Trying to Understand Bell's reasoning

[ThomasT]

Oops, that is not correct at all. For Type I PDC, they are HH>. For Type II, they are HV>.

That means, when you observe one to be H, you know with certainty what the polarization of the other is.

Not exactly. Since we don't (can't) know, and therefor can't say anything about, what the values of La and Lb are, then we can only say that, for |a-b| = 0 and 90 degrees, then if the polarizer at one end has transmitted a disturbance that resulted in a detection, then we can deduce what the result at the other end will be.

Since they don't produce entangled state stats, then presumably there's a range of |La - Lb| > 0 that allows the contingent deductions for |a-b| = 0 and 90 degrees, but not the full range of entangled state stats.

Anyway, La and Lb don't even have to represent optical vectors. |La - Lb| can be taken to denote the relationship between any relevant local hidden variable subset(s) of H. Or we can just leave it out. I'm not pushing an lhv description. I think that's impossible. This thread is discussing why that's impossible.

The point is that P(B|AH) /= P(B|H) holds for certain polarizer settings without implying ftl info transmission.

Since this violation of P(AB|H) = P(A|H)P(B|H) doesn't imply ftl info transmission, then P(AB|H) = P(A|H)P(B|H) isn't a locality condition, but rather, strictly speaking, it's a local hidden variable condition.

Per the OP, since P(AB|H) = P(A|H)P(B|H) doesn't hold for all settings, then it can't possibly model the situation that it's being applied to.

Per me, since P(AB|H) = P(A|H)P(B|H) requires that joint detection rate be expressed in terms of individual variable properties which don't determine it, then it can't possibly model the situation that it's being applied to.

The point of Bell's analysis was that lhv theories are ruled out because they would have to be in the separable form that he specified, and, as he noted, "the statistical predictions of quantum mechanics are incompatible with separable predetermination".

 

[ThomasT]

(Now of course, you deny that there is such a thing as Entanglement in the sense that it can be a state which survives the creation of the photon pair. But I don't.)

I don't know what you mean here. Could you elaborate please?

 

[DrChinese]

I don't know what you mean here. Could you elaborate please?

If one pushes local realism, one is asserting there is no ongoing connection between Alice and Bob. QM denies this. The connection is that Alice = Bob (at same settings) for any setting.

 

[DrChinese]

Not exactly. Since we don't (can't) know, and therefor can't say anything about, what the values of La and Lb are, then we can only say that, for |a-b| = 0 and 90 degrees, then if the polarizer at one end has transmitted a disturbance that resulted in a detection, then we can deduce what the result at the other end will be.

...

But you say that photon pairs with a joint common cause (or however you term it) and a definite polarization should produce Entangled State stats. They don't. Your assumption cannot be correct. Only ENTANGLED photons - pairs in a superposition - have the characteristic that they produce Entangled State statistics.

According to your revised explanation above, photons with the special case where we have HH> at 0 degrees should have HH> or VV> whenever A-B=0. But they don't, as I mention. Instead they have Product State stats. Hey, if the special case fails, how does your general case hold?

 

[ThomasT]

But you say that photon pairs with a joint common cause (or however you term it) and a definite polarization should produce Entangled State stats. They don't. Your assumption cannot be correct. Only ENTANGLED photons - pairs in a superposition - have the characteristic that they produce Entangled State statistics.

Entangled state stats are compatible with the assumption that the photons have a local common cause, say, via the emission process (you can interpret the emission models this way). It's just that you can't denote the entangled state in terms of the individual properties of the separated photons -- because that's not what's being measured in the joint context.

According to your revised explanation above, photons with the special case where we have HH> at 0 degrees should have HH> or VV> whenever A-B=0. But they don't, as I mention.

You said that there are cases where pdc photons exhibit the |a-b| = 0 and 90 degrees perfect correlations, but not the polarization entanglement stats. And I said ok, but that doesn't diminish the fact that assuming a local common cause for photons that do produce polarization entanglement stats is compatible with the perfect correlations and hence P(B|H) /= P(B|AH) holds for the detection contingencies at those angles without implying ftl info transmission.

 

[ThomasT]

If one pushes local realism, one is asserting there is no ongoing connection between Alice and Bob. QM denies this. The connection is that Alice = Bob (at same settings) for any setting.

I don't follow. Are you saying that qm says there's a nonlocal 'connection' between the observers? I don't think you have to interpret it that way.

 

[DrChinese]

I don't follow. Are you saying that qm says there's a nonlocal 'connection' between the observers? I don't think you have to interpret it that way.

Sure it does. There is a superposition of states. Observation causes collapse (whatever that is) based on the observation. According to EPR, that makes Bob's reality dependent on Alice's decision. Now, both EPR and Bell realized there were 2 possibilities: either QM is complete (no realism possible) or there is spooky action at a distance (locality not respected). But either way, the superposition means there is something different going on than a classical mixed state.

A local realist denies this, saying that there is no superluminal influence and that QM is incomplete because a greater specification of the system is possible. But Bell shows that QM, if incomplete, is simply wrong. That's a big pill to swallow, given 10,000 experiments (or whatever) that say it isn't.

 

[ThomasT]

Observation causes collapse (whatever that is) based on the observation. According to EPR, that makes Bob's reality dependent on Alice's decision.

Or, we can assume that the correlated events at A and B have a local common cause. And, standard qm is not incompatible with that assumption.

Now, both EPR and Bell realized there were 2 possibilities: either QM is complete (no realism possible) or there is spooky action at a distance (locality not respected).

EPR said that either qm is INcomplete (local realism possible) or there is spooky action at a distance (local realism impossible -- a detection at one end is instantaneously determining the reality at the other end -- in which case locality would be out the window). Qm is obviously incomplete as a physical description of the underlying reality. All you have to do is look at the individual results, wrt which, by the way, qm isn't incompatible with an lhv account of, to ascertain that. (But that doesn't entail that a viable lhv account of entanglement is possible.) The reason that the qm treatment is a 'complete', in a certain sense, account of the joint entangled situation is because the information necessary to predict individual detection SEQUENCES isn't necessary to predict joint detection RATES. But, again obviously, qm isn't, in the fullest sense, a complete account of the joint entangled context either, because it can't predict the order, the sequences, of the coincidental results. It can only predict the coincidence RATE, and for that all that's needed is |a - b| and the assumption that whatever |a - b| is analyzing is the same at both ends for any given coincidence window -- and that relationship, that sameness, is compatible with the assumption of a local common cause (even if qm doesn't explicitly say that, but, as I've mentioned, the emission model(s) can be interpreted that way).

But either way, the superposition means there is something different going on than a classical mixed state.

I agree. We infer that the superposition (via the preparation) has been experimentally realized when we observe that the entangled state stats have been produced -- which differ from the classical mixed state stats. But this has nothing to do with the argument(s) presented in this thread.

A local realist denies this, saying that there is no superluminal influence and that QM is incomplete because a greater specification of the system is possible.

I think we agree that lhv theories of entangled states are ruled out. We just differ as to why they're ruled out. But it's an important difference, and one worth discussing. I don't think that a greater specification of the system, beyond what qm offers, is possible. But I also think that it's important to understand why this doesn't imply nonlocality or ftl info transmission.

I do very much appreciate your comments and questions as they spur me to refine how I might communicate what I intuitively see.

But Bell shows that QM, if incomplete, is simply wrong. That's a big pill to swallow, given 10,000 experiments (or whatever) that say it isn't.

Qm, like any theory, can be an incomplete description of the underlying physical reality without being just simply wrong. I think Bell showed just what he said he showed, that a viable specification of the entangled state (ie., the statistical predictions of qm) is incompatible with separable predetermination. However, in showing that, he didn't show that separable predetermination is impossible in Nature, but only that the hidden variables which would determine individual detection SEQUENCES are not relevant wrt determining joint detection RATES. A subtle, but important, distinction.

Regarding billschnieder's argument, I'm not sure that what he's saying is equivalent to what I'm saying, but it seems to accomplish the same thing wrt Bell's ansatz, which is that it can't correctly model entanglement setups. (billschnieder might hold the position, with eg. 't hooft et al., that some other representation of local reality might be possible which would violate BIs, or that could be the basis for a new quantitative test which qm and results wouldn't violate. That isn't my position. I agree with Bell, you et al. who think that Bell's ansatz is the only form that an explicit lhv theory of entanglement can take, but since this form can't possibly model the situation it's being applied to, independent of the tacit assumption of locality, then lhv theories of entanglement are ruled out independent of the tacit assumption of locality. We simply can't explicate that tacit assumption wrt the joint context because that would require us to express the joint results in terms of variables which don't determine the joint results.)

Anyway, it seems that we can dispense with considerations of the minimum and maximum propagation rates of entangled particle 'communications' and, hopefully, focus instead on the real causes of the observed correlations. Quantum entanglement is a real phenomenon, and it's certainly reasonable to suppose that it's a result of the dynamical laws which govern any and all waves in any and all media. That is, it's reasonable to suppose that there are fundamental wave dynamics which apply to any and all scales of behavior.

After all, why is qm so successful? Could it be because wave behavior in undetectable media underlying quantum instrumental phenomena isn't essentially different than wave behavior in media that we can see?

With apologies to billschnieder for my ramblings, and returning the focus of this thread to billschnieder's argument, I think that he's demonstrated the inapplicability of Bell's ansatz to the joint entangled situation. And, since P(B|H)/=P(B|AH) holds without implying ftl info transmission, then the inapplicability of P(AB|H)=P(A|H)P(B|H) doesn't imply ftl info transmission.

Beyond this, the question of whether ANY lhv theory of entanglement is possible might be considered an open question. My answer is no based on the following consideration: All disproofs of lhv theories, including those not based directly on Bell's anstatz, involve limitations on the range of entanglement predictions due to explicitly local hidden variables a la EPR. But it's been shown that these variables are mooted in the joint (entangled) situation and explicit lhv formulations of entanglement bring us back to Bell's ansatz or some variation of it. So, lhv theories (of the sort conforming to EPR's notion of local reality anyway) seem to be definitively ruled out.

 

[ThomasT]

Apologies to billschnieder if I've got his argument wrong.

The usual:
1) Bell's ansatz correctly represents local-causal hidden variables
2). Bell's ansatz necessarily leads to Bell's inequalities
3). Experiments violate Bell's inequalities
Conclusion: Therefore the real physical situation of the experiments is not Locally causal.

Per billschnieder:
1) Bell's ansatz incorrectly represents local-causal hidden variables
2) Bell's ansatz necessarily leads to Bell's inequalities
3) Experiments violate Bell's inequalities
Conclusion: Therefore the real physical situation of the experiments is incorrectly represented by Bell's ansatz.

Per ThomasT:
1) Bell's ansatz correctly represents local-causal hidden variables
2) Bell's ansatz incorrectly represents the relationship between the local-causal hidden variables
3) The experimental situation is measuring this relationship
4) Bell's ansatz necessarily leads to Bell inequalities
5) Experiments violate Bell's inequalities
Conclusion: Therefore the real physical situation of the experiments is incorrectly represented by Bell's ansatz.

or to put it another way:
1) Bell's ansatz is the only way that local hidden variables can explicitly represent the experimental situation
2) This representational requirement doesn't express the relationship between the hidden variables
3) The experimental situation is measuring this relationship
etc.
Conclusion: Therefore the real physical situation of the experiments is, necessarily, incorrectly represented by Bell's ansatz.

We can continue with:
1) Any lhv representation of the experimental situation must conform to Bell's ansatz or some variation of it.
Then given the foregoing we can Conclude:
Therefore lhv representations of entanglement are impossible.

But of course, per billschnieders original point, this doesn't tell us anything about Nature.

 

[ThomasT]

JesseM, I'm here to learn. You didn't reply to my reply to your post where you stated:

If measurement A is at a spacelike separation from B, then isn't it clear that according to local realism, knowledge of A cannot alter your estimate of the probability of B if you were already basing that estimate on H, which encompasses every microscopic physical fact in the past light cone of B? To suggest otherwise would imply FTL information transmission ...

This isn't yet clear to me. If we assume a relationship between the polarizer-incident disturbances due to a local common origin (say, emission by the same atom), then doesn't the experimental situation allow that both Alice and Bob know at the outset (ie., the experimental preparation is in the past light cones of both observers) that if A=1 then B=1 and if A=0 then B=0 (and if A=1 then B=0, and vice versa) for certain settings without implying FTL transmission?

In a reply to billschnieder you stated:

... if P(B|L) was not equal to P(B|LA), that would imply P(A|L) is not equal to P(A|BL), meaning that learning B gives us some additional information about what happened at A, beyond whatever information we could have learned from anything in the past light cone of B ...

I agree that if P(B|L) /= P(B|AL) then P(A|L) /= P(A|BL), but doesn't the correctness of both of those expressions follow from the contingencies for certain settings which follow from the experimental preparation which is in the past light cones of both A and B?

So, it does seem that P(AB|L) /= P(A|L)P(B|L) without implying FTL transmission.

In another reply to billschnieder you stated:

Consider the possibility that you may not actually understand everything about this issue, and therefore there may be points that you are missing. The alternative, I suppose, is that you have no doubt that you already know everything there is to know about the issue, and are already totally confident that your argument is correct and that Bell was wrong to write that equation ...

Is it possible that the equation is wrong for the experimental situation, but that Bell was, in a most important sense, correct to write it that way vis EPR? Haven't hidden variables historically (vis EPR) been taken to refer to underlying parameters that would affect the prediction of individual results? If so, then wouldn't a formulation of the joint situation in terms of that variable have to take the form of Bell's ansatz? If so, then Bell's ansatz is, in that sense, correct. However, what if the underlying parameter that's being jointly measured isn't the underlying parameter that determines individual results? For example, if it's the relationship between the optical vectors of disturbances emitted during the same atomic transition, and not the optical vectors themselves, that's being jointly measured, then wouldn't that require a different formulation for the joint situation?

Do the assumptions that (1) this relationship is created during the common origin of the disturbances via emission by the same atom, and that (2) it therefore exists prior to measurement by the crossed polarizers, and that (3) counter-propagating disturbances are identically polarized (though the polarization vector of any given pair is random and indeterminable), contradict the qm treatment of this situation? If not, then might the foregoing be taken as an understanding of violations of BIs due to nonseparability of the joint entangled state?

I think that Bell showed just what he said he showed -- that the statistical predictions of qm are incompatible with separable predetermination. Which, according to my attempt at disambiguation, means that joint experimental situations which produce (and for which qm correctly predicts) entanglement stats can't be viably modeled in terms of the variable or variables which determine individual results.

Any criticisms of, or comments on, any part of the above viewpoint are appreciated.

 

[DrChinese]

Is it possible that the equation is wrong for the experimental situation, but that Bell was, in a most important sense, correct to write it that way vis EPR? Haven't hidden variables historically (vis EPR) been taken to refer to underlying parameters that would affect the prediction of individual results? If so, then wouldn't a formulation of the joint situation in terms of that variable have to take the form of Bell's ansatz? If so, then Bell's ansatz is, in that sense, correct. However, what if the underlying parameter that's being jointly measured isn't the underlying parameter that determines individual results? For example, if it's the relationship between the optical vectors of disturbances emitted during the same atomic transition, and not the optical vectors themselves, that's being jointly measured, then wouldn't that require a different formulation for the joint situation?

Do the assumptions that (1) this relationship is created during the common origin of the disturbances via emission by the same atom, and that (2) it therefore exists prior to measurement by the crossed polarizers, and that (3) counter-propagating disturbances are identically polarized (though the polarization vector of any given pair is random and indeterminable), contradict the qm treatment of this situation? If not, then might the foregoing be taken as an understanding of violations of BIs due to nonseparability of the joint entangled state?

Any criticisms of, or comments on, any part of the above viewpoint are appreciated.

QM does NOT imply that there anything exists prior to and independent of measurement, as we have told you at least 106 times. There are no local counter-propagating influences in the sense you describe either.

 

[ThomasT]

QM does NOT imply that there anything exists prior to and independent of measurement, as we have told you at least 106 times. There are no local counter-propagating influences in the sense you describe either.

I think you need to look at the emission models relevant to FandC and Aspect experiments.

Why don't you reply to this?:

Is it possible that the equation is wrong for the experimental situation, but that Bell was, in a most important sense, correct to write it that way vis EPR? Haven't hidden variables historically (vis EPR) been taken to refer to underlying parameters that would affect the prediction of individual results? If so, then wouldn't a formulation of the joint situation in terms of that variable have to take the form of Bell's ansatz? If so, then Bell's ansatz is, in that sense, correct. However, what if the underlying parameter that's being jointly measured isn't the underlying parameter that determines individual results? For example, if it's the relationship between the optical vectors of disturbances emitted during the same atomic transition, and not the optical vectors themselves, that's being jointly measured, then wouldn't that require a different formulation for the joint situation?

or this?:

I think that Bell showed just what he said he showed -- that the statistical predictions of qm are incompatible with separable predetermination. Which, according to my attempt at disambiguation, means that joint experimental situations which produce (and for which qm correctly predicts) entanglement stats can't be viably modeled in terms of the variable or variables which determine individual results.

 

[DrChinese]

I think you need to look at the emission models relevant to FandC and Aspect experiments.

Why don't you reply to this?:

...

or this?:

OK, in my opinion it is meaningless. Hey, you asked.

(I usually don't reply if I don't have something nice to say. Unless of course I'm pissed off.)

 

[ThomasT]

OK, in my opinion it is meaningless. Hey, you asked.

I don't think you understand it. Anyway, the post was directed at JesseM.

(I usually don't reply if I don't have something nice to say. Unless of course I'm pissed off.)

We both know that isn't true.

Like I said in the other thread, you're making my case.

 

[ThomasT]

OK, in my opinion it is meaningless.

You mean like this:

... Because I accept Bell, I know the world is either non-local or contextual (or both). If it is non-local, then there can be communication at a distance between Alice and Bob. When Alice is measured, she sends a message to Bob indicating the nature of the measurement, and Bob changes appropriately. Or something like that, the point is if non-local action is possible then we can build a mechanism presumably which explains entanglement results.

I hope that works out for you.

 

[DrChinese]

I hope that works out for you.

Don't go away mad.

I really wasn't trying to insult you. We all write funny stuff from time to time. As you say, there are plenty of my posts that sound like I am smoking something. (Of course, who knows...?)

 

[ThomasT]

Don't go away mad.

I really wasn't trying to insult you. We all write funny stuff from time to time. As you say, there are plenty of my posts that sound like I am smoking something. (Of course, who knows...?)

What would give you the impression that I was mad, or going away? I don't always take the time to put smileys. (I'm smiling right now, can you tell?)

We agree that BIs are violated. We agree, I think, on the meaning of hidden variable (per EPR elements of reality). What remains is to hash out the reason(s) for BI violations and GHZ inconsistencies, etc. I'm saying that this can be understood via the application of logic.

As for explaining the correlations in, say, optical Bell experiments, well, that's an optics, not a logic, problem.

The logic problem can be absolutely solved. The optics problem is a bit stickier, but the correlations are not mysterious, and don't need nonlocality, from an optics point of view.

The solutions to both the logic and the optics problems hinge on the idea (and application) of global or joint parameters.

No need for nonlocality. (It's a silly idea anyway. Don't you think?)


As for this thread, I think the OP's point has been made. QED

This deals with one part of the logic problem.

 

[Boy@n]

Thomas, so what's your logical explanation for quantum entanglement? You see it just as a result of false tests or as real natural phenomenon?

If real, and if I let my imagination free, how crazy would be the idea that by separating quantum entangled particles we create a quantum wormhole and thus changing state of one would affect the other at the same time?

 

[Boy@n]

Seems 'my' idea is not new, see: http://iopscience.iop.org/0295-5075/78/3/30005

 

[JesseM]

Sorry I missed this post earlier Thomas:

Based on H, which includes all values for |a-b|, the angular difference between the polarizer settings

H is intended to encompass local physical facts in the past light cone of both the measurements and the experimenter's choices about what measurement settings to use. So, H doesn't include the specific detector settings.

and all values for |L_a - L_b|, the emission-produced angular difference between the optical vectors of the disturbances incident on the polarizer settings, a and b

Can you explain what you mean by "optical vectors of the disturbances", and how they are supposed to interact with the detector setting to determine the outcome of each measurement? You never replied to this post where I suggested one possible interpretation of what you might mean, and why this interpretation wouldn't be able to explain the statistics predicted by QM:

can you explain the nature of the local hidden variables, and how they interact with the angle of the polarizer to give the probabilities of different outcomes? For example, maybe you're suggesting that each particle has an identical hidden variable giving the angle v of its polarization vector, and that to determine the probability a particle is detected we just take the angle of the polarizer it goes through (a or b) and the angle of the particle's polarization vector (which has the same value v for both particles) and calculate cos² of the angle between them (i.e. cos²(a-v) for the first particle going through polarizer a, and cos²(b-v) for the second particle going through polarizer b). If so, this would not give a coincidence rate of cos²(a-b), as you can see if you set a=b while making v different from a and b; in that case cos²(a-v)=cos²(b-v)=some number between 0 and 1, so there is some nonzero probability the two particles will give opposite results, despite the fact that cos²(a-b)=1 (this is basically the same argument I was making in the first paragraph of post 81, except I forgot to take cosine squared rather than just the cosine of the angles).

respectively, then when, eg., |a-b| = 0 and |L_a - L_b| = 0, then P(B|AH) /= P(B|H).

Why do you say that? Again, your model isn't clear.

In this case, we can, with certainty, say that if A = 1, then B = 1, and if A = 0, then B = 0. So, our knowledge of the result at A can alter our estimate of the probability of B without implying FTL information transmission.

Sure, but that's not a probability conditioned on H. If H includes everything in the past light cone of the measurements, it already includes information about everything that happened to the particle prior to measurement, including the hidden variables (like your 'optical vectors') that were given to the particles by the source. So though the result at A can alter your estimate of the probability of B if the source assigned both of them correlated hidden variables, if you already know everything in the past light cone of the measurement of B, then you already know whatever hidden variables were assigned to B by the source, so the result of A tells you nothing further about the probability of B in a local hidden variables model, i.e. P(B|H) = P(B|AH).

 

[JesseM]

This isn't yet clear to me. If we assume a relationship between the polarizer-incident disturbances due to a local common origin (say, emission by the same atom), then doesn't the experimental situation allow that both Alice and Bob know at the outset (ie., the experimental preparation is in the past light cones of both observers) that if A=1 then B=1 and if A=0 then B=0 (and if A=1 then B=0, and vice versa) for certain settings without implying FTL transmission?

Yes, but that just shows that P(AB) is different from P(A)*P(B), or that P(B|A) is different from P(B). If L represents everything that happened in the past light cone of the measurement B, then L will already include whatever hidden variables were assigned to the B-particle by the source, so if you know L then learning A will tell you nothing new about the hidden variables assigned to B by the source, which is why P(B|L) = P(B|LA).

I agree that if P(B|L) /= P(B|AL) then P(A|L) /= P(A|BL), but doesn't the correctness of both of those expressions follow from the contingencies for certain settings which follow from the experimental preparation which is in the past light cones of both A and B?

No, see above. Again, you seem not to understand that Bell's argument was explicitly based on considering the possibility that the correlations between A and B might be explained by common hidden properties assigned to the two particles by the source.

In another reply to billschnieder you stated:

Consider the possibility that you may not actually understand everything about this issue, and therefore there may be points that you are missing. The alternative, I suppose, is that you have no doubt that you already know everything there is to know about the issue, and are already totally confident that your argument is correct and that Bell was wrong to write that equation ...

Yes, and people who are challenging thoroughly mainstream claims, and believing they have noticed some obvious flaw that thousands of very intelligent physicists have been missing for decades, have a special responsibility to consider the possibility that they may not understand everything (if they have a reasonable amount of intellectual humility).

Is it possible that the equation is wrong for the experimental situation, but that Bell was, in a most important sense, correct to write it that way vis EPR? Haven't hidden variables historically (vis EPR) been taken to refer to underlying parameters that would affect the prediction of individual results? If so, then wouldn't a formulation of the joint situation in terms of that variable have to take the form of Bell's ansatz? If so, then Bell's ansatz is, in that sense, correct. However, what if the underlying parameter that's being jointly measured isn't the underlying parameter that determines individual results?

Bell's ansatz applies to all possible underlying parameters that qualify as "local hidden variables" (i.e. variables associated with a particular position such as the position of the particle, and variables whose value can only be causally influenced by events in their past light cone at any given moment).

For example, if it's the relationship between the optical vectors of disturbances emitted during the same atomic transition, and not the optical vectors themselves, that's being jointly measured, then wouldn't that require a different formulation for the joint situation?

See my question in the previous post about what you mean by "optical vectors". Are the optical vectors supposed to be local hidden variables?

Do the assumptions that (1) this relationship is created during the common origin of the disturbances via emission by the same atom, and that (2) it therefore exists prior to measurement by the crossed polarizers, and that (3) counter-propagating disturbances are identically polarized (though the polarization vector of any given pair is random and indeterminable), contradict the qm treatment of this situation? If not, then might the foregoing be taken as an understanding of violations of BIs due to nonseparability of the joint entangled state?

Again, I need clarification about whether "polarization vectors" are supposed to be local hidden variables, and if so how they are supposed to interact with polarizers to produce measurement outcomes. If they are local hidden variables, then Bell's theorem does apply to them, and the statistics that would result from these polarization vectors would obey the Bell inequalites. But the Bell inequalites are violated in QM (and experimentally), so the theory won't work.