A Crystal Clear illustration of the Bell illusion

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

Re: A Crystal Clear illustration of the Bell illusion

Postby gill1109 » Fri Apr 11, 2014 11:18 am

Ben6993 wrote:Michel, I have done more calculations following your reply.

CHSH statistic = E(a, b) − E(a, b′) + E(a′, b) + E(a′ b′). The settings a, a′, b and b′ are 0°, 90°, 45° and 135°, respectively

For the trivial case of a CHSH run of one pair of particles, CHSH = AB - AB' + A'B + A'B'

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".

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.

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.

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.

Now the expectation operator is linear, so we find E(AB) - E(AB') + E(A'B) + E(A'B') lies between -2 and 2.

All this in the limit of infinitely many repetitions and in the imaginary world where local hidden variables exist so that it makes sense to talk about the value of AB - AB' + A'B + A'B' for one particle pair, even though this value is "hidden".

Now we change gears and think of an experiment. If we do N repetitions and measure every time A and B, we can average the products of A and B. Call this average ave(AB). Note that it is random - if we do the same thing again, we can expect to get a different answer. It certainly will never (or almost never) equal E(AB) defined earlier. However it should tend to be only about 1/sqrt N off target, sometimes more, sometimes less, sometimes in one direction, sometimes in the other direction.

Do another finite number of repetitions, I don't mind if its the same number N or another number N'. For simplicity assume it's the same number. But this time measure A and B'. Calculate the average of the products and call it ave(AB').

Similarly for A'B and A'B'.

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.

Measure 4N particle pairs, N with each pair of settings, calculate ave(AB) - ave(AB') +ave(A'B) +ave(A'B')

It should be close to E(AB) - E(AB') + E(A'B) + E(A'B')

Which is not larger than 2 if local hidden variables well describe the mathematical physics of what is going on.

But can equal 2 sqrt 2 = 2.8 if quantum mechanics of the singlet state with the "optimal" set of measurement directions well describes the mathematical physics of what is going on.

So if ave(AB) - ave(AB') +ave(A'B) +ave(A'B') is larger than 2.4 (half way between 2 and 2.8) we would be advised to trash local hidden variables, because if local hidden variables theory had been true, something very unlikely has happened. While under QM predictions, what we have seen is quite plausible.

Of course if we saw ave(AB) - ave(AB') +ave(A'B) +ave(A'B') larger than 3.2 we should start worrying about QM because under QM it's not possible for E(AB) - E(AB') + E(A'B) + E(A'B') to be larger than 2.828...
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Re: A Crystal Clear illustration of the Bell illusion

Postby Ben6993 » Fri Apr 11, 2014 2:41 pm

Michel:
Yes, I see that now:
if there are four separate mini experiments there must be four different sets of particle pairs. So A cannot be in two different calculations, hence we need A1 and A2 instead of A etc.

So, using
(A1, B1, A2, B2', A3', B3, A4', B4) = (1, -1, -1, -1, 1, -1, -1, 1) for one particular set of outcomes for eight particles,
then your formula A1B1 - A2B2' + A3'B3 + A4'B4 = -4 which exceeds 2.

That is, maybe, a sort of eureka moment, but I need to think more about it!

I have followed a QM calculation [in an online lecture by Susskind] where Bell's Inequality is broken, but I cannot immediately see how that ties in with your formula above.


Richard:
I am glad that you have confused people among your friends, though one doesn't have to be confused to be your friend? Anyhow, I admit that I am unclear about CHSH.

I am OK on probability, but less than OK on physics theory and lab experiments. I will go through the details of your previous post and reply later.
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Re: A Crystal Clear illustration of the Bell illusion

Postby minkwe » Fri Apr 11, 2014 4:21 pm

Ben6993 wrote:Michel:
Yes, I see that now:
...
That is, maybe, a sort of eureka moment, but I need to think more about it!

I'm happy you are following.

I have followed a QM calculation [in an online lecture by Susskind] where Bell's Inequality is broken, but I cannot immediately see how that ties in with your formula above.

QM makes predictions for perform-able experiments only. So when you calculate E(a,b) from QM and get -cos(a-b) on the one hand, and calculate E(a,b') = -cos(a-b') on the other hand, those represent actual correlations. To get a violation, they simply do the calculation like:

E(a, b) − E(a, b′) + E(a′, b) + E(a′ b′) = -cos(a-b) + cos(a-b') - cos(a'-b) -cos(a'-b')

which for 0,22.5, 45,67.5, gives
-cos(-22.5) + cos(-67.5) - cos(22.5) - cos(-22.5) = -0.924 + 0.383 - 0.924 - 0.924 = -2.389, which violates the inequality.

But we now know the bounds for 4 separate sets is [-4, 4], we also know now know QM does not really violate it. If we insist on using the [-2,2] bounds, we are interpreting the QM correlations as counterfactual ones from the same set. But then we cannot at the same time assume the same QM distribution (ie, -cos(a,b)) applies for the counterfactual just as with the actual ones. The counterfactual distributions must be opposite to actual ones.

Richard's arguments are irrelevant because he is arguing that measuring the actual correlation E(AB) from the full population, and an average of it <AB> from a sample, should give you very similar values. He fails to understand that first you have to decide which inequality you want to use, and that fixes the kinds of terms you should be calculating. Picking the (-2,2) bounds implies counterfactual, while (-4,4) implies actual. If you calculate counterfactual terms, they cannot have the same probability distributions as the actual ones. Well, there is a special case in which they can, that is when the counterfactual probability is exactly the same as the factual one, such as with a fair coin. But the QM distribution is not one of those.

You many now understand what Adenier wrote about when he said:
http://arxiv.org/abs/quant-ph/0006014
Bell's Theorem was developed on the basis of considerations involving a linear combination of spin correlation functions, each of which has a distinct pair of arguments. The simultaneous presence of these different pairs of arguments in the same equation can be understood in two radically different ways: either as `strongly objective,' that is, all correlation functions pertain to the same set of particle pairs, or as `weakly objective,' that is, each correlation function pertains to a different set of particle pairs.
It is demonstrated that once this meaning is determined, no discrepancy appears between local realistic theories and quantum mechanics: the discrepancy in Bell's Theorem is due only to a meaningless comparison between a local realistic inequality written within the strongly objective interpretation (thus relevant to a single set of particle pairs) and a quantum mechanical prediction derived from a weakly objective interpretation (thus relevant to several different sets of particle pairs).
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Re: A Crystal Clear illustration of the Bell illusion

Postby gill1109 » Fri Apr 11, 2014 10:53 pm

Ben6993 wrote:Michel:
Yes, I see that now:
if there are four separate mini experiments there must be four different sets of particle pairs. So A cannot be in two different calculations, hence we need A1 and A2 instead of A etc.

So, using
(A1, B1, A2, B2', A3', B3, A4', B4) = (1, -1, -1, -1, 1, -1, -1, 1) for one particular set of outcomes for eight particles,
then your formula A1B1 - A2B2' + A3'B3 + A4'B4 = -4 which exceeds 2.

That is, maybe, a sort of eureka moment, but I need to think more about it!

I have followed a QM calculation [in an online lecture by Susskind] where Bell's Inequality is broken, but I cannot immediately see how that ties in with your formula above.


Richard:
I am glad that you have confused people among your friends, though one doesn't have to be confused to be your friend? Anyhow, I admit that I am unclear about CHSH.

I am OK on probability, but less than OK on physics theory and lab experiments. I will go through the details of your previous post and reply later.

Ben:

I believe that Michel confuses theory and experiment.

In theory, if LHV exist, then in that same theory, AB - AB' + A'B + A'B' exists too. One imaginary run of two particles. That doesn't mean anyone can observe it. It exists whether or not anyone does any measurement at all. Maybe nobody looks. Anyway, we are talking about a mathematical (abstract, imaginary) object. Well: you could simulate it on a computer. If you want to simulate a real experiment based on this model, then you let your computer create A, A', B, B'; you let the experimenter choose which setting pair to use, and then you output the corresponding pair of outcomes, e.g. A and B'. Of course if you want to simulate what the experimenter sees there is no point in "making" A' and B as well. You can just as well comment out the lines of code which make A' and B.

In experiment, in one run (one particle pair) Alice and Bob each choose one setting and each get to see one outcome.

In experiment, they repeat this many, many times to collect enough data, average products, and report averages of products, being sure to give standard errors or error bars as well. If the experiment is large enough then the observed averages will, with large probability, be close to theoretical expectation values (population averages). Now you can see if your pet theory and experiment match one another.

I have many confused friends and many not-confused friends. I am both often confused and confusing. C'est la vie. Celebrate diversity. Bohr: "great, now we have a contradiction, now we can make progress at last". Celebrate scientific clashing of opinion.

In my opinion we would do well to ban the words "inequality", "bound" and "violation" when we talk about experiment. We would do well to learn some elementary statistics. We have to realise that experiment brings in probability. With small probability our experimentally determined average can be very far from the truth. Experiment can mislead. Experiments have to be reproducible. If we see an extraordinary result we repeat the experiment again, and others try it to. The law of large numbers is on our side.
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Re: A Crystal Clear illustration of the Bell illusion

Postby minkwe » Sat Apr 12, 2014 9:52 am

gill1109 wrote:I believe that Michel confuses theory and experiment.

This is fantasy. I do no such thing. On the contrary I believe it is Richard that confuses experiment and theory. He writes in his papers that QM violates the CHSH, yet he doesn't want to answer whether those 4 QM correlations he uses to demonstrate the violation are predictions for a single set of particles (ie, counterfactual results), or predictions for different sets of particles (ie, all actual results). If he would clarify which of those two he is talking about, then we would know immediately the appropriate inequality to compare it with. But the magician's trick is to derive an inequality assuming a single set of particles, and apply it to correlations from distinct sets of particles. So the three questions reveal the illusion:

1. Is the CHSH derived assuming a single set of particles, or different sets of particles?
2. Are the terms from EPR-type experiments calculated from a single set of particles or different sets of particles?
3. Are the terms from QM predictions for a single set of particles or different sets of particles?

These are the questions Richard is struggling with. I suspect he knows the implications. If he answers:

1. Single set
2. Different sets
3. Different sets

The he would be correct. He knows this. But those answers undo most of his work on Bell's theorem, and all published experimental results proclaiming the demise of locality or realism. So he argues that those answers are correct, but it doesn't matter because as he claims, the results from different sets are just fair samples of the results from a single set anyway.

So I prove him wrong, by demonstrating that it does matter because the counter-factual probability distribution must be opposite to the actual one. Therefore the correlations from single sets are not the same as those from multiple sets. Knowing that I'm right about this, he comes up with a clever trick. He looks for a specific situation (his R-script) in which the counterfactual probability is equal to the actual one (cf 1 - X = X, if X = 0.5), since in this situation, the average value of the CHSH would be statistically close to 2 even for multiple sets. He now tries to claim that the fact that his specific situation does not produce averages much larger than 2, means that the CHSH upper bound for ALL local-realistic theorems must be not much larger than 2 either (statistically). Using my coin toss analogy, it is similar to arguing that since E(A) + E(B) is statistically very close to zero for tossing two different local realistic fair coins, it means the equality E(A) + E(B) = 0 apples to ALL local realistic coins (statistically). He argues that they can violate it sometimes but with high probability will not violate it much. Not only that, he now argues that we should not talk about bounds, and violations because they are confusing, even though he just submitted a paper about derivations of bounds, claiming that QM violates the bounds and how it all proves that we must accept non-realism.

Let me show again using his comments below some of his misunderstandings:
In theory, if LHV exist, then in that same theory, AB - AB' + A'B + A'B' exists too. One imaginary run of two particles. That doesn't mean anyone can observe it. It exists whether or not anyone does any measurement at all.

Yet, A, B, A', B' are all imaginary outcomes, in our theory, of the imaginary experiment. If an imaginary person measures our single imaginary pair of particles at angles (a,b), the same imaginary person can not at the same time measure the same imaginary pair of particles at angles (a',b'). However, they could have measured (a',b'), instead of (a,b). So in our imaginary run of two particles, only one of the outcomes AB, AB', A'B, A'B' is actual. The others are possible too but not actual. They are counterfactual. The word "exists" has been misused here. AB, AB', A'B, A'B' are all possible in our LHV theory but only one of them (the one measured) is actual, and the rest are counterfactual.

If our theory predicts that an outcome will be observed with probability P(X) = 0.75, it definitely means that the outcome will not be observed with a probability of 1-0.75 = 0.25. It definitely means the actual probability of X is 0.75 and the counter-factual probability of X is 0.25. It is silly to say the counterfactual distribution of X is the same as the actual one. And we are still talking of an abstract mathematical imaginary object.

We would do well to learn some elementary statistics. We have to realize that experiment brings in probability.

I have met people with doctorate degrees in statistics who make silly mistakes like I illustrated above because they lack basic understanding of the philosophy of reasoning and logic. Experiments have to be designed to answer a specific well-formed question, and the data analyzed accordingly. It is foolish to do an experiment, and hope that statistics will allow you to answer a poorly formed question.
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Re: A Crystal Clear illustration of the Bell illusion

Postby gill1109 » Sat Apr 12, 2014 6:16 pm

minkwe wrote:1. Is the CHSH derived assuming a single set of particles, or different sets of particles?
2. Are the terms from EPR-type experiments calculated from a single set of particles or different sets of particles?
3. Are the terms from QM predictions for a single set of particles or different sets of particles?

1. One population of particles
2. Different sets
3. One population of particles

minkwe wrote:the correlations from single sets are not the same as those from multiple sets.


Indeed, not the same.

But with large probability, they are close.
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Re: A Crystal Clear illustration of the Bell illusion

Postby minkwe » Sat Apr 12, 2014 8:43 pm

gill1109 wrote:
minkwe wrote:1. Is the CHSH derived assuming a single set of particles, or different sets of particles?
2. Are the terms from EPR-type experiments calculated from a single set of particles or different sets of particles?
3. Are the terms from QM predictions for a single set of particles or different sets of particles?

1. One population of particles
2. Different sets
3. One population of particles

Still not getting it, are you Richard. Remember the coin-toss example? Let me remind you:

1. Singe coin: E(A) + E(B) = 0, <A> = 0.25, <B> = -0.25, <A> + <B> = 0
2. Different coins: E(A) + E(B) <= 2, <A> = <B> = 0.25, <A> + <B> = 0.5
3. Different coins E(A) = E(B) = 0.25 QM, E(A) + E(B) = 0.5

I take it you believe QM makes predictions for the population. Now that is interesting because I've asked you many times and you've avoided answering. You may want to review Bell's critique of von Neumann, and Adenier's Paper. QM is a measurement theory, the predictions of QM deal with results of measurements only.

minkwe wrote:the correlations from single sets are not the same as those from multiple sets.

Indeed, not the same.
But with large probability, they are close.
[/quote]
Obviously false. See the coin-toss example above. -0.25 is not even close to 0.25. You may be able to find a specific equiprobable distribution for which that is true but generally it is false, as I have demonstrated.
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Re: A Crystal Clear illustration of the Bell illusion

Postby gill1109 » Sat Apr 12, 2014 11:54 pm

Still not getting it, Michel?
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Re: A Crystal Clear illustration of the Bell illusion

Postby 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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Re: A Crystal Clear illustration of the Bell illusion

Postby 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.
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Re: A Crystal Clear illustration of the Bell illusion

Postby 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.
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Re: A Crystal Clear illustration of the Bell illusion

Postby 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.
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Re: A Crystal Clear illustration of the Bell illusion

Postby 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"?
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Re: A Crystal Clear illustration of the Bell illusion

Postby 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.
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Re: A Crystal Clear illustration of the Bell illusion

Postby 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.
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Re: A Crystal Clear illustration of the Bell illusion

Postby 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!
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Re: A Crystal Clear illustration of the Bell illusion

Postby 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.
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Re: A Crystal Clear illustration of the Bell illusion

Postby 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.
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Re: A Crystal Clear illustration of the Bell illusion

Postby 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.
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Re: A Crystal Clear illustration of the Bell illusion

Postby 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
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