The CHSH inequality as a weakly objective result

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

Re: The CHSH inequality as a weakly objective result

minkwe wrote:
Justo wrote:There are 16 different values of hidden variables $\lambda_j=1,2\ldots 16$, the numbers are the indices numbering them.

Hidden variables are not measured, let alone numbered in experimental data. You are assuming the availability of information that is not available in experiments.

Of course, hidden variables are not measured. What the reasoing does is to show that if they existed the result obtained with the experimental values would have to be bounded by 2. Since the experimental result exceeds 2 the conclusion is that they cannot exist. That is why the experiments falsify the existence of the hidden variables.
The inequality is evaluated only with the measured data. The results falsify your assumptions.

minkwe wrote:
Justo wrote:What I have shown is that "each correlation function pertains to a different set of particle pairs." therefore they are weakly objective, and yes, of course, you can arrange them in a single 4xN (N=16) spreadsheet. The essential point is the four columns pertain to four different series of actual experiments.

You have not. You claim to but then you make an implicit assumption that the weakly objective case is the same as the strongly objective case (eq 24), and then proceed with the strongly objective case.
Justo wrote:You keep saying that but you just cannot say where, in what step, my reasoning fails or is wrong

I've mentioned several times and referenced the transition from equation (23) to (24). How can you claim that I have not shown where? You may disagree with me but to suggest that I haven't explicitly said where and how is just wrong.

I am sorry but I just can't make sense of that. Accepting that (23) is built up with actually measured experimental results (weakly objective), why is it incorrect to apply mathematical properties to put it in an equivalent form?. Of course, you do not measure (24), it is a mathematically equivalent form obtained with measured results. That is how mathematics is used to derive results all the time: you transform a given expression to an equivalent form where is it easy to evaluate and draw useful conclusions that were not evident in their original form.

minkwe wrote:Conceptually, your equation (23) is equivalent to 4 independent 2xN spreadsheets of outcomes. Your equation (24) is equivalent to a single 4xN spreadsheet of outcomes. And your equation (29) is equivalent to a single row from the single 4xN spreadsheet in equation (24). You can't derive the inequality without putting those numbers into a single 4xN spreadsheet as you did in equation (24). In fact, a spreadsheet that is not a 4xN spreadsheet can't be expected to obey the inequality. When you obtain experimental data you can't just compare it with the inequality without first converting the data to a 4xN spreadsheet. If this was not a necessary step, you would not have needed to do it before deriving the inequality.

Justo wrote:Yes, of course, that is what the derivation is all about. To prove that (23) is equivalent to 4 independent 2xN spreadsheets that reduce to one 4xN spreadsheet with actual data, i.e., "weakly objective".

So let me ask you a simple question. If I take 4 2xN spreadsheets from a weakly objective experiment, will you expect it to obey the inequality you derive without first being converted into a single 4xN spreadsheet? This is the key question.

Yes, I agree this is the key question. The answer is yes because they are mathematically equivalent unless you reject the laws of arithmetic. That is why the Bell theorem is a very elementary result. You just need arithmetic to understand it. You do not need to use delta functions, Fourier transforms, complex variables, etc. just arithmetic.
What happens is that if you do not transform the values contained in the 4 2xN spreadsheets into a mathematically equivalent arrange, the result is not evident. For instance, if I give you 100 numbers from 1 to 100 in a random configuration you cannot guess they are sequential numbers unless you order them. If you want to know the sum, you just order them and apply the formula for an arithmetic progression. That does not change the original value of the sum. It is just that simple end evident.

To evaluate the bound of the Bell inequality you transform the data contained in four 2xN spreadsheets into a single "ordered" 4xN spreadsheet so that you can obtain the bound of the inequality. You do not change the original experimental values, just apply to them valid arithmetic rules, namely, commutativity, associativity, and distributivity. There are no further intricacies involved.

What Adenier objected to is not that you cannot use arithmetic to evaluate the Bell inequality. He objected to the fact that the single 4xN spreadsheet does not contain real experimental values because the four columns are obtained from a single pair of particles (strongly objective interpretation).
What I proved is that, although Adenier is correct when saying that such interpretation is meaningless, the 4xN spreadsheet can be understood weakly objectively, i.e., containing results from 4 2xN spreadsheets of real experimental values, so it does make sense.
Justo

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Re: The CHSH inequality as a weakly objective result

Code: Select all
A1 [ 1  1  1 -1 -1 -1 -1 -1 -1  1] B1 [-1  1  1 -1 -1  1 -1 -1 -1  1] A2 [-1  1 -1 -1 -1  1 -1  1  1 -1] B2 [ 1 -1  1  1 -1 -1  1 -1 -1 -1] A3 [-1 -1  1  1  1 -1  1 -1 -1 -1] B3 [-1 -1  1  1  1  1 -1 -1 -1 -1] A4 [ 1 -1 -1 -1 -1  1 -1  1 -1  1] B4 [-1 -1 -1 -1 -1  1  1  1 -1  1] S = 2.4
minkwe

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Re: The CHSH inequality as a weakly objective result

minkwe wrote:
Code: Select all
A1 [ 1  1  1 -1 -1 -1 -1 -1 -1  1] B1 [-1  1  1 -1 -1  1 -1 -1 -1  1] A2 [-1  1 -1 -1 -1  1 -1  1  1 -1] B2 [ 1 -1  1  1 -1 -1  1 -1 -1 -1] A3 [-1 -1  1  1  1 -1  1 -1 -1 -1] B3 [-1 -1  1  1  1  1 -1 -1 -1 -1] A4 [ 1 -1 -1 -1 -1  1 -1  1 -1  1] B4 [-1 -1 -1 -1 -1  1  1  1 -1  1] S = 2.4

So with four sets of 10 observations each, you can violate the Bell inequality? You could violate Tsirelson’s inequality. You can even get S = 4. So what?

That is why we need a statistical independence assumption. You don’t understand probability theory, so you called it mumbo jumbo.

You don’t only need a probabilistic assumption, you also need error bars and p-values and all that. Or a prior distribution and Bayes theorem. As you like…
gill1109
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Re: The CHSH inequality as a weakly objective result

@qill1109 What a bunch of freakin' nonsense. Easy to exceed Tsirelson’s bound via CHSH. +1 +1 -(-1) +1 = 4. I even have a simulated curve that does it. Are you going to keep spewing pure nonsense forever?
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FrediFizzx
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Re: The CHSH inequality as a weakly objective result

minkwe wrote:
Code: Select all
A1 [ 1  1  1 -1 -1 -1 -1 -1 -1  1] B1 [-1  1  1 -1 -1  1 -1 -1 -1  1] A2 [-1  1 -1 -1 -1  1 -1  1  1 -1] B2 [ 1 -1  1  1 -1 -1  1 -1 -1 -1] A3 [-1 -1  1  1  1 -1  1 -1 -1 -1] B3 [-1 -1  1  1  1  1 -1 -1 -1 -1] A4 [ 1 -1 -1 -1 -1  1 -1  1 -1  1] B4 [-1 -1 -1 -1 -1  1  1  1 -1  1] S = 2.4

I could change the values and obtain 1.8, so what? It has nothing to do with our discussion.
Justo

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Re: The CHSH inequality as a weakly objective result

gill1109 wrote:So with four sets of 10 observations each, you can violate the Bell inequality? You could violate Tsirelson’s inequality. You can even get S = 4. So what?

That is why we need a statistical independence assumption. You don’t understand probability theory, so you called it mumbo jumbo.

You don’t only need a probabilistic assumption, you also need error bars and p-values and all that. Or a prior distribution and Bayes theorem. As you like…

Since you understand statistics and probability so clearly, why don't you address this part of my argument. You've been silent on it.

minkwe wrote:$A(\overrightarrow{a}, \overrightarrow{\lambda}) = \frac{1}{sign(\overrightarrow{a} \cdot \overrightarrow{\lambda})$
This function has values $\pm 1$ but you can't derive Bell's inequality with this type of function precisely because the domain of the function which is the space of vector pairs $\{\overrightarrow{a}, \overrightarrow{\lambda}\}$ excludes where $\overrightarrow{a} \perp \overrightarrow{\lambda}$.

Now if you take a product of two such functions
$f(\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{\lambda}) = A(\overrightarrow{a}, \overrightarrow{\lambda}) A(\overrightarrow{b}, \overrightarrow{\lambda})$, The domain of the product is the space of vector triples $\{\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{\lambda}, \}$ which excludes the regions where

$\{\overrightarrow{a} \perp \overrightarrow{\lambda} \} \cup \{ \overrightarrow{b} \perp \overrightarrow{\lambda}\}$.

The first observation of the consequences of this is that any probability distribution on the domains of the individual functions won't apply to the products. I think this could be another way of stating what local has been saying about separated vs joint measurements.

Secondly, looking at your equation 29, each of the products will have a different domain and therefore the $C(\lambda_i)$ will only be a valid expression for the common part of the domains of those functions.
minkwe

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Re: The CHSH inequality as a weakly objective result

Dear Michel

I would say that Bell’s theorem (what I call its mathematical content) doesn’t apply to it because your function “A” is not defined when a.lambda = 0. Bell’s theorem is about functions A and B taking values +/-1 and it always goes without saying that they are assumed to be defined everywhere. And it’s about a probability distribution rho which doesn’t depend on the settings.

You can violate the conclusion of the theorem by violating the conditions. You can prove new theorems if you relax the conditions. Jan-Åke Larsson and I have done that for the detection loophole and the coincidence loophole. The CHSH upper bound gets larger. I showed in my unpublished arXiv preprint on your simulation models how they satisfy our adjusted bounds.

The detection loophole works by violating the conditions of the CHSH inequality. A detection loophole model rejects lambda when some condition involving a and b and lambda is not satisfied. This means one is effectively sampling lambda from its conditional distribution given that the condition is satisfied. This conditional distribution can naturally depend on a and/or b. If it violates CHSH, it certainly must depend on a and b.

Yours
Richard
gill1109
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Re: The CHSH inequality as a weakly objective result

PS to Michel: I think that "local" has been saying something else, I think he has been saying that entanglement will somehow break down when particles become more and more separated. I think this is also what Donald Grant has been arguing. And many people argued it before. I think neither of them believe in the non-local collapse of the wave function of particles 1 and 2 together, when just particle 1 is measured. But if you don't think of the wave function as being real, but you just use it as a handy tool in doing calculations, then maybe you would be less worried. That's called Shut Up and Calculate. And Bell called the FAPP trap (FAPP = For All Practical Purposes).

I don't think "local" is thinking about the detection loophole. But I might be wrong.

You said "looking at your equation 29". Equation 29 in which publication? If I write a product of two functions I'm silently assuming (like most mathematicians do, I think, but I might be wrong) that we are talking about two functions with the same domain, otherwise their product is not defined.
gill1109
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Re: The CHSH inequality as a weakly objective result

@gill1109 I can't believe you are still trying to discuss meaningless stuff. It is quite simple. The math of QM is faulty. Can it be fixed? Not sure and don't really care since we have the way Nature works without resorting to QM.
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FrediFizzx
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Re: The CHSH inequality as a weakly objective result

gill1109 wrote:PS to Michel: I think that "local" has been saying something else, I think he has been saying that entanglement will somehow break down when particles become more and more separated.

Shameless liar Gill is lying again. I have explicitly rejected this misrepresentation at least 3 or 4 times but this loser continues to misrepresent my thinking. Get it through your stupid narc head, Gill, I do not appeal to decoherence as the particles separate. Stop misrepresenting me.

One cannot sample a joint distribution with separated (marginal) measurements. That has nothing to do with decoherence. I'm happy that minkwe too acknowledges this simple reality. Gill cannot acknowledge this reality because it is devastating to his mysterian thesis. So instead he is forced to dissemble and misrepresent. Disgusting!
local

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Re: The CHSH inequality as a weakly objective result

local wrote:
gill1109 wrote:PS to Michel: I think that "local" has been saying something else, I think he has been saying that entanglement will somehow break down when particles become more and more separated.

Shameless liar Gill is lying again. I have explicitly rejected this misrepresentation at least 3 or 4 times but this loser continues to misrepresent my thinking. Get it through your stupid narc head, Gill, I do not appeal to decoherence as the particles separate. Stop misrepresenting me.

One cannot sample a joint distribution with separated (marginal) measurements. That has nothing to do with decoherence. I'm happy that minkwe too acknowledges this simple reality. Gill cannot acknowledge this reality because it is devastating to his mysterian thesis. So instead he is forced to dissemble and misrepresent. Disgusting!

"local", I said that I didn't know what you meant. I guessed and I guessed wrong. Your behaviour is the disgusting behaviour. You seem obsessed with something I must have done long ago. Apparently your feelings got hurt and you just can't get over it. Get a life!
gill1109
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Re: The CHSH inequality as a weakly objective result

gill1109 wrote:"local", I said that I didn't know what you meant. I guessed and I guessed wrong.

You are a shameless liar. I have told you several times right here on this forum what I believe in this regard, but you continue to feign ignorance and misrepresent me. Now your childish taunts expose you further.
local

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Re: The CHSH inequality as a weakly objective result

local wrote:
gill1109 wrote:"local", I said that I didn't know what you meant. I guessed and I guessed wrong.

You are a shameless liar. I have told you several times right here on this forum what I believe in this regard, but you continue to feign ignorance and misrepresent me. Now your childish taunts expose you further.

“Local”, you used to be one of the most gentlemanly and courteous persons on the forum. A breath of fresh air. I always enjoyed your well thought out comments. What has come over you?

Anyway, please remind me what you believe in this regard. I’m not as young as I once was. I believe Michel would be interested too.
gill1109
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Re: The CHSH inequality as a weakly objective result

Now the shameless lying narcissist is trying to gaslight us. Pathetic.
local

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Re: The CHSH inequality as a weakly objective result

Ok guys, let's get back on topic! Now!
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FrediFizzx
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