# Where can I found explanation on Bell's Inequality ?

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

Thanks for help .

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Homework Helper
Gold Member
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.

Locrian
In the search function! Seriously!

Gold Member
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.)

Staff Emeritus
I highly, highly recommend DrChinese's site for anything and everything on Bell and entanglement.

Zz.

Gold Member
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.

Gold Member
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.

Edgardo
Hello ngkamsengpeter,

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.

Type in google "American Journal of Physics" and Browse "All Online Issues"
http://scitation.aip.org/dbt/dbt.jsp?KEY=AJPIAS [Broken]
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 [Broken]
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 [Broken]
You have to read this paper! It really explains what is meant by "local realism" in a nice way (yummy, quantum cakes ).

[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 [Broken]
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

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nightlight
This is not the other half of the story.

You're right, of course. It is not the 'other half' of the story at all, but the 'real story' 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 Bell tests. Please do not take this simple thread off topic.

Yep, those evil deniers. From Einstein, Planck, Schrodinger, 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, or in plain language without euphemisms, there have to exist violations that do violate inequalities (as opposed to the present "violations" which do not violate 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 (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.

Gold Member
nightlight said:
Yep, those evil deniers[/url]. From Einstein, Planck, Schrodinger, 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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nightlight
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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Staff Emeritus

Zz.

slyboy
The following papers were recommended by slyboy:

Wow, somebody was listening!

Edgardo
slyboy said:
Wow, somebody was listening!

Of course!
By the way, thanks for posting the papers slyboy,
I really enjoyed reading them, especially the quantum cakes.

snooper007
You may consult Bell's Book "Speakable and unspeakable in quantum physics"