Why is superdeterminism not the universally accepted explanation of nonlocality?

[lugita15]

The rate of individual detection doesn't vary with the measurement parameter, but the rate of coincidental detection does vary with the measurement parameter. So, what would you infer from this?

But there isn't some magical thing called "joint detection" or "coincidence detection". Rather, each experimenter just does individual detection of each photon, and records the results. We draw conclusions about the "rate of coincidental detection" AKA the correlation based on the results of individual detections. Since there is no such thing as coincidence detection, and correlation is nothing but correlation of individual detections, an analysis of entanglement cannot consist, even in principle, of anything other than asking what determines the results of individual detection.

 

[Joncon]

If you could phrase this a bit less anthropically, that would be helpful. Photons aren't people.

I agree, that's why I double-quoted "choose". Okay, to put it another way, what determines which function (individual/coincidental) is applied to the photons?

We're talking about different measurement parameters. Is it unreasonable to suppose that these different measurement parameters are measuring different underlying parameters?

But they're not different measurement parameters. Each photon has it's polarization measured. That's it.

 

[ThomasT]

But there isn't some magical thing called "joint detection" or "coincidence detection".

Who said anything about magic? The term rate of coincidental detection refers to a statistical accumulation, and that statistical accumulation varies as the measurement parameter varies. The term rate of individual detection also refers to a statistical accumulation, and that statistical accumulation doesn't vary as the measurement parameter varies. I asked what you might infer from this fact.

Since there is no such thing as coincidence detection, and correlation is nothing but correlation of individual detections ...

Of course there's such a thing as coincidence detection. What do you think Bell tests are about? The term Bell correlations refers to correlations between θ, the angular difference between the separated polarizers, and the rate of coincidental detection.

... an analysis of entanglement cannot consist, even in principle, of anything other than asking what determines the results of individual detection.

I would guess that that's what a lot of people think. And therein lies much of the confusion surrounding the meaning of Bell's theorem.

Anyway, of course an analysis of entanglement can consist of something other than asking what determines the results of individual detection. It starts with recognizing that the rates of individual and coincidental detection are determined by different parameters.

 

[ThomasT]

I agree, that's why I double-quoted "choose". Okay, to put it another way, what determines which function (individual/coincidental) is applied to the photons?

The measurement parameter.

But they're not different measurement parameters.

Yes they are. The orientation of an individual polarizer is a different measurement parameter than the angular difference between two polarizer orientations.

 

[lugita15]

Who said anything about magic? The term rate of coincidental detection refers to something, and that something varies as the measurement parameter varies. There's also something called rate of individual detection, and that something doesn't vary as the measurement parameter varies. I asked what you might infer from this fact.

But whatever these rates are, they do not arise full-grown from the head of Zeus, do they? They are calculated solely from the results of individual detections of photons. Thus the only thing that can affect these rates are those results. So explaining the "rate of coincidence detection" consists of another more and nothing less than explaining the results of individual detection.

Of course there's such a thing as coincidence detection. What do you think Bell tests are about? The term Bell correlations refers to correlations between θ, the angular difference between the separated polarizers, and the rate of coincidental detection.

There is no experimental procedure called "coincidence detection", so the term "rate of coincidence detection" is highly misleading. Coincidences aren't "detected" experimentally, they are a consequence of individual detections.

Anyway, of course an analysis of entanglement can consist of something other than asking what determines the results of individual detection. It starts with recognizing that the rates of individual and coincidental detection are determined by different parameters.

They are both entirely determined by the same thing, the results of individual detections; that is, whether photon A from pair N goes through the polarizer oriented at the angle θ, to which the answer is either yes or no. I don't know how you can possibly disagree with this.

 

[Joncon]

Yes they are. The orientation of an individual polarizer is a different measurement parameter than the angular difference between two polarizer orientations.

But when photon A encounters polarizer A there's no such thing as "angular difference between two polarizer orientations". A (photon or polarizer) has no knowledge of what is happening at B.

 

[ThomasT]

@ Joncon and lugita15,

I think this is a case of "not seeing the forest for the trees". There are two different measurement contexts to consider. The results wrt which are determined by different parameters, both measurement and assumed underlying.

I'm going to take a time out now. Please reread what I've written. Think about it some more. And I'll get back to you in a few hours.

 

[ThomasT]

But when photon A encounters polarizer A there's no such thing as "angular difference between two polarizer orientations".

Right, this is an individual measurement context. Do you think there's a difference between this measurement context and the one where coincidental detections are correlated with θ?

 

[ThomasT]

They are both entirely determined by the same thing ... I don't know how you can possibly disagree with this.

Read my most recent posts again. I'll get back to you.

 

[ThomasT]

There is no experimental procedure called "coincidence detection" ...

Sure there is. There's circuitry that matches detection attributes which operates according to calculations based on the photon emission source and the distance between the polarizers.

... so the term "rate of coincidence detection" is highly misleading. Coincidences aren't "detected" experimentally, they are a consequence of individual detections.

They're a consequence of matching individual detection attributes wrt calculated coincidence intervals.

Whether coincidental detections are counted 'on the fly' by circuitry built into the experimental design, or after the fact via time stamps, the fact is that the basic datum of entanglement setups (eg., Bell tests) is called coincidental detection, and the rate of coincidental detection varies as a function of θ, the angular difference between the polarizer settings.

So, given that the rate of individual detection doesn't vary as a function of polarizer setting, then what can you infer from this?

They are both entirely determined by the same thing ...

No. Incorrect inference. This doesn't follow from the known experimental results.

 

[lugita15]

Sure there is. There's circuitry that matches detection attributes which operates according to calculations based on the photon emission source and the distance between the polarizers.
They're a consequence of matching individual detection attributes wrt calculated coincidence intervals.

But these are just contingent facts about experimental design. Consider an idealized experiment where one photon pair is sent out every hour by a source which is exactly at the midpoint between two polarizers, which catch every single photon with perfect accuracy. In that case all each experimenter has as far as data goes is a list of yes or no answers as to whether the photon went through the polarizer or not. There are no time stamps, distance measurements, coincidence intervals, or anything like that.

Whether coincidental detections are counted 'on the fly' by circuitry built into the experimental design, or after the fact via time stamps, the fact is that the basic datum of entanglement setups (eg., Bell tests) is called coincidental detection, and the rate of coincidental detection varies as a function of θ, the angular difference between the polarizer settings.

No, in the Bell test setup I described above, the basic datum is whether the experimenter sees a photon go through the polarizer or not. I think the word "correlation" is a much better term for what you call the "rate of coincidental detection". It is just the correlation between individual polarization measurements of photons, and as such all its properties are determined by whatever determines the results of individual polarization measurements. And the nonlinear relationship between the correlation and the angle is also entirely determined by whatever determines whether a photon goes through a polarizer or not.

So, given that the rate of individual detection doesn't vary as a function of polarizer setting, then what can you infer from this?

All a local determinist might infer from this is that the decision of whether to go through the polarizer or not is based on some local hidden variable, but we human beings don't know the value of this variable, so to us it seems like an unpredictable 50-50 chance whether it will go through.

No. Incorrect inference. This doesn't follow from the known experimental results.

But the argument is not based on the known data from practical experiments done so far; if you wanted to respond to Bell's theorem in that way you could be like zonde, who believes that Bell tests to date have experimental loopholes, and that quantum mechanics will be disproved as soon as we improve our experimental capabilities. The argument I'm making is more fundamental: it is that it is impossible for a local determinist to believe that all the experimental predictions of quantum mechanics are correct, without regard to the practical difficulties of testing these predictions. It took us a while to do any Bell tests at all, but that did not change the validity of Bell's theorem.

 

[ThomasT]

There is no experimental procedure called "coincidence detection" ...

There's circuitry that matches detection attributes which operates according to calculations based on the photon emission source and the distance between the polarizers.

... so the term "rate of coincidence detection" is highly misleading. Coincidences aren't "detected" experimentally, they are a consequence of individual detections.

They're a consequence of matching individual detection attributes wrt calculated coincidence intervals.

But these are just contingent facts about experimental design. Consider an idealized experiment where one photon pair is sent out every hour by a source which is exactly at the midpoint between two polarizers, which catch every single photon with perfect accuracy. In that case all each experimenter has as far as data goes is a list of yes or no answers as to whether the photon went through the polarizer or not. There are no time stamps, distance measurements, coincidence intervals, or anything like that.

But my reply was in reply to your reply that "there's no experimental procedure called 'coincidence detection'. And of course there is an experimental procedure called coincidence detection.

And in reply to that you propose an idealized experiment that has nothing to do with what we're talking about.

The fact of the matter is that wrt Bell tests there are time stamps, distance measurements, and coincidence intervals. So, you're going to have to deal with them.

 

[lugita15]

But my reply was in reply to your reply that "there's no experimental procedure called 'coincidence detection'. And of course there is an experimental procedure called coincidence detection.

And in reply to that you propose an idealized experiment that has nothing to do with what we're talking about.

The fact of the matter is that wrt Bell tests there are time stamps, distance measurements, and coincidence intervals. So, you're going to have to deal with them.

But we're not talking about the practical ability of Bell tests today to definitively disprove local determinism. (There are of course several experimental loopholes to Bell, and people like zonde rely on them to cling onto a local deterministic view, accepting the fact that future experiments may disprove their views.) We're discussing the deeper issue of whether a local determinist can believe that all the experimental predictions of quantum mechanics are true, and that includes what QM has to say about idealized setups like the one I outlined.

 

[ThomasT]

... in the Bell test setup I described above, the basic datum is whether the experimenter sees a photon go through the polarizer or not.

That's the basic datum for rate of individual detection. Wrt rate of coincidental detection, the basic datum is coincidental detection.

I think the word "correlation" is a much better term for what you call the "rate of coincidental detection".

Rate of coincidental detection has a specific technical meaning. It doesn't, by itself, refer to correlation. It refers to rate of coincidental detection.

It is just the correlation between individual polarization measurements of photons, and as such all its properties are determined by whatever determines the results of individual polarization measurements.

That's just incorrect. Rate of coincidental detection certainly does not refer to the correlation between individual polarization measurements of photons.

Bell test correlations refers to the correlation between the angular difference between the polarizers and the rate of coincidental detection.

And the nonlinear relationship between the correlation and the angle is also entirely determined by whatever determines whether a photon goes through a polarizer or not.

Also incorrect.

Here's what's known. The rate of individual detection doesn't vary with polarizer orientation. The rate of coincidental detection does vary with the angular difference between polarizer orientation. How can these two different experimental contexts be measuring the same underlying parameter?

... the argument is not based on the known data from practical experiments done so far ...

Well, no, your argument isn't. No offense, but from what you've written it doesn't seem that you're all that knowledgeable about Bell tests. Is that the case?

If so, just admit it and then DrC et al. can help you learn about them. They certainly helped me. I'm still more or less quite ignorant ... but a bit less so thanks to their help.

 

[ThomasT]

But we're not talking about the practical ability of Bell tests today to definitively disprove local determinism.

Right, we're talking about the practical ability of Bell tests to definitively rule out Bell-type LR models of quantum entanglement, and how that can be explained in a way that still allows the assumptions of locality and determinism.

We're discussing the deeper issue of whether a local determinist can believe that all the experimental predictions of quantum mechanics are true, and that includes what QM has to say about idealized setups like the one I outlined.

No, it doesn't include idealized setups like the one you outlined because that idealized setup is a nonsequitur.

I've asked you a specific question, that you still haven't answered, about what you would infer from the experimental facts that, wrt Bell tests, the rate of individual detection does not vary as a function of polarizer orientation, while the rate of coincidental detection does vary as a function of the angular difference between polarizer orientations. So, what might you infer from this?

 

[lugita15]

Right, we're talking about the practical ability of Bell tests to definitively disprove Bell-type LR models of quantum entanglement, and how that can be explained in a way that still allows the assumptions of locality and determinism.

If that's your only point, then you and I have no quarrel. Not only am I willing to concede that the philosophical stance you call local determinism has not been ruled out by experiment, I am also willing to concede that what you call the "Bell-type LR models of quantum entanglement" have not been definitively disproven, due to various kinds of experimental loopholes, and there is reason to believe that we might not be able to do a loophole-free Bell test for the forseeable future.

No, it doesn't include idealized setups like the one you outlined because that idealized setup is a nonsequitur.

Why is it a nonsequitur? What I am trying to argue is that a local determinist must disagree with at least some of the experimental predictions of quantum mechanics. The particular predictions he disagrees with might be difficult or nearly impossible from a practical point of view to test (as in the case of my idealized setup), but the disagreement exists all the same. To answer the OP's question, this is why local determinism is not usually considered an acceptable interpretation of quantum mechanics, unlike the many worlds interpretation or nonlocal deterministic interpretations like Bohmian mechanics. In a (non-superdeterministic) local deterministic universe, there must exist an experiment which disproves quantum mechanics. This is, in my view, the heart of Bell's theorem. Do you disagree with this?

I've asked you a specific question, that you still haven't answered, about what you would infer from the experimental facts that, wrt Bell tests, the rate of individual detection does not vary as a function of polarizer orientation, while the rate of coincidental detection does vary as a function of the angular difference between polarizer orientations. So, what might you infer from this?

I responded to your question in a previous post of mine, but I probably didn't do justice to whatever your intent was:
"All a local determinist might infer from this is that the decision of whether to go through the polarizer or not is based on some local hidden variable, but we human beings don't know the value of this variable, so to us it seems like an unpredictable 50-50 chance whether it will go through." And I'll add that a local determinist would say that the reason a comparison of individual detection results yields a correlation which depends on the relative angle of the polarizers is that both photons contain the same basic hidden variable information, so when we turn our polarizers to different angles we're finding out different parts of this shared information.

 

[ThomasT]

What I am trying to argue is that a local determinist must disagree with at least some of the experimental predictions of quantum mechanics.

And at least one of the things that I'm trying to argue is that a local determinist doesn't have to disagee with any of the experimental predictions of QM.

In a (non-superdeterministic) local deterministic universe, there must exist an experiment which disproves quantum mechanics.

Why? QM is in certain respects a nonmechanistic acausal theory, and certainly wrt the quantum entanglements produced via Bell tests. Whether QM is at odds with local determinism is pretty much a matter of interpretation as far as I can tell.

This is, in my view, the heart of Bell's theorem. Do you disagree with this?

I think that Bell's theorem showed that an LR model of quantum entanglement encoding certain constraints is necessarily incompatible with standard QM. No more, and no less.

I responded to your question in a previous post of mine, but I probably didn't do justice to whatever your intent was ...

It's a straightforward question. Here it is again.

Wrt Bell tests, the rate of individual detection does not vary as a function of polarizer orientation, while the rate of coincidental detection does vary as a function of the angular difference between polarizer orientations.

What might you infer from this?

 

[Demystifier]

Demystifer, if pilot waves don't go faster than light, then what explains the nonlocality of entanglement? Does the quantum potential propagate faster than light?

Bohmian mechanics (BM) is not nonlocal because something propagates faster than light. Instead, BM is nonlocal because velocity and acceleration of one particle at a given time depends on the positions of other particles (with which it is entangled) at the same time, no matter haw far these particles are.

Also, am I wrong in my impression that a particle's trajectory right now is determined in part by the apparatuses it knows, based on nonlocal interaction, that it's going to encounter later?

In the context of nonrelativistic BM, you are wrong. In the context of relativistic BM, the answer depends on what exactly do you mean by "later".

 

[ThomasT]

Bohmian mechanics (BM) is not nonlocal because something propagates faster than light. Instead, BM is nonlocal because velocity and acceleration of one particle at a given time depends on the positions of other particles (with which it is entangled) at the same time, no matter how far these particles are.

So, this isn't nonlocality in the sense of ftl propagations, or nonlocality in the sense of spooky action at a distance. But just nonlocality in a formal sense? Thus, the same sort of nonlocality that might be inferred wrt to the standard QM formalism.? This has been your recent program, right?

 

[Demystifier]

So, this isn't nonlocality in the sense of ftl propagations, or nonlocality in the sense of spooky action at a distance. But just nonlocality in a formal sense? Thus, the same sort of nonlocality that might be inferred wrt to the standard QM formalism.? This has been your recent program, right?

Well, not exactly. There is some sense in which BM is "more nonlocal" than orthodox QM. This perhaps is best viewed in the solipsistic hidden-variable interpretation, which interpolates between Bohmian and orthodox interpretation:
http://xxx.lanl.gov/abs/1112.2034

 

[ThomasT]

Well, not exactly. There is some sense in which BM is "more nonlocal" than orthodox QM. This perhaps is best viewed in the solipsistic hidden-variable interpretation, which interpolates between Bohmian and orthodox interpretation:
http://xxx.lanl.gov/abs/1112.2034

Thanks for the reply. I have an intuitive grasp of your writings, but some of the technical details are currently beyond me.

But back to the OP. Although it appears as though the OP originator might have gotten temporarily banned. Anyway, what is your opinion of my recent replies to lugita15 and Joncon? Do they make sense to you? Do you think that one can believe that the LR program is ruled out, while still maintaining a belief in locality and determinism?

 

[Demystifier]

But back to the OP. Although it appears as though the OP originator might have gotten temporarily banned. Anyway, what is your opinion of my recent replies to lugita15 and Joncon? Do they make sense to you? Do you think that one can believe that the LR program is ruled out, while still maintaining a belief in locality and determinism?

You would help me by pointing to a specific post which you would like me to comment.

 

[bohm2]

First of all, I thought the nonlocal stuff like entanglement was handled through the pilot wave, not the quantum potential.

The difficult and interesting question with respect to Bohm's concept of quantum potential (Q) is specifying which physical object(s) cause this potential and how and why. Bohm argued for an "informational field" interpretation of Q, but this view has been criticized by other "Bohmians" as being very obscure. For instance:

In the context of quantum physics, Bohm and Hiley postulated that ‘active information’ (which is carried by the wave field and represented by the quantum potential) determines a quantum particle’s path and its velocity by using the particle’s own energy. The Active Information Hypothesis opens up a whole host of questions and issues that are extremely problematic. Consider first the difficulties encountered with particle structure. Quantum particles would require complex internal structures with which the ‘active information’ is processed in order that the particle be directed through space. Bohm and Hiley readily acknowledge this: The fact that the particle is moving under its own energy, but being guided by the information in the quantum field suggests that an electron or other elementary particle has a complex and subtle inner structure (e.g., perhaps even comparable to that of a radio) (1993, 37).

Reflections on the deBroglie–Bohm Quantum Potential
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/riggs_2008.pdf

For such reasons, some "minimalist" Bohmians (Durr, Goldstein, etc.) try to dispense with Q completely but other problems arise. For example, without Q, are particle trajectories by themselves sufficient to explain quantum phenomena ("problem of trajectories")? Other "Bohmians" attempt to employ the quantum potential concept but dispense with the information field suggesting that "primitive" forces existing on their own in addition to particles (e.g. Belousek):

Energy Content of Quantum Systems and the Alleged Collapse of the Wavefunction
http://arxiv.org/ftp/arxiv/papers/0910/0910.2834.pdf

Formalism, Ontology and Methodology in Bohmian Mechanics
https://springerlink3.metapress.com...oqulc13h34tv0ihv21kj2&sh=www.springerlink.com

 

[lugita15]

Bohmian mechanics (BM) is not nonlocal because something propagates faster than light. Instead, BM is nonlocal because velocity and acceleration of one particle at a given time depends on the positions of other particles (with which it is entangled) at the same time, no matter haw far these particles are.

What is the explanation given in Bohmian mechanics for the dependence of velocity and acceleration on the position of other particles?

 

[lugita15]

And at least one of the things that I'm trying to argue is that a local determinist doesn't have to disagee with any of the experimental predictions of QM.

OK, now the discussion is getting back on track. So consider again the idealized setup I described earlier, since we are trying to deal with the issue of whether local determinists must disagree with the predictions of QM in principle, not whether practical considerations make it difficult to test this disagreement. For this setup, which of the following do you disagree with:
1. The only experimental data collected is the results of individual detection events, so all the experimenter records is a yes or no answer as to whether a given photon went through the polarizer or not.
2. What you call the "rate of coincidental detection" in this case is just a correlation of individual detection results from the two experimenters.
3. Thus, explaining any properties, like θ-dependence, of the correlation between individual detection results involves no more and no less than explaining the results themselves.
4. It is an experimental prediction of QM that there is perfect correlation between detection results if the polarizers are set to the same angle.
5. You are a local determinist who agrees with all the predictions of QM, so you conclude that the particles are not communicating with each other faster-than-light, but rather that the two photons in a pair are using the same function P(θ) to decide whether to go through the polarizer oriented at an angle θ or not, where they go through the polarizer if P(θ)=1 and they don't go through if P(θ)=0.

I hope you agree with these five points.

It's a straightforward question. Here it is again.

Wrt Bell tests, the rate of individual detection does not vary as a function of polarizer orientation, while the rate of coincidental detection does vary as a function of the angular difference between polarizer orientations.

What might you infer from this?

I don't really have a very interesting answer to your question, but here goes. A local determinist, based on my 5 points above, would say that the two photons are consulting the same function P(θ), but humans don't know the details of this function, so it seems like it's a random 50-50 thing whether a photon goes through or not. However, if we make individual measurements on both photons, then we an find out the values of the function P at two different angles, so looking at the results of both measurements make things look a bit less random, and we can draw more inferences about the function P.

 

[Demystifier]

What is the explanation given in Bohmian mechanics for the dependence of velocity and acceleration on the position of other particles?

BM does not provide such an explanation. Instead, it POSTULATES the existence of such dependence and shows that such a postulate can explain all measurable quantum phenomena.

 

[ThomasT]

2. What you call the "rate of coincidental detection" in this case is just a correlation of individual detection results from the two experimenters.

I have to disagree with this the way it's stated. What's called "rate of coincidental detection" (not just by me, but in all of the literature on Bell tests afaik) isn't "just a correlation of individual detection results from the two experimenters", because that implies that what's being correlated in the joint (entanglement) context is the individual detection results. But that's not what's being correlated in that context. Rather, what's being correlated in the joint context is the rate of coincidental detection wrt the angular difference between the polarizers. The angular difference between polarizer settings is a different measurement parameter than the angular setting of one polarizer, and the rate of coincidental detection is a different detection statistic than the rate of individual detection.

3. Thus, explaining any properties, like θ-dependence, of the correlation between individual detection results involves no more and no less than explaining the results themselves.

First of all, a point wrt notation. θ, that is, capital Theta, usually refers to the angular difference between polarizer settings. θ isn't correlated with individual detection results. It's correlated with coincidental detection results. So, a phrase like " ... θ-dependence, of the correlation between individual detection results ...", is contrary to both the predictions and the experimental results in that there are only three combined settings (that is, angular differences, ie., θ) where individual detection results are correlated, afaik. They are 0, 45 and 90 degree angular differences between polarizers. Other than at those θ, individual detections aren't correlated.

5. You are a local determinist who agrees with all the predictions of QM, so you conclude that the particles are not communicating with each other faster-than-light, but rather that the two photons in a pair are using the same function P(θ) to decide whether to go through the polarizer oriented at an angle θ or not, where they go through the polarizer if P(θ)=1 and they don't go through if P(θ)=0.

This is just the wrong way to frame it, imho. I don't know what else to say. The function that determines whether or not a photon is transmitted by an individual polarizer should not be inferred to be the same function that determines coincidental detection. And this is, afaik, a reasonable inferential distinction to make wrt the extant experimental results. Why? Because coincidental detection varies as a function of θ, the global or joint measurement parameter, which suggests that it's a function of an underlying constant, and is not varying as a function of the, presumably, randomly varying underlying parameter that, presumably, determines individual detection.

 

[lugita15]

I have to disagree with this the way it's stated. What's called "rate of coincidental detection" (not just by me, but in all of the literature on Bell tests afaik) isn't "just a correlation of individual detection results from the two experimenters", because that implies that what's being correlated in the joint (entanglement) context is the individual detection results. But that's not what's being correlated in that context. Rather, what's being correlated in the joint context is the rate of coincidental detection wrt the angular difference between the polarizers. The angular difference between polarizer settings is a different measurement parameter than the angular setting of one polarizer, and the rate of coincidental detection is a different detection statistic than the rate of individual detection.

ThomasT, I feel like we're arguing semantics. Let me just ask you this: do you agree that in the idealized setup I described, there is no experimental procedure called "coincidence detection", only individual detection events?

First of all, a point wrt notation. θ, that is, capital Theta, usually refers to the angular difference between polarizer settings. θ isn't correlated with individual detection results. It's correlated with coincidental detection results. So, a phrase like " ... θ-dependence, of the correlation between individual detection results ...", is contrary to both the predictions and the experimental results in that there are only three combined settings (that is, angular differences, ie., θ) where individual detection results are correlated, afaik. They are 0, 45 and 90 degree angular differences between polarizers. Other than at those θ, individual detections aren't correlated.

OK, I think this is more semantics. In the terminology that I've seen more often used, if you have an angle at which an individual detection result for one photon completely determines the individual detection result for the other photon, we say that there is perfect correlation (or perfect anticorrelation as the case may be). If there is not perfect correlation, there can still be correlation, described by a correlation coefficient. If the photons are doing the exact same thing, as occurs when both polarizers are at the same angle, the correlation is 100%. If you turn the polarizers 45 degrees apart, you get a 50% correlation, meaning that given the information of what one photon has done you can predict what the other one will do with 50% certainty. Etc.

So we turn each polarizers at various angles, and we record data like "Photon 1 in pair 55 went through detector 1 turned at an angle of 40 degrees." (Remember, I'm talking about the idealized setup I described.) So at the end, for each individual angle setting the experimenter has written a long list of yes or no answers as to whether each photon went through or not. As he looks through the list, he sees no apparent pattern; regardless of what angle he turns the polarizer to, it seems like half of the photons go through, and the other half do not. Then the two experimenters have a meeting and compare their results, and for each angle pair (θ1,θ2) they calculate the correlation coefficient R(θ1,θ2). They find that R(θ1+C,θ2+C)=R(θ1,θ2) for all C, so they conclude it's not the absolute angles that are most important, only the difference θ=|θ1-θ2|, so we can just say R(θ).

Now do you agree or disagree that in my idealized setup, R(θ) is determined entirely by whatever determines the individual detection results? I really don't know how you can disagree with this, because the yes's and no's the experimenters recorded were entirely based on the individual results, and the calculation of R(θ) was done entirely be analyzing those yes's and no's.

Once we're agreed on this, we can discuss the more substantive issues, such as the point even zonde (who is a local determinist) agreed with, that once you accept that there is perfect correlation at identical polarizer settings, as a local determinist you MUST believe that the universe obeys Bell's inequality (even if you believe that this Bell inequality is too difficult to test for practical purposes).

 

[lugita15]

BM does not provide such an explanation. Instead, it POSTULATES the existence of such dependence and shows that such a postulate can explain all measurable quantum phenomena.

OK, in which of the two real differential equations does this dependence occur? (I'm probably asking a really obvious question.)

 

[Demystifier]

OK, in which of the two real differential equations does this dependence occur? (I'm probably asking a really obvious question.)

You seem to need a brief course in Bohmian mechanics. See e.g.
http://xxx.lanl.gov/pdf/quant-ph/0611032.pdf
In particular, the answer to your question above is Eq. (1). But please, before asking further trivial questions, read the WHOLE paper first!

For a complementary bottom-up introduction to Bohmian mechanics you may also see
Sec. 2 "Essential and inessential aspects of Bohmian interpretation" of
http://xxx.lanl.gov/pdf/1112.2034.pdf
In this case, the answer to your question is given by the LAST equation (rather than first), Eq. (18).