## Evidence that QM does not violate Bell's inequalities

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

### Re: Evidence that QM does not violate Bell's inequalities

Heinera wrote:I promised myself I wouldn't bother anymore, but weak willpower makes me try one more time to teach someone some elementary probability theory:

Because the expected mean of a randomly selected sample from a larger population is the same as the mean of the population itself, we have the following equalities when the sets of j,k,l,m are randomly selected subsets of the set of i:

$\langle A_iB_i\rangle=\langle A_jB_j\rangle$
$\langle A_iD_i\rangle =\langle A_kD_k\rangle$
$\langle C_iB_i\rangle =\langle C_lB_l\rangle$
$\langle C_iD_i\rangle= \langle C_mD_m\rangle$

We now do the trivial substitution from

$\langle A_iB_i\rangle - \langle A_iD_i\rangle + \langle C_iB_i\rangle + \langle C_iD_i\rangle \leq 2$

to get

$\langle A_jB_j\rangle - \langle A_kD_k\rangle + \langle C_lB_l\rangle + \langle C_mD_m\rangle \leq 2$, which is the CHSH inequality.

I don't think that can be right for CHSH. The CHSH string is about two iterations (trials) minimum.
So $\langle A_iB_i\rangle$ and $\langle A_iD_i\rangle$ can't be in the same iteration for the first expression. But then in the second expression the A's are not the same in the first and second expectation terms, etc.
FrediFizzx
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### Re: Evidence that QM does not violate Bell's inequalities

FrediFizzx wrote:I don't think that can be right for CHSH. The CHSH string is about two iterations (trials) minimum.

Well that was wrong. In a real experiment, there would have to be at least 4 iterations minimum. Keep that in mind when evaluating CHSH.
FrediFizzx
Independent Physics Researcher

Posts: 2905
Joined: Tue Mar 19, 2013 7:12 pm
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### Re: Evidence that QM does not violate Bell's inequalities

Heinera wrote:I promised myself I wouldn't bother anymore, but weak willpower makes me try one more time to teach someone some elementary probability theory:

Promise yourself to learn some basic statistics before you speak next time. And before you respond to this thread any further, I strongly suggest you read post #1, very carefully

Heinera wrote:$\langle A_iB_i\rangle=\langle A_jB_j\rangle$
$\langle A_iD_i\rangle =\langle A_kD_k\rangle$
$\langle C_iB_i\rangle =\langle C_lB_l\rangle$
$\langle C_iD_i\rangle= \langle C_mD_m\rangle$

As clearly explained in post #1, the above is impossible. So again, go back to the first page and read the argument in post #1, and save yourself from further embarrassment. Make sure you do not miss the part where it is shown that the above is impossible. If for some reason you do not like me personally (evidently), such that you have a bias against valid arguments made by me, perhaps you may like to read a purely mathematics paper which pre-dates Bell, and shows exactly the same thing rigorously http://www.panix.com/~jays/vorob.pdf. Do not be deceived that your naive "probability reasoning" is valid. Such arguments are made all the time by novices who do not understand a shred of probability theory. You can read some more examples in Chapter 15 of Jaynes Book, Probability Theory: The Logic of Science. (http://www-biba.inrialpes.fr/Jaynes/cc15b.pdf)

In short, you have no clue what you are talking about. Just because you are friends with, and hang around a few old-school statisticians does not mean you understand probability theory.

Heinera wrote:The extra degrees of freedom is of no use to the modeler (or nature), since he/she can't make any use of them due to the random selection of settings.

Please also do yourself a favor and read-up on Bertrands paradox. Random sampling of "hidden variables" is an oxymoron. To randomly sample any variable you need to know ALL the parameters that influence its values and exactly how the values change. If you do not understand this, read this article, specifically related to Bell's inequality, in which a counterexample demonstrating this pitfall is presented

http://arxiv.org/abs/0907.0767
minkwe

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Joined: Sat Feb 08, 2014 10:22 am

### Re: Evidence that QM does not violate Bell's inequalities

"minkwe" should like this: Bell (1981): "It is notable in this argument that nothing is said about the locality, or even localizability, of the variables lambda. They could well include, for example, QM state vectors"
Guest

### Re: Evidence that QM does not violate Bell's inequalities

Perhaps Guest should review this thread to find out what the discussion here is all about. Lambda is completely irrelevant to the topic of discussion here. Read specifically post #1 and then my last response to Heinera from Sat Aug 29th.
minkwe

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