Bell's derivation; socks and Jaynes

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Discussion Overview

The discussion centers around Bell's theorem, specifically focusing on the example of Bertlmann's socks and the implications of Jaynes' criticism of Bell's equation no. 11. Participants explore the definitions and implications of probability calculations involving hidden variables, particularly in the context of local realistic theories.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about the definitions and notation in Bell's paper, particularly regarding the role of the variable "lambda" in probability calculations.
  • Another participant argues that if "X" correlates with Bertlmann wearing a pink sock, then the conditional probability P1(pink|X) would be greater than 0.5, suggesting a need for a more nuanced understanding of the correlations involved.
  • A later reply clarifies that "X" represents an invisible random function that determines sock color, asserting that the probability of observing a pink sock remains 0.5 when averaged over many trials.
  • Participants discuss the implications of Bell's reasoning regarding the correlation between the colors of socks on Bertlmann's feet, noting that observing one color provides information about the other.
  • One participant introduces a mathematical representation of the probabilities, indicating that the correlation between the two socks is negative, suggesting independence in their selection.
  • Another participant challenges the interpretation of Bell's model, emphasizing that knowing the hidden variable (Bertlmann's mood) would lead to a complete correlation between the outcomes, contradicting the independence suggested by earlier calculations.

Areas of Agreement / Disagreement

Participants express differing views on the implications of Bell's theorem and the role of hidden variables. While some agree with Jaynes' perspective, others challenge the interpretations and calculations presented, indicating that the discussion remains unresolved with multiple competing views.

Contextual Notes

Participants acknowledge limitations in their understanding of the definitions and implications of the variables involved, as well as the mathematical steps required to fully grasp the arguments being made. The discussion also highlights the dependence on specific interpretations of Bell's theorem and the assumptions underlying the probability calculations.

  • #91
DrChinese said:
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?
 
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  • #92
rlduncan said:
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?
 
  • #93
DrChinese said:
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?
 
  • #94
harrylin said:
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.
 
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  • #95
rlduncan said:
[..] 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).
 
  • #96
lugita15 said:
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. :smile:

PS: I think that Herbert's proof deserves to be a separate topic - it looks really good and no need for a lambda!
 
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  • #97
harrylin said:
Thanks, that may very well provide the answer on my Mermin question and it looks very interesting. :smile:

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.
 
  • #98
harrylin said:
[..] I think that Herbert's proof deserves to be a separate topic - it looks really good and no need for a lambda!
lugita15 said:
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
 

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