A new simulation of the EPR-Bohm correlations

[minkwe]

OK, how exactly do you think that point 8 'hammers the final nail' into my argument? Just use the table of values like I provided to illustrate what you think you're doing in that point, because to be honest, it appears about as clear as mud to me.

Go back and read all 8 points. You agree to point (4). Points 5,6,7 simply lay out the implications of point (4). Point 8 shows that those implications are unrealizable. It is not possible to do the required rearrangments starting with 4 independent 2xN spreadsheets Unless you want to now recant yet again your agreement with point (8), which you are allowed to do obviously. But I have an even more stark example to present if and when you do that, so tread carefully.

[Jochen]

Point (8) proves that point (4) is false. In other words, the QM predictions for are not the same as the QM predictions for. In other words, you guys (including Bell) have been using the wrong QM predictions to claim violation.

The QM prediction for is given by , with , where is the singlet state. The QM prediction for is given by , with , where is the singlet state. Notice something? Since in both cases, the same measurement operators are used, and the same state is used, the same predictions are obtained.

Likewise if you perform re-orderings on the table that keep the correlators unchanged.

[Jochen]

Go back and read all 8 points. You agree to point (4). Points 5,6,7 simply lay out the implications of point (4). Point 8 shows that those implications are unrealizable.

I'm sorry, but your point 8 is nothing but a confused mess. You've muddled your way into some erroneous belief. Try to make things more clear: think about the actual table of values as assigned by the HV theory. There, it's plain that there is no table such that the value of the CHSH quantity exceeds 2. Is this clear to you? If not, just write down a few lines, and you'll see it. And that's all that's needed; it's just that simple. Whatever you're doing with the re-orderings and such can't change that value. Plainly, row-rearrangements don't change that value. So, what's not clear about this to you? Or are you going to continue being evasive?

[minkwe]

Point (8) proves that point (4) is false. In other words, the QM predictions for are not the same as the QM predictions for.

The QM prediction for
...
Likewise if you perform re-orderings on the table that keep the correlators unchanged

Your first problem is that you always like to talk about predictions of one term, which you then extrapolate to the others. So you are missing the point. You have to talk about all 4 at once. The question is what is the QM prediction for the CHSH, ie all 4 terms.

Your second problem is that you have not realized that for a single set of particle pairs prodicing 4 outcomes we have a single 4xN spreadsheet and the CHSH follows. This was point (1). Even if you make paired copies of the 4xN spreadsheet into 4 separate 2xN spreadsheets, and perform independent row permutations on each of the resulting 2xN spreadsheet, the CHSH inequality still follows. This was point (2).
But for 4 independent disjoint sets of particle pairs producing outcomes , which corresponds to 4 separate 2xN spreadsheets. The inequality for this scenario is not the, but . This was point (3). Heine agrees, though you disagree; perhaps because you believe the 4 independent disjoint sets from point (3) are the same as the 4 2xN spreadsheets from point (2), so you claim they are statistically equivalent. This was point (4). In points (5), (6) and (7), I flesh out the implication of the claimed statistical independence. In other words, I prove that the inequality will only apply to the independent disjoints sets of point (3), if the operations outlined in points (5), (6) and (7) are possible, and only then will those sets be statistically equivalent as you claim.

Finally in point (8), I show that it is not possible to carry out the operations implied by (5), (6) and (7), therefore the claims in point (4) fail.

I'm sorry, but your point 8 is nothing but a confused mess.

So why did you agree to it if you believed it was confused mess??? Perhaps now realizing the failure of your argument, you are just diverting with ad-hominem.

You keep repeating that there is no table which violates the CHSH. But that points (1) and (2) already laid out this fact that there is no 4xN table which violates the CHSH since the inequality immediately follows. I don't know who you are trying to convince with an argument that nobody is contesting. I can easily give you an 8xN spreadsheet of outcomes which violates the CHSH inequality. The whole point of the excercise was to show exactly under what conditions 4 independent disjoint 2xN spreadsheets, (or a single 8xN spreadsheet), will obey the inequality. And as laid out in points 5-7, only when row permutations can be done to rearrange the 2xN spreadsheets such that for all practical purposes columns with similar letters are almost identical. Point 8 shows that this can not be done.

You keep repeating that "whatever you're doing with the re-orderings and such can't change that value. Plainly, row-rearrangements don't change that value". Of course, all the row-rearrangements done in points (2), (5), (6), (7) and (8) do not change the expectation values! The point you do not get, perhaps because you still do not appreciate that there is a difference between the sets in point (3) and those in points (2), is that point 4 implies that those rearrangements must be possible if point (4) is true. But point (8) shows that those rearrangements are not possible, therefore point (4) is false.

You may want to go back and read all 8 points again more carefully this time to understand the point.

[Heinera]

There is no point in me addressing all eight points, since I basically agree with all of them. So what?

Good! You agree with all the 8 points! That wasn't so hard that it needed almost a week to extract.

Point (8) proves that point (4) is false.

No, it does not.

[minkwe]

No, it does not.

Yes it does.

[Heinera]

No, it does not.

Yes it does.

You use the word "independent" in a confusing manner. Point 4 is only correct if the data are generated by a LHV-model; and if so, point 8 does not contradict it.

[Jochen]

Point (8) proves that point (4) is false. In other words, the QM predictions for are not the same as the QM predictions for.

The QM prediction for
...
Likewise if you perform re-orderings on the table that keep the correlators unchanged

Your first problem is that you always like to talk about predictions of one term, which you then extrapolate to the others. So you are missing the point. You have to talk about all 4 at once. The question is what is the QM prediction for the CHSH, ie all 4 terms.

Which all will be the same, as well.

But for 4 independent disjoint sets of particle pairs producing outcomes , which corresponds to 4 separate 2xN spreadsheets. The inequality for this scenario is not the, but .

Not if all of the observables are sampled from the same probability distribution, i.e. not if a table exists such that the observed values are given by its entries, which is always the case for a LHV model. You can simply join these four tables to one, in this form:

Code: Select all

  Alice    |    Bob   
  A  |  C  |  B  |  D 
(A_i)|     |(B_i)|     
     |(C_j)|     |(D_j)
     |(C_k)|(B_k)|     
(A_l)|     |     |(D_l),


where by I simply mean the full list of entries in the A column of the i-spreadsheet. The blank entries can be filled with arbitrary values. Once again, it is clear that the list obeys the inequality, i.e. the value of the CHSH quantity is for all possible ways of completing the table bounded by two. If you challenge this conclusion, the onus is on you: provide a table of values such that .

[minkwe]

You use the word "independent" in a confusing manner. Point 4 is only correct if the data are generated by a LHV-model; and if so, point 8 does not contradict it.

I told you to read all the points carefully before addressing them. You claimed you agreed with all of them, now you are trying to find things to disagree with?

Do not forget that point (4) was given as the reason why the QM predictions for should be the same as the QM predictions for

Therefore it does not help your argument one bit, to argue that they are only equal for LHV models.

[minkwe]

Code: Select all

  Alice    |    Bob   
  A  |  C  |  B  |  D 
(A_i)|     |(B_i)|     
     |(C_j)|     |(D_j)
     |(C_k)|(B_k)|     
(A_l)|     |     |(D_l),


Now you are invoking Gill's failed argument. It is a trick, to try to circumvent the problem, but the trick does not work because the rows which you sampled for the set of particles is not available to be sampled for the set of particles, therefore you have a dependency between the sets of particles. You can not use such an argument when we are discussing 4 disjoint independent sets , , , like in experiments. The dice example I provided already debunks this.

The only way is to start from an 8xN spreadsheet and show what conditions need to be met for the inequality to apply, and then see if those conditions can be met in an experiment. This is what I have done in points 5-8.

[Jochen]

Code: Select all

  Alice    |    Bob   
  A  |  C  |  B  |  D 
(A_i)|     |(B_i)|     
     |(C_j)|     |(D_j)
     |(C_k)|(B_k)|     
(A_l)|     |     |(D_l),


Now you are invoking Gill's failed argument. It is a trick, to try to circumvent the problem, but the trick does not work because the rows which you sampled for the set of particles is not available to be sampled by the set of particles, therefore you have a dependency between the sets of particles. You can not use such an argument when we are discussing 4 disjoint independent sets , , , like in experiments.

No, we have 4N independent particle pairs. On the first N particle pairs, Alice always measured A, and Bob always measured B. On the second N particle pairs, Alice always measured C, and Bob always measured D. On the third N particle pairs, Alice always measured C, Bob always measured B. On the last N particle pairs, Alice always measured A, Bob always measured D. So, all of these sets are independent.

[minkwe]

No, we have 4N independent particle pairs. On the first N particle pairs, Alice always measured A, and Bob always measured B. On the second N particle pairs, Alice always measured C, and Bob always measured D. On the third N particle pairs, Alice always measured C, Bob always measured B. On the last N particle pairs, Alice always measured A, Bob always measured D. So, all of these sets are independent.

So? You do not have a 4xN spreadsheet. Why do you think the measured values should have more weight than the arbitrary values you decide to fill the spreadsheet with.
Once you start adding arbitrary values in order to produce a 4xN spreadsheet, you change the results, unless you want to add zeros. This trick doesn't work either. It is the same trick you accuse others of doing, only then you call it "detection loophole".

[Jochen]

No, we have 4N independent particle pairs. On the first N particle pairs, Alice always measured A, and Bob always measured B. On the second N particle pairs, Alice always measured C, and Bob always measured D. On the third N particle pairs, Alice always measured C, Bob always measured B. On the last N particle pairs, Alice always measured A, Bob always measured D. So, all of these sets are independent.

So? You do not have a 4xN spreadsheet.

Err, yes I do, I showed you how to create it...?

[minkwe]

Code: Select all

  Alice    |    Bob   
  A  |  C  |  B  |  D 
(A_i)|     |(B_i)|     
     |(C_j)|     |(D_j)
     |(C_k)|(B_k)|     
(A_l)|     |     |(D_l),


So do you believe QM cannot generate this spreadsheet? Or do you believe such spreadsheets cannot be produced from the experiments which claim violation of the CHSH? Otherwise what is your point exactly?

If you mean that any data which can be placed in a table like this can never violate the inequality, that is an admission that nothing whatsoever can ever violate the CHSH because every experiment involving 4 disjoint sets of particle pairs can be placed in such a table by simple recombination like you suggest. So there must be something very wrong mathematically with the claim the QM violates it.

The point remains that your spreadsheet above is not a 4xN spreadsheet. It is 4 separate 2xN spreadheets simply stacked on each other. For the CHSH to apply to it, it must be possible to row permutations within each of the sections such that All the outcomes almost match the outcomes and the outcomes almost match the outcomes and the outcomes almost match the outcomes and the outcomes almost match the outcomes. But since only row permutations are permitted in each section, and there is a cyclic combination of letters, it is not possible to do the rearrangements. The last rearrangement will undo the first one. This is point (8).

[Heinera]

You use the word "independent" in a confusing manner. Point 4 is only correct if the data are generated by a LHV-model; and if so, point 8 does not contradict it.

I told you to read all the points carefully before addressing them. You claimed you agreed with all of them, now you are trying to find things to disagree with?

No, I said I basically agreed with them, which means that I found them lacking in rigor, and e.g. point 4 needed qualifications. But my main argument is that your chain of reasoning does not invalidate Bell's proof, so I see no point in going into details about it. Why don't you just point to the specific error you think he made in his proof?

Do not forget that point (4) was given as the reason why the QM predictions for should be the same as the QM predictions for

They are not the same, nor does your point (4) give a reason for it.

[minkwe]

No, I said I basically agreed with them

Do not forget that point (4) was given as the reason why the QM predictions for should be the same as the QM predictions for

They are not the same, nor does your point (4) give a reason for it.

Exactly, they are not the same. That is the whole point of the argument, to demonstrate that they are not the same. Had you read all 8 points carefully, you should have understood this already. Jochen claims they are the same. Point (4) is a claim that he made, which I simply formalized so that there is no doubt about what he meant. Bell says they are. If you believe Bell's theorem, then you also believe that they are the same, because Bell used QM predictions for to claim violation in an inequality which contains .

So I'm happy you no longer believe Bell's theorem, since you now do not believe that they are the same. That is why I asked you earlier to tell me what the correct QM expectation values should be for .

If you recall, the premise of Bell's theorem was "If QM is accurate, then ...". It turns out, it should have been "If Bell and his followers are accurate about what QM says, then ...". Clearly, you guys have been using the wrong QM predictions for the CHSH terms.

[Heinera]

No, I said I basically agreed with them

Do not forget that point (4) was given as the reason why the QM predictions for should be the same as the QM predictions for

They are not the same, nor does your point (4) give a reason for it.

Exactly, they are not the same. That is the whole point of the argument, to demonstrate that they are not the same.

They are not the same in QM. They are the same when the data is generated by a LHV model. You need to understand the difference.

[minkwe]

Exactly, they are not the same. That is the whole point of the argument, to demonstrate that they are not the same.

They are not the same in QM. They are the same when the data is generated by a LHV model. You need to understand the difference.

Go back and read points (1) to (8) again carefully. The argument shows that they are not the same period. They are not the same for QM, they are not the same for LHV. You should convince Jochen of that. He was the one claiming (and continues to do so) that they are the same for QM. But if you continue to believe Bell's theorem, please tell us what the correct QM predictions should be for , since those are the terms in the CHSH inequality.

If you like, prefix it with "basically", so that you can have a way out later.

[Heinera]

But if you continue to believe Bell's theorem, please tell us what the correct QM predictions should be for , since those are the terms in the CHSH inequality.

That is an epression that only makes sense for a LHV model, and not QM. So QM does not predict anything for that expression. You still don't understand that the CHSH inequality applies to LHV models only. Next!

[minkwe]

please tell us what the correct QM predictions should be for , since those are the terms in the CHSH inequality.

That is an epression that only makes sense for a LHV model, and not QM. So QM does not predict anything for that expression.

Get your head out of the sand already. If QM does not predict anything for those terms, how then can any sane person claim that the QM prediction for those terms violates the CHSH? How can somebody like yourself who believes it is not possible to provide QM values for those terms, also believe Bell's theorem which is based on substituting the supposed QM predictions for those term into the expression.

It is not reasonable to believe mutually contradictory statements at the same time. So again, the CHSH is



Show us exactly how it is possible for QM to violate this inequality. When stuck in a hole, stop digging!