Is action at a distance possible as envisaged by the EPR Paradox.

[DrChinese]

I'm just trying to understand the correlation between the angular difference in the polarizer settings and coincidental detection. It doesn't 'seem' mysterious. That is, the optics principle that applies to the observed coincidence count when both polarizers are on one side, would seem to be applicable when there's one polarizer on each side.

Except that it doesn't apply to ordinary streams of identically polarized photon pairs coming from a PDC crystal. According to your ideas, it should. You would predict Entangled State stats (cos^2 theta) and you instead see Product State (.5*(.5+cos^2 theta)). So your prediction is flat out incorrect.

I re-iterate: where is your REFERENCE?

 

[JesseM]

We're talking about optical Bell tests, right? I think I phrased it as the 'coincidental photon flux'.

Please review the context of this exchange. I said "Well, can you present your local optical explanation in detail, either here or on a new thread?" and you replied "It isn't 'my' optical explanation. It's optics." Naturally I took this to imply you thought there could be a local optical explanation for the cos^2(a-b) statistics seen in entanglement experiments, perhaps one involving Malus' law (which can indeed be derived from classical electromagnetism, a completely local theory). Did I misunderstand? Are you not claiming that the statistics can be explained in terms of local properties that travel along with the two beams (or the individual photons) that were assigned to them by the source?

In certain optical Bell tests the coincidence rate is proportional to cos^2(a-b). From your knowledge of quantum optics, do you think that that indicates or requires that something nonlocal or ftl is happening in those experiments?

It does require that if we adopt a "realist" view of the type I discussed in post #101 of the Understanding Bell's Logic thread, and if we assume each measurement has a single unique outcome (so many-worlds type explanations are out), and if the experiment meets various observable requirements like sufficiently high detector efficiency and a spacelike separation between measurements.

The joint probability P(AB) is not being modeled as the product of P(A)*P(B) by Bell's equation. Do you disagree?

My thinking has been that it reduces to that.

Yes, of course I disagree, you're just totally misunderstanding the most basic logic of the proof which is assuming a perfect correlation between A and B whenever both experimenters choose the same detector setting. It's really rather galling that you make all these confident-sounding claims about Bell's proof being flawed when you fail to understand something so elementary about it! Could you maybe display a tiny bit of intellectual humility and consider the possibility that it might not be that the proof itself is flawed and that you've spotted a flaw that so many thousands of smart physicists over the years have missed, that it might instead be you are misunderstanding some aspects of the proof?

If you want an example where two variables are statistically dependent in their marginal probabilities but statistically independent when conditioned on some other variable, you might consider the numerical example I provided in this post, where P(T,U) is not equal to P(T)*P(U) but P(T,U|V) is equal to P(T|V)*P(U|V):

in your example there seem to be two measured variables, T which can take two values {received treatment A, received treatment B} and another one, let's call it U, which can also take two values {recovered from disease, did not recover from disease}. Then there is also a hidden variable we can V, which can take two values {large kidney stones, small kidney stones}. In your example there is a marginal correlation between variables T and U, but there is still a correlation (albeit a different correlation) when we condition on either of the two specific values of V. So, let me modify your example with some different numbers. Suppose 40% of the population have large kidney stones and 60% have small ones. Suppose those with large kidney stones have an 0.8 chance of being assigned to group A, and an 0.2 chance of being assigned to group B. Suppose those with small kidney stones have an 0.3 chance of being assigned to group A, and an 0.7 chance of being assigned to B. Then suppose that the chances of recovery depend only one whether one had large or small kidney stones and is not affected either way by what treatment one received, so P(recovers|large kidney stones, treatment A) = P(recovers|large kidney stones), etc. Suppose the probability of recovery for those with large kidney stones is 0.5, and the probability of recovery for those with small ones is 0.9. Then it would be pretty easy to compute P(treatment A, recovers, large stones)=P(recovers|treatment A, large stones)*P(treatment A, large stones)=P(recovers|large stones)*P(treatment A, large stones)=P(recovers|large stones)*P(treatment A|large stones)*P(large stones) = 0.5*0.8*0.4=0.16. Similarly P(treatment A, doesn't recover, small stones) would be P(doesn't recover|small stones)*P(treatment A|small stones)*P(small stones)=0.1*0.3*0.6=0.018, and so forth.

In a population of 1000, we might then have the following numbers for each possible combination of values for T, U, V:

1. Number(treatment A, recovers, large stones): 160
2. Number(treatment A, recovers, small stones): 162
3. Number(treatment A, doesn't recover, large stones): 160
4. Number(treatment A, doesn't recover, small stones): 18
1. Number(treatment B, recovers, large stones): 40
2. Number(treatment B, recovers, small stones): 378
3. Number(treatment B, doesn't recover, large stones): 40
4. Number(treatment B, doesn't recover, small stones): 42

If we don't know whether each person has large or small kidney stones, this becomes:

1. Number(treatment A, recovers) = 160+162 = 322
2. Number(treatment A, doesn't recover) = 160+18 = 178
3. Number(treatment B, recovers) = 40+378 = 418
4. Number(treatment B, doesn't recover) = 40+42=82

So here, the data shows that of the 500 who received treatment A, 322 recovered while 178 did not, and of the 500 who received treatment B, 418 recovered and 82 did not. There is a marginal correlation between receiving treatment B and recovery: P(treatment B, recovers)=0.418, which is larger than P(treatment B)*P(recovers)=(0.5)*(0.74)=0.37. But if you look at the correlation between receiving treatment B and recovery conditioned on large kidney stones, there is no conditional correlation: P(treatment B, recovers|large stones) = P(treatment B|large stones)*P(recovers|large stones) [on the left side, there are 400 people with large stones and only 40 of these who also received treatment B and recovered, so P(treatment B, recovers|large stones) = 40/400 = 0.1; on the right side, there are 400 with large stones but only 80 of these received treatment B, so P(treatment B|large stones)=80/400=0.2, and there are 400 with large stones and 200 of those recovered, so P(recovered|large stones)=200/400=0.5, so the product of these two probabilities on the right side is also 0.1] The same would be true if you conditioned treatment B + recovery on small kidney stones, or if you conditioned any other combination of observable outcomes (like treatment A + no recovery) on either large or small kidney stones.

If you like I could also show you how something similar would be true in my scratch lotto example, which is even more directly analogous to the situation being considered in Aspect-type experiments.

If you don't think that's ok, then how would you characterize the separability of the joint state (ie., the expression of locality) per Bell's (2)?

I would characterize it in terms of A and B being statistically independent only when conditioned on the value of the hidden variable λ. They are clearly not statistically independent otherwise, and Bell makes it explicit that he assumes there is a perfect correlation between their values when both experimenters choose the same detector setting. For example, in the introduction to the original paper he says:

Since we can predict in advance the result of measuring any chosen component of \sigma_2, by previously measuring the same component of \sigma_1, it follows that the result of any such measurement must actually be predetermined.

Likewise in http://cdsweb.cern.ch/record/142461/files/198009299.pdfpapers Bell writes on p. 11:

Let us summarize once again the logic that leads to the impasse. The EPRB correlations are such that the result of the experiment on one side immediately foretells that on the other, whenever the analyzers happen to be parallel. If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independent of the intervention on the other side, by signals from the source and by the local magnet setting.

If the value of measurement A "immediately foretells" the value of measurement B when the settings on both sides are the same, that means there's a perfect correlation between the value of A and the value of B when conditioned only on the fact that both sides used the same setting (and not conditioned on any hidden variables)--do you disagree?

 

[JesseM]

I'm just trying to understand the correlation between the angular difference in the polarizer settings and coincidental detection. It doesn't 'seem' mysterious.

Well, you are going to have to do some precise reasoning rather than just relying on feelings about how things "seem" if you want to understand Bell's arguments.

That is, the optics principle that applies to the observed coincidence count when both polarizers are on one side, would seem to be applicable when there's one polarizer on each side.

If you are doing an experiment which matches the condition of the Bell inequalities that says each measurement must yield one of two binary results (rather than a continuous range of intensities), then even if "both polarizers are on one side" it would be impossible to reproduce the cos^2 relationship between the angles of the two polarizers in classical optics, despite the fact that Malus' law applies in classical optics. Do you disagree? In post #896 I outlined some ways you might design a detector to yield one of two binary outcomes in an experiment based on classical optics:

You are free to design your detectors in a classical optics experiment so that they can only yield two outcomes rather than a continuous range of intensities--for example, you design it so that if the intensity of the light that made it through the polarizer was above a certain threshold a red light would go off, and if the intensity was at or below that threshold a green light would go off. Likewise you might design the detector so the probability or a red light going off vs. a green light going off would depend on the reduction in intensity as the light went through the polarizer--say if the intensity was reduced by 70%, there'd be a 70% chance the red light would go off and a 30% chance the green light would go off.

But no matter how you design your classical detector to give one of two binary outcomes based on how much light passes through it, you can never get a violation of the Bell inequalities in classical optics.

 

[my_wan]

"One to one quantitative correspondence" between what and what? the cos^2 in Malus' law is for the difference between the angle of a polarizer and the polarization angle of a beam hitting it at the same location, the cos^2 in entanglement experiments is for the difference in angles between two polarizers at completely different locations making measurements on different particles. There's no way to use the first cos^2 law to derive the second one, whatever ThomasT may think.

Of course the polarizer at the same location in the classic optics case, with no path references for individual photons. That's one of the reasons EPR correlations are sensitive to certain realism claims that standard optics is not. The quantitative correspondence results when you apply the same same location rules to the photon polarizers interactions plus standard conservation requiring photon pairs be anticorrelated, if you insist on rotational invariance at every level. These two conditions lead to an apparent contradiction between the statics we invariable measure and the statistics and the statistics we apparently would have gotten using any other choice of settings besides what we actually measured, if the path through the polarizer was a real property of the photon.

Why a "greater range of presumptions"? Standard optics can be derived from Maxwell's laws, which is a perfect example of a local realist theory of physics, so Bell's theorem definitely applies to anything in optics (and it's impossible to use classical optics to get a violation of Bell inequalities).

The "greater range of presumptions" allowed is because the standards optics case alone does not have a reference case to question (in principle) how this set of photons would have been detected had we chosen detector settings differently. Maxwell's equations also described fields, leaving the particle behavior more or less out. How would you define the set of all individual variables such a field can define?

Note the original EPR paper hinged on conservation law. The randomized polarizations of the emitter alone statistically demands rotational invariance, irrespective of any underlying mechanism. Thus Malus law + conservation + statistical rotational invariance does lead to the same statistical contradictions.

We are left with a *fundamentally* statistical theory in which statistical outcomes can be deterministically determined in some cases, but lacks variables that can even in principle explain how the outcomes are predetermined.

Malus' law is only based on the difference in angle between the beam and the polarizer, so it doesn't get violated depending on how your coordinate system defines the angle of the beam. Are you suggesting otherwise?

EXACTLY! Malus law is dependent only on the angle difference. Now note: A randomly polarized emitter physically must, irrespective of and underlying or lack of mechanism, be rotational invariant. So as long as 3 rules always apply, Malus law, rotational invariance, and conservation law, then BI violations must occur. If, statistically, rotational invariance applies, as it physically must for a randomly polarized beam, it does not mean the individual events defined by individual detections must also be rotational invariant, any more than Malus law.

I'm not entirely convinced by my own arguments, but I would appreciate more than hand waving the issues. Now, to argue against this, two things would be acceptable and appreciated:
1) Reject that rotational invariance can be induced simply by randomizing the polarization of the emitter, and explain why.
2) Accepting 1), explain why, if Malus law is dependent solely on angle difference and rotational invariance is dependent solely on randomized polarizations (not individual detection events), it could be expected that EPR correlations should depend on more than just the angle difference between the detector pairs.

You could also try to show that Malus law can be applied to any coordinate rotation rather than just a difference in rotation. You could also try to explain why Malus law + conservation + statistical rotational invariance does not lead to the same statistical contradictions.

 

[JesseM]

The quantitative correspondence results when you apply the same same location rules to the photon polarizers interactions plus standard conservation requiring photon pairs be anticorrelated, if you insist on rotational invariance at every level.

Again, "quantitative correspondence" between what and what? Are you claiming that if we "apply the same same location rules to the photon polarizers interactions plus standard conservation requiring photon pairs be anticorrelated", that uniquely leads us to the statistics seen in QM? If so, what "same location rules" are you talking about, given that Malus' law deals with continuous decreases in intensity rather than the binary fact about whether a photon passes through a polarizer?

Note the original EPR paper hinged on conservation law. The randomized polarizations of the emitter alone statistically demands rotational invariance, irrespective of any underlying mechanism. Thus Malus law + conservation + statistical rotational invariance does lead to the same statistical contradictions.

Well, see above, it's not clear to me what you mean by "Malus law" in the context of detecting individual photons rather than looking at how the intensity of an electromagnetic wave changes when it passes through a polarizer.

 

[my_wan]

Again, "quantitative correspondence" between what and what? Are you claiming that if we "apply the same same location rules to the photon polarizers interactions plus standard conservation requiring photon pairs be anticorrelated", that uniquely leads us to the statistics seen in QM? If so, what "same location rules" are you talking about, given that Malus' law deals with continuous decreases in intensity rather than the binary fact about whether a photon passes through a polarizer?

I'm only looking at how a photon responds to the polarizer it comes in contact with irrespective of what a distant correlated photon does, which requires Malus law in all cases. This also entails that a detector offset from the default photon polarization has some likelihood of passing that photon 'as if' it possessed that polarization. These odds defined by Malus law. Now to add an assumption: these photons have properties that predetermine how they will respond to any polarizer setting, such that an identical twin photon would have responded to a polarizer with the same arbitrary setting the same way. Opposite for anti-twins. Now, as long as the properties of the photons in the beam is, as a group, randomized such that rotational invariance must be maintained, and Malus law (with relative offsets) is required for all cases, the predeterminism assumption leads to BI violations, irrespective of any other consideration.

Here's the challenge: you CANNOT construct a local deterministic variable set, independent of QM, BI, etc., that respects Malus law for any arbitrary setting and rotational invariance without violating BI. You will invariably be stuck with the same relative offset requirements that Malus law is predicated on. This results without any reference to QM whatsoever. The effect may be local, at the point where photon meets polarizer, but the counterfactual requirement that the photon polarizer interaction is predetermined in all cases is effectively equivalent to what an anti-twin is doing light years away.

Are you seeing the difficulty here, when the impossibility logic is turned on its head? The same impossibility Bell demonstrated also points to an impossibility of maintaining Malus law without violating BI. Of course, as you noted, Malus law can be derived from Maxwell's equations, which is a classical field theory. So, unless you can deny the validity of the challenge, what does this say about the "reality" of classical fields? Perhaps the deterministic variables are transfinite? I don't know, but if you can successfully reject the validity of the challenge I'll be indebted to you.

 

[DrChinese]

Are you seeing the difficulty here, when the impossibility logic is turned on its head? The same impossibility Bell demonstrated also points to an impossibility of maintaining Malus law without violating BI. Of course, as you noted, Malus law can be derived from Maxwell's equations, which is a classical field theory. So, unless you can deny the validity of the challenge, what does this say about the "reality" of classical fields? .

Yes, this is true (about Malus). However, this has nothing to do with some kind of "challenge" or impossiblity. Your logic does not work:

Malus-> Bell Inequality violation
QM-> Malus-> Bell Inequality violation

This is perfectly reasonable.

 

[my_wan]

Yes, this is true (about Malus). However, this has nothing to do with some kind of "challenge" or impossiblity. Your logic does not work:

Malus-> Bell Inequality violation
QM-> Malus-> Bell Inequality violation

This is perfectly reasonable.

Not real sure I follow. Not even sure how to guess what you intended to say. My best guess is your saying "QM-> Malus-> Bell Inequality violation" is "perfectly reasonable", but still can't grok your intended meaning with any confidence.

If your summing up what I said as "Malus-> Bell Inequality violation" it's more than a little overly simplified, as is the implicit QM and BI issues. Are you saying that "Malus-> Bell Inequality violation" doesn't work, while "QM-> Malus-> Bell Inequality violation" does?

What I'm saying is that, even if you forget everything you know about QM, and merely try to construct a local realistic variable set that respects Malus law without violating BI, you can't do it. It is you who keeps insisting the similarity between Malus law and QM is an illusion, yet here I am presumptuously interpreting you to say Malus law is a QM law.

Here's an example of what you can't do. Define a set of photons with predefined properties which entails that 50% of all randomly polarized photons are predetermined to pass a polarizer at any angle. Then require the predetermined photon paths to switch paths through the polarizer according to Malus law as you rotate the polarizer. Now try and get this same predefined set of photons to continue honoring Malus law when you pick a pair of counterfactual detector setting in which neither setting is 0. It will not work, and this doesn't even involve correlations, only paths taken by a predefined set of photons through a variable polarizer setting. Without correlation you don't have a uniquely QM phenomena, yet BI violation persist in simple classical paths through a polarizer.

Does it now make sense why the QM requirement (I think) you imposed is not necessary for BI? Not even correlations are required, only assumptions of classical paths. Of course Maxwell's equations, in spite of being a classical construct, has no requirement of presuming photon trajectories represent a classical path, due to its field theoretic construction.

 

[JesseM]

I'm only looking at how a photon responds to the polarizer it comes in contact with irrespective of what a distant correlated photon does, which requires Malus law in all cases.

How does Malus' law apply to individual photons, though? The classical version of Malus' law requires uniformly polarized light with a known polarization angle, are you talking about a photon that's known to be in a polarization eigenstate for a polarizer at some particular angle? In that case, whatever the angle v of the eigenstate, I think the probability the photon would pass through another angle at angle a would be cos^2(v-a). But when entangled photons are generated, would they be in such a known polarization eigenstate? If not it seems like you wouldn't be able to talk about Malus' law applying to individual members of the pair.

Of course, as you noted, Malus law can be derived from Maxwell's equations, which is a classical field theory. So, unless you can deny the validity of the challenge, what does this say about the "reality" of classical fields? Perhaps the deterministic variables are transfinite? I don't know, but if you can successfully reject the validity of the challenge I'll be indebted to you.

But with electromagnetic waves in Maxwell's equations there's no probabilities involved, Malus' law just represents a deterministic decrease in intensity. So there's no case where two detectors at different angles a and b have a probability cos^2(a-b) of opposite results, including the fact that they give opposite results with probability 1 with the detectors at the same angle. This is true even if you design the detectors to give one of two possible outputs depending on the decrease in intensity, as I suggested in post #896 to ThomasT. So no violations of BI and no reason Maxwell's laws can't be understood as a local realist theory, so I'm not sure why you have a problem with the reality of classical fields.

 

[DrChinese]

Not real sure I follow. Not even sure how to guess what you intended to say. My best guess is your saying "QM-> Malus-> Bell Inequality violation" is "perfectly reasonable", but still can't grok your intended meaning with any confidence.

If your summing up what I said as "Malus-> Bell Inequality violation" it's more than a little overly simplified, as is the implicit QM and BI issues. Are you saying that "Malus-> Bell Inequality violation" doesn't work, while "QM-> Malus-> Bell Inequality violation" does?

What I'm saying is that, even if you forget everything you know about QM, and merely try to construct a local realistic variable set that respects Malus law without violating BI, you can't do it. It is you who keeps insisting the similarity between Malus law and QM is an illusion, yet here I am presumptuously interpreting you to say Malus law is a QM law.

Here's an example of what you can't do. Define a set of photons with predefined properties which entails that 50% of all randomly polarized photons are predetermined to pass a polarizer at any angle. Then require the predetermined photon paths to switch paths through the polarizer according to Malus law as you rotate the polarizer. Now try and get this same predefined set of photons to continue honoring Malus law when you pick a pair of counterfactual detector setting in which neither setting is 0. It will not work, and this doesn't even involve correlations, only paths taken by a predefined set of photons through a variable polarizer setting. Without correlation you don't have a uniquely QM phenomena, yet BI violation persist in simple classical paths through a polarizer.

Does it now make sense why the QM requirement (I think) you imposed is not necessary for BI? Not even correlations are required, only assumptions of classical paths. Of course Maxwell's equations, in spite of being a classical construct, has no requirement of presuming photon trajectories represent a classical path, due to its field theoretic construction.

OK, ask this: so what if Malus rules out local realistic theories per se? You are trying to somehow imply that is not reasonable. Well, it is.

We don't live in a world respecting BIs while we do live in one which Malus is respected. There is no contradiction whatsoever. You are trying to somehow say Malus is classical but it really isn't. It is simply a function of a quantum mechanical universe. So your logic needs a little spit polish.

 

[billschnieder]

If you are doing an experiment which matches the condition of the Bell inequalities that says each measurement must yield one of two binary results...

This requirement by itself is unreasonable because according to Malus law, it is normal to expect that some photons will not go through the polarizer. Therefore Bell's insistence on having only binary outcomes (+1, -1) goes off the boat right from the start. He should have included a non-detection outcome too.

 

[DevilsAvocado]

(my emphasis)

... Yes, of course I disagree, you're just totally misunderstanding the most basic logic of the proof which is assuming a perfect correlation between A and B whenever both experimenters choose the same detector setting. It's really rather galling that you make all these confident-sounding claims about Bell's proof being flawed when you fail to understand something so elementary about it! Could you maybe display a tiny bit of intellectual humility and consider the possibility that it might not be that the proof itself is flawed and that you've spotted a flaw that so many thousands of smart physicists over the years have missed, that it might instead be you are misunderstanding some aspects of the proof?

JesseM, thank you so very much for these very intelligent and well expressed words! You’ve hit the nail! THANKS!

And I can guarantee you that you are not the only one exasperated on ThomasT’s general attitude.

 

[my_wan]

OK, ask this: so what if Malus rules out local realistic theories per se? You are trying to somehow imply that is not reasonable. Well, it is.

We don't live in a world respecting BIs while we do live in one which Malus is respected. There is no contradiction whatsoever. You are trying to somehow say Malus is classical but it really isn't. It is simply a function of a quantum mechanical universe. So your logic needs a little spit polish.

The claim that my logic needs a little spit polish is absolutely valid. That's part of why I debate these issues here, to articulate clear my own thinking on the matter.

I'm not making claims about what is or isn't reasonable. Here's the thing, so long as the terms "local" and "realistic" are well defined to be restricted to X and Y conceptions of those terms, I have no issue with the claim that X and/or Y conceptions are invalid. To generalize that claim as evidence that all conception of those terms is likewise invalid is technically dishonest. Reasonable? Perhaps.., but also presumptuous. It may not rise to the level of presumptuousness the realist in general tend toward, but I find it no less distasteful. It would likewise be a disservice to academically lock those terms as representative of certain singular conceptions.

Then there is a more fundamental theoretical issue. Correctly identifying the issues leading to certain empirical results can play an essential role in extending theory in unpredictable ways. To simply imply that if Malus alone can lead to BI violations is a vindication of some status quo interpretation is unwarranted. Your concretion is misplaced. Often the point of questioning the reason X is false is not to establish a claim of its truth value, but to gain insight to a wider range of questions. Teachers that would respond to enumerations of all the possible reasons something was false with: but the point is that it's false, missed the point entirely.

So, in spite of the justifications implied by Malus consequences lacking contradiction, what does it indicate when a preeminent classical theoretical construct predicts a consequence that violates BI? It certainly does NOT indicate that realism, as narrowly defined by EPR and Bell, erred in ruling out a particular form of realism. It does in fact question the generalization of BI to a broader range of conceptions of realism. It also directly brings into question the relevance of nonlocality, when the polarizer path version, resulting from a classical field construct, doesn't even have an existential partner to correlate with. The difficulties might even be a mathematical decomposition limitation, some akin to a la Gödel maybe? It also begs the question, if Maxwell's equations can produce a path version of BI violations, what besides quanta and the Born rule is fundamentally unique to QM, notwithstanding the claim of being fundamental?

I don't have the answers, but I'm not going to restrict myself to BI tunnel vision either.

 

[JesseM]

This requirement by itself is unreasonable because according to Malus law, it is normal to expect that some photons will not go through the polarizer. Therefore Bell's insistence on having only binary outcomes (+1, -1) goes off the boat right from the start. He should have included a non-detection outcome too.

I'm pretty sure that in experiments with entangled photons, there is a difference between non-detection and not making it through the polarizer. For example, if you look at the description and diagram of a "typical experiment" in this section of the wikipedia article on Bell test loopholes, apparently if the two-channel polarizer like "a" doesn't allow a photon through to be detected at detector D+, it simply deflects it at a different angle to another detector D-, so the photon can be detected either way.

 

[my_wan]

Had to get some sleep after that last post, I go too long sometimes.

How does Malus' law apply to individual photons, though? The classical version of Malus' law requires uniformly polarized light with a known polarization angle, are you talking about a photon that's known to be in a polarization eigenstate for a polarizer at some particular angle? In that case, whatever the angle v of the eigenstate, I think the probability the photon would pass through another angle at angle a would be cos^2(v-a). But when entangled photons are generated, would they be in such a known polarization eigenstate? If not it seems like you wouldn't be able to talk about Malus' law applying to individual members of the pair.

Yes, I'll restate this again. This is the statistics I have verified as an exact with Malus law expressed sole in terms of intensity for all pure or mixed polarization state beams, as well as cases of passage through arbitrary multiple polarizers. Malus consistency is predicated on modeling intensity, but it even perfectly models EPR correlations with the caveats given. It's a straight up assumption that individual photons, randomly polarized as a group or not, has a very definite default polarization. The default polarization is unique only in that it is the only polarization at which a polarizer with a matching setting effectively has a 100% chance of passing that photon. The odds of any given photon passing a polarizer that is offset from that default is defined by a straight up assumption that ∆I (intensity) constitutes a ∆p (odds), i.e., for any arbitrary theta offset from the individual photons default ∆I = ∆p.

But with electromagnetic waves in Maxwell's equations there's no probabilities involved, Malus' law just represents a deterministic decrease in intensity. So there's no case where two detectors at different angles a and b have a probability cos^2(a-b) of opposite results, including the fact that they give opposite results with probability 1 with the detectors at the same angle. This is true even if you design the detectors to give one of two possible outputs depending on the decrease in intensity, as I suggested in post #896 to ThomasT. So no violations of BI and no reason Maxwell's laws can't be understood as a local realist theory, so I'm not sure why you have a problem with the reality of classical fields.

Yes, neither does Maxwell's equations explicitly recognize the particle aspect of photons, thus lacked any motivation for assigning probabilities to individual photons. But as noted, ∆I = ∆p perfectly recovers the proper Malus predicted intensities in all pure and mixed state beams, as well as ∆I in stacked (series) polarizer cases. The EPR case is a parallel case involving anti-twins.

At no point, in modeling Malus intensities or EPR correlation, did I use cos^2(a-b), where a and b represented different polarizers. I've already argued with ThomasT over this point. I used cos^2(theta), where theta is defined solely as the offset of the polarizer relative to the photon that actually comes in contact with that polarizer. In fact, since the binary bit field that predetermined outcomes already had cos^2(theta) statistically built in, I didn't even have to calc cos^2(theta) at detection time. I merely did a linear one to one count into the bit field defined by theta (between polarizer and the photon that actually came in contact with it) alone, took that bit and passed it if it was a 1, diverted if 0. I used precisely the same rules, in the computer models, in both Malus intensity and parallel EPR cases, and only compared EPR correlations after the fact.

To clarify, the bit field I used to predetermine outcomes, to computer model both Malus intensities and EPR parallel cases, set a unique bit for each offset, such that a photon that passed at a given offset could sometimes fail at a lesser offset. The difficulties arose only the the EPR modeling case when it only successfully modeled BI violations correlations when one or the other detector was defined as 0. Yet uniformly rotating the default polarizations of the randomly polarized beam changed which individual photons took what path it had no effect whatsoever on the BI violated statistics. The EPR case, like the Malus intensities, was limited to relative coordinates only wrt detector settings. Absolute values didn't work, in spite of the beam rotation statistical invariance with individual photon path variance.

Maxwell's equations didn't assign a unique particulate identity to individual photons. Yet, if consider classically distinct paths as a real property of a particulate photon (duality), you can construct BI violations from path assumptions required to model Malus law. It's easy to hand wave away when were talking a local path through a local polarizer, until you think about it. In fact the path version of BI violation only become an issue when you require absolute arbitrary coordinates, rather than relative offsets, to model. The same issue that is the sticking point in modeling EPR BI violations.

 

[my_wan]

I was looking over DrC's Frankenstein particles and read the wiki page JesseM linked:
http://en.wikipedia.org/wiki/Loopholes_in_Bell_test_experiments
Where it mentions a possible failure of of rotational invariance and realized it should be possible, if the Malus law assumptions I used is valid, to construct a pair of correlated beams that explicitly fails rotational invariance.

I need to think through it more carefully, but it would involve using a PBS to split both channels from the source emitter. Use a shutter to selectively remove some percentage of both correlated pairs of a certain polarization, and recombine the remainder. Similar to DrC's Frankenstein setup. Done such that all remaining photons after recombination should have a remaining anti-twin, which, as a group, has a statistically preferred polarization. The only photons that can be defined as observed, and their partners, are no longer present in the beam to effect the correlation statistics. Then observe the effects on correlation statistics at various common detector settings and offsets. The possible variations of this is quiet large.

Edit: A difficulty arises when you consider that while photons are being being shuttered in one side of the polarized beam, before recombination, any photon that takes the other path at that time can be considered detected. Non-detection in QM can sometime qualify as a detection in QM.

 

[ThomasT]

... it might instead be you are misunderstanding some aspects of the proof ...

Of course, that's why I'm still asking questions.

The joint probability P(AB) is not being modeled as the product of P(A)*P(B) by Bell's equation.

My thinking has been that it reduces to that. Just a stripped down shorthand for expressing Bell's separability requirement. If you don't think that's ok, then how would you characterize the separability of the joint state (ie., the expression of locality) per Bell's (2)?

I would characterize it in terms of A and B being statistically independent only when conditioned on the value of the hidden variable λ. They are clearly not statistically independent otherwise ...

A and B are not independent in their marginal probabilities (which determine the actual observed frequencies of different measurement outcomes), only in their probabilities conditioned on λ.

Ok, you seem to be saying that P(AB)=P(A) P(B) isn't an analog of Bell's (2). You also seem to be saying that Bell's (2) models A and B as statistically independent for all joint settings except (a-b)=0. Is this correct?

My thinking has been that Bell's(2) is a separable representation of the entangled state, and that this means that it models the joint state in a factorable form. Is this correct? If so, then is this the explicit expression of Bell locality in Bell's (2).

 

[DevilsAvocado]

JesseM, please correct me if I’m wrong, but haven’t you already answer the question above perfectly clear??

... Yes, and this was exactly the possibility that Bell was considering! If you don't see this, then you are misunderstanding something very basic about Bell's reasoning. If A and B have a statistical dependence, so P(A|B) is different than P(A), but this dependence is fully explained by a common cause λ, then that implies that P(A|λ) = P(A|λ,B), i.e. there is no statistical dependence when conditioned on λ. That's the very meaning of equation (2) in Bell's original paper, that the statistical dependence which does exist between A and B is completely determined by the state of the hidden variables λ, and so the statistical dependence disappears when conditioned on λ. Again, please tell me if you disagree with this.

Could we also make it as simple that even a 10-yearold can understand, by stating:

Bell's(2) is not about entanglement, Bell's(2) is only about the Hidden variable λ.​

 

[JesseM]

Of course, that's why I'm still asking questions.

I'm glad you're still asking questions, but if you don't really understand the proof, and you do know it's been accepted as valid for years by mainstream physicists, doesn't it make sense to be a little more cautious about making negative claims about it like this one from an earlier post?

I couldn't care less if nonlocality or ftl exist or not. In fact, it would be very exciting if they did. But the evidence just doesn't support that conclusion.

On to the topic of probabilities:

Ok, you seem to be saying that P(AB)=P(A) P(B) isn't an analog of Bell's (2). You also seem to be saying that Bell's (2) models A and B as statistically independent for all joint settings except (a-b)=0. Is this correct?

No. In any Bell test, the marginal probability of getting either of the two possible results (say, spin-up and spin-down) should always be 0.5, so P(A)=P(B)=0.5. But if you're doing an experiment where the particles always give identical results with the same detector setting, then if you learn the other particle gave a given result (like spin-up) with detector setting b and you're using detector setting a, then the conditional probability your particle gives the same result is cos^2(a-b). So if A and B are identical results, in this case P(AB)=P(B)*P(A|B)=0.5 * cos^2(a-b), so as long as a and b have an angle between them that's something other than 45 degrees (since cos^2(45) = 0.5), P(AB) will be different than P(A)*P(B), and there is a statistical dependence between them.

My thinking has been that Bell's(2) is a separable representation of the entangled state, and that this means that it models the joint state in a factorable form. Is this correct? If so, then is this the explicit expression of Bell locality in Bell's (2).

It shows how the joint probability can be separated into the product of two independent probabilities if you condition on the hidden variables λ. So, P(AB|abλ)=P(A|aλ)*P(B|bλ) can be understood as an expression of the locality condition. But he obviously ends up proving that this doesn't work as a way of modeling entanglement...it's really only modeling a case where A and B are perfectly correlated (or perfectly anticorrelated, depending on the experiment) whenever a and b are the same, under the assumption that there is a local explanation for this perfect correlation (like the particles being assigned the same hidden variables by the source that created them).

 

[DrChinese]

The claim that my logic needs a little spit polish is absolutely valid. That's part of why I debate these issues here, to articulate clear my own thinking on the matter.

That is why I participate too.

 

[DrChinese]

This requirement by itself is unreasonable because according to Malus law, it is normal to expect that some photons will not go through the polarizer. Therefore Bell's insistence on having only binary outcomes (+1, -1) goes off the boat right from the start. He should have included a non-detection outcome too.

Not with beam splitters! (Non-detection is not an issue ever, as we talk about the ideal case. Experimental tests must consider this.)

 

[DrChinese]

I want to make an important statement that counters the essence of some of the arguments being presented about "non-detections" or detector effeciency.

A little thought will tell you why this is not much of an issue. If we have a particle pair A, B and we send them through a beam splitter with detectors at both output ports, we should end up with one of the following 4 cases:

1. A not detected, B not detected.
2. A detected, B not detected.
3. A not detected, B detected.
4. A detected, B detected.

However we won't actually know when case 1 occurs, correct? But unless the chance of 1 is substantially greater than either 2 or 3 individually (and probability logic indicates it should be definitely less - can you see why?), then we can estimate it. If case 4 occurs 50% of the time or more, then 1 should occur less than 10% of the time. This is in essence a vanishing number, since visibility is approaching 90%. That means cases 2 and 3 are happening only about 1 in 10, which would imply case 1 of about 1%.

So you have got to claim all of the "missing" photons are carrying the values that would prove a different result. And this number is not much. I guess it is *possible* if there is a physical mechanism which is responsible for the non-detections, but that would also make it experimentally falsifiable. But you should be aware of how far-fetched this really is. In other words, in actual experiments cases 2 and 3 don't occur very often. Which places severe constraints on case 1.

 

[DevilsAvocado]

It shows how the joint probability can be separated into the product of two independent probabilities if you condition on the hidden variables λ. So, P(AB|abλ)=P(A|aλ)*P(B|bλ) can be understood as an expression of the locality condition. But he obviously ends up proving that this doesn't work as a way of modeling entanglement...it's really only modeling a case where A and B are perfectly correlated (or perfectly anticorrelated, depending on the experiment) whenever a and b are the same, under the assumption that there is a local explanation for this perfect correlation (like the particles being assigned the same hidden variables by the source that created them).

This must mean that my "10-yearold explanation" is correct, and hopefully this information can even make sense to ThomasT:

Bell's(2) is not about entanglement, Bell's(2) is only about the Hidden variable λ.​

No. In any Bell test, the marginal probability of getting either of the two possible results (say, spin-up and spin-down) should always be 0.5, so P(A)=P(B)=0.5. But if you're doing an experiment where the particles always give identical results with the same detector setting, then if you learn the other particle gave a given result (like spin-up) with detector setting b and you're using detector setting a, then the conditional probability your particle gives the same result is cos^2(a-b). So if A and B are identical results, in this case P(AB)=P(B)*P(A|B)=0.5 * cos^2(a-b), so as long as a and b have an angle between them that's something other than 45 degrees (since cos^2(45) = 0.5), P(AB) will be different than P(A)*P(B), and there is a statistical dependence between them.

Could we make a 'simplification' of this also, and say:

According to QM predictions, all depends on the relative angle between the polarizers a & b. If measured parallel (0º) or perpendicular (90º) the outcome is perfectly correlated/anticorrelated. In any other case, it’s statistically correlated thru QM predictions cos^2(a-b).

Every outcome on every angle is perfectly random for A & B, with one 'exception' for parallel and perpendicular, where the outcome for A must be perfectly correlated/anticorrelated to B (still individually perfectly random).​

Correct?

 

[DevilsAvocado]

... However we won't actually know when case 1 occurs, correct?

DrC, could you help me out? I must be stupid...

If we use a beam splitter, then we always get a measurement, unless something goes wrong. Doesn’t this mean we would know that case 1 has occurred = nothing + nothing??

 

[DrChinese]

DrC, could you help me out? I must be stupid...

If we use a beam splitter, then we always get a measurement, unless something goes wrong. Doesn’t this mean we would know that case 1 has occurred = nothing + nothing??

That is the issue everyone is talking about, except it really doesn't fly. Normally, and in the ideal case, a photon going through a beam splitter comes out either the H port or the V port. Hypothetically, photon Alice might never emerge in line, or might not trigger the detector, or something else goes wrong. So neither of the 2 detectors for Alice fires. Let's say that happens 1 in 10 times, and we can see it happening because one of the Bob detectors fires.

Ditto for Bob. There might be a few times in which the same thing happens on an individual trial for both Alice and Bob. If usual probability laws are applied, you might expect something like the following:

Neither detected: 1%.
Alice or Bob not detected, but not both: 18%.
Alice and Bob both detected: 81%.

I would call this visibility of about 90% which is about where things are at in experiments these days. But you cannot say FOR CERTAIN that the 1 case only occurs 1% of the time, you must estimate using an assumption. But if you *assert* that the 1 case occurs a LOT MORE OFTEN than 1% and you STILL have a ratio of 81% to 18% per above (as these are experimentally verifiable of course), then you have a lot of explaining to do.

And you will need all of it to make a cogent argument to that effect. Since any explanation will necessarily be experimentally falsifiable. The only way you get around this is NOT to supply an explanation. Which is the usual path when this argument is raised. So visibility is a function of everything involved in the experiment, and it is currently very high. I think around 85% + range but it varies from experiment to experiment. I haven't seen good explanations of how it is calculated or I would provide a reference. Perhaps someone else knows a good reference on this.

 

[JesseM]

This must mean that my "10-yearold explanation" is correct, and hopefully this information can even make sense to ThomasT:

Bell's(2) is not about entanglement, Bell's(2) is only about the Hidden variable λ.​

Basically I'd agree, although I'd make it a little more detailed: (2) isn't about entanglement, it's about the probabilities for different combinations of A and B (like A=spin-up and B=spin down) for different combinations of detector settings a and b (like a=60 degrees, b=120 degrees), under the assumption that there is a perfect correlation between A and B when both sides use the same detector setting, and that this perfect correlation is to be explained in a local realist way by making use of hidden variable λ.

Could we make a 'simplification' of this also, and say:

According to QM predictions, all depends on the relative angle between the polarizers a & b. If measured parallel (0º) or perpendicular (90º) the outcome is perfectly correlated/anticorrelated. In any other case, it’s statistically correlated thru QM predictions cos^2(a-b).

Every outcome on every angle is perfectly random for A & B, with one 'exception' for parallel and perpendicular, where the outcome for A must be perfectly correlated/anticorrelated to B (still individually perfectly random).​

Correct?

By "perfectly random" you just mean that if we look at A individually or B individually, without knowing what happened at the other one, then there's always an 0.5 chance of one result and an 0.5 chance of the opposite result, right? (so P(A|a)=P(B|b)=0.5) And this is still just as true when talk about the "exception" case of parallel or perpendicular detectors (as you point out when you say 'still individually perfectly random'), so it could be a little misleading to call this an "exception", but otherwise I have no problem with your summary.

 

[DevilsAvocado]

... I haven't seen good explanations of how it is calculated or I would provide a reference. Perhaps someone else knows a good reference on this.

Thanks for the info DrC.

 

[DevilsAvocado]

... this perfect correlation is to be explained in a local realist way by making use of hidden variable λ.

Yes, this is obviously the key.

By "perfectly random" you just mean that if we look at A individually or B individually, without knowing what happened at the other one, then there's always an 0.5 chance of one result and an 0.5 chance of the opposite result, right? (so P(A|a)=P(B|b)=0.5) And this is still just as true when talk about the "exception" case of parallel or perpendicular detectors (as you point out when you say 'still individually perfectly random'), so it could be a little misleading to call this an "exception", but otherwise I have no problem with your summary.

Correct, that’s what I meant. Thanks!

 

[billschnieder]

Not with beam splitters! (Non-detection is not an issue ever, as we talk about the ideal case. Experimental tests must consider this.)

1) Non-detection is present in every bell-test experiment ever performed
2) The relevant beam-splitters are real ones used in real experiments, not idealized ones that have never and can never be used in any experiment.

Bell should still have considered non-detection as one of the outcomes in addition to (-1, and +1). If you are right that non-detection is not an issue, the inequalities derived by assuming there are three possible outcomes right from the start, should also be violated. But if you do this and end up with an inequality that is no longer violated, then non-detection IS an issue.

 

[billschnieder]

A little thought will tell you why this is not much of an issue. If we have a particle pair A, B and we send them through a beam splitter with detectors at both output ports, we should end up with one of the following 4 cases:

1. A not detected, B not detected.
2. A detected, B not detected.
3. A not detected, B detected.
4. A detected, B detected.

Correct.
In Bell's treatment, only case 4 is considered, the rest are simply ignored or assumed to not be possible.

However we won't actually know when case 1 occurs, correct? But unless the chance of 1 is substantially greater than either 2 or 3 individually (and probability logic indicates it should be definitely less - can you see why?), then we can estimate it. If case 4 occurs 50% of the time or more, then 1 should occur less than 10% of the time. This is in essence a vanishing number, since visibility is approaching 90%. That means cases 2 and 3 are happening only about 1 in 10, which would imply case 1 of about 1%.

This is not even wrong. It is outrageous. Case 1 corresponds to two photons leaving the source but none detected, cases 2-3 correspond to two photons leaving the source and only one detected on any of the channels. In Bell test experiments, coincidence-circuitry eliminates 1-3 from consideration because there is no way in the inequalities to include that information. The inequalities are derived assuming that only case 4 is possible.

To determine likelihood of each case from relative frequencies, you will need to count that specific case, and divide by the total number for all cases (1-5), or alternatively, all photon pairs leaving the source. Therefore, the relative frequency will be the total number of the specific case observed divided by the total number of photon pairs produced by the source.
ie: P(caseX) = N(caseX) / { N(case1) + N(case2) + N(case3) + N(case4)}

If you are unable to tell that case 4 has occurred, then you can never know what proportion of the particle pairs resulted in any of the cases, because N(case4) is part of the denominator!

So when you say "if case 4 occurs 50% of the time", you have to explain what represents 100%.
for example consider the following frequencies, for the case in which 220 particle pairs are produced and we have:

case 1: 180
case 2: 10
case 3: 10
case 4: 20

Since according to you, we can not know when case 1 occurs, then our total is only (40)
according to you, P(case4) = 50% and P(case2) = 25% P(case 3) = 25%
according to you, P(case1) should be vanishingly small since P(case4) is high.

But as soon as you realize that our total is actually 220 not 40 as you mistakenly thought,
P(case1) now becomes 82%, for exactly the same experiment, just by correcting the simple error you made.
It is even worse with Bell because according to him, cases 1-3 do not exist so his P(case4) is 100%, since considering even only case 2 and 3 as you suggested would required including a non-detection outcome as well as (+1 and -1).

Now that this blatant error is clear, let us look at real experiments to see which approach is more reasonable, by looking at what proportion of photons leaving the source is actually detected.

For all Bell-test experiments performed to date, only 5-30% of the photons emitted by the detector have been detected, with only one exception. And this exception, which I'm sure DrC and JesseM will remind us of, had other more serious problems. Let us make sure we are clear what this means.

It means of almost all those experiments usually thrown around as proof of non-locality, P(case4) has been at most 30% and even as low as 30% in some cases. The question then is, where did the whopping 70% go?

Therefore it is clear first of all by common sense, then by probability theory, and finally confirmed by numerous experiments that non-detection IS an issue and should have been included in the derivation of the inequalities!