Where can I found explanation on Bell's Inequality ?

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Discussion Overview

The discussion centers around Bell's inequality theorem, with participants seeking explanations and resources for understanding the theory. The scope includes philosophical implications, mathematical interpretations, and references to various educational materials and papers related to Bell's theorem.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asks for a detailed explanation of Bell's inequality theorem and resources for learning about it.
  • Another participant shares a positive experience reading a philosophy book that explains Bell's inequalities without assuming prior physics knowledge, emphasizing its accessibility.
  • Several participants provide links to online resources and papers that discuss Bell's theorem, including technical and simplified versions of the mathematics involved.
  • Some participants recommend specific papers and authors known for their work on Bell's theorem, highlighting their relevance and clarity.
  • A debate emerges regarding the validity of certain references, with one participant arguing that some suggested sites focus on denying Bell tests rather than explaining them.
  • Another participant challenges the notion of "deniers," arguing that historical figures could not have denied Bell tests as they were not alive when Bell published his work.
  • There is a contention over the interpretation of Bell's theorem and its implications, with participants expressing differing views on the validity of Bell tests and the nature of non-local effects.

Areas of Agreement / Disagreement

Participants express a mix of agreement on the value of certain resources while also presenting competing views on the interpretation and implications of Bell's theorem. The discussion remains unresolved regarding the validity of certain claims about Bell tests.

Contextual Notes

Some participants reference specific papers and educational materials that may require subscriptions or prior knowledge to fully understand. The discussion also highlights the complexity and contentious nature of interpretations surrounding Bell's theorem.

ngkamsengpeter
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What is Bell's inequality theorem ?
Where can I find the details explanation of this theory ?


Thanks for help .
 
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I learned about Bell's inequalities in a... philosophy book! It was great because the author, assumed no prior knowledge of physics, but also adressed the reader as very learning-capable. So he was able to plow through all the pre-requiste physics with a minimum use of equations before getting to Bell's inequality, and manage to make the reader understand perfectly* the meaning of every symbols in the mathematical form of Bell's inequality before getting on to discussing its philosophical implications.

Perhaps you could have access to such a document in your nearest education establishment. :smile:
 
In the search function! Seriously!
 
The Stanford/Shimony reference given by jtbell is absolutely top-notch.

I will also pass on some pages I keep on my site for this purpose. If you want to read the 3 original papers crucial to the subject (including Bell's paper), you can see all in PDF format:

EPR, Bell and Aspect: The Original References

If you are interested in a very easy version of the math, but following Mermin's variation of Bell's Inequality, try:

Bell's Theorem with Easy Math

And if you are interested in something following Bell more closely, but a little easier to understand than Bell, try:

Bell's Theorem and Negative Probabilities

(This one assumes you already understand the basic ideas of Bell, but perhaps not the actual math.)
 
I highly, highly recommend DrChinese's site for anything and everything on Bell and entanglement.

Zz.
 
nightlight said:
For the other half of the story you can check:
...

This is not the other half of the story. These sites have little to do with explaining Bell and everything to do with denying Bell tests. Please do not take this simple thread off topic.
 
ZapperZ said:
I highly, highly recommend DrChinese's site for anything and everything on Bell and entanglement.

Zz.

Thanks ZapperZ for the kind words.

One of my links is brand new - Bell's Theorem with Easy Math. It is actually a result of a link you had asked about a while back - I thought it could be reformulated for easier understanding. Any comments are appreciated.
 
  • #10
Hello ngkamsengpeter,

check out this thread here: https://www.physicsforums.com/showthread.php?t=82446

There I mentioned the following paper, that is very(!) good :

[1] Daniel M. Greenberger, Michael A. Horne, Abner Shimony, Anton Zeilinger
"Bell's theorem without inequalities", American Journal of Physics Vol. 58 (12), December 1990.
Have a look at the Appendix where Bell's inequality is derived.

To download the paper do the following:
Type in google "American Journal of Physics" and Browse "All Online Issues"
http://scitation.aip.org/dbt/dbt.jsp?KEY=AJPIAS
Go to Volume 58, to December and search for the title.
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000058000012001131000001&idtype=cvips&gifs=Yes
You will need a subscription, which your university will probably have.


The following papers were recommended by slyboy:

[2] "The mystery of the quantum cakes," P.G. Kwiat and L. Hardy, Am. J. Phys. 68, 33 (2000).
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000068000001000033000001&idtype=cvips&gifs=Yes
You have to read this paper! It really explains what is meant by "local realism" in a nice way (yummy, quantum cakes :biggrin: ).


[3] "Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories", Hardy L.
PHYS REV LETT 68: (20) 2981-2984 MAY 18 1992
http://prola.aps.org/abstract/PRL/v68/i20/p2981_1
You could read this after having read [2], since [2] is based on this one. I should mention that I really understood what [2] and [3] were about after the following paper:


[4]"Quantum mysteries refined", N. David Mermin, American Journal of Physics 62, October 1994, page 880-887.
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000062000010000880000001&idtype=cvips&gifs=Yes
Read especially page 881 right bottom side! (I had to read it several times until I got it. Then suddenly the papers [2] and [3] became clear to me).


[5] "Hidden Variables and the Two Theorems of John Bell", N. David Mermin, Rev. Mod. Phys. 65, 803–815 (1993)
http://prola.aps.org/abstract/RMP/v65/i3/p803_1
I haven't read this yet.
 
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  • #11
This is not the other half of the story.

You're right, of course. It is not the 'other half'[/color] of the story at all, but the 'real story'[/color] behind the hype. Sorry for confusion, I was just trying to be generous.

These sites have little to do with explaining Bell and everything to do with denying[/color] Bell tests. Please do not take this simple thread off topic.

Yep, those evil deniers. From Einstein, Planck, Schrödinger, de Broglie, Fermi,... through Jaynes, Barut, Marshall, Santos,... Since statement of facts is not a "denial", in order to "deny Bell tests" there has to be a test that violated Bell's inequalities -- there has to exist the so-called loophole free violation of Bell's inequalities[/color], or in plain language without euphemisms, there have to exist violations that do violate[/color] inequalities (as opposed to the present "violations" which do not violate[/color] any classical inequalities). Since no such violation (that violates) exists, the only sin of the deniers is their failure to show the officially required degree of faith and enthusism for some future violations[/color] (that do violate). With that kind of unhelpful attitude, the evil deniers may even scare off the venture capital and military funding for Quantum Computing, Quantum Cryptography... startups. Who needs that.
 
  • #12
nightlight said:
Yep, those evil deniers[/url]. From Einstein, Planck, Schrödinger, de Broglie, Fermi,...

Nightlight, you have a distorted sense of the language which does not serve the novice reader of this thread. With the exception of de Broglie, these famous people you cited could NEVER have denied Bell tests because they died before Bell published his paper. Please, don't bother to explain this blatant inaccuracy in another post.

If you want to debate the validity of Bell tests (yet again zzzzz), please start another thread. This thread is about Bell's Theorem.
 
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  • #13
Nightlight, you have a distorted sense of the language which does not serve the novice reader of this thread.

Readers should decide for themselves what serves them and what doesn't. Half truths or misinformation usually don't serve anyone but those pushing them.

With the exception of de Broglie, these famous people you cited could NEVER have denied Bell tests because they died before Bell published his paper.

They didn't know the specific inequality, but they rejected its implications (the nonlocal effects in general). Hence, from the general rejection of non-local effects, any special case, such as Bell's inequality violation, is automatically rejected.

If you want to debate the validity of Bell tests (yet again zzzzz),

There is nothing to debate about the well known fact that no experimental violation of Bell's inequalities was ever obtained, assuming the conventional meaning of term violation (i.e. that the counts violate the inequality). Of course, if one redefines words so that plain violation is called "loophole free violation" while the plain non-violation is called just "violation" then, yes, you get "violation", or anything else you could wish (say, you choose to call your Toyota as "Rolls Royce", and now you're driving "Rolls Royce").
 
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  • #14
Please do NOT hijack this thread. The OP asked for an explanation for Bell theorem. If you wish to rehash this DEBATE, start your own thread!

Zz.
 
  • #15
The following papers were recommended by slyboy:

Wow, somebody was listening!
 
  • #16
slyboy said:
Wow, somebody was listening!

Of course! :biggrin:
By the way, thanks for posting the papers slyboy,
I really enjoyed reading them, especially the quantum cakes.
 
  • #17
You may consult Bell's Book "Speakable and unspeakable in quantum physics"
 

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