Is this new version of the CHSH inequality valid?

[Joy Christian]

So long as you have a single Nx4 spreadsheet, you will never violate the CHSH, not even by spooky action at a distance.

This elementary point is precisely the one Fred has been making as well, which Gill has completely failed to understand. I find that extraordinary.

[Joy Christian]

Let me recapitulate the central logical fallacy in Gill's argument. In any real experiment one can only counterfactually obtain the results like

AB or AB' or A'B or -A'B'.

Gill decides to replace the disjunctions "or" in this set of possible results by conjunctions "and", and proceeds to replace the above results with

AB and AB' and A'B and -A'B'.

Anyone familiar with Logic-101 should be able to recognize at once what is wrong with replacing disjunctions with conjunctions like this.

[FrediFizzx]

Well... there is someone else here besides Richard that doesn't understand it because they voted yes on the poll. ???

This fact makes his chapter 9 here completely invalid as it is then impossible for anything to violate his false new version CHSH "challenge".

[gill1109]

My "new version" of CHSH is not new. It is good old CHSH.

The starting point of section 2 of my paper is the trivial observation that you will never violate CHSH with a single Nx4 spreadsheet. I'm glad everyone is agreed on this point, at least.

I go on to show in that section, that if you randomly select four sets of rows from that spreadsheet, and compute the four correlations separately on each of the four pieces, you'll almost never (I bound the probability explicitly ) violate CHSH by more than a small amount (statistical error).

Nobody has commented on this so far, but I suppose that means that they accept my probability calculations and understand what I'm talking about there.

The point of section 9 is that you'll almost never violate CHSH by more than a small amount when you run a local realist computer simulation of a Bell-CHSH experiment according to a stringent but fair protocol. For this I have to build a bridge between the computer simulation program and the spreadsheet of Section 2. Minkwe has told me in private communication that I am not allowed to do this and/or I have no reason to do this, but the fact remains I can do it, and I do have a reason: it is a "Gedankenexperiment" designed to enable us to prove a theorem about computer programs like his own. Well... first we have to agree what we are going to do with the 0's which his simulation produces. If we let them stand, and compute the correlations including the 0 outcomes as true 0's, the CHSH inequality will (with large probability, and up to a small margin of error) hold. As is easy to verify if one just collects the data which his simulation generates, and analyses it properly.

It seems that the argument is too subtle for many to appreciate.

To recapitulate: in section 9 of the paper I explain how to generate a single Nx4 spreadsheet from a computer program designed to simulate a Bell-CHSH experiment in a local realist way and under stringent (but fair) requirements on settings, timing, and outcomes. I show how the actual simulation output (four correlations each based on a separate, random, subset of the runs) is actually the same as the result obtained in the manner of section 2 (random selection of rows from an Nx4 spreadsheet).

Extraordinary indeed, that so few people manage to get the point.

So long as you have a single Nx4 spreadsheet, you will never violate the CHSH, not even by spooky action at a distance.

This elementary point is precisely the one Fred has been making as well, which Gill has completely failed to understand. I find that extraordinary.

Try reading the paper carefully. Just sections 2 and 9.

Remark to Fred: what is the vote supposed to be on? Where is the "new version of CHSH" in my paper? I have given some alternative derivations of the good old inequality, and everyone agrees that it necessarily holds in the Nx4 spreadsheet case! Nobody has disputed the extension to correlations computed by randomly selecting rows. We have only just started talking about Section 9, which is where interesting things start happening, for those interested in the limitations of local realistic computer simulation of Bell-CHSH experiments.

Everybody has known for the last 50 years that in order to violate Bell you have to circumvent it. (I am paraphrasing one of Joy's rather wise remarks here). That is to say: if you don't satisfy the assumptions under which it is derived, you're not subject to the conclusion.

Michel's computer program does this by use of the conspiracy loophole: his "states" are selected according to which settings are being used by Alice and Bob. Pearle (1970) etc etc etc... long long history. "Christian 1.0" circumvented it by redefining correlation. Sanctuary circumvents it by multiplying observed correlations by 2. (He has a local realistic model which gives CHSH = 1 times sqrt 2, so he has to double that, in order to "reproduce" the singlet correlations). Accardi also used the "multiply observed correlations by 2 trick", long ago! He multiplied the outcomes on both sides by sqrt 2.

One has to hide these tricks deeply in a lot of mathematics and a lot of words, so that people won't notice, but you cannot escape the necessity of circumventing an iron law of mathematics and logic. The iron law being the elementary point which Fred and Joy admit to being true, together with a little probability calculation. The average of a sample is with large probability close to the mean of the population, provided ...

[Joy Christian]

Michel's computer program does this by use of the conspiracy loophole: his "states" are selected according to which settings are being used by Alice and Bob.

This is entirely false. The settings a and b are chosen completely freely in Michel's simulation. The states are NOT selected according to which settings are chosen.

The argument in your paper, however, is based on an elementary logical fallacy. In any real experiment one can only counterfactually obtain the results like

AB or AB' or A'B or -A'B'.

You decide to replace the disjunctions "or" in this set of possible results by conjunctions "and", and proceed to replace the above results with

AB and AB' and A'B and -A'B'.

Anyone familiar with Logic-101 should be able to recognize at once what is wrong with replacing disjunctions with conjunctions in this manner.

[gill1109]

I suggest you study Michel's code before you make claims like that about it, Joy.

There is no state in Michel's model unless the state has passed a test which depends on the two settings a and b.

They are selected according to which settings are chosen.

[FrediFizzx]

My "new version" of CHSH is not new. It is good old CHSH.

The starting point of section 2 of my paper is the trivial observation that you will never violate CHSH with a single Nx4 spreadsheet. I'm glad everyone is agreed on this point, at least.

Sorry, but it is not "good old CHSH". Not even close. This is "good old CHSH".

E(a, b) + E(a, b') + E(a', b) - E(a', b') <= 2

Quantum theory can violate that expression. Quantum theory cannot violate your expression. If you think it can, please give a proof that it can.

In Chapter 9 you state something about N=800. If you think quantum theory can violate the way you have specified the rules in chapter 9, you should be able to provide a proof that quantum theory can violate it with N = 800. Until you can provide that proof, there is no reason for further discussion about this. I say what you have setup in chapter 9 is impossible for anything to show violation.

[gill1109]

I don't understand your problems, Fred. In sections 2 and 9 of my paper I give a probability inequality for computer-simulated local realistic strict protocol Bell-CHSH type experiments. The inequality says that, in such a computer simulation experiment, violation of CHSH by some small amount (replace "2" by "2 + epsilon") has low probability, if N is large. It does not say that that violation is impossible. I gave you a possible data-set which exhibited a large violation (we saw something close to 2 sqrt 2).

In other words, something rather unusual has happened. Not impossible, just rather unlikely.

[minkwe]

Richard,
I notice the lack of response to any of my posts for over a week. Does that mean you now understand the issue? Or will you simply say read section 2 and 9.

Specifically, I see no response to:

The fact that we have 4 independent terms from 4 different sets of particles. If we derive an inequality based on that fact we get:

<A1B1> + <A2B2'> + <A3'B3> - <A4'B4'> <= 4

You haven't said if you disagree with this inequality. If you do, say so.
...
how about you simply measure each particle twice so that you will get A and A' at Alice and B and B' at Bob for a single particle pair. Clearly this is really what you are asking. It is certainly possible to do this in a python program and I've done it. This will give you your single spreadsheet with 4xN. And it will never violate the CHSH even if you include memory effects. Nobody I know of has ever suggested that such a result will violate the CHSH.
...
When calculating the CHSH, you are still calculating

<A1B1> + <A2B2'> + <A3'B3> - <A4'B4'>

in which no terms shares any thing with any other. No factorization is possible since none of the rows used to calculate each of the paired terms is used for any other, so the upper limit for this is still 4.

...

- We both agree that experiments are measuring 4 different sets of particles.
- We both agree that for 4 sets of particles the inequality is

<A1B1> + <A2B2'> + <A3'B3> - <A4'B4'> <= 4

Now you believe, some ways of using randomness allows you to reduce this expression to

<A1B1> + <A2B2'> + <A3'B3> - <A4'B4'> <= 2

Please show it mathematically, making all assumptions explicit

Specific responses, other than, see chapters 2 and 9 will be appreciated.

[gill1109]

Dear Minkwe

I am sorry, it is pretty clear to me that you don't have a clue what my paper is about. (The same holds for Fred ... so never mind, this is nothing personal). I'm getting tired of trying to explain.

If you can't read and understand sections 2 and 9 of my paper, which are *only* about computer programs, not about physics, then my paper is not for you. Too bad.

Richard

[minkwe]

So you have no response. Too bad.

[gill1109]

So you have no response. Too bad.

I have no *new* response. It seems to me that you haven't understood the statement of Theorem 1. Can you read what it says? Do you not believe it?

Too bad if you don't. There's nothing much more I can say. The proof is in the appendix of the paper. Pretty elementary probabilty.

[FrediFizzx]

Yes, and you have proven that NOTHING can violate your version of CHSH. Not even quantum theory. So what you have done in Chapter 9 is completely useless for anyone. Now that is really amusing!

[gill1109]

Yes, and you have proven that NOTHING can violate your version of CHSH. Not even quantum theory. So what you have done in Chapter 9 is completely useless for anyone.

Where do you get this (to me, seemingly) totally crazy idea, Fred? What the hell do you mean by "my version of CHSH", anyway? I am still not aware of having done anything terribly original in this paper. The main novelty is to carefully distinguish between finite N averages and infinite N limits, and even there, I am just redoing something I did 15 years ago, but in a more simple context (no memory effects). No controversy about it.

I am wondering if maybe you are one of those people who don't understand the technique of proving something by assuming the opposite of what you want to prove, and then deriving a contradiction? (I know a lot of very clever experimental physicists who belong to this category, you would be in good company).

[FrediFizzx]

viewtopic.php?f=6&t=6&start=50#p139

On page 3 you define <AB> = (1/N)Sum_j=1 to n(A_j B_j). With that definition and the definition that A, A', B and B' are + or - 1, your expression for CHSH can not be violated by anything including QM. Now, I would suggest that you pick different definitions. But it may not be possible and still have it come out right.

[minkwe]

I am wondering if maybe you are one of those people who don't understand the technique of proving something by assuming the opposite of what you want to prove, and then deriving a contradiction? (I know a lot of very clever experimental physicists who belong to this category, you would be in good company).

The pitfall of this technique is that you can't be sloppy in clearly specifying all your assumptions, miss just one and your proof goes up in flames. I know a lot of clever mathematicians and physicists who thought they had proven something this way only to be shown a hidden assumption which turned out to be false. Some of them are still in denial.

http://arxiv.org/pdf/1108.3583v1.pdf

[gill1109]

You are referring to a mathematical lemma. That is not "how I define CHSH for experimental data". I am just marshalling my soldiers. Summarizing some elementary mathematical facts. You should now read on, and see what comes out of this. In particular, notice the definition of <AB>_{obs}.

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=6&start=50#p139

On page 3 you define <AB> = (1/N)Sum_j=1 to n(A_j B_j). With that definition and the definition that A, A', B and B' are + or - 1, your expression for CHSH can not be violated by anything including QM. Now, I would suggest that you pick different definitions. But it may not be possible and still have it come out right.

[gill1109]

Well, we could have a long discussion as to who is in denial: Karl Hess and Walter Philip (RIP), or yours truly. Start a new thread if you really want to discuss http://arxiv.org/pdf/1108.3583v1.pdf

But the rules of this forum are to be scientific, objective. Talk about the content. The maths and the physics. Not about the psychology of your opponents, please.

... you can't be sloppy in clearly specifying all your assumptions, miss just one and your proof goes up in flames. I know a lot of clever mathematicians and physicists who thought they had proven something this way only to be shown a hidden assumption which turned out to be false. Some of them are still in denial. http://arxiv.org/pdf/1108.3583v1.pdf

[FrediFizzx]

You are referring to a mathematical lemma. That is not "how I define CHSH for experimental data". I am just marshalling my soldiers. Summarizing some elementary mathematical facts. You should now read on, and see what comes out of this. In particular, notice the definition of <AB>_{obs}.

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=6&start=50#p139

On page 3 you define <AB> = (1/N)Sum_j=1 to n(A_j B_j). With that definition and the definition that A, A', B and B' are + or - 1, your expression for CHSH can not be violated by anything including QM. Now, I would suggest that you pick different definitions. But it may not be possible and still have it come out right.

It doesn't matter if it is <A_j B_j> or <A_j B_j>_obs or <A_j B_j>_lim. None of them will make your eq. (6) true. I know what your intentions are in that paper but your math doesn't support your intentions. Again, I am just offering some constructive criticism here.

[gill1109]

It doesn't matter if it is <A_j B_j> or <A_j B_j>_obs or <A_j B_j>_lim. None of them will make your eq. (6) true. I know what your intentions are in that paper but your math doesn't support your intentions. Again, I am just offering some constructive criticism here.

OK, seems we are home then. My intention was to prove Bell's theorem. What you say is not criticism but affirmation. You confirm that if local hidden variables existed, then equation (6) couldn't be true. Yet equation (6) is predicted by quantum mechanics.