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Understanding bell's theorem: why hidden variables imply a linear relationship? 
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#109
Apr612, 11:07 PM

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#110
Apr612, 11:19 PM

P: 915

it's hard for the human imagination/mind to comprehend (or think further)....what we mean by no cause and effect..... the below is trivial (not important): does not the Copenhagen interpretation say lets not go there (not talk about it, shut up and calculate) rather than its totally random? or does it depends upon who you ask about the interpretation of the Copenhagen interpretation? ..:) 


#111
Apr612, 11:46 PM

P: 1,583

At a more fundamental level, I suppose the cos^2 in this case arises from the the fact that photon polarization is related to spin angular momentum, and angular momentum is based on rotations, so the mathematics of rotations gives us sines and cosines. But we have a problem: the wave function in QM is supposed to represent the probability of getting of a particle getting a certain experimental outcome. So it seems like although we can say that the wave function does describe the probability the photon will be detected at a particular point on the screen of a double slit apparatus, it seems like we cannot say that it describes the probability of the photon going through one slit vs the other slit (where there are no detectors at the slits). The way it looks is that a wave goes through the slits, but then when then there is a detection event, then suddenly the wave function translates into probabilities of the particle being measured having certain attributes. So it's as if the quantum object behaves as a wave until it's measured, behaves as a particle with definite attributes after it's measured. Thus the Copenhagen interpretation was born. If you want to see more discussion along these lines, you can read a chapter from the Feynman Lectures on Physics (I can give you a scan), or watch one of Feynman's Character of Physical Law videos. Bottom line, in some sense you can say that waveparticle duality is to blame for the strangeness of quantum entanglement. 


#112
Apr612, 11:50 PM

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#113
Apr712, 04:38 AM

P: 1,414

Let me say this right now. I feel pretty certain that ttn (Travis Norsen), DrC (David Schneider), zonde, lugita, Demystifier (Nikolic), billschnieder, Gordan Watson, unusualname, harrylin (and anybody I left out) and all the other contributors to this and other 'Bell' threads know a lot more about this stuff than I do. So, it would probably be best if you don't ask me any more questions about this. The Bell stuff is mainly a philosophical consideration, and wading through the language surrounding it, and eliminating the bs and irrelevant considerations is a daunting task. I hope that you and others stick with it so that maybe one day you can explain it to me and other laypersons in a way that we can understand it. I've expressed my ideas/opinions, and now I will fade back into the peanut gallery, and hopefully learn something new. 


#114
Apr712, 05:30 AM

P: 1,414

It's not that one of your steps (assumptions) is necessarily wrong, it's that one of your steps might not necessarily be expressing what's actually happening in the underlying reality. The problem, the situation, is that we have no way of knowing, because of the limitations imposed by our sensory faculties. 


#115
Apr712, 07:32 AM

P: 915

it has been a great discussion/thread......:) DrChinese, Lugita and others have passionately/patiently answered the posts and shared some interesting new information/knowledge. They has also helped, some of us, understand Bell's theorem faster. thanks DrC, Lugita and others. 


#116
Apr712, 09:26 AM

P: 1,414

If you're just starting out in this, then I hope you have the time to keep at it until you're satisfied that you fully understand it. 


#117
Apr712, 12:56 PM

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#118
Apr712, 04:57 PM

P: 1,414

The only thing that can be concluded from any BellLR model of quantum entanglement is that something pertaining to the formal LR restrictions makes the model nonviable. The precise relationship between the model, any model, even viable ones, and an underlying reality remains unknown. If the source of disagreement between model and results can be precisely identified as something in the model which clearly is incompatible wrt the experimental design and execution, then that should be taken as the effective cause of the nonviability. Regarding your proof, is your step 3 the only way to conceptualize the experimental situation? If not, then does it establish that nature is nonlocal? 


#119
Apr712, 11:40 PM

P: 1,583

You can, of course, dispute that the particles have agreed in advance which angles to go through and which angles not to go through, in which case you should dispute step 2. But if you have accepted step 2, and thus believe that the particles have instructions as to exactly which angles to go through and which angles not to go through, then the transitive property of equality forces you to accept step 3. If you agree with me up to there, I don't know how you can disagree with step 3, which is completely trivial. Similarly, I see local determinism (excluding superdeterminism) as a view that IS distinguishable experimentally from quantum mechanics, and thus it can't be fairly called an "interpretation". 


#120
Apr912, 06:02 AM

P: 1,414

Then again, I suppose you could say that step 2 in some sense implies step 3. So, maybe we should look more closely at step 2. The way it's stated is rather ... pedestrian and a bit too anthropomorphic, I must say. What are some other ways of stating the inference(s) that might be drawn from step 1? 


#121
Apr912, 08:42 AM

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#122
Apr1012, 08:19 AM

P: 3,186

Many pairs that were detected in Weih's experiment, were interpreted as "nonentangled"; removing those from the analysis yielded a result conform the prediction of QM, while including them yielded a different result. "Local realistic" simulations were shown to be capable of matching all those results. Because of that kind of subtleties my comment was (and still is): It seems to me that here (that is, in your abovementioned comment) is a partial misunderstanding, for there is a "twist" on this: the correlation may be perfect for those pairs that are called "entangled pairs". 


#123
Apr1012, 08:40 AM

P: 3,186




#124
Apr1012, 08:54 AM

Sci Advisor
PF Gold
P: 5,299

But we wouldn't expect perfect correlations from pairs that are not entangled, would we! (Unentangled pairs have a match rate closer to 75%) It is pretty clear that we need some way to define what is an entangled pair. That definition is a time coincidence window. The window ultimately defines the correlation, not the other way around. Logically, pairs in which one arrives quite late might be suspect as to whether they are still polarization entangled. On the other hand, no source is perfect. Please note that it is also possible to convert the same source into entangled pairs that are NOT polarization entangled. Using Type I PDC, simply align both crystals identically and they will produce pairs with known polarization in the Product State. You can then look at that sample and see that the time coincidence window is reasonable (since you will see the same distribution of times). Ultimately, you only get Bell state stats with entanglement. It would not be reasonable to include pairs that are not entangled if you can avoid it. 


#125
Apr1012, 09:41 AM

P: 3,186

It was merely to illustrate that the argument that Thomas presented can look good due to lack of knowledge of the very thing that it is about. Another example that is less close to home: it could have looked good to state over a century ago that since Newton's mechanics work so well, we see no reason to assume that it doesn't work for MMX and the extremely unlikely possibility of length contraction is a loophole that soon will be closed. 


#126
Apr1012, 10:00 AM

P: 1,414

@ DrC and harrylin,
Regarding the statement: If so, then if detection and pairing efficiencies were perfect, then would you expect anything to be different regarding experimental BI violation and the incompatibility of the predictions of QM and LR? 


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