Is the Quantum Randi Challenge (QRC) valid?

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

Re: Is the Quantum Randi Challenge (QRC) valid?

Postby minkwe » Sun Feb 16, 2014 1:18 pm

gill1109 wrote:
minkwe wrote:It is similar to claiming that the expression "women are shorter than men" is not true, by using height data from one set of randomly selected people without regard for gender, and gender data from a disjoint set of randomly selected people without regard for height. Its bad statistics.


This is amusing. Let me turn it around. Suppose we are interested in the average difference in height between a husband and wife. We could take a sample of married couples, and average the differences.

But ... we could also take a random sample of married couples, and average the heights of the women; we could take another, independent, random sample of married couples, and average the heights of the men. The difference between the two averages is a decent estimator of the average difference in height within married couples.

Statistics is a powerful tool.


Maybe you can describe to us exactly how you "selected a random set of couples" then you may start seeing the problem. It is very easy to lie using statistics. But only the uninitiated will be fooled. For any description of your random selection method you can come up with, I will be able to come up with a new hidden variable that defeats it. Up for the challenge? It is impossible to screen-off a hidden variable in your sample selection. You should know this.
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby gill1109 » Sun Feb 16, 2014 1:20 pm

The upper bound on E(a, b) + E(a', b) + E(a, b') - E(a', b') by any theory whatever is 4.

The upper bound on E(a, b) + E(a', b) + E(a, b') - E(a', b') in quantum mechanics is 2 sqrt 2 (Tsirelson's inequality).

Note that to get from 2 sqrt 2 to 4 we have to abandon quantum physics but we don't have to abandon "no action at a distance". Alice still can't see what Bob is doing. (cf. the theory of Rohrlich-Popescu boxes, https://en.wikipedia.org/wiki/Quantum_nonlocality).

minkwe wrote:
FrediFizzx wrote:Something is not quite right with your analysis for the "true CHSH" as it has been mathematically proven that the upper bound on
E(a, b) + E(a', b) + E(a, b') - E(a', b') is 2sqrt(2).


I do not agree with that, do you have a paper where that prove is presented, I'll like to break it apart and show you the flaw. Are you perhaps referring to the calculation in which each term is calculated using QM independently, or are you referring to the derivation of the CHSH. Note that you can not have two mathematical proofs disagreeing with each other so if you say there is a mathematical proof showing an upper bound of 2 root 2, and also a mathematical proof showing an upper bound of 2, something must be wrong somewhere.

But I think I did notice that sometimes when QRC's CHSH is violated, it was like 3.9 so I think you are right about it is doing <A1B1> + <A2B2'> + <A3'B3> - <A4'B4'>. If that is the case then that is a mistake in the QRC. But perhaps not a serious mistake. I will check this out further. Thanks.

Remember I've been saying the upper bound is 4, so 3.9 is pretty close to the bound. Do you agree that the upper bound of <A1B1> + <A2B2'> + <A3'B3> - <A4'B4'> is 4?
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby minkwe » Sun Feb 16, 2014 1:24 pm

I will like to see the how you prove this E(a, b) + E(a', b) + E(a, b') - E(a', b') <= 2√2 usng QM. Please present the proof and be prepared to defend it.
This is what I said earlier about this:
Besides, the claimed QM violation of the standard CHSH is not even a valid calculation as far as QM is concerned since the full expression implies that we can simply combine separate observations of non-commuting observables to obtain the joint measurement result. That this is a grave error has escaped many people including Gill but guess who first used this argument to disprove a so-called "proof" of no hidden variables? Bell himself!

Bell wrote:Of course the explanation is well known: A measurement of a sum of non-commuting observables cannot be made by combining trivially the results of separate observations on the two terms -- it requires a quite distinct experiment.
...
But this explanation of the non-additivity of allowed values also establishes the non-triviality of the additivity of expectation values.


By calculating the QM expectation values of each pair separately and then adding them trivially, everyone who claims violation of the CHSH is making this mistake. But note something, the reason why you can't do this, is the same reason why you can't make statements about joint properties by using disjoint measurements, just expressed differently.
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby gill1109 » Sun Feb 16, 2014 1:28 pm

minkwe wrote:Maybe you can describe to us exactly how you "selected a random set of couples" then you may start seeing the problem. It is very easy to lie using statistics. But only the uninitiated will be fooled. For any description of your random selection method you can come up with, I will be able to come up with a new hidden variable that defeats it. Up for the challenge? It is impossible to screen-off a hidden variable in your sample selection. You should know this.


Let's suppose the set of couples is finite but large, say it consists of N couples. I list them. Each couple has a number, from 1 up to N.

There are of course many ways to take two samples such that we are able to validly base statistical inference on the results. One way is the following: I take my two random samples by taking first a random sample of size n1 without replacement from the set {1, ..., N}, then a random sample of size n2 without replacement from the set of remaining couples.

My assumptions are that heights of human beings are bounded so that all means, variances .. are well defined and are finite.

It seems that you still didn't study the appendix to my paper where all the probability calculations are contained. There, I have a population of N items (rows of a spreadsheet). Say: N = 800. I split this population into four at random by choosing, independently and at random, for each row, a number 1, 2, 3 or 4.

You are criticising a piece of mathematics by gut-instinct without actually studying the explicit justification which I give for the results. Sorry, naive gut intuitions about probability and about statistics might well be completely wrong.
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby gill1109 » Sun Feb 16, 2014 1:30 pm

minkwe wrote:I will like to see the how you prove this E(a, b) + E(a', b) + E(a, b') - E(a', b') <= 2√2 usng QM. Please present the proof and be prepared to defend it.

I told you: Tsirelson's inequality. Ask Google? The mathematics is rather non-trivial. It's a very famous theorem.

B.S. Cirel’son (1980) (modern spelling: Tsirelson). Quantum generalizations of Bell’s inequality. Letters in Mathematical Physics 4, 93–100.
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby minkwe » Sun Feb 16, 2014 1:41 pm

gill1109 wrote:Let's suppose the set of couples is finite but large, say it consists of N couples. I list them. Each couple has a number, from 1 up to N.

There are of course many ways to take two samples such that we are able to validly base statistical inference on the results. One way is the following: I take my two random samples by taking first a random sample of size n1 without replacement from the set {1, ..., N}, then a random sample of size n2 without replacement from the set of remaining couples.


What if the heights of men increase during the day from a lowest value at dawn to the highest value at dusk. Your random sampling will be meaningless unless you considered time of day in your random sampling. Want to have another try?
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby FrediFizzx » Sun Feb 16, 2014 5:15 pm

OK, so the QM upper bound for CHSH is 2sqrt(2). The way CHSH is implemented in the QRC the upper bound is 4. So if a Bell test model is between 2 and 4, then I think that is OK for the QRC since it violates the 2 bound. Can we agree on that?

BTW, sorry if the tex images are broken in other posts; seems like the Codecogs LaTeX server is down where the images are generated from. If anyone knows of a better solution for LaTeX, let me know.
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby gill1109 » Sun Feb 16, 2014 11:01 pm

No I don't want to have another try. You are not criticising my approach but you are telling me that the height of each person in a couple is not a well-defined single number. You had better tell me how you want to define the height of the man, the height of the woman, and the difference between the heights. Then we can start talking about how to sample them.

minkwe wrote:
gill1109 wrote:Let's suppose the set of couples is finite but large, say it consists of N couples. I list them. Each couple has a number, from 1 up to N.

There are of course many ways to take two samples such that we are able to validly base statistical inference on the results. One way is the following: I take my two random samples by taking first a random sample of size n1 without replacement from the set {1, ..., N}, then a random sample of size n2 without replacement from the set of remaining couples.


What if the heights of men increase during the day from a lowest value at dawn to the highest value at dusk. Your random sampling will be meaningless unless you considered time of day in your random sampling. Want to have another try?
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby gill1109 » Sun Feb 16, 2014 11:04 pm

FrediFizzx wrote:BTW, sorry if the tex images are broken in other posts; seems like the Codecogs LaTeX server is down where the images are generated from. If anyone knows of a better solution for LaTeX, let me know.

Hi Fred, sometimes the TeX images are not there the first time you look at a page but do turn up when you reload.

Math in html has of course been a major head-ache for years. I would prefer Mathjax. Making little .png images and scattering them about the text is not the best solution.

http://www.mathjax.org
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby minkwe » Mon Feb 17, 2014 6:57 am

gill1109 wrote:No I don't want to have another try. You are not criticising my approach but you are telling me that the height of each person in a couple is not a well-defined single number. You had better tell me how you want to define the height of the man, the height of the woman, and the difference between the heights. Then we can start talking about how to sample them.

minkwe wrote:
gill1109 wrote:Let's suppose the set of couples is finite but large, say it consists of N couples. I list them. Each couple has a number, from 1 up to N.

There are of course many ways to take two samples such that we are able to validly base statistical inference on the results. One way is the following: I take my two random samples by taking first a random sample of size n1 without replacement from the set {1, ..., N}, then a random sample of size n2 without replacement from the set of remaining couples.


What if the heights of men increase during the day from a lowest value at dawn to the highest value at dusk. Your random sampling will be meaningless unless you considered time of day in your random sampling. Want to have another try?


Exactly. Now you are getting it. Unless I tell you the exact nature of the hidden variables, (aka no longer hidden). Any claims of random sampling is naive. Now do you understand the importance Accardis work?
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby thray » Mon Feb 17, 2014 7:14 am

" ... you are telling me that the height of each person in a couple is not a well-defined single number."

It isn't, Richard. Quantum theory in general and the "QRC" in particular assume perfect information; i.e., that there are well defined singular properties, like the pips on the sides of a die. That leads to probabilistic calculations that are not present in a deterministic local hidden variables framework of continuous measurement functions.

"You had better tell me how you want to define the height of the man, the height of the woman, and the difference between the heights. Then we can start talking about how to sample them."

Why would one want to tell you how to sample when no sampling in required?

If we considered that all M and W are bounded above and below by minimum and maximum values, say 4 feet and 8 feet, with an average of 6 feet, that doesn't mean that we know anything about the height of an individual. There are short men and tall women. We can only say, that when separated into groups M and W, the average of W is say 5 feet 4 inches and the average of M is say 5 feet 10 inches. Neither of those values have anything to say about the upper and lower bounds, nor about the random W who is 5-10 and the random M who is 5-4. Nor does it say anything about the pair whose W is 5-10 and M is 5-4.

Just as we don't have perfect information of how the heights of pairs of women and men are distributed, we don't have perfect information of how quantum probabilities are distributed. We do know, however, that strong quantum correlations are empirical; that is the well defined single number. Quantum theory and the "QRC" assume without proof that it is a probabilistic result -- the "QRC" is supported by the same nonconstructive method of proving its own assumptions that burdens quantum theory.

If there were no way to show that this statistical analysis is false, one would be justified in assuming it is true. There is such a way, however.

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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby gill1109 » Mon Feb 17, 2014 8:28 am

Minkwe, Tom,

Let's talk about classical computer simulations of local realistic models of EPR-B (CHSH) experiments performed according to a strict protocol - the kind of strict protocol which Bell always had in mind and which he described at great length in his "Bertlmann's socks" papers. This is what QRC is about. This is what my CHSH challenge is about. That is what Sections 2 and 9 of my 1207.5103 are about.

Whether you are coding in R or in Python you have the possibility to save/restore/set all random seeds of the built-in random generator of the programming language which you are using. This makes your code exactly reproducible - same inputs, same outputs. This allows objective definition of counterfactual outcomes of all the possible measurements (within the model which is being simulated by your code). This enables my probability calculations concerning what happens when the sequence of settings are chosen externally, at random.

After we have understood this "toy universe" we can go on to discuss the real world, physics, real experiments, and the metaphysics of "counterfactual definiteness". But let's get some objective mathematical facts settled, out front, on the table, first.

Richard

PS could you please both be mindful of the ground rules of this forum? Please keep "on topic". The present thread was started by Fred and he asked a particular question. Your last posts in this thread don't seem to have any bearing on it at all. If you want to start a discussion on a new topic, go ahead.
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby thray » Mon Feb 17, 2014 1:43 pm

That's pretty slippery, Richard. You rig the rules to "prove" the facts we all know -- that Bell's inequality is violated in all Bell-Aspect type experiments, and that the arithmetic part of Bell's theorem is correct. Your proof, however, amounts to proving what we already know empirically and axiomatically -- the real surprise would be find that it doesn't work -- so I could just as well say that the motion of the sun is Apollo driving his fiery chariot across the heavens and dare you to prove me wrong. It would be a mistake to assume that either Minkwe or I are mathematically naive.

You simply refuse to acknowledge that the local hidden variable model is not probabilistic. Bell's framework is entirely classical, and so also not probabilistic. It does not become probabilistic simply because one thinks Baye's theorem is the only way to explain what we clearly observe. Unfortunately for your view, it isn't the only way -- there is an objective way, one that does not invoke personal belief.

And that exposes the "QRC" for the pseudo-science that it is -- using classical science to "prove" what one assumes of an imagined quantum reality independent of the classical domain. I am beginning to judge that Joy Christian is right to say or imply that Bell's followers do not honor Bell.

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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby FrediFizzx » Mon Feb 17, 2014 2:22 pm

OK, so if a test model exceeds the bound of 2.82 for QRC's CHSH, then that is also not a valid model. So this is a bit of a mistake in QRC that a model could exceed the bound of 2.82. However, easy to fix.
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby FrediFizzx » Mon Feb 17, 2014 5:00 pm

gill1109 wrote:
FrediFizzx wrote:BTW, sorry if the tex images are broken in other posts; seems like the Codecogs LaTeX server is down where the images are generated from. If anyone knows of a better solution for LaTeX, let me know.

Hi Fred, sometimes the TeX images are not there the first time you look at a page but do turn up when you reload.

Math in html has of course been a major head-ache for years. I would prefer Mathjax. Making little .png images and scattering them about the text is not the best solution.

http://www.mathjax.org


It looks like Codecogs.com finally got their rendering server fixed. Hopefully it won't break again as this is the easiest solution for LaTeX. But I will work on implementing MathJax into the forum. It's much more complicated though. I'm going to have to upgrade the software for the forum also; hope it doesn't break anything. :D
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby gill1109 » Tue Feb 18, 2014 8:18 am

FrediFizzx wrote:OK, so if a test model exceeds the bound of 2.82 for QRC's CHSH, then that is also not a valid model. So this is a bit of a mistake in QRC that a model could exceed the bound of 2.82. However, easy to fix.


Huh? With CHSH, in any one experiment with N separate pairs of measurements on N pairs of particles, each of the N setting pairs chosen independently at random from one of four different possible setting pairs, the outcome (sum of three correlations minus a fourth) can be anything between -4 and +4. However under local realism, the chance that it is bigger than 2 + epsilon is smaller than (something like) A exp( - N B epsilon^2) for some constants A and B which I can tell you, if you really want to know them. Similarly under QM but now with 2 replaced by 2 sqrt 2 (Tsirelson's inequality instead of Bell-CHSH).

You are not taking account of the statistical error. Bell's inequality is about theoretical mean values. But experiments only give us sample averages. Experimentalists put error bars on their correlations and do some statistics to show that they got a result exceeding the bound set by local realism by some very large number of standard deviations!

Similarly, in an event-based simulation, we have to take account of statistical error.

That's why Vongehr's QRC requires perfect anti-correlation on equal settings, and that the model violates the three-correlation Bell inequality (three different setting pairs) about 99% of the time (many repeats of the experiment, all with N = 800).

My old CHSH challenge, once off, one-on-one bet, wager 4000 Euro, requires that just one experiment with N = 40 000 yields a result at least half way between 2 and 2 sqrt 2. I figured out that this was a pretty safe bet on my side. Because of exponential inequalities for large deviations of sub-martingales ...
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby FrediFizzx » Sun Feb 23, 2014 3:05 pm

Sorry folks, I had a transcribing mistake in the Mathematica notebook file for the QRC here that John Reed pointed out to me. During my copy and paste job I forgot to change for N1 and NE1 the proper angles values of - pi/8 instead of - 3pi/8. The corrected notebook file can be found here. And here is a jpeg image of it.

Image
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby FrediFizzx » Wed Mar 05, 2014 10:32 am

Another mea culpa folks. John Reed discovered that I left out the -alpha[j] on N_E2 above. So please make that correction if you have downloaded the notebook file. I believe that it should be completely correct now however, a new version is coming. Watch this space.
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby gill1109 » Thu Mar 06, 2014 2:32 am

It would be so nice if both John and you, Fred, would try out R! So much easier to use, and so much easier to share with others. Joy already has his own Rpubs page!

http://rpubs.com/jjc

See also

http://rpubs.com/chenopodium

http://rpubs.com/gill1109
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Re: Is the Quantum Randi Challenge (QRC) valid?

Postby FrediFizzx » Thu Mar 06, 2014 12:04 pm

Why don't you setup the QRC in R and run the simulations thru it? It would be a good comparison. I'm quite busy enough for now learning Mathematica. I love it. Has some really great features.
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