Bell & CHSH type inequalities and experiments

[FrediFizzx]

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

I'm not party to the experiment. I'm just pointing out inconsistencies in Richards choice of how to interpret the data. I see no reason why it should take forever anyway. All I'm saying is that each correlation be calculated on a separate set of particles. You can generate one list of vectors but you must sample without replacement so that no pair of vectors contributes to more than one correlation. Only then will it be equivalent to 4 separate sets.

[Heinera]

All I'm saying is that each correlation be calculated on a separate set of particles. You can generate one list of vectors but you must sample without replacement so that no pair of vectors contributes to more than one correlation.

Joy has suggested that the entire list of vectors should be published on the Internet for further analysis. So if research group 1 decides to sample a set to compute E(a,b), this set is now somehow contaminated? So that if research group 2 now comes along, and by chance samples the same set and want to test for E(a',b') they have to be stopped somehow?

[Joy Christian]

All I'm saying is that each correlation be calculated on a separate set of particles. You can generate one list of vectors but you must sample without replacement so that no pair of vectors contributes to more than one correlation. Only then will it be equivalent to 4 separate sets.

I agree, as you already know.

And as you have kindly noted, this is what I have been arguing for years:

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

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

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

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

and

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

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

The experimental procedure described in my paper is unambiguous.

[gill1109]

Joy has time and time again said that it is a matter of complete indifference to him, whether the data coming out of the experiment is split into four parts or not.

Regarding the bet about the outcome of the experiment he has already agreed to the procedure http://rpubs.com/gill1109/Bet.

We are waiting for translations into Python, Mathematica, and Java. Only then can we present our protocol to the adjudicators Andrei Khrennikov, Hans de Raedt and Gregor Weihs, and start advertising it more widely, in an attempt to gain crowd-funding for the experiment.

Obviously if N is large and if correlation E(90, 135) is calculated by first sampling about one quarter of the rows of the two files of directions, its value will tend to be pretty similar to E(90, 135) calculated using both complete files. And the same, for the other three correlations. Joy thinks that - E(0, 45) + E(0, 135) - E(90, 45) - E(90, 135) will be close to 2.8, I think it will be close to 2. Whether the four terms are computed on the complete two data-sets or each is computed on a separate pair of sub-sets chosen by random sampling done once and for all by myself and submitted to the adjudicators on a USB stick before the experiment, is pretty irrelevant, and I don't see the point in introducing further uncertainty (noise) and complexity into the experiment. The specification in Joy's paper is crystal clear. Time and time again he has said that he stands by every word he has written.

The advertising for the experiment will make use of the images



The experiment generates four points which Joy hopes are close to the blue balls, I hope are close to the red crosses. The less noise there is in the experiment, the better. The less noise there is on this forum, the better.

[minkwe]

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

Richard, surely you understand that Joy means N could be the same for the 4 separate sets or it could be different.

Now this is what I said earlier that got Heinera so worked up:

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

The discussion in this thread confirms this already. Joy has agreed that he meant separate separate sums. Yet you keep claiming contrary to fact that Joy has not, so that you can go back to insisting on a single set. Why?

BTW your previous post was probably posted here in error. You probably wanted to post it in another more appropriate thread as it appears not to have anything to do with this thread.

[gill1109]

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

Richard, surely you understand that Joy means N could be the same for the 4 separate sets or it could be different.

Sure, so what?
It could be the same or it could be different, as far as he is concerned.
But it will be the same according to the rest of the paper, which he also authored.
You know the expression "the truth, the whole truth, and nothing but the truth"?
It's important to be aware of the whole truth. Just part of it is not enough.

The paper explains that first we let N spheres explode.
Then computer image-processing software calculates directions u_k and -u_k for each pair of hemispheres.

Now we have two files of directions.

The paper explains that next, E(a, b) is calculated for a huge number of random pairs of directions a and b, using the same two files of directions every single time.

In Joy and my bet we'll take just four cleverly chosen pairs (0, 45), (0, 135), (90, 45) and (90, 135). They have been chosen to maximize the statistical power of the experiment. In order to optimize use of our resources. To give the most bang for our buck.

For the same reason it is better to calculate each correlation on all the data, not on a random subsample of the data. That would be a criminal waste of resources, an attempt to cloak the crystal clear message of the data in statistical noise.

Joy has already agreed to http://rpubs.com/gill1109/Bet. There is no point in introducing further random noise into the experiment by repeating the whole experiment four times and calculating each correlation with the data from just one of the four experiments. Complete waste of resources.

Yes we have drifted off topic yet again.

Let's talk about Joy's experiment on the thread devoted to Joy's experiment.
Let's talk about the proof of the abominable CHSH inequality in its own thread.
Let's talk about my stupid little R experiment on its own thread.
We can talk about Joy's theoretical work in a thread devoted to that.

[minkwe]

So let us get back on topic. What have we learned in this thread?

1. That the CHSH is derived from only 4 functions from a single set of particle pairs and involves counterfactual mutually dependent terms.
2. That EPR experiments calculate mutually independent correlations from 8 functions derived from 4 sets of particle pairs with no counterfactual terms
3. That the true upper bound for the experiments is 4 not 2
4. That apparent violation of the CHSH proves only the trivial facts that (a) We are not using counterfactual terms as we should have (b) that we are not using mutually dependent terms as we should have, (c) we are not using the same number of degrees of freedom as we should have.
5. None of those reasons have anything whatsoever to do with realism or, locality, or loopholes.
6. That QM does not violate the proper upper bound for the experimental situation it is predicting for.


Adenier's was therefore correct 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).

There is therefore absolutely no conflict between QM, Experiments and local hidden variable theories.

[gill1109]

So let us get back on topic. What have we learned in this thread?
1. That the CHSH is derived from only 4 functions from a single set of particle pairs and involves counterfactual mutually dependent terms.
2. That EPR experiments calculate mutually independent correlations from 8 functions derived from 4 sets of particle pairs with no counterfactual terms
3. That the true upper bound for the experiments is 4 not 2
4. That apparent violation of the CHSH proves only the trivial facts that (a) We are not using counterfactual terms as we should have (b) that we are not using mutually dependent terms as we should have, (c) we are not using the same number of degrees of freedom as we should have.
5. None of those reasons have anything whatsoever to do with realism or, locality, or loopholes.
6. That QM does not violate the proper upper bound for the experimental situation it is predicting for.

1. What do you mean by "four functions"? There are three functions in usual proofs of Bell's theorem: Alice's measurement function; Bob's measurement function; and the probability density of the hidden variable. The derivation assumes a local hidden variables theory. A local hidden variables theory ensures the "existence" of A(a, lambda), A(a', lambda), B(b, lambda), B(b', lambda) in the mathematical sense. So "counterfactual" or not, whatever that means, these objects all exist, mathematically. Even if the particles don't leave the source, A(a, lambda), A(a', lambda), B(b, lambda), B(b', lambda) all "exist" in the mathematical sense. If I write down a mathematical model for your computer simulation programs, they all exist. Whether or not you actually have lines of code computing these things, they exist. Whether or not we run your program, they exist. We can reason with them. We can mathematically derive properties of the output of your computer programs, using their existence.
2. EPR experiments do not involve any functions at all.
3. Yes the only upper bound which one can give to the value of CHSH that one can observe in an experiment is 4.
4. Apparent violation of CHSH does not "prove" anything, in the sense with which you use the word "prove". Experiments can't prove anything, in the sense with which you use the word "prove".
5. Irrelevant, because of preceding remarks
6. Irrelevant, because of preceding remarks

Experiments do not violate bounds. Experiments generate results which either fit to one theory or to another theory or to neither.

I imagine you know about Popper's criterion of falsifiability. I predict that Joy's experiment is going to falsify Joy's theory. So far, no experiment has falsified LHV. The experimenters hope that they might succeed, in the next five years. I am not sure whether or not they will make it.

Of course, the word falsifiable has to be understood in a statistical sense. The CERN experiment did not falsify the theory that the Higgs Boson does not exist. It only produced results which would have been almost impossible if the Higgs Boson did not exist. Not actually impossible.

Similarly, a succesful loophole free Bell-CHSH experiment, which so far has never been performed, would be an experiment which produces results which are almost impossible if LHV would be true. Not actually impossible.

Read Popper! Learn statistics! Logic and philosophy is not enough.

[FrediFizzx]

I predict that Joy's experiment is going to falsify Joy's theory.

Only macroscopically if E(a, b) != -a.b for the macroscopic experiment. The quantum experiments themselves support Joy's theory microscopically.

[gill1109]

I predict that Joy's experiment is going to falsify Joy's theory.

Only macroscopically if E(a, b) != -a.b for the macroscopic experiment. The quantum experiments themselves support Joy's theory microscopically.

So far, no experiment has disproved local hidden variables theory.

So far, the experiments do not discriminate between quantum theory, Joy's theory, and local hidden variables theories.

[Joy Christian]

I predict that Joy's experiment is going to falsify Joy's theory.

Only macroscopically if E(a, b) != -a.b for the macroscopic experiment. The quantum experiments themselves support Joy's theory microscopically.

So far, no experiment has disproved local hidden variables theory.

So far, the experiments do not discriminate between quantum theory, Joy's theory, and local hidden variables theories.

Hallelujah!!! You have earned my respect for being the first Bell-believer to acknowledge this fact about my local-realistic framework (it is not yet a full theory).

[minkwe]

1. What do you mean by "four functions"?

Go back and read the first post. Then read up the difference between a random variable and a function. Then you might learn that a,a',b,b' are not random variables in the context of the CHSH.

2. EPR experiments do not involve any functions at all.

Sad that you have been reduced to silly nitpicking. The outcome of experiments are modeled as the result of a function of a random variable.

3. Yes the only upper bound which one can give to the value of CHSH that one can observe in an experiment is 4.

Good. Finally. But I don't see you withdrawing your baloney paper, yet. I don't see you withdrawing your claim that realism is untenable.

4. Apparent violation of CHSH does not "prove" anything

It certainly proves misapplication of the CHSH to the situation, in every sense of the word "prove".

Experiments do not violate bounds. Experiments generate results which either fit to one theory or to another theory or to neither.

Tell that to Bell proponents after you withdraw your papers claiming violation of the CHSH.

Similarly, a succesful loophole free Bell-CHSH experiment, which so far has never been performed, would be an experiment which produces results which are almost impossible if LHV would be true. Not actually impossible.

Every experiment is loophole free. Theories have loopholes not experiments. A successful Bell-CHSH experiment requires actual measurement of counterfactual results, a contradiction. A successful Bell-CHSH experiment is impossible to perform. That is an unsurmountable loophole in Bell's theorem.
By your logic, a spectator who spots a magicians trick and unravels the illusion has, a loophole.

[gill1109]

So far, no experiment has disproved local hidden variables theory.
So far, the experiments do not discriminate between quantum theory, Joy's theory, and local hidden variables theories.

Hallelujah!!! You have earned my respect for being the first Bell-believer to acknowledge this fact about my local-realistic framework (it is not yet a full theory).

Copied from another thread, but I it does belong here too:

I don't know what it a Bell-believer is. I doubt I am a Bell believer. I do believe QM is seriously inadequate.

Bell offered four *alternative* positions which one might like to take in view of his analysis ("Bertlmann's socks" paper. Read it!!!). Later he admitted there exists a fifth, which I christened "Bell's fifth position" in a paper more than 10 years ago.

I think Bell's analysis is correct but I don't know which of the five positions consequently needs to be adopted. This is partly a metaphysical issue and partly a matter of experiment. ... Experiment is inconclusive. Metaphysics is partly a matter of taste.

I keep an open mind on all this.

[minkwe]

There is no conflict whatsoever between QM and LHV theories. We have identified the logical error which leads to the presumed conflict. As Richard's friend Adenier described it:

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).

Yes the only upper bound which one can give to the value of CHSH that one can observe in an experiment is 4.

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"?

[gill1109]

We have identified the logical error which leads to the presumed conflict.

No. "We" are barking up a wrong tree. (For some reason the image of a dog barking away at some tree where he thought he saw some cat disappear, sticks in my mind. The cat actually is sitting at home eating a nice fat mouse, and laughing.)

Where is the report of your experimental findings on doing my experiment, and where is the Python code for Joy's experiment?

[minkwe]

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"?

[gill1109]

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.

[Xray]

….

I can email the CHSH original to anyone who would like to see it. We could also set up a shared dropbox folder of key papers. Anyone interested?

Gill,

I would welcome a copy. Is PM OK for this purpose?

Has there been any progress on your dropbox idea? I support it.

Xray

[gill1109]

Dear Xray

What is PM?

Email me, and I'll email you the CHSH article,

So far no-one else expressed interest in a shared dropbox folder but of course it remains an option.

Richard

[FrediFizzx]

PM = private messaging on the forum. Sorry, attachments aren't allowed in PM's. But you can swap email addresses via PM.