Bell's theorem/Proofs

While this page begins as chatty and personal, anyone may edit this page to improve it.

I'm merely starting a conversation, and this could simply be imaginary, but the original voice is authentic. --Abd (discuss • contribs) 13:12, 7 September 2015 (UTC)

It was written on the page supra that elementary proofs of Bell's theorem were "all over the internet." I looked at a page and it wasn't there, so I tagged this with a clarification template. But why not just use Goggle? Yes, they are all over the internet, but I found only one good one. It was buried deep as http://www.physics.umd.edu/courses/Phys270/Jenkins/Griffiths_EPR_BellInequality_Excerpt.pdf

Proofs of Bell's theorem are all over the internet, but the number one hit is fringe science:

Googling "Bell's theorem Elementary proof," 461,000 hits. Great! I was worried it might be "all over." the number one hit is:


 * Disproof of Bell's Theorem | Libertes Philosophica. the blog of Joy Christian flogging a book and soliciting donations for research. At the top of the page is
 * Why is this evidence so feared by the dark forces?
 * "This evidence" was incomprehensible. I can see, then, why it's feared. It causes the brain of anyone who reads it to implode and descend into conspiracy theories. However, the "dark forces" page looks interesting. It does not use the phrase "dark forces." This might be worth some exploration, but not here.

I tried another search on "Elementary proof of Bell's inequality" The number one hit?

Wikipedia! [queue fireworks] (permanent link)
 * There have also been repeated claims that Bell's arguments are irrelevant because they depend on hidden assumptions that, in fact, are questionable—though none of these claims have ever achieved much support. For example, E. T. Jaynes[26] claimed in 1989 that there are two hidden assumptions in Bell's theorem that could limit its generality. According to him:

Bell interpreted conditional probability P(X|Y) as a causal inference, i.e. Y exerted a causal inference on X in reality. However, P(X|Y) actually only means logical inference (deduction). Causes cannot travel faster than light or backward in time, but deduction can.
 * Bell's inequality does not apply to some possible hidden variable theories. It only applies to a certain class of local hidden variable theories. In fact, it might have just missed the kind of hidden variable theories that Einstein is most interested in.

However, Richard D. Gill has argued that Jaynes misunderstood Bell's analysis. Gill points out that in the same conference volume in which Jaynes argues against Bell, Jaynes confesses to being extremely impressed by a short proof by Steve Gull presented at the same conference, that the singlet correlations could not be reproduced by a computer simulation of a local hidden variables theory.[27] According to Jaynes (writing nearly 30 years after Bell's landmark contributions), it would probably take us another 30 years to fully appreciate Gull's stunning result.

For our purposes here, we might be most interested in Gull's proof.
 * [27] Gill, Richard D. (2003). "Time, Finite Statistics, and Bell's Fifth Position". Proc. of "Foundations of Probability and Physics - 2", Ser. Math. Modelling in Phys., Engin., and Cogn. Sc. (Växjö Univ. Press). 5/2002: 179–206. arXiv:quant-ph/0301059.


 * Gull's proof is here: http://www.mrao.cam.ac.uk/~steve/maxent2009/ http://www.mrao.cam.ac.uk/~steve/maxent2009/images/bell.pdf  and I discuss it here: http://arxiv.org/abs/1312.6403 Gill110951 (discuss • contribs) 05:48, 14 September 2015 (UTC)

Just collecting some more proofs, in Google sequence for me:


 * A simple proof of Bell’s inequality, blog.
 * Bell's Theorem with Easy Math, David R. Schneider.
 * SEE SPOT RUN: A SIMPLE PROOF OF BELL'S THEOREM, Nick Herbert.
 * A simple proof of Bell's inequality. Lorenzo Maccone, arXiv paper.
 * A basic introduction to Bell's Inequality, Youtube video.
 * Simplest proof of Bell's inequality - John Boccio This is only a copy of the Maccone paper. Clue? Study that first?
 * and then the Libertes Philosophica page shows up. Nice place to stop for now.


 * Bell Inequality Excerpt was linked in prefatory material, from a book by David Griffiths on Quantum Mechanics. Bell's theorem is covered on pdf page 15, book page 376.


 * Hardy and Kwiat's quantum cakes proof, based on Hardy's proof "without inequalities". Am. J. Phys. 68 (1), January 2000, 33-36.

There is a lot of confusion as to what Bell's theorem actually is. Did Bell himself prove a theorem? He was a physicist. He did once refer to "his theorem" and what he referred to was a proof of the CHSH inequality. In other words, according to Bell himself, his "theorem" is a rather trivial mathematical inequality. What most people call Bell's theorem is a statement belonging to the field of metaphysics, not to mathematics, that quantum physics and local realism are incompatible. Gill110951 (discuss • contribs) 09:15, 14 September 2015 (UTC)