by **minkwe** » Wed Aug 26, 2015 7:08 am

Heinera wrote:There is no problem. My model does not respect the bound of 2, because of its non-locality. All local models wil have a bound of 2.

This is complete and utter garbage and if I did not suspect that Heine may really be completely clueless about this, I would have concluded that he was lying through his teeth.

The dependence and independence we are talking about, have no relationship to locality/non-locality. I have already shown since post #1 that it is impossible to satisfy the conditions required to compare the experimental and QM expectations with Bell's inequalities -- even if the model/experiment is fully local realistic. Heine simply ignores the argument.

He does not deny that Bell's inequality is the following:

,

which makes use of the four terms

all defined for the same set of outcomes

He presents a simulation which is equivalent to the terms each calculated from 8 separate columns of outcomes:

recombined into 4 independent paired spreadsheets, yielding the 4 terms

. He then calculates the expression

and finds that the value is greater than 2. But this is to be expected because the terms in this expression are statistically independent. Note that there are 8 columns of data in 4 independent pairs in the data from his simulation, whereas there are 4 columns of data with cyclic dependent pairing in Bell's inequality. Note also that the origin of the upper bound is entirely due to this fact. It is the dependencies or lack thereof that determine the upper bound of the inequality, so a proper understanding of it's presence or absence is crucial to any understanding of Bell's theorem.

As you can see in every proof of the CHSH or Bell's inequality (

https://en.wikipedia.org/wiki/Bell%27s_ ... inequality for example), There are only 4 columns of data

, recombined into pairs such that the cyclic dependency of the paired terms is present. What is often missing is that the subscripts are left out which allows them to later confusingly or intentionally mislead by assuming there are only 4 columns of data in

, since without subscripts, all the As, Bs, Cs and Ds look alike and you can simply say

.

When presented with this obvious fact, Heine then proceeds first to make the incredible claim that he is indeed calculating

not

Heinera wrote:As shown in post #1, you are calculating the independent terms

which are definitely not the terms in Bell's inequality.

My model does indeed produce

. Read the code again.[/quote]

Obviously anyone with a shred of statistics training should be able to see that if Heine is right that he is calculating

, then it means

. Only then can his claim be true. An easy statistics test of this claim is to calculate the cross correlation between

or

or

, or

. If those columns of data are equivalent, then those correlations will be significantly different from zero. This is what Fred has shown in

viewtopic.php?f=6&t=181&start=110#p5302 and found that the cross correlations if you substitute A_i for A_k becomes zero and the same for the rest of them. Therefore Heine is calculating

not

like he claims, and therefore the upper bound is 4 not 2.

So what has this got to do with non-locality or locality? Nothing whatsoever, as shown in the first post of this thread, if you start with 4 random statistically independent sets of outcome pairs from any source whatsoever (local or non-local), it is impossible to carry out the required row-permutations in order to demonstrate that all the equivalences

are simultaneously true. Some of them might be the same but all of them can not be simultaneously the same as verly clearly explained in post #1. It does not matter whether we are dealing with a local or a non-local model. Therefore it is a mathematical error to assume that all the expectation values are simultaneously equal, ie

Some of them may be equal, but they can not all be simultaneously equal. This was clearly explained in post #1. Bell's believers simply ignore the argument.

You may have heard noises about sample of a population having the same value as population. You will note that when this bogus argument is presented, they always talk about a single value, not 4 values simultaneously. But they ignore one very crucial detail. The expectations in Bell's inequality are not equivalent to independent random samples. They are heavily dependent on each other. You can not replace them with independent random samples. Bell's followers repeatedly proclaim how Bell's theorem forces us to rethink the freedom of the experimenter, but it is the complete opposite. The problem is not that the experimenters are not free enough to measure what they want. The problem is that they are too free compared to the freedom assumed in Bell's inequality. Therefore the push to have even more perfectly random and perfectly free experimental situations is completely misguided as far as the inequalities are concerned.

Even worse, the problem described above is fatal. The only solution is to put Bell's theorem in the garbage bin where it belongs. See

http://link.springer.com/article/10.100 ... 010-9461-z for a slightly different take of these ideas.

[quote="Heinera"]

There is no problem. My model does not respect the bound of 2, because of its non-locality. All [b]local[/b] models wil have a bound of 2.[/quote]

This is complete and utter garbage and if I did not suspect that Heine may really be completely clueless about this, I would have concluded that he was lying through his teeth.

The dependence and independence we are talking about, have no relationship to locality/non-locality. I have already shown since post #1 that it is impossible to satisfy the conditions required to compare the experimental and QM expectations with Bell's inequalities -- even if the model/experiment is fully local realistic. Heine simply ignores the argument.

He does not deny that Bell's inequality is the following:

[tex]\langle A_iB_i\rangle - \langle A_iD_i\rangle + \langle C_iB_i\rangle + \langle C_iD_i\rangle \leq 2[/tex],

which makes use of the four terms [tex]\langle A_iB_i\rangle ,\; \langle A_iD_i\rangle ,\; \langle C_iB_i\rangle ,\; \langle C_iD_i\rangle[/tex] all defined for the same set of outcomes [tex]A_i, B_i, C_i, D_i[/tex]

He presents a simulation which is equivalent to the terms each calculated from 8 separate columns of outcomes: [tex]A_j, B_j, A_k, D_k, C_l, B_l, C_m, D_m[/tex] recombined into 4 independent paired spreadsheets, yielding the 4 terms [tex]\langle A_jB_j\rangle ,\; \langle A_kD_k\rangle ,\; \langle C_lB_l\rangle ,\; \langle C_mD_m\rangle[/tex]. He then calculates the expression

[tex]\langle A_jB_j\rangle - \langle A_kD_k\rangle + \langle C_lB_l\rangle + \langle C_mD_m\rangle[/tex] and finds that the value is greater than 2. But this is to be expected because the terms in this expression are statistically independent. Note that there are 8 columns of data in 4 independent pairs in the data from his simulation, whereas there are 4 columns of data with cyclic dependent pairing in Bell's inequality. Note also that the origin of the upper bound is entirely due to this fact. It is the dependencies or lack thereof that determine the upper bound of the inequality, so a proper understanding of it's presence or absence is crucial to any understanding of Bell's theorem.

As you can see in every proof of the CHSH or Bell's inequality (https://en.wikipedia.org/wiki/Bell%27s_theorem#Derivation_of_CHSH_inequality for example), There are only 4 columns of data [tex]A_i, B_i, C_i, D_i[/tex], recombined into pairs such that the cyclic dependency of the paired terms is present. What is often missing is that the subscripts are left out which allows them to later confusingly or intentionally mislead by assuming there are only 4 columns of data in [tex]A_j, B_j, A_k, D_k, C_l, B_l, C_m, D_m[/tex], since without subscripts, all the As, Bs, Cs and Ds look alike and you can simply say [tex]A, B, C, D[/tex].

When presented with this obvious fact, Heine then proceeds first to make the incredible claim that he is indeed calculating

[tex]\langle A_iB_i\rangle - \langle A_iD_i\rangle + \langle C_iB_i\rangle + \langle C_iD_i\rangle[/tex]

not

[tex]\langle A_jB_j\rangle - \langle A_kD_k\rangle + \langle C_lB_l\rangle + \langle C_mD_m\rangle[/tex]

[quote="Heinera"]

As shown in post #1, you are calculating the independent terms [tex]E11_i,\; E12_j,\; E21_k,\; E22_l[/tex] which are definitely not the terms in Bell's inequality. [/quote]

My model does indeed produce [tex]E11_i,\; E12_i,\; E21_i,\; E22_i[/tex]. Read the code again.[/quote]

Obviously anyone with a shred of statistics training should be able to see that if Heine is right that he is calculating [tex]\langle A_iB_i\rangle - \langle A_iD_i\rangle + \langle C_iB_i\rangle + \langle C_iD_i\rangle2[/tex], then it means [tex]A_j = A_k = A_i,\; B_j = B_l = B_i,\; C_l =C_m = C_i,\; D_k = D_m = D_i[/tex]. Only then can his claim be true. An easy statistics test of this claim is to calculate the cross correlation between [tex](A_j,\; A_k)[/tex] or [tex](B_j, B_l)[/tex] or [tex](C_l, C_m)[/tex], or [tex](D_k, D_m)[/tex]. If those columns of data are equivalent, then those correlations will be significantly different from zero. This is what Fred has shown in http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=181&start=110#p5302 and found that the cross correlations if you substitute A_i for A_k becomes zero and the same for the rest of them. Therefore Heine is calculating [tex]E11_i,\; E12_j,\; E21_k,\; E22_l[/tex] not [tex]E11_i,\; E12_i,\; E21_i,\; E22_i[/tex] like he claims, and therefore the upper bound is 4 not 2.

So what has this got to do with non-locality or locality? Nothing whatsoever, as shown in the first post of this thread, if you start with 4 random statistically independent sets of outcome pairs from any source whatsoever (local or non-local), it is impossible to carry out the required row-permutations in order to demonstrate that all the equivalences [tex]A_j \equiv A_k,\; B_j \equiv B_l,\; C_l \equiv C_m,\; D_k \equiv D_m[/tex] are simultaneously true. Some of them might be the same but all of them can not be simultaneously the same as verly clearly explained in post #1. It does not matter whether we are dealing with a local or a non-local model. Therefore it is a mathematical error to assume that all the expectation values are simultaneously equal, ie

[tex]\langle A_jB_j\rangle = \langle A_iB_i\rangle,\; \langle A_kD_k\rangle = \langle A_iD_i\rangle ,\; \langle C_lB_l\rangle = \langle C_iB_i\rangle ,\; \langle C_mD_m\rangle = \langle C_iD_i\rangle[/tex]

Some of them may be equal, but they can not all be simultaneously equal. This was clearly explained in post #1. Bell's believers simply ignore the argument.

You may have heard noises about sample of a population having the same value as population. You will note that when this bogus argument is presented, they always talk about a single value, not 4 values simultaneously. But they ignore one very crucial detail. The expectations in Bell's inequality are not equivalent to independent random samples. They are heavily dependent on each other. You can not replace them with independent random samples. Bell's followers repeatedly proclaim how Bell's theorem forces us to rethink the freedom of the experimenter, but it is the complete opposite. The problem is not that the experimenters are not free enough to measure what they want. The problem is that they are too free compared to the freedom assumed in Bell's inequality. Therefore the push to have even more perfectly random and perfectly free experimental situations is completely misguided as far as the inequalities are concerned.

Even worse, the problem described above is fatal. The only solution is to put Bell's theorem in the garbage bin where it belongs. See http://link.springer.com/article/10.1007%2Fs10701-010-9461-z for a slightly different take of these ideas.