## 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

Justo wrote:You just say my is not weakly objective but you don't say why and where my reasoning fails.

I have. From this paper https://arxiv.org/pdf/2012.10238v5.pdf Equation (23) is where you list 4 different sums each over the same set of hidden variables. From equation (23) you extract (equation (29) by converting the linear combination of sums into the sum of a linear combination over the same set of lambdas. Think for a second what this operation means. It means you went from adding/subtracting a global property of each individual dataset (ie, the average of the paired product of outcomes), to taking the average of the sum/difference individual properties of the combined dataset. Equation (23) can be evaluated from data stored on 4 independent spreadsheets of pairs of outcomes. All you need is to calculate the average of each spreadsheet and use just the averages to calculate (23). Because of this, the ordering is not that important for (23).

Equation (24) can only be evaluated on a single spreadsheet containing all outcome pairs. This is because you must calculate the individual products and then combine them for each row before doing the summation. You can't do this without re-ordering! This is the implicit assumption. On its face, as a purely mathematical operation, it appears legitimate, however, you then claim that your equations (23 to 29) represent the results of a weakly objective experiment. But for the weakly objective case, the re-ordering required to proceed from (23) is impossible. I've explained it multiple times already using multiple examples and even posted code to demonstrate it.

Let me try explaining a different way. Say we perform a weakly objective experiment and obtain some data from it. Let us assume that the data from this experiment are in fact due to local hidden variables. Let us also assume that we perform N iterations from each of the weakly objective runs, and let us also assume that the fair sampling assumption applies and N is large enough such that the distributions of the hidden variables that produced the data are exactly the same for all 4 sets, except for the fact that each set is a separate random experiment with different orderings of the hidden variables. In this case, we have satisfied all your assumptions leading up to (23).

Our task now is to calculate similar to your (23) to verify if it agrees with (28).

Note that in our weakly objective experiment, the outcomes represented by do not necessarily represent the results from the same lambda. The only information we have is that all the data in each run result from the same distribution of lambda. The orderings are random for each independent run. It's similar to tossing a coin 100 times in two independent experiments and obtaining 50 heads and 50 tails in each but the ordering of the outcomes will be random and independent between the two sets.

But, take a closer look at equation (24). Let us try to express in a similar manner to (24). We can't unless we make an assumption about the ability to reorder the data. After reordering the values in all the columns will match each other not just in relative frequencies but also in the pattern and order, and similarly for , and . If this reordering is impossible, then we can't expect equations (24 to 29) to apply to this data and therefore we can't expect the upper bound of 2 to apply to weakly objective experimental outcomes.

To see that it is impossible to reorder the data, let us try to do the re-orderings required. We can apply the permutation to such that . This creates the match . This takes care of . To take care of . We can apply the permutation to to obtain the match . Note that every permutation we apply must be applied to both columns of each independent spreadsheet, in order to keep corresponding pairs of values on each row together. Therefore after applying and we now also end up with a the columns and . But we still need to make the and columns match and , plus whatever permutation we apply to must be the same permutation we apply to in order to keep rows together. Unfortunately this is impossible to complete because we need to apply to to obtain the match but we need a different incompatible permutation to get the match
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The CHSH inequality as a weakly objective result

The reason why it is weakly objective is too simple and elementary: there can only be a "finite" number of hidden variables(HV) therefore they have no other option but to repeat their values in different experiments.

As explained above, this is wrong. It is not simply a matter of repeating the same values. The ordering is also important.

Let me explain that in even more simple terms: if you toss two different coins many times in two different series of experiments: their results will have to repeat because there are only two different results.

True, but you are missing the point. Say we have a coin-reading machine. The machine works by accepting one of two settings (H=head or T=tail). A coin is tossed into an opening above the machine, causing a green LED to flash if the coin comes up the same side as the setting and a red LED flashes otherwise. We perform an experiment with the machine set to H. After very many tosses, we calculate the relative frequency of green LEDs. We repeat the experiment setting the machine to T and after very many tosses, we calculate the relative frequency of green LEDs.

This experiment is weakly objective because we did not measure the heads and tails in the same experiment, even though we measured the same coin. If we evaluate the expression P(H) + P(T) for this experiment, each term would correspond to an independent experiment. We could write it as

1)
Where represents the outcome.
We can assume that the same hidden variables are at play for both experiments but that is not enough to convert the above expression to

2)

In fact, this expression is strongly objective. Because it implies that you are evaluating from each individual toss. Let us say we decided to measure both H and T in the same experiment. If we set the machine to H and get a green flash we record H=1 and if we get a red flash, we record T=1 and vice versa. In this case, it is valid to write

3)

because we have the joint data already ordered in pairs. In the weakly objective case, we don't have that. We must order the data first before we are allowed to combine the sums that way. In fact, this precise coin toss example easily demonstrates how relationships derived from strongly objective scenarios can fail woefully if applied to weakly objective data.

For example, looking at equation (3) above, it is obvious that therefore
4) . Here we have proved the strongly objective equality of P(H) + P(T) = 1.

However, this relationship can easily be violated by the weakly objective experiment represented by equation (1). All you need to see this is consider the weakly objective experiment where we set the machine to H, and obtained green flashes 80% of the time. P(H) = 0.8, and then in a separate independent run we set the machine to T and obtained green flashes 70% of the time P(T) = 0.7. P(H) + P(T) = 1.5 =/= 1. How come? The same coin, the same machine, the same hidden variables. The only difference is that in one case we used the strongly objective result to derive the equality and in the other case we used the weakly objective experiment to violate the equality. This experiment demonstrates explicitly that despite appearing innocent, the transition from equation (1) to equation (2) includes a hidden assumption that is false. Because once you have equation (2), the equality (4) follows.

This is exactly the same assumption that you make in going from equation (23) to equation (24,29) in your paper.

This shows that you do not understand my derivation. I agree with you and Adenier (not with Gill) that strongly objective is meaningless. So, whatever it is that you explain to Gill I would probably agree with you but that obviously cannot explain my mistake because my argument is different.

I understand your paper very well. I've explained the problem in many different ways, I've provided code that demonstrates the issue, I've provided a simple-to-understand coin-toss example above which shows you exactly the issue.

A key claim in your paper is that your expressions represent the weakly objective case. But equation (24, 29) is strongly objective and going from (23) to (24) involves the hidden assumption that the experimental data from a weakly objective experiment can be re-ordered such that the corresponding repeated columns match each other. This assumption is false as I have now demonstrated multiple times.
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The CHSH inequality as a weakly objective result

gill1109 wrote:I’m glad you recall that story. But you misreport it. It was not about the correlation, but about the average difference. You can sample husbands. You can sample wives. The difference between the averages estimates the mean difference between heights in a husband and wife couple.

Provided, of course, that the populations of husbands and wives are in one-to-one correspondence and the samples are random samples.

I think that you think the story is daft because you don’t understand statistics and probability very well.

For the simple type of statistics that you do daily, that may be enough but you just need to scratch the surface just a bit and realize how wrong you are. If I tell you that the average absolute height difference between married couples is 5 inches, good luck using your technique to prove or disprove it through separate disjoint random samples of married men and women.

In fact if you never do joint measurements of married couples, you may end up easily in a situation in which your measurements give you zero. If the average height of men and women are the same, and short people prefer to marry more than 5 inches taller than themselves, then you easily have the average absolute height difference between married couples being higher than 5 inches, and yet your expert randomized experiment will give you zero. You can't measure joint properties separately. This was the point you missed. Tell me what you think is wrong with my proof, or with Justo’s proof.

I've done both already to great detail. In addition, as Justo correctly points out, you are quite confused about the meaning of "Counterfactual definiteness". And as I've explained to you previously, you are also confused about the meanings of "Realism", "Locality", "Randomness" and "Freedom". This is obvious from your papers and we have discussed that many times.
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The CHSH inequality as a weakly objective result

Ok, here @minkwe describe two supposedly different experiments:
minkwe wrote:The machine works by accepting one of two settings (H=head or T=tail). A coin is tossed into an opening above the machine, causing a green LED to flash if the coin comes up the same side as the setting and a red LED flashes otherwise.

versus

minkwe wrote: Let us say we decided to measure both H and T in the same experiment. If we set the machine to H and get a green flash we record H=1 and if we get a red flash, we record T=1 and vice versa.

Please explain how these two are fundamentally different, anyone. Let's say that in the first experiment, we chose the setting H. Then both experiments are the same. If we choose setting T, then it's just a convention of switching colours (interpreting red as green).
Heinera

Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

### Re: The CHSH inequality as a weakly objective result

minkwe wrote:In fact if you never do joint measurements of married couples, you may end up easily in a situation in which your measurements give you zero. If the average height of men and women are the same, and short people prefer to marry more than 5 inches taller than themselves, then you easily have the average absolute height difference between married couples being higher than 5 inches, and yet your expert randomized experiment will give you zero.

Hahaha, @minkwe! Think! If men and women have the same average height, how can then men on average have a shorter wife?

Moaahhhaaa. Please give us a numerical example. Heinera

Posts: 917
Joined: Thu Feb 06, 2014 1:50 am

### Re: The CHSH inequality as a weakly objective result

minkwe wrote:
Justo wrote:You just say my is not weakly objective but you don't say why and where my reasoning fails.

I have. From this paper https://arxiv.org/pdf/2012.10238v5.pdf Equation (23) is where you list 4 different sums each over the same set of hidden variables. From equation (23) you extract (equation (29) by converting the linear combination of sums into the sum of a linear combination over the same set of lambdas. Think for a second what this operation means. It means you went from adding/subtracting a global property of each individual dataset (ie, the average of the paired product of outcomes), to taking the average of the sum/difference individual properties of the combined dataset. Equation (23) can be evaluated from data stored on 4 independent spreadsheets of pairs of outcomes. All you need is to calculate the average of each spreadsheet and use just the averages to calculate (23). Because of this, the ordering is not that important for (23).

Great! Now I can finally make sense of your objections. Each sum arises from four different series of experiments performed with different settings. That's Adenier's weakly objectiveness.
Notice that if each spreadsheet registers individual outcomes, to obtain the four sums of (23) we need to combine the results of each spreadsheet and reduce them according to eq (21) so that we finally obtain only 16 rows in each spreadsheet. Permuting is the same as reordering.

minkwe wrote:Equation (24) can only be evaluated on a single spreadsheet containing all outcome pairs. This is because you must calculate the individual products and then combine them for each row before doing the summation. You can't do this without re-ordering! This is the implicit assumption. On its face, as a purely mathematical operation, it appears legitimate, however, you then claim that your equations (23 to 29) represent the results of a weakly objective experiment. But for the weakly objective case, the re-ordering required to proceed from (23) is impossible. I've explained it multiple times already using multiple examples and even posted code to demonstrate it.

I think here you went astray. We do not care about the real order, in fact, we cannot know what is the real order because we do not even know whether hidden variables exist. The important point is that if hidden variables existed, we could have reordered them to obtain the desired result. The real order is irrelevant because the final result does not depend on whether your order them or not.
Take this example: writhe two numbers in two cards, say 1 and 2. Extract them without substitution: I can predict the result of the sum of your cards 1 + 2 =3 although I do not know in what order you actually extracted them, your extraction could have been first 2 and then 1, it is irrelevant.
Your objection to my derivation is similar to saying that I can't predict the result of the sum or your cards because I don't know the order in which you extracted them.

minkwe wrote:Let me try explaining a different way. Say we perform a weakly objective experiment and obtain some data from it. Let us assume that the data from this experiment are in fact due to local hidden variables. Let us also assume that we perform N iterations from each of the weakly objective runs, and let us also assume that the fair sampling assumption applies and N is large enough such that the distributions of the hidden variables that produced the data are exactly the same for all 4 sets, except for the fact that each set is a separate random experiment with different orderings of the hidden variables. In this case, we have satisfied all your assumptions leading up to (23).

Our task now is to calculate similar to your (23) to verify if it agrees with (28).

Note that in our weakly objective experiment, the outcomes represented by do not necessarily represent the results from the same lambda. The only information we have is that all the data in each run result from the same distribution of lambda. The orderings are random for each independent run. It's similar to tossing a coin 100 times in two independent experiments and obtaining 50 heads and 50 tails in each but the ordering of the outcomes will be random and independent between the two sets.

But, take a closer look at equation (24). Let us try to express in a similar manner to (24). We can't unless we make an assumption about the ability to reorder the data. After reordering the values in all the columns will match each other not just in relative frequencies but also in the pattern and order, and similarly for , and . If this reordering is impossible, then we can't expect equations (24 to 29) to apply to this data and therefore we can't expect the upper bound of 2 to apply to weakly objective experimental outcomes.

To see that it is impossible to reorder the data, let us try to do the re-orderings required. We can apply the permutation to such that . This creates the match . This takes care of . To take care of . We can apply the permutation to to obtain the match . Note that every permutation we apply must be applied to both columns of each independent spreadsheet, in order to keep corresponding pairs of values on each row together. Therefore after applying and we now also end up with a the columns and . But we still need to make the and columns match and , plus whatever permutation we apply to must be the same permutation we apply to in order to keep rows together. Unfortunately this is impossible to complete because we need to apply to to obtain the match but we need a different incompatible permutation to get the match

When you say "We can't unless we make an assumption about the ability to reorder the data" basically reduces to the validity of arithmetic, you do not need to actually reorder anything. You only need to know that is possible. In other words, whether you do it or not doesn't change the result. You reorder only to facilitate the calculation, that is what mathematical properties are useful for.
Your permutation scheme is an unnecessary complication, however, it is easy to see that it does not invalidate my final result.
Say we have four unordered spreadsheets. Don't touch the first one. Now reorder each of the other three such that they coincide with the first spreadsheet. There you have all four in the same order.
Justo

Posts: 83
Joined: Fri Aug 20, 2021 8:20 am

### Re: The CHSH inequality as a weakly objective result

minkwe wrote:
gill1109 wrote:I’m glad you recall that story. But you misreport it. It was not about the correlation, but about the average difference. You can sample husbands. You can sample wives. The difference between the averages estimates the mean difference between heights in a husband and wife couple.

Provided, of course, that the populations of husbands and wives are in one-to-one correspondence and the samples are random samples.

I think that you think the story is daft because you don’t understand statistics and probability very well.

For the simple type of statistics that you do daily, that may be enough but you just need to scratch the surface just a bit and realize how wrong you are. If I tell you that the average absolute height difference between married couples is 5 inches, good luck using your technique to prove or disprove it through separate disjoint random samples of married men and women.

I suggest you test your assertions by doing a little simulation experiment.

According to basic probability theory, E(X - Y) = E(X) - E(Y) as long as E(|X|) < infty, E(|Y|) < infty. As long as the mean height of men and of women is finite, there is nothing wrong in what I told you.

It is true that I forget to mention that finiteness condition till now. Sorry. I was keeping things simple.
gill1109
Mathematical Statistician

Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

### Re: The CHSH inequality as a weakly objective result

Justo wrote:Great! Now I can finally make sense of your objections. Each sum arises from four different series of experiments performed with different settings. That's Adenier's weakly objectiveness.
Notice that if each spreadsheet registers individual outcomes, to obtain the four sums of (23) we need to combine the results of each spreadsheet and reduce them according to eq (21) so that we finally obtain only 16 rows in each spreadsheet. Permuting is the same as reordering.

And if you are able to do that you will end up with pairs of identical columns and you essentially have a 4xN spreadsheet which is the same as the strongly objective experiment. Your argument is essentially that for EPRB Weakly objective = Strongly objective.

I think here you went astray. We do not care about the real order, in fact, we cannot know what is the real order because we do not even know whether hidden variables exist. The important point is that if hidden variables existed, we could have reordered them to obtain the desired result. The real order is irrelevant because the final result does not depend on whether your order them or not.

I did not. You perhaps haven't understood it. The order is relevant because you rely on it in order to derive the upper bound of 2 starting at equation (24). All the steps leading up to the upper bound of 2 rely on the order. Therefore the inequality only applies to reordered data, that is the point. Even if the hidden variables existed, you don't know it so you have to to the permutations as explained in my previous post, but you can't. It is impossible.

Take this example: writhe two numbers in two cards, say 1 and 2. Extract them without substitution: I can predict the result of the sum of your cards 1 + 2 =3 although I do not know in what order you actually extracted them, your extraction could have been first 2 and then 1, it is irrelevant.
Your objection to my derivation is similar to saying that I can't predict the result of the sum or your cards because I don't know the order in which you extracted them.

That's a silly example. You wouldn't suggest it if you actually understood my point. It doesn't have all the required elements. You should address the coin-tossing machine example. It is simple enough but has all the components.

When you say "We can't unless we make an assumption about the ability to reorder the data" basically reduces to the validity of arithmetic, you do not need to actually reorder anything.

Absolutely not. Notice I've not once said your arithmetic was wrong. I've said your assumption that your equations represent the weakly objective scenario was false.

Your permutation scheme is an unnecessary complication, however, it is easy to see that it does not invalidate my final result.
Say we have four unordered spreadsheets. Don't touch the first one. Now reorder each of the other three such that they coincide with the first spreadsheet. There you have all four in the same order.

Here are the 4 spreadsheets from a weakly objective experiment

Please explain how you reorder the last three so that all the corresponding columns match as they should.

Finally even if you are able to do the re-ordering, you will end up with a single 4xN spreadsheet, which is the strongly objective scenario. Therefore you are essentially arguing that the strongly objective scenario and the weakly objective scenario are essentially the same. If that is your argument, now please answer my coin-tossing machine example.
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The CHSH inequality as a weakly objective result

gill1109 wrote:According to basic probability theory, E(X - Y) = E(X) - E(Y) as long as E(|X|) < infty, E(|Y|) < infty. As long as the mean height of men and of women is finite, there is nothing wrong in what I told you.

It is true that I forget to mention that finiteness condition till now. Sorry. I was keeping things simple.

Come on Richard, don't play games. Are you ready to claim that E(|X - Y|) = |E(X) - E(Y)|?

minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The CHSH inequality as a weakly objective result

minkwe wrote:
gill1109 wrote:According to basic probability theory, E(X - Y) = E(X) - E(Y) as long as E(|X|) < infty, E(|Y|) < infty. As long as the mean height of men and of women is finite, there is nothing wrong in what I told you.

It is true that I forget to mention that finiteness condition till now. Sorry. I was keeping things simple.

Come on Richard, don't play games. Are you ready to claim that E(|X - Y|) = |E(X) - E(Y)|?

Michel, I’m not playing games. I don’t understand the relevance of your question. |E(X) - E(Y)| = |E(X - Y)| </= E(|X - Y|). So what?

I am building on standard results in probability theory concerning existence of expectation values and linearity of the expectation operator which perhaps you’re not familiar with. I would be happy to explain.
gill1109
Mathematical Statistician

Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

### Re: The CHSH inequality as a weakly objective result

gill1109 wrote:
minkwe wrote:
gill1109 wrote:According to basic probability theory, E(X - Y) = E(X) - E(Y) as long as E(|X|) < infty, E(|Y|) < infty. As long as the mean height of men and of women is finite, there is nothing wrong in what I told you.

It is true that I forget to mention that finiteness condition till now. Sorry. I was keeping things simple.

Come on Richard, don't play games. Are you ready to claim that E(|X - Y|) = |E(X) - E(Y)|?

Michel, I’m not playing games. I don’t understand the relevance of your question. |E(X) - E(Y)| = |E(X - Y)| </= E(|X - Y|). So what?

I am building on standard results in probability theory concerning existence of expectation values and linearity of the expectation operator which perhaps you’re not familiar with. I would be happy to explain.

Especially the part where I explained:

minkwe wrote:For the simple type of statistics that you do daily, that may be enough but you just need to scratch the surface just a bit and realize how wrong you are. If I tell you that the average absolute height difference between married couples is 5 inches, good luck using your technique to prove or disprove it through separate disjoint random samples of married men and women.
In fact if you never do joint measurements of married couples, you may end up easily in a situation in which your measurements give you zero. If the average height of men and women are the same, and short people prefer to marry more than 5 inches taller than themselves, then you easily have the average absolute height difference between married couples being higher than 5 inches, and yet your expert randomized experiment will give you zero. You can't measure joint properties separately. This was the point you missed. You are obviously still missing the point.
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The CHSH inequality as a weakly objective result

Ah, thanks! You were talking about the average *absolute* height difference. I was talking about the average (signed) difference.

Fortunately, *my* example is relevant to the CHSH discussion, yours isn't!

You can measure *some* joint properties separately.

So now, we can go back to where we were and you can tell me where I went wrong in the derivation of my version of CHSH. Or you can show Justo where he was wrong in his. Both of us emphasize the need for a statistical assumption and a statistical argument to arrive at inferences about real-world experimental data.

BTW Justo and I have disagreed over the use of the phrase "counterfactual definiteness". We had no disagreement at all over matters of substance, as far as I am aware. Only terminology. We come from different scientific fields and our native cultures and languages are different, too. [Cool mean perfidious Englishman versus passionate Hispanic].
gill1109
Mathematical Statistician

Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

### Re: The CHSH inequality as a weakly objective result

minkwe wrote:Here are the 4 spreadsheets from a weakly objective experiment

Please explain how you reorder the last three so that all the corresponding columns match as they should.

You have four columns with 16 different rows each. Rows are numbered from 1 to 16 in different order.
Are you telling me that you can't change the order of the rows to make them appear in sequential order in each column?

minkwe wrote:Finally even if you are able to do the re-ordering, you will end up with a single 4xN spreadsheet, which is the strongly objective scenario. Therefore you are essentially arguing that the strongly objective scenario and the weakly objective scenario are essentially the same.

Here is how Adenier defined weakly objective and strongly objected:
"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."

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.
Justo

Posts: 83
Joined: Fri Aug 20, 2021 8:20 am

### Re: The CHSH inequality as a weakly objective result

Justo wrote:
minkwe wrote:Here are the 4 spreadsheets from a weakly objective experiment

Please explain how you reorder the last three so that all the corresponding columns match as they should.

You have four columns with 16 different rows each. Rows are numbered from 1 to 16 in different order.
Are you telling me that you can't change the order of the rows to make them appear in sequential order in each column?

Where did the numbers come from. There are no numbers in those spreadsheets. These are experimental outcomes. The hidden variables are hidden and not measured. All you have are outcomes.

Here is how Adenier defined weakly objective and strongly objected:
"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."

Take a look at the coin-tossing machine example. The above definition applies. For some reason, you are avoiding addressing it.

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.

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.

What I've explained is that it is not possible to relate data from a weakly objective experiment with the inequality you derived.
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The CHSH inequality as a weakly objective result

gill1109 wrote:Fortunately, *my* example is relevant to the CHSH discussion, yours isn't!

Unfortunately for you mine is relevant to EPRB and yours is absolutely not. Joint measurement is important in EPRB. You can't recover joint properties by measuring separately.
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The CHSH inequality as a weakly objective result

minkwe wrote:
gill1109 wrote:Fortunately, *my* example is relevant to the CHSH discussion, yours isn't!

Unfortunately for you mine is relevant to EPRB and yours is absolutely not. Joint measurement is important in EPRB. You can't recover joint properties by measuring separately.

The purpose of a Bell experiment is not to recover joint properties. It is to disprove local realism.

minkwe wrote: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.
What I've explained is that it is not possible to relate data from a weakly objective experiment with the inequality you [Justo] derived.

The inequality is proven by use of an assumption of statistical independence on top of local realism. The data is not converted into an Nx4 spreadsheet. The data consists of four 2x2 tables with usually different total numbers of trials. For each setting pair, the table contains the number of (+ +), (+ -), (- +), and (- -) outcomes.
gill1109
Mathematical Statistician

Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

### Re: The CHSH inequality as a weakly objective result

minkwe wrote:
Justo wrote:
minkwe wrote:Here are the 4 spreadsheets from a weakly objective experiment

Please explain how you reorder the last three so that all the corresponding columns match as they should.

You have four columns with 16 different rows each. Rows are numbered from 1 to 16 in different order.
Are you telling me that you can't change the order of the rows to make them appear in sequential order in each column?

Where did the numbers come from. There are no numbers in those spreadsheets. These are experimental outcomes. The hidden variables are hidden and not measured. All you have are outcomes.

There are 16 different values of hidden variables , the numbers are the indices numbering them.

minkwe wrote:Take a look at the coin-tossing machine example. The above definition applies. For some reason, you are avoiding addressing it.

I am avoiding it because I would have to say the same I am trying to say already here.

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.

You keep saying that but you just cannot say where, in what step, my reasoning fails or is wrong

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.

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".

minkwe wrote:What I've explained is that it is not possible to relate data from a weakly objective experiment with the inequality you derived.

No, you have not. You should identify where the mistake is. You just keep telling me it is not possible but do not say where or in what step there is a mistake.
Your argument seems to be that you can't reorder data, but that is just absurd.
It seems that you believe that we're talking about "actually" reordering the data. No, that is not the idea, the idea is that it is possible to reorder data and that, if arithmetic is true, reordering cannot change the result, which in this case is the bound 2 for the inequality.

I think the discussion is going nowhere. You just keep saying what I did is wrong and to justify your claim you invent examples of your own that have nothing to do with my derivation.
I really appreciate your reading of my paper but we should stop here.
Justo

Posts: 83
Joined: Fri Aug 20, 2021 8:20 am

### Re: The CHSH inequality as a weakly objective result

gill1109 wrote:
minkwe wrote:
gill1109 wrote:Fortunately, *my* example is relevant to the CHSH discussion, yours isn't!

Unfortunately for you mine is relevant to EPRB and yours is absolutely not. Joint measurement is important in EPRB. You can't recover joint properties by measuring separately.

The purpose of a Bell experiment is not to recover joint properties. It is to disprove local realism.

What a bunch of freakin' nonsense. All the experiments do is try to validate quantum mechanics. Nothing more; nothing less. They actually have nothing to do with Bell's junk physics theory and Gill's junk theory.   .
FrediFizzx
Independent Physics Researcher

Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
Location: N. California, USA

### Re: The CHSH inequality as a weakly objective result

Justo wrote:There are 16 different values of hidden variables , 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.
minkwe wrote:Take a look at the coin-tossing machine example. The above definition applies. For some reason, you are avoiding addressing it.

I am avoiding it because I would have to say the same I am trying to say already here.

That's unfortunate because I don't think you have understood the issue and I took the time to describe it using that example to help you see it.
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.

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.

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.

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.

minkwe wrote:What I've explained is that it is not possible to relate data from a weakly objective experiment with the inequality you derived.

No, you have not.

I have, multiple times. You just don't understand it. Here is the latest attempt:
minkwe wrote:Say we perform a weakly objective experiment and obtain some data from it. Let us assume that the data from this experiment are in fact due to local hidden variables. Let us also assume that we perform N iterations from each of the weakly objective runs, and let us also assume that the fair sampling assumption applies and N is large enough such that the distributions of the hidden variables that produced the data are exactly the same for all 4 sets, except for the fact that each set is a separate random experiment with different orderings of the hidden variables. In this case, we have satisfied all your assumptions leading up to (23).

Our task now is to calculate similar to your (23) to verify if it agrees with (28).

Note that in our weakly objective experiment, the outcomes represented by do not necessarily represent the results from the same lambda. The only information we have is that all the data in each run result from the same distribution of lambda. The orderings are random for each independent run. It's similar to tossing a coin 100 times in two independent experiments and obtaining 50 heads and 50 tails in each but the ordering of the outcomes will be random and independent between the two sets.

But, take a closer look at equation (24). Let us try to express in a similar manner to (24). We can't unless we make an assumption about the ability to reorder the data. After reordering the values in all the columns will match each other not just in relative frequencies but also in the pattern and order, and similarly for , and . If this reordering is impossible, then we can't expect equations (24 to 29) to apply to this data and therefore we can't expect the upper bound of 2 to apply to weakly objective experimental outcomes.

To see that it is impossible to reorder the data, let us try to do the re-orderings required. We can apply the permutation to such that . This creates the match . This takes care of . To take care of . We can apply the permutation to to obtain the match . Note that every permutation we apply must be applied to both columns of each independent spreadsheet, in order to keep corresponding pairs of values on each row together. Therefore after applying and we now also end up with a the columns and . But we still need to make the and columns match and , plus whatever permutation we apply to must be the same permutation we apply to in order to keep rows together. Unfortunately this is impossible to complete because we need to apply to to obtain the match but we need a different incompatible permutation to get the match

Note that my arguments are directed at specific steps and equations in your paper.

You should identify where the mistake is. You just keep telling me it is not possible but do not say where or in what step there is a mistake.

Obviously, you don't understand what I'm saying, otherwise, you won't ask me to show you a mistake. I've never claimed that you made a mistake. I've claimed that you made an implicit assumption that is false for weakly objective data.

Your argument seems to be that you can't reorder data, but that is just absurd.
It seems that you believe that we're talking about "actually" reordering the data. No, that is not the idea, the idea is that it is possible to reorder data and that, if arithmetic is true, reordering cannot change the result, which in this case is the bound 2 for the inequality.

So then answer my 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?
Reordering can't change the result of equation (23) but reordering can change the result of equation (24). This is the part you don't get. Reordering can't change but reordering can change the upper bound, this is the reason why you rely on implicit reordering to derive the upper bound of 2. If only you would address the coin-reading machine example, you would see it. But you don't want to.
minkwe

Posts: 1441
Joined: Sat Feb 08, 2014 10:22 am

### Re: The CHSH inequality as a weakly objective result

minkwe wrote:
Justo wrote:There are 16 different values of hidden variables , 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.

Justo is not assuming the availability (to you or to me) of information that is not available in experiments to the experimenters.

Just because certain things assumed to exist in a physics theory are not observed does not mean that a theoretician cannot deduce, using logic and mathematics, the physical consequences of those assumptions. That's what theoretical physicists do all the time!
gill1109
Mathematical Statistician

Posts: 2812
Joined: Tue Feb 04, 2014 10:39 pm
Location: Leiden

PreviousNext 