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A Simple Proof Of Bell's Theorem 
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#1
Jul2010, 08:17 AM

PF Gold
P: 322

I've been following up a lot regarding the fascinating stuff I read here.
I recently came across this page; http://quantumtantra.com/bell2.html I know that the author and the other material on that site would be considered new age crackpottery by most here at PF, but anyway, that page for me is a simple and lucid explaination, just within my level of undesrtanding of these things. Had it been a little more complex, I would not have understood it. So I'm gald I found it, though I have a few questions;  What do others think of the explanation ?  Has it been proven by repeated experiment/s, or is it pure theory / maths ?  If it HAS been proven by experiments, to what extent if any, has it been put to practical use ? I mean, instantanious communication between particles at any distance .. WOW ! Any feedback would be appreciated. Thanks. 


#2
Jul2110, 10:14 AM

Sci Advisor
PF Gold
P: 5,288

The only thing I object to is Nick's claim to have the shortest proof. I think this is shorter, the actual proof being 8 paragraphs. It is certainly written by a better looking person (that being moi). http://drchinese.com/David/Bell_Theorem_Easy_Math.htm 


#3
Jul2210, 03:31 AM

P: 1,414

What it does tell you is that if the light incident on the polarizers is modelled in terms of discrete and separable "instruction sets" or "coded messages", then it would be expected that the rate of coincidental detection would vary linearly as a function of the angular difference between the polarizer settings. What it doesn't tell you is that it's been known for about 200 years that light doesn't behave in this way. The simplest way to illustrate this is to move one of the polarizers to the other side so that both polarizers are between the emitter and detector A or between the emitter and detector B. The results are exactly the same as when one polarizer is on side A and one polarizer is on side B. With both polarizers on one side, the rate of coincidental detection is the same as the rate of detection on the side that both polarizers are on. Now, DrC might tell you that this is just a coincidence. DrC might even tell you that optical laws have nothing to do with optical Bell tests. But keep in mind that DrC is just a computer programmer of unknown competence. He's not a physicist. He's not an expert in optics, certainly not quantum optics. And, he's not an expert logician or mathematician. People who are experts in these fields have published papers showing that violations of BIs do not imply anything about nature. Who are you going to believe? If you want to get at the truth of things, and be satisfied that you understand everything involved, then just ignore all the above and do your own research. Learn about classical and quantum optics. Read as much as you can of the relevant papers on Bell, GHZ, Hardy, etc. And come to your own conclusions. This should take you at least a couple of years unless you're ridiculously intelligent. Then, hopefully, you can explain this stuff to me in a way that I can actually understand it. 


#4
Jul2210, 04:05 AM

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P: 8,470

A Simple Proof Of Bell's Theorem



#5
Jul2210, 06:57 AM

P: 1,414

I think that most physicists would say that nature is evolving according to local and discoverable underlying dynamics. Am I wrong? Read the papers by Hess, et al., then I'll have some more for you to look at. Start with the papers that I linked to please. And please, no more nitpicky obfuscating responses on stuff that I've written. I'm just a curious amateur. I don't know what your qualifications are, but the people who wrote the papers I want you to critique are the real deal. 


#6
Jul2210, 08:10 AM

PF Gold
P: 322

ThomasT and JesseM, thank you also for the replies. Even though you guys are at odds on this, I am really interested in what you're each saying, and avidly taking it all in  to the best of my QP abilities anyway (which are pretty much zilch). 


#7
Jul2210, 08:48 AM

Sci Advisor
PF Gold
P: 5,288

Also: Besides being charming and handsome, I am also modest. So don't dismiss me!! 


#8
Jul2210, 08:50 AM

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PF Gold
P: 5,288

As a side note, I would recommend disregarding everything ThomasT says. Either that, or read it along with the morning comics. 


#9
Jul2210, 08:57 AM

P: 2,284

Fun aside, thanks for the link to the other proof, I enjoyed that a great deal. 


#10
Jul2210, 08:59 AM

PF Gold
P: 322

Antinomy itself is often instructive ! 


#11
Jul2210, 09:06 AM

Sci Advisor
P: 8,470

Perhaps by "same law" you just mean that the classical Malus' law for polarized light and the law for entangled particles both involve a cos^2? The problem is that although the equation can be written in a similar form for both laws, the physical meaning of the symbols is completely different, so from a physical perspective they cannot be called the "same". If you write cos^2(ab) in the classical context a would be the polarization angle of the light, b would be the angle of a single polarizer, and cos^2 would be giving the reduction in intensity of the light as it passes through the polarizer; but if you write cos^2(ab) in the quantum context, a and b would both be polarizer angles, there would be no term for the polarization of the light, and cos^2 would be giving the probability that both photons give the same binary result (both passing through their polarizers, or neither). 


#13
Jul2210, 05:01 PM

P: 1,414




#14
Jul2210, 05:49 PM

P: 1,414

Possible Experience: from Boole to Bell http://arxiv.org/PS_cache/arxiv/pdf/...907.0767v2.pdf Published in: EPL, 87 (2009) 60007 Extended BooleBell inequalities applicable to quantum theory http://arxiv.org/PS_cache/arxiv/pdf/...901.2546v2.pdf The second paper, still in the works, on the extended BooleBell inequalities, provides a detailed account of why BIs are violated and why their violation doesn't imply nonlocality in nature. Now consider, say, an Aspect or F and C optical Bell test setup where you have an emitter of entangled photons between two polarizers, a and b, between two detectors, A and B, respectively. Take the polarizer, a, and place it between the emitter and the polarizer, b. So, on the left side there is just a detector, A, and on the right side there are polarizers, a and b, between the emitter and detector B. The right side is now a polarimeter. It produces results in accord with Malus Law, as all polarimeters do. And the coincidence rate, ie. F(AB), is the same as with the original setup, .5 cos^2 ab, in the ideal. But Herbert, vis Bell, requires that the polarimeter produce a linear relationship between ab and rate of detection. This is why I said that light was being required by Herbert, vis Bell, to behave in a way contrary to what thousands of polarimetric experiments have shown. So, JesseM, thanks for bearing with me. I'm hoping that we might go through at least one of the papers I linked to. It will be very instructional for me, as well as probably for a lot of noncontributing readers of this thread. Maybe just take a page every few days or so and post your comments. Take it slow, because, you're right, at the moment I don't fully understand them. 


#15
Jul2310, 07:06 AM

PF Gold
P: 322

Yes, I read what you said. On another post, you also said "I'm just a curious amateur" Well, if you are an amatuer, I'm a babe in the wilderness. I'm gonna keep reading 'round here, and see if I can understand (let alone agree or disagree with) anything. It's fun though :) 


#16
Jul2310, 10:27 AM

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P: 8,470

The first paper did appear in a peerreviewed publication, the epl journal, perhaps because it didn't make the strong claim that the example they provided was actually a local realist violation of the LeggettGarg inequality or any other Bellian inequality, you can interpret the paper as just being about an analogous inequality that fails to hold because the conditions under which the data is collected and indexed are different from those assumed in the derivation of LeggettGarg (as well as the conditions assumed in the derivation of Boole's original inequality). The second paper, on the other hand, doesn't appear to have been published anywhere outside of arxiv.org (see google scholar search here), which doesn't require peerreview. I haven't read through it in detail, but skimming it the argument appears similar to the first paper, in that they are considering situations where the procedure by which data is collected and indexed does not conform to the conditions stipulated by Bell inequalities (or the conditions needed for a derivation of Boole's own inequality). In fact they mention the exact same example involving doctors and patients from the earlier paper on pp. 2527 of this second paper. They do claim that it is possible to explicitly violate Bell's theorem with locally causal models on p. 28: If you have followed the authors' argument in this second paper and think they show it would be possible to get a BI violation in this type of simulation, please explain. Likewise if you think they show it would be possible to get a violation of a BI in a scenario that matches all the observable experimental conditions stipulated in the derivation of the inequality, please explain. But if you haven't really followed the argument of the paper, and are just citing a paper you don't understand to support your claim that there is widespread disagreement among physicists about whether Bell's theorem showed QM was incompatible with all local realist theories, then one can show the absurdity of this claim just by noting that you're pointing to a nonpeerreviewed paper uploaded to arxiv.org which has led to no real reactions from the physics community (in the form of other physicists citing the paperonly four papers have cited it so far, two by De Raedt), and that physics textbooks which mention Bell's theorem uniformly present it as a valid demonstration that QM is incompatible with local models. Assuming you should have written cos^2 (ab) for the original setup, your altered setup above will not give the same results. After all, given perfectly efficient detection, on the left side every photon sent out by the emitter should be detected at A, since there are no polarizers to reflect photons sent to the left. On the right side, even if a and b are at the same angle so cos^2(ab)=1, it is quite possible for some of the entangled photons to be reflected by polarizers at that angle rather than passing through, in which case the coincidence rate in this setup is not cos^2 (ab). 


#17
Jul2310, 10:30 AM

P: 2,284

Now this is interesting reading; like alt I feel I'm learning from reading this discussion. Back on track, life is good.



#18
Jul2810, 01:10 AM

P: 3,408

Paraphrased from Nick Herbert's book Quantum Reality, the following (borrowed from the OP's http://quantumtantra.com/bell2.html) is the best (simplest) account I have found to date for the Bell inequality (SPOT stands for Single Photon Orientation Tester):



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