), with large probability.

So that's the rational of a CHSH experiment. Choose N large enough that 1/sqrt N is of order of size, say, 0.01."

Yes, Ok. But for the case where A' and B' are counterfactuals, there is no chance of exceeding 2 no matter how small we pick N.

by **gill1109** » Mon Apr 14, 2014 5:41 am

minkwe wrote:Richard, have you withdrawn your papers which claim on the basis of alleged violations of the CHSH by experiments and QM that "realism is untenable"?

No.

by **minkwe** » Mon Apr 14, 2014 5:23 am

gill1109 wrote:To Michel: I cannot see your posts anymore.

Liar.

gill1109 wrote:"No upper bound can ever be violated even by experimental error"

True ... but irrelevant.

minkwe wrote:Richard, have you withdrawn your papers which claim on the basis of alleged violations of the CHSH by experiments and QM that "realism is untenable"?

by **gill1109** » Mon Apr 14, 2014 12:59 am

"No upper bound can ever be violated even by experimental error"

True ... but irrelevant.

Time to move on.

by **minkwe** » Sun Apr 13, 2014 1:19 pm

gill1109 wrote:The problem with Michel's reasoning is that he does not realize the difference between a theoretical prediction of an expectation value (population or ensemble mean) and a sample average. I get the impression he has no idea what is an error bar or standard error. What is a p-value. Having no comprehension at all of the difference between experiment and theory, makes it rather difficult to discuss said difference.

Lies. No upper bound can ever be violated even by experimental error. I've given you plenty of opportunity to provide one example with as much experimental error as you like which violates it and you have been unable to do so. Every time you bring a new word from your statistician's tool box and it is summarily dismissed. This time it is "error bar" and "standard error". So I ask you again:

Produce 4xN experimental data which violates the CHSH by even 0.00000000000000001. You can write any code to generate the data, and introduce as much noise and experimental error as you like in the data. All I ask is that you demonstrate your claims that upper bounds can be violated statistically by producing sample 4xN data which violates it statistically. Your speed of light example doesn't cut it.

To Michel: I cannot see your posts anymore.

You cannot extinguish the sun by refusing to look at it. I'm not worried. You'll be back.

by **gill1109** » Sun Apr 13, 2014 12:36 pm

The problem with Michel's reasoning is that he does not realize the difference between a theoretical prediction of an expectation value (population or ensemble mean) and a sample average. I get the impression he has no idea what is an error bar or standard error. What is a p-value. Having no comprehension at all of the difference between experiment and theory, makes it rather difficult to discuss said difference.

To give an example. There is a theory that nothing goes faster than light, and the speed of light in vacuum has by now been determined to quite a few significant figures. Let's pretend that it is 3, according to present day theory, in suitable units.

Suppose an experimenter measures the speed of some newly discovered particles and observes that they travel at the speed of 3.02 (0.1), standard error in parenthesis. Would he say that he has empirically proved a violation of the upper bound of 3?

Suppose on the other hand that he observerd a speed of 3.02 (0.001). What would he now say?

I recall a recent experiment falling in the second category.

To Michel: I cannot see your posts anymore. I won't, till you have fulfilled two modest requests which I made some days ago. You'll have to email me to let me know you are ready.

by **minkwe** » Sun Apr 13, 2014 6:19 am

gill1109 wrote:Still not getting it, Michel?

Yes you still are not getting it.

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