Is this new version of the CHSH inequality valid?

[minkwe]

Section 9 explains how, given a computer program like his, we would be able to construct the Nx4 spreadsheet discussed in Section 2, and deduce that CHSH should apply to the output of the computer experiment.

A computer simulation like mine does not generate an Nx4 spreadsheet. No experiment can ever generate a single Nx4 spreadsheet.

Why is his able to violate CHSH?

It is able to violate it because it does not generate a single Nx4 spreadsheet which the CHSH requires. The same applies to the real experiments. So long as you have a single Nx4 spreadsheet, you will never violate the CHSH, not even by spooky action at a distance. But in experiments and in the simulation you have 4 different disjoint spreadsheets which should not be expected to obey the CHSH if reasoning correctly.

Here is the argument again, which I do not see a response to:

From a single spreadsheet you have 4 columns A, A', B, B' each with values +/-1 and length N. (4xN)
AB + AB' + A'B - A'B' = +/-2
A(B+B') +A'(B-B')

This is correct (for a single spreadsheet), since we have only 4 columns which we've recombined to generate the 4 pairs AB, AB', A'B, A'B'. The factorization which is crucial to obtain the inequality is then proper (for a single spreadsheet).

However, in experiments in which 4 different sets of particles are used, we have 4 different spreadsheets (A1, A1', B1, B1'),(A2, A2', B2, B2'), (A3, A3', B3, B3'), (A4, A4', B4, B4') : In the first spreadsheet, we only use A1 and B1, in the second A2B2', in the third A3'B3 and in the fourth A4'B4'.

Which means contrary to the single spreadsheet case, we have not recombined only 4 columns to generate 4 pairs, rather each pair shares absolutely zero columns with the others. Therefore Gill's assumption that

A1B1 + A2B2' + A3'B3 - A4'B4' = +/-2

Is False, and the factorization is not possible, which means the upper limit of the inequality is 4 not 2.

Richard can I please get a specific response to this point?

[minkwe]

The outcome "0" is allowed as well as +/-1. The observed correlations are computed on the post-selected samples, post-selected according to both particles getting detected. He needs to get rid of this bug. It will be a difficult job.

There is no bug. In the real world in which Alice is at a remote location and Bob is at a remote location, there is no way to decide which detection at Alice corresponds to which detection at Bob without bringing the results together after the experiment and doing post-processing. In the real world you will never have a detector which records 100.00000..% of detected particles. So let's say N = 1 billion, and you have as perfect a detector as is possible in the real world. Let us assume that your detector is so good that you only lose a single particle. so if you obtain N-1 outcomes at Alice and N outcomes at Bob, please tell me how you will know which of the 1 billion at Bob does not have a counterpart, if you do not compare Bob's result with Alice with some additional assumptions added in. Note you already have 1 billion different possible combinations with just a single particle missing. Now let us make it worse by eliminating only 1 % of the particles.

Besides, you have written a paper which says that the CHSH can not be violated by an experiment with efficiency above 88 percent. So no need to talk of Eberhard inequality until we are clear about the CHSH. And by the way the expression:

AB + AB' + A'B - A'B' <= 2
A(B+B') +A'(B-B')

Is valid even for outcomes +1, 0, -1. So the CHSH inequality is valid for a single spreadsheet which includes outcomes of 0 too. Bell himself proved this a while ago. The presence of 0 is not a reason why the CHSH should be violated. But the presence of more than one spreadsheet is definitely a reason.

In any case my simulation can work without the 0 outcome if you want. All that is needed is to generate more than one spreadsheet, like is done in the real world and in models of the real world and you can violate it.

Richard, I need a specific response why my simulation should not be expected to generate 4 different spreadsheets from 4 different sets of particles just like is done in the real world.

[gill1109]

Dear Michel

Of course your simulation may be expected to do exactly that: "generate 4 different spreadsheets from 4 different sets of particles". I am explaining how we could use it to do more than that. We could use it to generate one spreadsheet from which your four "experimental data" spreadsheets could be extracted, each one corresponding to a different (random) set of rows. The reason we can do that is because a properly protocolled computer simulation of such an experiment is a classical physical system, a local-realistic physical system.

On a technical note, you may indeed include the zero's in your calculation of <AB>_{obs} etc: take the product of all the outcomes for which Alice tried to measure A and Bob tried to measure B, including the runs for which either or both outcome is zero, and divide by the total number of runs involved, i.e. including the runs for which either or both outcome was zero.

There was an earlier question on which you asked for a specific response. I'll answer that next in a separate posting.

Richard

[gill1109]

Dear Michel

You also asked for a response to the remark "A computer simulation like mine does not generate an Nx4 spreadsheet. No experiment can ever generate a single Nx4 spreadsheet."

There are two issues here. Let's look at the second first, your second sentence "No experiment can ever generate a single Nx4 spreadsheet".

Well obviously, typical experiments on quantum systems can't do that, since one cannot measure two incompatible observables at the same time - measuring one changes the statistics of a subsequent measurement of the other. On the other hand, in Christian's famous proposed experiment with exploding colourful balls (which apparently needs to be performed in zero gravity and and at close to zero temperature), his description of the experiment makes it clear that it can and does generate a single Nx4 spreadsheet. Apparently when one tries to bring the data from the two wings of the experiment together, one is travelling on some kind of Möbius strip, and left and right get exchanged on the way, so the data collected in the lab where the correlations are calculated is not the same as the data collected at the two locations and merged.

First issue: a computer simulation like yours does not generate an Nx4 spreadsheet. No of course it doesn't. But we could easily make it do that. Let's suppose you don't have any zero outcomes, and let's suppose you are not using any memory effects. Let's suppose you allow me to supply the measurement settings (two lists of length N, binary). Let's suppose that Python allows us to save/set/restore the random seed of any random generators which you are using. Let's suppose your programme outputs the final settings and outcomes, and leaves the post-processing to who-ever wants to try.

Then I do the following. I save the random seed before any further computations, let N=1 and let the setting pair be 1, 1, and get two outcomes A and B. I then reset the random seed to the saved value, let N=1 and let the setting pair be 1, 2 and get two outcomes A and B'. Because computations in Python are deterministic and reproducible and because your programs respect locality, the value of A this second time is the same as the value of A the first time. I go on trying all the four setting pairs (1,1), (1,2), (2,1), (2,2), generating four separate pairs (A,B), (A, B'), A', B), (A', B'). But the two values of A are the same, and the two values of A' are the same, and the two values of B are the same, and the two values of B' are the same! Since your model is local-realistic and normal Python programs are deterministic and reproducible.

Then I go on in the obvious way to get a complete set of counterfactual outcomes for the second run. And so on.

The point is that the spread-sheet which I compile in this way, together with two series of settings of length N, generates the same four subsets of actually observed data as when we run your program in the standard way, starting from the same initial seed, and being fed the same series of settings.

Hence by the maths of my Section 2, the CHSH inequality will be satisfied with large probability up to a small error margin, as long as N is reasonably large, and I am allowed to generate my settings completely at random.

If you want to use the memory loophole things are more complicated but it all works out the same in the end, thanks to martingale theory and some results which I worked out 10 or more years ago.

Hope this clarifies things.
Richard

[gill1109]

I suggest to Minkwe that he carefully reads sections 2 and 9 of my paper. They are about event-based simulations of rigorous Bell-CHSH type experiments. No need to get into a philosophical muddle discussing what realism should or should not mean.

I have read the paper carefully, my arguments are based on the content of the paper, which includes claims of "mathematical existence". I haven't brought up any argument which the paper does not prompt. It is odd to write a paper claiming that "realism as a physical principle is not tenable" and then not want to talk about philosophical issues.

Dear Minkwe

Let's postpone discussion of philosophical (metaphysical) issues till after we have clarified various mathematical facts. I am enthusiastic to talk about metaphysics but we cannot do that if we can't agree on some simple mathematical issues.

Richard

[minkwe]

Dear Michel

Of course your simulation may be expected to do exactly that: "generate 4 different spreadsheets from 4 different sets of particles". I am explaining how we could use it to do more than that. We could use it to generate one spreadsheet from which your four "experimental data" spreadsheets could be extracted, each one corresponding to a different (random) set of rows. The reason we can do that is because a properly protocolled computer simulation of such an experiment is a classical physical system, a local-realistic physical system.

If I understand correctly you want to stack the 4 different spreadsheets on top of each other so that you get a single spreadsheet, and then randomize the rows. Of course you can imagine that the 4 different spreadsheets originate from one giant one like that, but note that this does not change anything. 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 are back to the snake head and length problem.

Do you agree with this?

[minkwe]

Richard,
You are misunderstanding something very fundamental. Let me try to explain it to you:

What is the purpose of this excercise? Why are we even here trying to argue about anything? Let me tell you why. Because some people, you included, on the basis of some actually performed experiments, have claimed that particles do not have hidden properties when you are not measuring them. Or if you prefer, that particles instantaneously send signals faster than light at the moment of measurement to affect a remote outcome. Please keep this in mind as we discuss because it is very important.

Now let us state some very basic uncontroversial facts:

(1) No particle can ever be measured more than once so no experiment will ever measure counterfactual outcomes.
(2) No experimenter can ever control hidden variables in an experiment which he knows absolutely nothing about.
(3) If hidden variables exist, then particles have them, and so do instruments.
(4) If nature wants to have memory effects, and non-detection of some particles, or any other property, we have no right to forbid it unless and until we have direct experimental evidence that such effects are contrary to observed experimental facts.

More below ...

[minkwe]

Continuing, now let us see what you are asking:

Then I do the following. I save the random seed before any further computations, let N=1 and let the setting pair be 1, 1, and get two outcomes A and B. I then reset the random seed to the saved value, let N=1 and let the setting pair be 1, 2 and get two outcomes A and B'. Because computations in Python are deterministic and reproducible and because your programs respect locality, the value of A this second time is the same as the value of A the first time. I go on trying all the four setting pairs (1,1), (1,2), (2,1), (2,2), generating four separate pairs (A,B), (A, B'), A', B), (A', B'). But the two values of A are the same, and the two values of A' are the same, and the two values of B are the same, and the two values of B' are the same! Since your model is local-realistic and normal Python programs are deterministic and reproducible.

Then I go on in the obvious way to get a complete set of counterfactual outcomes for the second run. And so on.

You are asking me to modify my simulation such that it allows you to control all the hidden variables, measure 100% of all particles, rewind time and re-measure the particles you just measured at counterfactual angles, in order to get your 4xN spreadsheet.

Now what do you expect this pointless exercise to tell you about the central question we are all interested in, whether hidden variables exist or not, and whether any experiment ever performable can produce a single 4xN spreadsheet? What use is it if I write a simulation which does absolutely nothing to answer the important question facing us?

What you are asking is unreasonable, and does nothing to answer any question. But there is a simple solution: Let us consider the practical situation of real experiments. The fact that we have 4 independent terms from 4 different sets of particles. Let us derive an inequality based on that which I have done.

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

You haven't said if you disagree with this inequality. If you do, say so. Now produce me an experiment or simulation which violates this inequality. You can use any loophole you like, and you can use any spooky action or nonlocality or non-reality you like.

[minkwe]

One other point. I can even make your request simpler for you. Rather than resetting random number generators, 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, even if you include memory effects. 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.

But the point I've been repeatedly telling you which you do not understand is that, this exercise will be meaningless. Nothing you glean from it will mean anything either as far as QM is concerned, or as far as real experiments are concerned. In the real world, you can not control all the hidden variables, and you can not measure a particle more than once. Do you understand this?

To write a simulator which is meaningful, you have to be as close to the real world as possible and simulate things that are reasonable to expect in the real world. Anything else is fantasy.

[minkwe]

Richard, let us make things even more clear.

- 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 so that we may see how you are able to obtain the CHSH starting with 4 different sets of particles.

[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