Understanding bell's theorem: why hidden variables imply a linear relationship?

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 Quote by San K i was asking, in general, about non-entangled single photons.....sorry forgot to mention
OK, then the explanation is even simpler. The photon is initially described by a wave function that is in a superposition of polarization states. Then when the photon is hits the polarizer, the wave function collapses, and photon acquires a state of definite polarization, either polarized parallel to the polarizer or polarized perpendicular to the polarizer, each of these two outcomes has a 50% chance of happening.
 what does "completely random" mean? is there cause and effect?
In the traditional Copenhagen interpretation, wave function collapse is truly random, in the sense that there is no cause and effect.
 take 100 photons un-entangled photons (in an indeterminate state)....why do only 50% of them pass through?
The Cophenhagen interpretation says there is no reason for this, there is just a non-deterministic element to the universe.
 is that predetermined, cause and effect, or totally random? what does an indeterminate state mean? what do we mean by "inherent randomness" ?
In the Copenhagen interpretation collapse is totally random, so that absolutely nothing determines what the outcome will be.
 second question: when we rotate the polarizer by a few degrees: do the same 50 photons pass through or does the composition changes?
Copenhagen says that each photon goes through or doesn't go through at random, so which 50 (on average) of the 100 photons are going to go through is not determined in advance at all.
 at some point/interaction ......says QM (?)......we/photons reach the edge.....the edge of cause/effect and enter into the world of "inherent" randomness.....
Yes, at least according to the Copenhagen interpretation, which is the "standard" or "orthodox" view of QM. There are of course many other interpretations. For instance, Bohmian mechanics says that the apparent randomness of particle behavior is just due to our ignorance of (nonlocal) hidden variables associated with the particles. Many Worlds says that all possible outcomes occur in separate universes, and our mind is also there in these multiple universe, so the fact that we seem to observe outcome A rather than outcome B just means we happened to end up in a universe in which outcome A occurs. Roger Penrose's interpretation says that there is no randomness at all, and that the outcomes of all experiments can be determined in advanced just by calculating a mathematical function, but the only problem is that this function cannot be calculated by a computer (or Turing machine); but he believes that this uncomputable mathematical function CAN be calculated by humans, because he believes that the insightful abilities of the human mind surpasses that of any computer, because he believes that the human mind is based on quantum mechanics (see his books The Emperor's New Mind or Shadows of the Mind for more info).
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 Quote by lugita15 In the Copenhagen interpretation collapse is totally random, so that absolutely nothing determines what the outcome will be.
Lugita, i agree with all of what you said in your post.

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? ..:)
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 Quote by San K good answer, however my question was how cos came....:)?
At a shallow level, the way quantum mechanics works is that you have to calculate the probability amplitude of a particle in state A to be measured in state B. In this case, state A is a superposition of polarization states and state B is the state of definite polarization parallel to the polarizer. Then you take the square of the absolute value of the probability amplitude to find the actual probability. When you do this straightforward calculation, the result happens to be cos^2.

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.
 cos came from the de broglie waves......
Yes, in some sense you could say that the sinusoidal functions come from the fact that in QM particles are described by wave functions, which is very different than how particles work classically.
 now laws of probability are (linear/simple) additive for particles
The laws of probability have the same form regardless of what kinds of objects you're talking about.
 are the laws of probability (linear) additive for waves? or do the have cosine in them
The laws of probability are still (sub)additive, for both particles and waves, but that's not the question you should be asking. Rather the issue is, if you take two simple waves, is the square of the amplitude of their sum less than or equal to the sum of the squares of their amplitudes? That is, if wave 1 has amplitude A1, wave 2 has amplitude A2, and wave 3, which is the superposition of waves 1 and 2, has amplitude A3, is A3^2 always less than or equal to A1^2 +A2^2? The answer to that is no.

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 wave-particle duality is to blame for the strangeness of quantum entanglement.
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 Quote by San K 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? ..:)
The doctrine of Copenhagen is total randomness of the results of wave function collapse. It's more when you ask questions like "is the wave function real" or "what constitutes a measurement for the purposes of wave function collapse" that Copenhagen people may give you the "shut up and calculate" attitude.
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 Quote by San K ... what is co-incidental detection? is it (experiments using) entangled photons detected by a co-incidence counter?
Yes, or some other means of pairing individual results. It's what DrC is talking about in his challenge.

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.
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 Quote by lugita15 My steps are concerned with local determinism in general. But what do you mean by separable? Do you mean in the sense of factorization of probability distributions, as Bell did in his original proof? Such a factorization is not used in Herbert's proof.
Herbert says that his line of reasoning embodies the independence of spacelike separated events as the assumption of locality. If your proof is a recounting of Herbert's proof, then your proof does this also. In which step of your proof is this explicated?

 Quote by lugita15 I don't know how much help I can be, because I honestly don't know where I am "encoding restrictions" in my reasoning. I do ultimately arrive at a restriction, AKA the bell inequality, but I get that restriction as a conclusion of the argument, not an assumption of the argument. So if this conclusion is wrong then one of the steps must be wrong.
The conclusion isn't wrong if it follows from your assumptions. You say, and I agree, that your conclusion follows from your assumptions. So, what we have to look at is your assumptions in order to ascertain whether we can conclude that an underlying reality, ie., nature, must be nonlocal.

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.

 Quote by lugita15 I agree that there is ample experimental evidence for many of the predictions of QM. But a key prediction of QM used in the proof is the fact that you get perfect correlation at identical angle settings, and this has not been definitively demonstrated, because there are various experimental loopholes that in principle could be exploited to construct a local deterministic theory. But yes, the preponderance of evidence is in favor of the correctness of QM's experimental predictions.
Ok, so we, and most everybody else, agrees on that.

 Quote by lugita15 Determinism may be unfalsifiable on its own, but the combination of determinism and other assumptions may be falsifiable.
In which case, then what you might be falsifying would be a certain expression of those other assumptions, such as a particular expression of locality -- but not determinism.

 Quote by lugita15 I presume you mean locality in the sense of the principle of locality, which is just a synonym for local determinism.
Locality, in the usual sense, means that nothing propagates faster than the speed of light. Determinism means that events or states at t = 1 are a consequence of events or states at t = 0. Determinism isn't incompatible with ftl propagations. But it is incompatible with instantaneous action at a distance.

 Quote by lugita15 I'm still trying to find out how you think I'm "restricting" or "conceptualizing" local determinism.
That's what I'm trying to find out. It's your proof. You tell me.

 Quote by lugita15 But I'm not deducing facts of nature here ...
Then we're on the same page. You, and Herbert, and Bell aren't necessarily saying anything about nature.
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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.
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 Quote by San K i won't ask you anymore.
But certainly keep on asking the others. They know a bit more. (And of course you can still ask me anything, and if I don't feel certain that I know the answer, then I'll try to find the time to look it up ... but of course you can do that also.)

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.
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 Quote by ThomasT Herbert says that his line of reasoning embodies the independence of spacelike separated events as the assumption of locality. If your proof is a recounting of Herbert's proof, then your proof does this also. In which step of your proof is this explicated?
Well, if by "independence of spacelike separated events" you mean that the behavior of particle 1 is independent of the setting of polarizer 2, and vice versa, then yes, I am assuming that that is part of the definition of local determinism. Is that what you dispute? If so, then step 2 would be the step you should disagree with me on.
 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.
But there are some things that are the same regardless of the universe we live in. Step 1 is a prediction of quantum mechanics, and this prediction will be the same in every universe, although presumably it will be a correct prediction in some universes and an incorrect prediction in others. Step 3 is an application of the transitive property of equality, and step 4 is an application of the laws of probability, and I hope you agree that those apply equally well in all universes. So we come back to step 2.
 Determinism isn't incompatible with ftl propagations. But it is incompatible with instantaneous action at a distance.
This is irrelevant to what we're discussing, but why do you think instantaneous action at a distance is incompatible with determinism?
 That's what I'm trying to find out. It's your proof. You tell me.
But I don't think I am assuming some restrictions on what a local deterministic theory can look like. Rather, I am CONCLUDING a restriction, the Bell inequality, from the assumptions of local determinism and perfect correlation at identical angles.
 Then we're on the same page. You, and Herbert, and Bell aren't necessarily saying anything about nature.
We're not on the same page, because under the assumption that QM is correct in its experimental predictions, I most definitely AM saying something about nature.
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 Quote by lugita15 Well, if by "independence of spacelike separated events" you mean that the behavior of particle 1 is independent of the setting of polarizer 2, and vice versa, then yes, I am assuming that that is part of the definition of local determinism. Is that what you dispute? If so, then step 2 would be the step you should disagree with me on.
But step 2 doesn't specify any particular way of expressing that. That comes with step 3. So, it would seem that step 3 is where the actual restriction is introduced.

 Quote by lugita15 ... why do you think instantaneous action at a distance is incompatible with determinism?
Because determinism has to do with the temporal causal order of events. Instantaneous action at a distance between A and B precludes this. It says that A and B are happening simultaneously.

 Quote by lugita15 But I don't think I am assuming some restrictions on what a local deterministic theory can look like. Rather, I am CONCLUDING a restriction, the Bell inequality, from the assumptions of local determinism and perfect correlation at identical angles.
The restriction has to be introduced before the conclusion of a linear correlation between θ and rate of coincidental detection. Since step 2 doesn't express any particular literal restriction, then it has to be step 3. That is, you've chosen to express the assumption of independence (locality) in a certain way, and expressing it that way entails the conclusion that the correlation between θ and rate of coincidental detection must be linear.

 Quote by lugita15 We're not on the same page, because under the assumption that QM is correct in its experimental predictions, I most definitely AM saying something about nature.
The physical interpretation of QM has been an open question since the theory was first formulated. As far as I can tell it will always be an open question.

The only thing that can be concluded from any Bell-LR 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?
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 Quote by ThomasT But step 2 doesn't specify any particular way of expressing that. That comes with step 3. So, it would seem that step 3 is where the actual restriction is introduced.
ThomasT, you have the uncanny ability of focusing on steps I consider to be unimportant. Step 3 says "In order for the agreed-upon instructions (to go through or not go through) at -30 and 30 to be different, either the instructions at -30 and 0 are different or the instructions at 0 and 30 are different." Let me ask you this, is the following general statement true? "If A and C are different, either A and B are different or B and C are different." For example, "If the color of your pants and shoes are different, then the color of your pants and socks are different, or the color of your socks and shoes are different." (In this case, A="the instruction at -30", B="the instruction at 0", and C="the instruction at 30".) If you cannot tell that this statement is true, consider the equivalent statement "If A and B are the same, and B and C are the same, then A and C are the same." You should recognize that as the transitive property of equality, and presumably that is not in despite.

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.
 Because determinism has to do with the temporal causal order of events. Instantaneous action at a distance between A and B precludes this. It says that A and B are happening simultaneously.
This is entirely irrelevant to our discussion, but do you not consider Newton's theory of gravitation to be deterministic, since it has instantaneous action at a distance? And would consider Bohmian mechanics to be nondeterministic, since it too has instantaneous action at a distance?
 The restriction has to be introduced before the conclusion of a linear correlation between θ and rate of coincidental detection. Since step 2 doesn't express any particular literal restriction, then it has to be step 3. That is, you've chosen to express the assumption of independence (locality) in a certain way, and expressing it that way entails the conclusion that the correlation between θ and rate of coincidental detection must be linear.
But I am not making any assumption of locality or independence in step 3! Step 2 is where I say the particles have determined in advance, exactly what angles to go through and what angles not to go through. So they have a list of the instructions of the form "If you see a 20 degree polarizer, go through", "If you see a 40 degree polarizer, don't go through", etc., a list they have agreed upon in advance when they were emitted from the source.

If you agree with me up to there, I don't know how you can disagree with step 3, which is completely trivial.
 The physical interpretation of QM has been an open question since the theory was first formulated. As far as I can tell it will always be an open question.
Yes, there are some philosophical views that are indistinguishable experimentally from quantum mechanics, so they can fairly be called interpretations. Copenhagen, Many Worlds, and Bohmian mechanics are good examples of those. But not all possible viewpoints are indistinguishable experimentally from quantum mechanics. For instance, Schrodinger himself originally viewed the wave function as a literal gas that surrounded the nucleus of the atom, and that the magnitude of the wave function was indication the thickness of the gas. But this view was rejected after it was found that when measured, an electron was detected as a particle, not a wave.

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".
 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?
As I said, step 3 is not the step where locality is invoked. Step 3 is an unimportant step where I'm just saying something of the form "If A≠C, then A≠B or B≠C" (an application of the transitive property of equality), so that I can apply the laws of probability and say "The probability that A≠B or B≠C is less than or equal to the probablity that A≠B plus the probability that B≠C" and thus conclude that "The probability that A≠C is less than or equal to the probablity that A≠B plus the probability that B≠C", which is the Bell inequality I'm after.
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 Quote by lugita15 ThomasT, you have the uncanny ability of focusing on steps I consider to be unimportant.
They must all have some importance, otherwise I suppose that you wouldn't bother expressing them.
 Quote by lugita15 Step 3 says "In order for the agreed-upon instructions (to go through or not go through) at -30 and 30 to be different, either the instructions at -30 and 0 are different or the instructions at 0 and 30 are different." Let me ask you this, is the following general statement true? "If A and C are different, either A and B are different or B and C are different." For example, "If the color of your pants and shoes are different, then the color of your pants and socks are different, or the color of your socks and shoes are different." (In this case, A="the instruction at -30", B="the instruction at 0", and C="the instruction at 30".) If you cannot tell that this statement is true, consider the equivalent statement "If A and B are the same, and B and C are the same, then A and C are the same." You should recognize that as the transitive property of equality, and presumably that is not in despute.
No, that's not in dispute. What's in dispute is the manner in which some have chosen to restrict the argument. Is it possible that the transitive property of equality expressed in terms of things that we can count at our level of macroscopic apprehension might have nothing to do with locality/nonlocality in a realm of behavior removed from our sensory apprehension and, presumably, underlying instrumental behavior -- at least wrt the way that the dilemma has so far been framed?

 Quote by lugita15 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.
There's at least one other way of conceptualizing the reason for identical detection attributes at identical settings. Namely, that the separated polarizers are analyzing, filtering exactly the same thing wrt any given pair of entangled particles. In which case, the expected result would be in line with the QM predictions and Malus Law.

 Quote by lugita15 This is entirely irrelevant to our discussion ...
I think so too. But you're the one who's including determinism in this.

 Quote by lugita15 ... but do you not consider Newton's theory of gravitation to be deterministic, since it has instantaneous action at a distance?
I'm not aware of any contention or hypothesis of instantaneous action at a distance associated, by Newton, with the relationships that his equations specify. For those who want to infer nonlocality from the equations, then that's on them. The equations express an observationally confirmed relationship. Is it possible that that relationship might be due to local interactions/transmissions? Yes, of course it is, in the sense of gravitational systems.

 Quote by lugita15 And would consider Bohmian mechanics to be nondeterministic, since it too has instantaneous action at a distance?
Yes, insofar as dBB is interpreted to explicate nonlocality, then it's nondeterministic. Just relational, just as standard QM is relational, not causal.

 Quote by lugita15 But I am not making any assumption of locality or independence in step 3!
But that's where it takes a particular form that must affect the conclusion. Simply assuming locality, in terms of independence, is inconsequential until that assumption is put into a form that will impact the reasoning or the experimental predictions.

 Quote by lugita15 Step 2 is where I say the particles have determined in advance, exactly what angles to go through and what angles not to go through.
Yes, but step 2 doesn't put it into a form that will impact the reasoning. Step 3 does that.

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?
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 Quote by ThomasT They must all have some importance, otherwise I suppose that you wouldn't bother expressing them.
Yes, it's just that step 3 is a relatively trivial and unimportant step, at least to my mind.
 No, that's not in dispute. What's in dispute is the manner in which some have chosen to restrict the argument. Is it possible that the transitive property of equality expressed in terms of things that we can count at our level of macroscopic apprehension might have nothing to do with locality/nonlocality in a realm of behavior removed from our sensory apprehension and, presumably, underlying instrumental behavior -- at least wrt the way that the dilemma has so far been framed?
In step 3, I'm not "restricting the argument" or assuming anything at all about locality, nonlocality, or independence. All I'm doing is applying the transitive property of equality.
 There's at least one other way of conceptualizing the reason for identical detection attributes at identical settings. Namely, that the separated polarizers are analyzing, filtering exactly the same thing wrt any given pair of entangled particles. In which case, the expected result would be in line with the QM predictions and Malus Law.
OK, but whatever you're talking about it has absolutely nothing to do with step 3.
 I think so too. But you're the one who's including determinism in this.
Yes, and determinism to me means that the future can be determined with complete certainty given the present.
 I'm not aware of any contention or hypothesis of instantaneous action at a distance associated, by Newton, with the relationships that his equations specify. For those who want to infer nonlocality from the equations, then that's on them. The equations express an observationally confirmed relationship. Is it possible that that relationship might be due to local interactions/transmissions? Yes, of course it is, in the sense of gravitational systems.
Again, this is irrelevant for our discussion, but if Newton's theory of gravitation were correct, we could use it to send messages instantaneously: just move around a mass here, and the gravitational field all over the universe would be immediately measured to have a change.
 Yes, insofar as dBB is interpreted to explicate nonlocality, then it's nondeterministic. Just relational, just as standard QM is relational, not causal.
I think your view of determinism is not how the term is generally understood.
 But that's where it takes a particular form that must affect the conclusion. Simply assuming locality, in terms of independence, is inconsequential until that assumption is put into a form that will impact the reasoning or the experimental predictions.
As I said, in step 3 I am not at all putting the assumption of locality or independence into any form. I am not invoking such notions in any way. All I am doing is starting from step 2, which says that that the particles have agreed on what angles to go through, and applying the transitive property of equality.
 Yes, but step 2 doesn't put it into a form that will impact the reasoning. Step 3 does that.
No, step 3 does nothing of the sort.
 Then again, I suppose you could say that step 2 in some sense implies step 3.
Yes, it certainly does.
 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?
I agree that the phrasing in step 2 is a little anthropomorphic, but we can easily change the phrasing without changing the meaning. For instance, instead of saying that the particles have AGREED in advance what angles to go through and not to go through, we can say that it is DETERMINED in advance what angles both particles will go through and what angles they will not go through.
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 Quote by ThomasT Neither am I. DrC is pretty familiar/fluent wrt the experiment and simulation you mentioned. I think he might agree with: "Since the correlation is perfect at θ = 0° for the entangled pairs that are detected, then I see no reason to assume that it would be different if all entangled pairs could be detected." But I don't know.
Hi I'm pretty sure that the experimental results to which I referred disqualified that statement in the way as I indicated. But apparently my example wasn't sufficiently clear, so I'll rephrase it.

Many pairs that were detected in Weih's experiment, were interpreted as "non-entangled"; 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 above-mentioned 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".
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 Quote by ThomasT [..] 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. [..]
I thought the same of you and others! The only thing I do in this group while I'm trying to learn more by listening is to give now and then my 2cts which I happened to pick up elsewhere...
PF Gold
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 Quote by harrylin Many pairs that were detected in Weih's experiment, were interpreted as "non-entangled"; 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 marching 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 above-mentioned 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".
Yes, that is true. And as you widen the window, you get a lower correlation rate.

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.
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 Quote by DrChinese Yes, that is true. And as you widen the window, you get a lower correlation rate. [..] 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.
Obviously; I certainly would not suggest the contrary!

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.
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@ DrC and harrylin,

Regarding the statement:
 Quote by ThomasT Since the correlation is perfect at θ = 0° for the entangled pairs that are detected, then I see no reason to assume that it would be different if all entangled pairs could be detected.
The situation seems to be that for entangled pairs that are detected, then the correlation is perfect at θ = 0°. Is this the case?

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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