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

[San K]

As lugita15 says, this is exactly the idea (or its equivalent) that was considered PRIOR to Bell. But you will quickly find that works fine when the angle settings are identical, but generally does not work out at many combinations of settings.

0/120/240 are good examples - take the DrChinese challenge! See how close you can get the match rate (comparing AB, BC, AC) to 25% (the QM value) for 10 photons.

Photon 1:
A=0 degrees is +
B=120 degrees is +
C=240 degrees is -

So AB is a match, but AC and BC are not. 1 of 3.

Photon 2:
A=0 degrees is -
B=120 degrees is +
C=240 degrees is -

So AC is a match, but AB and BC are not. 1 of 3.

Photon 3:
A=0 degrees is -
B=120 degrees is -
C=240 degrees is -

So AC, AB and BC are matches. 3 of 3.

Etc. to 10 or whatever.

You win the challenge if your average rate is lower than 1/3. Again, the QM prediction is 1/4. It should be clear that the ONLY way to "win" over a suitably large sample is to know in advance which 2 settings will be selected for each photon in our trial. But if I do that (being independent of you and not knowing whether you marked a + or a - for each photon's settings) after you mark your values, the rate of matches will converge on 1/3 or more.

Agreed, could not win the DrChinese challenge...:)

question (and I will search on the net too) what are the QM calculations and assumptions to arrive at 1/4?

 

[San K]

I see what you mean now, from your post #95.

great

That seems to work for rate of individual detection, but not for rate of coincidental detection.

interesting.

what is co-incidental detection? is it (experiments using) entangled photons detected by a co-incidence counter?

Afaik, QM doesn't provide a causal explanation for either the random individual result sequences, or the random coincidental result sequences, or the predictable correlation between θ and rate of coincidental detection.

ok

 

[DrChinese]

Agreed, could not win the DrChinese challenge...:)

question (and I will search on the net too) what are the QM calculations and assumptions to arrive at 1/4?

A - B = -120 degrees
A - C = -240 "
B - C = -120 "

These are all equivalent for the function cos^2(theta), which is the formula for the QM prediction.

cos^2(-120) = .25
cos^2(-240) = .25
cos^2(-120) = .25

So no matter which pair you consider, the QM expectation is 1/4.

 

[ThomasT]

Sorry, I had to get it approved. Now you can read my post. (It doesn't contain any new info, just the reasoning I've already been giving, for easy reference.)

Ok. That makes it handy.

No, i do not say that. I say that we must infer from my line of reasoning that local determinism is incompatible with the experimental predictions of quantum mechanics being completely correct.

What you (and Bell and Herbert) are saying is that expressing coincidental detection in terms of a separable local predetermination is incompatible with the QM-predicted and observed correlation between θ and rate of coincidental detection. Which I agree with.

I am not arbitrarily placing restrictions. I am *logically deducing* such restrictions, i.e. the Bell inequality, from certain assumptions. If you disagree with my conclusion, you must either disagree with the assumption of local determinism, or you must believe that my reasoning is flawed.

Wrt Bell's formulation, it's clear where the restrictions come from and how they affect the predictions of any LR model that encodes those restrictions. Wrt your and Herbert's proofs, it's not so clear to me -- so, if you could clarify that it would help.

The proofs show that either nature is nonlocal, nature is nondeterministic, or that quantum mechanics is incorrect, in principle, in at least some of its experimental predictions.

More precisely, the proofs show that any model or line of reasoning embodying certain restrictions must be incompatible with QM and experiment. What are the restrictions, and how did they become part of the model or line of reasoning? Does employing these restrictions prove that nature is nonlocal? Imo, no.

It's been well established that the QM predictions are correct. Regarding determinism, it's an unfalsifiable assumption. So all you're dealing with is locality. So, what you're saying your proof proves is that nature is nonlocal (which is what Herbert says). But, what you've shown is that a particular way of conceptualizing coincidental detection is incompatible with QM and experiment. You can infer, from a certain conceptualization and line of reasoning that nature is nonlocal, but whether or not that inference is warranted depends on what's involved in the model or line of reasoning, and whether or not that inference is a fact of nature can only be ascertained by observing a nonlocal transmission.

But I'm not logically proving that nature must be nonlocal.

Yet that seems to be what you said above, and it is what Herbert says his proof proves, and you present your steps as a simplified recounting of Herbert's proof.

So the burden of proof is still on you to either identify a step in my reasoning your disagree with or to agree with the conclusion of my reasoning.

I think you (and Bell and Herbert) have proved what I said above. If you don't claim that your proof proves that nature is nonlocal, then we're basically on the same page.

 

[lugita15]

Yes it is. Agreed Lugita.

question: why do 50% photons going through a polarizer? What is QM's explanation for that? Is the (indeterminate state) photon's interaction with the polarizer -- totally random or is it cause and effect?

According to (the standard interpretation of) quantum mechanics, you have a wave function for the two-particle system, so the polarizations of the particles are in a superposition of states, until one of the photons is detected by one of the polarizers (say the first polarizer). Then the wave function of the system collapses (nonlocally and instantaneously), putting both photons in the same definite polarization state. The collapse will either make both particles polarized in the direction of the first polarizer, or make both particles polarized perpendicular to the direction of the first polarizers. Which of these two things will happen is considered to be a 50-50 chance event, because wave function collapse is according to (the standard interpretation of) QM completely random.

So then if the collapse makes the photons polarized in the direction of the first polarizer, the first photon will go through the first polarizer. If the collapse makes the photons polarized perpendicular to the first polarizer, then the first photon doesn't go through. So to someone just looking at the first polarizer, he always sees random 50-50 results.

What about the second polarizer? Well, the second photon is now in a definite polarization state, either parallel or perpendicular to the angle of the first polarizer. So now if the second polarizer is oriented at the same angle as the first one, the second photon will do the same thing the first one did. If the second polarizer is oriented at a different angle, then the second photon will randomly either go through or not go through, with a probability of going through equal to the cosine squared of the difference between the polarization angle of the photon and the angle of the second polarizer. But if someone was just looking at the second polarizer they won't know what angle the first polarizer was turned to or whether the first photon went through or not, so he won't know what angle the second photon was polarized along before it hit, and thus to him it will seem to go through or not go through with random 50-50 chance.

Does that make sense?

 

[San K]

A - B = -120 degrees
A - C = -240 "
B - C = -120 "

These are all equivalent for the function cos^2(theta), which is the formula for the QM prediction.

cos^2(-120) = .25
cos^2(-240) = .25
cos^2(-120) = .25

So no matter which pair you consider, the QM expectation is 1/4.

good answer, however my question was how cos came...:)

cos came from the de broglie waves...

now laws of probability are (linear/simple) additive for particles

are the laws of probability (linear) additive for waves? or do the have cosine in them?

 

[San K]

According to (the standard interpretation of) quantum mechanics, you have a wave function for the two-particle system, so the polarizations of the particles are in a superposition of states, until one of the photons is detected by one of the polarizers (say the first polarizer). Then the wave function of the system collapses (nonlocally and instantaneously), putting both photons in the same definite polarization state. The collapse will either make both particles polarized in the direction of the first polarizer, or make both particles polarized perpendicular to the direction of the first polarizers. Which of these two things will happen is considered to be a 50-50 chance event, because wave function collapse is according to (the standard interpretation of) QM completely random.

i was asking, in general, about non-entangled single photons...sorry forgot to mention

what does "completely random" mean? is there cause and effect?

Does that make sense?

surely and it was good to rehearse the 50-50 logic

however I am asking something else.take 100 photons un-entangled photons (in an indeterminate state)...why do only 50% of them pass through?

is that predetermined, cause and effect, or totally random? what does an indeterminate state mean? what do we mean by "inherent randomness" ?

second question: when we rotate the polarizer by a few degrees:

do the same 50 photons pass through or does the composition changes?

I also realize that we may not have to answer to any of the above questions, however can be important for future researchat some point/interaction ...says QM (?)...we/photons reach the edge...the edge of cause/effect and enter into the world of "inherent" randomness...

 

[lugita15]

What you (and Bell and Herbert) are saying is that expressing coincidental detection in terms of a separable local predetermination is incompatible with the QM-predicted and observed correlation between θ and rate of coincidental detection. Which I agree with.

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.

Wrt Bell's formulation, it's clear where the restrictions come from and how they affect the predictions of any LR model that encodes those restrictions. Wrt your and Herbert's proofs, it's not so clear to me -- so, if you could clarify that it would help.

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.

To go through the steps again, 1 is a prediction of QM, 3 uses the transitive property of equality, and 4 uses the laws of probability. Thus 2, in my view, is the only step that can possibly be disputed by someone. And yet it seems so obvious to me that a local determinist who accepts 1 must accept 2.

It's been well established that the QM predictions are correct.

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.

Regarding determinism, it's an unfalsifiable assumption.

Determinism may be unfalsifiable on its own, but the combination of determinism and other assumptions may be falsifiable.

So all you're dealing with is locality.

I presume you mean locality in the sense of the principle of locality, which is just a synonym for local determinism. But it would be slightly improper to call a theory which violated local determinism a "nonlocal" theory, because "nonlocal" to my mind means that causality can propagate faster than the speed of light. But you can have, for instance, a nondeterministic theory in which there are no FTL influences.

So, what you're saying your proof proves is that nature is nonlocal (which is what Herbert says).

I mean exactly what I said: assuming that QM is completely correct in all its experimental predictions, we may reject local determinism.

But, what you've shown is that a particular way of conceptualizing coincidental detection is incompatible with QM and experiment.

I'm still trying to find out how you think I'm "restricting" or "conceptualizing" local determinism.

You can infer, from a certain conceptualization and line of reasoning that nature is nonlocal, but whether or not that inference is warranted depends on what's involved in the model or line of reasoning, and whether or not that inference is a fact of nature can only be ascertained by observing a nonlocal transmission.

But I'm not deducing facts of nature here, I'm trying to make logical deductions. My argument is of the form "If the universe has property A, then it must have property B." But the question of whether it actually has property B is dependent on whether in fact it has property A. (Property A is local determinism+perfect correlations at identical angle settings, and property B is the Bell inequality.) And the question of whether local determinism is logically incompatible with the experimental predictions of QM is a question to be decided logically, not experimentally. So as I said, the burden of proof is on you to disagree with my steps or agree with my conclusion.

Yet that seems to be what you said above, and it is what Herbert says his proof proves, and you present your steps as a simplified recounting of Herbert's proof.

It is a restatement of Herbert's proof, but I just feel he worded his conclusion a bit too strongly.

I think you (and Bell and Herbert) have proved what I said above. If you don't claim that your proof proves that nature is nonlocal, then we're basically on the same page.

But the only reason I do not make that claim is that current Bell tests have certain practical limitations and loopholes. But assuming that an ideal loophole-free Bell test, of the kind Herbert discusses, were to definitively demonstrate that the predictions of QM are completely correct, then I am certainly willing to reach the conclusion that we can reject local determinism (excluding unfalisifiable assumptions of superdeterminism, of course).

 

[lugita15]

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).

 

[San K]

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 let's 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? ..:)

 

[lugita15]

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.

 

[lugita15]

does not the Copenhagen interpretation say let's 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.

 

[ThomasT]

... 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.

 

[ThomasT]

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?

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.

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.

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.

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.

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.

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.

 

[San K]

So, it would probably be best if you don't ask me any more questions about this.

i won't ask you anymore.

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.

 

[ThomasT]

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.

 

[lugita15]

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.

 

[ThomasT]

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.

... 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.

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.

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?

 

[lugita15]

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.

 

[ThomasT]

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.

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?

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.

This is entirely irrelevant to our discussion ...

I think so too. But you're the one who's including determinism in this.

... 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.

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.

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.

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?

 

[lugita15]

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.

 

[harrylin]

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".

 

[harrylin]

[..] 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...

 

[DrChinese]

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.

 

[harrylin]

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.

 

[ThomasT]

@ DrC and harrylin,

Regarding the statement:

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?

 

[DrChinese]

@ DrC and harrylin,

Regarding the statement:

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?

I wouldn't expect anything to be different, no. As we move towards better setups, the number of standard deviations of violation should increase. It does. IIRC, Aspect was about 5, Weihs et al was 30 and we are over 100 now in some experiments.

 

[San K]

As we move towards better setups, the number of standard deviations of violation should increase.

did not get this.

are you saying that the (photons) violation of BI will increase with better instruments?

i.e. we will detect photons that violated BI with even greater degree?

however don't they have to be within the cosine curve?

 

[DrChinese]

did not get this.

are you saying that the (photons) violation of BI will increase with better instruments?

i.e. we will detect photons that violated BI with even greater degree?

Sort of. Keep in mind that there are a lot of components along the way from the source to the detector. We would like to catch and detect as many pairs as possible. Early setups had problems producing a good stream of pairs. Also problems detecting them reliably. Clearly, the issue is that we don't want there to be some kind of hidden bias in the mechanism. But in a perfect world, I would expect better detection of bigger streams to lead to higher deviations from the related BI boundary value.

 

[jtbell]

As we move towards better setups, the number of standard deviations of violation should increase. It does. IIRC, Aspect was about 5, Weihs et al was 30 and we are over 100 now in some experiments.

did not get this.

are you saying that the (photons) violation of BI will increase with better instruments?

i.e. we will detect photons that violated BI with even greater degree?

As experimental setups get better and we collect more data, the uncertainty in our measurements (measured in terms of "standard deviation") becomes smaller. Pulling numbers out of my hat, suppose the Bell inequality requires local realistic theories to predict x > 0.7 for a particular setup.

Now suppose we actually measure x = 0.5 ± 0.2 where 0.2 is the standard deviation of our measurements. We've violated the BI by one standard deviation. Most physicists would consider that suggestive, but not very conclusive.

We improve our measurements and collect more data, and we now get x = 0.51 ± 0.02. It's consistent with our previous measurement in absolute terms, but now we've violated the BI by about ten standard deviations. Most physicists would consider this to be very significant. As DrC has pointed out, some experiments have actually done much better than this.

 

[San K]

the uncertainty in our measurements (measured in terms of "standard deviation") becomes smaller.

...yes that is what i was asking, thanks jtbell. so the uncertainty becomes smaller...vastly improving credibility of the experiment/hypothesis...agreed..

however stays within the cosine curve?

 

[DrChinese]

however stays within the cosine curve?

Yup, tighter and tighter.

 

[ThomasT]

did not get this.

are you saying that the (photons) violation of BI will increase with better instruments?

i.e. we will detect photons that violated BI with even greater degree?

however don't they have to be within the cosine curve?

What DrC and jtbell said, and here's my two cents since it was my statement that was being questioned.

One can calculte proximity to some BI associated with some experimental setup assuming that everything is perfect, and those calculations show that Bell LR models satisfy BIs by a certain amount and QM violates BIs by a certain amount.

My statement in question was basically that if everything was perfect, then that wouldn't be expected to change.

But everything isn't perfect. A Bell inequality associated with a particular experiment (eg., Aspect 1982) might express something like S <= 0. The average for a number of runs was S_exp = .101 ± .020, with the experiment violating the BI by 5 standard deviations.

Regarding agreement between the QM predictions and the observed results, there's usually some slight difference. For example, wrt the above experiment the QM prediction was S_qm = .112 .

Improving efficiencies in Bell tests both decreases the standard deviation, and increases the agreement between the QM curve and the result curve.

 

[San K]

thanks DrC and ThomasT

- can we think of an experiment (that/which uses a different logic/aspect of reality) other than Bell's test that supports QE?

- for entanglement it occur, do the two particles have to always physically (locally) interact first?

- what is swapping of entanglement between two pairs of photons?

the below is not important/central to our discussion/goal (there are still some parts of BI that I have not read yet):

- why is it convenient/easier to discuss BI in terms of mismatches rather than matches?
- why do we deal with only three orientations (0, 120, 240)? --- this i guess is just for illustration purposes, we could go with more than 3
- why will the photon always pass through exactly 2 of the 3 orientations?

 

[harrylin]

@ DrC and harrylin,

Regarding the statement:

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?

The situation seems to be that for those pairs that are detected and labeled "entangled pairs" after following a tight data selection procedure, the correlation is nearly perfect for θ = 0°.
In one LR model to which I already referred - if I understood it correctly - then if detection and pairing efficiencies were 100% (which may be impossible according to the model) and with correct labeling according to that model, the result would be different from QM.

 

[ThomasT]

- can we think of an experiment (that/which uses a different logic/aspect of reality) other than Bell's test that supports QE?

Not sure what you mean. Are you asking whether there are quantum experiments that produce quantum entanglement that aren't specifically designed to be tests of a Bell inequality?

- for entanglement it occur, do the two particles have to always physically (locally) interact first?

Afaik, no. But there has to be some common, locally propagated, influence, or force, or torque ... whatever, introduced and interacting with certain entities (and it might be thousands, even millions, of atoms) that produces an entanglement relationship between those entities.

- what is swapping of entanglement between two pairs of photons?

Your most recent questions are beyond the scope of the subject of this thread. Start a new thread, and hopefully some more knowledgeable people will reply to your question(s). But first do a search of PF and arxiv.org articles on this.

- why is it convenient/easier to discuss BI in terms of mismatches rather than matches?

I don't know that it is. Afaik, Bell test results are usually reported in terms of coincidental matches not coincidental mismatches.

I suppose you might be referring to Herbert's proof, which, to me, makes no sense. I mean that wrt what he says his proof proves. Herbert says that his proof proves that nature is nonlocal. Which, imho, is just silly. Wrt Herbert's proof proving that an LR model of entanglement is incompatible with QM, then, yes, it is one way of demonstrating that. It's also a way of demonstrating that a particular expression of locality is incompatible with experimental results. The reason(s) why this is not a disproof of locality in nature wrt quantum entanglement, or support for nonlocality in nature wrt quantum entanglement are subtle, pertaining to the relationship between an LR-restricted formalism and an experimental design, and beyond the scope of this thread.

- why do we deal with only three orientations (0, 120, 240)? --- this i guess is just for illustration purposes, we could go with more than 3

Well, three is all you need. But it doesn't have to be those particular settings. In fact, if you want to go with Herbert's proof, then you just need two values of θ ... some θ, and then 2θ.

- why will the photon always pass through exactly 2 of the 3 orientations?

Don't know what you mean. Photons don't always pass through 2 different orientations. Sometimes the result is 1,0 or 0,1. Anyway, since there are only 2 possible orientations in a given trial, ie., the settings of the polarizers a and b, then what are you referring to by "3" orientations?

 

[ThomasT]

The situation seems to be that for those pairs that are detected and labeled "entangled pairs" after following a tight data selection procedure, the correlation is nearly perfect for θ = 0°.

Ok.

In one LR model to which I already referred - if I understood it correctly - then if detection and pairing efficiencies were 100% (which may be impossible according to the model) and with correct labeling according to that model, the result would be different from QM.

Well, yeah. The calculational result is different from QM now, wrt both practical and presumed ideal situations. It's always going to be different. What's your point?

 

[harrylin]

Ok.
Well, yeah. The calculational result is different from QM now, wrt both practical and presumed ideal situations. It's always going to be different. What's your point?

My point was to answer your question and regretfully I forgot what your point was.
Anyway, getting back to the topic: I guess that in such an alternative interpretation of "ideal situation", the relationship will be linear (both in LR theory and in Weih's experimental data).

 

[ThomasT]

My point was to answer your question and regretfully I forgot what your point was.

Well, that was wrt a statement that was a bit off topic. So, nevermind.

Anyway, getting back to the topic: I guess that in such an alternative interpretation of "ideal situation", the relationship will be linear (both in LR theory and in Weih's experimental data).

You might be right about that. I don't know.

In which case I might be wrong in saying to the OP that hidden variables don't imply a linear correlation between θ and rate of coincidental detection. But the fact of the matter, afaik, is that they don't. Simply due to the fact that there are LR models of quantum entanglement which predict a cosine, not a linear, correlation between θ and rate of coincidental detection. Even DrC will agree with this. Ask him.

 

[San K]

Not sure what you mean. Are you asking whether there are quantum experiments that produce quantum entanglement that aren't specifically designed to be tests of a Bell inequality?

yes

Don't know what you mean. Photons don't always pass through 2 different orientations. Sometimes the result is 1,0 or 0,1. Anyway, since there are only 2 possible orientations in a given trial, ie., the settings of the polarizers a and b, then what are you referring to by "3" orientations?

0, 120, 240 <--- three orientations, we'll go step at a time

http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/bell.html

http://www.upscale.utoronto.ca/PVB/Harrison/BellsTheorem/BellsTheorem.html

 

[ThomasT]

Are you asking whether there are quantum experiments that produce quantum entanglement that aren't specifically designed to be tests of a Bell inequality?

yes

Ok. I would suppose so. But I don't know. DrC, jtbell, et al. can probably answer this for you. Google it.

You asked:

- why will the photon always pass through exactly 2 of the 3 orientations?

To which I answered:

Don't know what you mean. Photons don't always pass through 2 different orientations. Sometimes the result is 1,0 or 0,1. Anyway, since there are only 2 possible orientations in a given trial, ie., the settings of the polarizers a and b, then what are you referring to by "3" orientations?

To which you replied:

0, 120, 240 <--- three orientations, we'll go step at a time

Ok, now I know what you mean by the three orientations. These are the θ (the angular difference between polarizer settings) that might be used in a Bell test. They can have any values. Wrt the θ you gave, 120° and 240° are the same θ.

But your question still isn't clear to me. You said "the photon", singular.

Are you thinking of the "three orientations" as individual polarizer offsets from the horizontal 0° setting?

 

[lugita15]

(I'm replying to a post from another thread)

Hi lugita. How do you go from step 2 to step 3?

I told you, all that's required is a trivial use of the transitive property of equality. Based on step 2, we assume it is determined in advance what angles both particles would go through and what angles they both wouldn't go through. Let us call the angles the two particles will go through "good angles", and the angles the two particles will not go through "bad angles". So for each angle, we can ask the question "Is the angle good?" or in other words "Is this one of the angles for which it is determined in advance that the particles will go through?" This is of course a yes or no question. If the answer to this question is "yes" for a particular angle, i.e. if the angle is "good", we say the instruction at that angle is "yes". If the answer is "no" for a particular angle, i.e. the angle is "bad", then we say that the instruction at that angle is "no' (The word "instruction" is just an arbitrary word I'm using. If you want to use another word for it that's fine.)

So for instance, if the two particles would go through the angle 30 degrees, then we say the instruction at 30 is "yes". If the two particles would not go through the angle 20 degees, then we say that the instruction at 20 is "no". (Remember, by step 2 the instructions, i.e. the answers to the yes or no question "would the particle go through at this angle", are determined in advance.) Are we good up to here? So far I've just been talking about what we can say based on step 2.

Now for the logic to go from step 2 to step 3. By the transitive property of equality, we get the following:
(*)If the instruction at -30 is the same as the instruction at 0, and the instruction at 0 is the same as the instruction at 30, then the instruction at -30 is the same as the instruction at 30.

(For example, if the instructions at -30 and 0 are both "yes", and the instructions at 0 and 30 are both "yes", then all three instructions are yes, and similarly if you replace all the yes's with no's.)

I hope you see that the statement (*) really is trivial, and I hope you also see that the statement (*) is completely equivalent to the statement in my step 3. If you don't see either of these, please tell me.

 

[ThomasT]

(I'm replying to a post from another thread)
I told you, all that's required is a trivial use of the transitive property of equality. Based on step 2, we assume it is determined in advance what angles both particles would go through and what angles they both wouldn't go through. Let us call the angles the two particles will go through "good angles", and the angles the two particles will not go through "bad angles". So for each angle, we can ask the question "Is the angle good?" or in other words "Is this one of the angles for which it is determined in advance that the particles will go through?" This is of course a yes or no question. If the answer to this question is "yes" for a particular angle, i.e. if the angle is "good", we say the instruction at that angle is "yes". If the answer is "no" for a particular angle, i.e. the angle is "bad", then we say that the instruction at that angle is "no' (The word "instruction" is just an arbitrary word I'm using. If you want to use another word for it that's fine.)

So for instance, if the two particles would go through the angle 30 degrees, then we say the instruction at 30 is "yes". If the two particles would not go through the angle 20 degees, then we say that the instruction at 20 is "no". (Remember, by step 2 the instructions, i.e. the answers to the yes or no question "would the particle go through at this angle", are determined in advance.) Are we good up to here? So far I've just been talking about what we can say based on step 2.

Now for the logic to go from step 2 to step 3. By the transitive property of equality, we get the following:
(*)If the instruction at -30 is the same as the instruction at 0, and the instruction at 0 is the same as the instruction at 30, then the instruction at -30 is the same as the instruction at 30.

(For example, if the instructions at -30 and 0 are both "yes", and the instructions at 0 and 30 are both "yes", then all three instructions are yes, and similarly if you replace all the yes's with no's.)

I hope you see that the statement (*) really is trivial, and I hope you also see that the statement (*) is completely equivalent to the statement in my step 3. If you don't see either of these, please tell me.

Suppose you assume, from the observation in step 1, that the angular difference between polarizer settings is measuring a relationship between entangled photons that isn't varying from entangled pair to entangled pair. How would you proceed from that assumption?

 

[lugita15]

Suppose you assume, from the observation in step 1, that the angular difference between polarizer settings is measuring a relationship between entangled photons that isn't varying from entangled pair to entangled pair. How would you proceed from that assumption?

Um, I'm not sure what this has to do with what I'm saying. Are you saying that you agree or disagree that step 2 follows from step 1? If you disagree, I can try to explain the logic.

Also, given what I said in the post you're responding to, do you now accept that step 3 is a trivial consequence of step 2?

 

[ThomasT]

Um, I'm not sure what this has to do with what I'm saying. Are you saying that you agree or disagree that step 2 follows from step 1? If you disagree, I can try to explain the logic.

Your step 1 says:
1. Entangled photons behave identically at identical polarizer settings.

There are a number of things that might be inferred from this. Your step 2 says:
2. The believer in local hidden variables says that the polarizer angles the photons will and won't go through are agreed upon in advanced by the two entangled photons.

Ok, so there's something wrt the incident optical disturbances that will determine whether or not they're transmitted by the polarizing filters.

Your step 3 says:
3. 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.

Where did that come from? What's the relationship between your step 3 and your step 2? Please express steps 2 and 3 in non-anthropomorphic terms. Ie., from the observation noted in step 1, then what might you infer about the properties of the optical disturbances incident on the polarizers in any given coindicence interval?

 

[harrylin]

[I wrote: [..] getting back to the topic: I guess that in such an alternative interpretation of "ideal situation", the relationship will be linear (both in LR theory and in Weih's experimental data).]

[..] You might be right about that. I don't know.

In which case I might be wrong in saying to the OP that hidden variables don't imply a linear correlation between θ and rate of coincidental detection. But the fact of the matter, afaik, is that they don't. Simply due to the fact that there are LR models of quantum entanglement which predict a cosine, not a linear, correlation between θ and rate of coincidental detection. Even DrC will agree with this. Ask him.

I hope that he will see this remark and comment on it, as it's very much on topic; I do think that hidden variables imply a linear relationship with 100% detection and without "data picking".

 

[lugita15]

Where did that come from? What's the relationship between your step 3 and your step 2? Please express steps 2 and 3 in non-anthropomorphic terms.

I think I spelled out the logic in going from step 2 to step 3 pretty well in post #142, and I did so in non-anthropomorphic terms. Tell me if you don't understand something in that post.

 

[lugita15]

I hope that he will see this remark and comment on it, as it's very much on topic; I do think that hidden variables imply a linear relationship with 100% detection and without "data picking".

There's a small subtlety here that was covered earlier this thread. You should really use the term "sublinear" or "at most linear". That's because the Bell inequality in (say) Herbert's proof is of the form A is less than or equal to B+C, not of the form A=B+C, which is what's required for linearity. So you CAN have some kind of nonlocal correlation, but that will only make the result differ even further from the predictions of QM. The local deterministic theory that has the closest possible agreement with QM is one in which the correlation is linear, and we know that even such a theory differs significantly from the predictions of QM.

 

[ThomasT]

I hope that he will see this remark and comment on it, as it's very much on topic; I do think that hidden variables imply a linear relationship with 100% detection and without "data picking".

Here's a hidden variable model, assuming ideal efficiencies, that produces a nonlinear relationship.

https://www.physicsforums.com/showpost.php?p=3856186&postcount=54

 

[harrylin]

There's a small subtlety here that was covered earlier this thread. You should really use the term "sublinear" or "at most linear". That's because the Bell inequality in (say) Herbert's proof is of the form A is less than or equal to B+C, not of the form A=B+C, which is what's required for linearity. So you CAN have some kind of nonlocal correlation, but that will only make the result differ even further from the predictions of QM. The local deterministic theory that has the closest possible agreement with QM is one in which the correlation is linear, and we know that even such a theory differs significantly from the predictions of QM.

Ok, that makes sense!