Bell's derivation; socks and Jaynes

[harrylin]

I thought you were using it to demonstrate that classical data can violate a Bell Inequality. If you weren't intending that, then my apologies. But if you were, then I will say it is not a suitable analogy. A suitable analogy would be one like particle spin or polarization.

Bell was using it to make it plausible that classical data must obey his method of probability analysis. I mentioned why I find both Lille/Lyon and particle spin useless for illustrating such things as particle spin in post #55. For me Lille-lyon is too difficult to analyse and it doesn't include the detection aspects well. What do you find unsuited about Lille-Lyon?

 

[harrylin]

In regards to Jaynes’ view: Bell incorrectly factored a joint probability; it may be informative to analyze the data set presented by N. David Mermin in his article: “Is the moon there when nobody looks? Reality and the quantum theory.” [..]

Now that you bring it up, I was going to bring up Mermin as a separate topic but perhaps the answer on my question is very simple: can anyone tell me how his equality of 0.5 follows from (or, as he presents it, is) Bell's inequality?

 

[rlduncan]

So let me see if I have this straight. If you apply the probability analysis (either dependent or independent in your example), you would predict .5333 (actually a minimum). The quantum prediction is .5 which agrees to actual experiments.

Well, I would say Bell's point works nicely. Focusing on his factorization is a mistake. Once you know of Bell, I think it is easier to simply require that counterfactual cases must have a probability >=0. Which is the requirement of realism, going back to EPR and the famous "elements of reality".

Thanks for the comments.

The data shows that the events A and B are dependent not independent, an assumption made by Bell. The P(A)*P(B/A) ≠ P(A)*P(B). Can you exlain how Bell got it right using an invalid assumption?

 

[lugita15]

Now that you bring it up, I was going to bring up Mermin as a separate topic but perhaps the answer on my question is very simple: can anyone tell me how his equality of 0.5 follows from (or, as he presents it, is) Bell's inequality?

Rather than examining Mermin, you might want to look at Nick Herbert's exposition "quantumtantra.com/bell2.html" . It's written in a style like Mermin's, but the example used is even simpler. This example was the one Bell used in talks to popular audiences, as he said that it was simplest known Bell inequality.

 

[harrylin]

[..] The data shows that the events A and B are dependent not independent, an assumption made by Bell. The P(A)*P(B/A) ≠ P(A)*P(B). Can you exlain how Bell got it right using an invalid assumption?

It appears that you don't have lambda in your analysis. That is however necessary to test his assumption (see the discussion on the first page of this thread).

 

[harrylin]

Rather than examining Mermin, you might want to look at Nick Herbert's exposition "quantumtantra.com/bell2.html" . It's written in a style like Mermin's, but the example used is even simpler. This example was the one Bell used in talks to popular audiences, as he said that it was simplest known Bell inequality.

Thanks, that may very well provide the answer on my Mermin question and it looks very interesting.

PS: I think that Herbert's proof deserves to be a separate topic - it looks really good and no need for a lambda!

 

[lugita15]

Thanks, that may very well provide the answer on my Mermin question and it looks very interesting.

PS: I think that Herbert's proof deserves to be a separate topic - it looks really good and no need for a lambda!

Yes, it would be nice to have a thread on Herbert's proof.

 

[harrylin]

[..] I think that Herbert's proof deserves to be a separate topic - it looks really good and no need for a lambda!

Yes, it would be nice to have a thread on Herbert's proof.

So, I started that topic here:
https://www.physicsforums.com/showthread.php?t=589134