Bell & CHSH type inequalities and experiments

[Heinera]

Sorry for being dense, but I guess your answer to my question is that it is uncontroversial that none of the four correlations would change?

Heinera,
S = E(a,b) - E(a,b') + E(a,b') + E(a',b')
What in your opinion is the upper bound for S when the expectation values are independent and each has bounds [-1,+1]?

My poor brain prefers to take one question at a time. So, is it uncontroversial that none of the four correlations would change?

[gill1109]

Sorry for being dense, but I guess your answer to my question is that it is uncontroversial that none of the four correlations would change?

Heinera,
S = E(a,b) - E(a,b') + E(a,b') + E(a',b')
What in your opinion is the upper bound for S when the expectation values are independent and each has bounds [-1,+1]?

My poor brain prefers to take one question at a time. So, is it uncontroversial that none of the four correlations would change?

Can your poor brain take this: They would change a little, but most likely, they wouldn't change much.

[minkwe]

You claimed in this thread that this argument sank Bell's boat. I am proving to you, by actually doing the experiment we are talking about

You are asking me to do a simulation not an experiment. You should know the difference. Obviously most people understood that I'm referring to actual CHSH type experiments with photons/electrons or other quantum particles in my question 3. I didn't think we'll start playing semantic games about what an experiment means. Again, you already agree with my argument so I don't know what you keep forcefully arguing about, or bringing up irrelevant simulations for. You can discuss that in another thread.

[gill1109]

You claimed in this thread that this argument sank Bell's boat. I am proving to you, by actually doing the experiment we are talking about

You are asking me to do a simulation not an experiment. You should know the difference. Obviously most people understood that I'm referring to actual CHSH type experiments with photons/electrons or other quantum particles in my question 3. I didn't think we'll start playing semantic games about what an experiment means. Again, you already agree with my argument so I don't know what you keep forcefully arguing about, or bringing up irrelevant simulations for. You can discuss that in another thread.

I disagreed with the last line of your argument. You know, the posting you made at the beginning of this thread? The last sentences are wrong. The final conclusion does not follow from the earlier parts of your argument.

I'm asking you to do an experiment. A real CHSH experiment. In a situation where a well-known LHV model is true. No quantum particles.

You wrote at the end of your first posting to this thread

In a genuine CHSH experiment, the terms must be related to each other in the same way as the terms of the CHSH inequality are related to each other. No such experiment has ever been performed.

You say "must be related". Your deduction is false. You are wrong.

You spent days getting us to agree with some totally uncontroversial and uninteresting facts which we all knew before. They are irrelevant.

[minkwe]

But a LHV model can't have independent terms.

Earlier, I described this claim as rubbish. I thought I should be more kind and actually explain why it is rubbish.

Pick two random sets of people from a population. Call the sets 1 and 2. Measure the Heights and Weights of the people in each set, denote them H1, W1, H2, W2. Nobody doubts that Heights and Weights are local realistic variables (although the pedantic may argue that they are not hidden ).

H1 is not mutually independent from W1, but H2 is mutually independent from H1 and W1. So we see that LHV can and do have independent terms when they are derived from disjoint sets, even if the terms from a single set are not independent?

[gill1109]

But a LHV model can't have independent terms.

Earlier, I described this claim as rubbish. I though I should be more kind and actually explain why it is rubbish.

Pick two random sets of people from a population. Call the sets 1 and 2. Measure the Heights and Weights of the people in each set, denote them H1, W1, H2, W2. Nobody doubts that Heights and Weights are local realistic variables (although the pedantic may argue that they are not hidden ).

H1 is not mutually independent from W1, but H2 is mutually independent from H1 and W1. So we see that LHV can and do have independent terms when they are derived from disjoint sets, even if the terms from a single set are not independent?

Great example.

Measure the heights in one set, and the weights in the other. The mean height from one random sample minus the mean weight from the other random sample is a perfectly valid estimate of the mean value of the difference between a randomly selected person's height and weight.

So this shows that separate samples can be used to draw inference about things which are not measured in either sample separately.

[Heinera]

My poor brain prefers to take one question at a time. So, is it uncontroversial that none of the four correlations would change?

Can your poor brain take this: They would change a little, but most likely, they wouldn't change much.

That's great! So if the original correlations (all computed on the whole set) didn't violate the CHSH inequality (CHSH<2), and the correlations computed on four disjoint random subset would not change much, we can now conclude that the four latter correlations would still not significantly violate the CHSH inequality, since term by term, they are approximately equal to the original correlations?

[gill1109]

My poor brain prefers to take one question at a time. So, is it uncontroversial that none of the four correlations would change?

Can your poor brain take this: They would change a little, but most likely, they wouldn't change much.

That's great! So if the original correlations (all computed on the whole set) didn't violate the CHSH inequality (CHSH<2), and the correlations computed on four disjoint random subset would not change much, we can now conclude that the four latter correlations would still not significantly violate the CHSH inequality, since term by term, they are approximately equal to the original correlations?

Yes Heinera, you are home. They might violate it a little, but in all probability they won't violate it by much.

[Mikko]

Pick two random sets of people from a population. Call the sets 1 and 2. Measure the Heights and Weights of the people in each set, denote them H1, W1, H2, W2. Nobody doubts that Heights and Weights are local realistic variables (although the pedantic may argue that they are not hidden ).

H1 is not mutually independent from W1, but H2 is mutually independent from H1 and W1. So we see that LHV can and do have independent terms when they are derived from disjoint sets, even if the terms from a single set are not independent?

Here you are again unclear about the meaning of "independent". The H1 and H2 are samples from the same population, so they are not independent (in some sense of the word). W1 is not independent of H1, as you note, so by transitivity, W1 is not independent of H2, either.

[gill1109]

Pick two random sets of people from a population. Call the sets 1 and 2. Measure the Heights and Weights of the people in each set, denote them H1, W1, H2, W2. Nobody doubts that Heights and Weights are local realistic variables (although the pedantic may argue that they are not hidden ).

H1 is not mutually independent from W1, but H2 is mutually independent from H1 and W1. So we see that LHV can and do have independent terms when they are derived from disjoint sets, even if the terms from a single set are not independent?

Here you are again unclear about the meaning of "independent". The H1 and H2 are samples from the same population, so they are not independent (in some sense of the word). W1 is not independent of H1, as you note, so by transitivity, W1 is not independent of H2, either.

You are using the word independent in two different senses here, Mikko. "Statistical independence" is a concept in probability theory. It refers to the joint probability distribution of several random variables. "Mathematical independence" is a word in mathematics and logic meaning that two variables can each be chosen freely in their respective domains. ie the domain of the pair is a Cartesian product. "Choose" means here choosing in the mathematical sense, which just means "mathematical existence".

Michel seems to use the word "independent" in a lot of different senses, some of them more or less recognisable from mathematics, others not (at least, not to me).

[minkwe]

Mikko,
I have been specific that I'm talking about mutual dependence. Two random variables are mutually dependent if knowing one of them gives you some information about the other. Because of the relationship between height, and weight, knowing the height of one person tells me something about his weight. Knowing the height of another person tells me nothing about the weight of the other person.

For a single set with A(a,λ), B(b,λ), A(a',λ), B(b',λ) well defined. Knowing E(a,b) tells you something about E(a,b') and E(a',b), knowing E(a',b') tells you something about E(a,b') and E(a',b), knowing E(a',b') and E(a,b) tells you exactly everything about E(a,b') and E(a',b). And when I say exactly, I'm not just talking about the final values obtained. I'm talking about all the individual outcomes that result in the final values. Remember that the inequality was not derived from the final values, it was derived from those individual values, by factorizing them *under the integral*! So the CHSH is a a very specific relationship between lists of outcomes derived by looking at the relationships between the individual values. It is not a relationship between averages as some tend to think. You cannot derive the CHSH starting from the final values *after* integration as is obvious by looking at the expression

S = E(a,b) - E(a,b') + E(a',b) + E(a',b')

Each of the terms on the right hand side has bounds [-1,+1].
1. What will the upper bound of S be if each of those terms is *independent* of each other (pick your choice of the meaning of independent).
2. Are the terms calculated from disjoint sets of particles in Aspect type experiment *independent* of each other? (use the same definition of independent you picked above).

Richard has already accepted that the terms from experiment are independent.


Let us attempt to prove the CHSH starting with the final expectation values and see that it can not be done if the terms are mutually independent. If the upper bound of S is considered to be 2, then when E(a,b), E(a',b) and E(a',b') are at their maximum values, of 1, then E(a,b') must be at its maximum value of 1. You'll notice that if you place an upper bound of 2 on that expression, then knowing three of the values, places very strong constraints on what the third value must be. Clearly they are mutually dependent not independent in that case.

[minkwe]

Yes Heinera, you are home. They might violate it a little, but in all probability they won't violate it by much.

I recommend these articles:

http://vixra.org/pdf/1305.0129v1.pdf
http://arxiv.org/pdf/quant-ph/0006014.pdf

Maybe if it's not me making the argument, both of you will get past your mental block.

[Heinera]

But a LHV model can't have independent terms.

This is just rubbish.

I'll just repeat my request: Why don't you construct one, and prove us all wrong?

[FrediFizzx]

From what I gather from this thread is that CHSH derived by Bell 1971 is basically "rigged". Nothing can violate its bound of 2. Not even QM. And it is easy to see from what I presented here that the calculation for an experiment (or even a simulation) the bound is 4. So I do believe Michel is right.

[FrediFizzx]

I'll just repeat my request: Why don't you construct one, and prove us all wrong?

No need to. Joy Christian has already done that.

[Heinera]

From what I gather from this thread is that CHSH derived by Bell 1971 is basically "rigged". Nothing can violate its bound of 2. Not even QM. And it is easy to see from what I pres available, phsical ented here that the calculation for an experiment (or even a simulation) the bound is 4. So I do believe Michel is right.

No. If I can write a computer program where I am allowed to do anythng, I can achieve 4, given that I can use all algebraically information available, physically sensible or not.. If someone restricts me to a LHV model (source can't know the settings, one detector can't now the other setting, etc.), the best I can do is 2. QM is somewhere in between..

[FrediFizzx]

From what I gather from this thread is that CHSH derived by Bell 1971 is basically "rigged". Nothing can violate its bound of 2. Not even QM. And it is easy to see from what I presented here that the calculation for an experiment (or even a simulation) the bound is 4. So I do believe Michel is right.

No. If I can write a computer program where I am allowed to do anythng, I can achieve 4, given that I can use all algebraically information available, physically sensible or not.. If someone restricts me to a LHV model (source can't know the settings, one detector can't now the other setting, etc.), the best I can do is 2. QM is somewhere in between..

Then what are you going to do about Joy's classical local realistic model that gives the exact predictions of QM? It proves that you and Bell's CHSH is wrong.

[minkwe]

But a LHV model can't have independent terms.

This is just rubbish.

I'll just repeat my request: Why don't you construct one, and prove us all wrong?

I've proved you wrong without constructing one. Joy has proved you wrong by constructing one.

[Heinera]

Then what are you going to do about Joy's classical local realistic model that gives the exact predictions of QM? It proves that you and Bell's CHSH is wrong.

Good to se a smile there I guess I'll just conclude that Joy's proof is wrong, and keep smiilng

[gill1109]

Heinera said "But a LHV model can't have independent terms"
This is just rubbish.

I'll just repeat my request: Why don't you construct one, and prove us all wrong?

I've proved you wrong without constructing one. Joy has proved you wrong by constructing one.

No, Joy has not constructed one. His construction is no construction. He is is confused about the difference between "for all" and "there exists". He thinks he showed something exists, but if you look closely, it doesn't exist.