# Why is superdeterminism not the universally accepted explanation of nonlocality?

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 Quote by lugita15 I'm including things like polarization vectors in the description of the particular function P for a particular entangled pair, rather than including them as an input of the function. This is just an arbitrary choice in how I'm defining things, so it shouldn't affect anything.
You've discretized the possible values of λ, a presumably continuous underlying parameter, in terms of dichotomized detector outputs. Is this the point where LR models of entanglement become incompatible with QM ... and the design of Bell tests?
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 Quote by ThomasT λ is meant to denote the polarization (angle) of the incident optical disturbance. a (or b) denotes the polarizer setting. So, from standard optics, individual detection is the function, cos2(a - λa), or in the same way for the B side.
You still haven't told me how any of this determines whether a particular photon goes through the polarizer or not.
 Quote by ThomasT You've asked, quite rightly I think, which of your steps would a more comprehensive local deterministic view disagree with. It's the step (in your steps) from which a linear correlation between θ and rate of coincidental detection is necessitated. So, which step, in your opinion, is that?
I'll summarize the argument up to the point where I think logical necessity enters the picture: the two photons in a pair exhibit identical behavior at identical angle settings, therefore the particles have coordinated in advance which polarizer angles they will go through and which ones they won't. From just this much, I think linear correlation is necessitated. The rest is just spelling out the chain of logical deduction.
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 Quote by ThomasT You've discretized the possible values of λ, a presumably continuous underlying parameter, in terms of dichotomized detector outputs. Is this the point where LR models of entanglement become incompatible with QM ... and the design of Bell tests?
In step 3, all I'm saying is that the two photons, right when they are created, agree in advance what polarizer angles to go through and what angles not to go through. (I'm talking about individual polarizer settings, not angle difference.) How they choose which angles they want to go through and which ones not to is irrelevant. They could do it using some polarization vector or anything else. But the point is that they've made a definite decision about what angles are "good" and what angles are "bad". And it is just this information that I am calling P(θ).

I think if you do not believe that the particles have chosen the good and bad angles in advance, but you believe in identical behavior at identical polarizer settings, you cannot sensibly call yourself a local determinist.
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 Quote by lugita15 You still haven't told me how any of this determines whether a particular photon goes through the polarizer or not.
Afaik, there's no way to determine that.

But, in one way of modelling it, the rate of individual detection (ie., the photon flux), per unit time, is,

cos2(a - λa)

 Quote by lugita15 I'll summarize the argument up to the point where I think logical necessity enters the picture: the two photons in a pair exhibit identical behavior at identical angle settings ...
Wrt your points this would be:

 Quote by lugita15 2. One of these [QM] experimental predictions is that entangled photons are perfectly correlated when sent through polarizers oriented at the same angle ...
From this I might infer that entangled photons are created via some common causal mechanism, and that their underlying properties are therefore related (which is in line with the QM treatment).

 Quote by lugita15 ... therefore the particles have coordinated in advance which polarizer angles they will go through and which ones they won't.
Wrt, say, Aspect 1982, the QM treatment is that the polarizer-incident optical disturbances are related wrt the conservation of angular momentum. The net effect of this assumption is that wrt θ = 0° coincidental detection attributes will be (1,1) or (0,0).

This isn't in conflict with LR predictions, and doesn't necessitate a linear correlation between θ and rate of coincidental detection.

 Quote by lugita15 From just this much, I think linear correlation is necessitated.
Well, that can't be it. Because identical detection attributes at EPR settings don't necessitate a linear correlation between θ and rate of coincidental detection. So, it has to be some other step.
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 Quote by lugita15 In step 3, all I'm saying is that the two photons, right when they are created, agree in advance what polarizer angles to go through and what angles not to go through. (I'm talking about individual polarizer settings, not angle difference.) How they choose which angles they want to go through and which ones not to is irrelevant. They could do it using some polarization vector or anything else. But the point is that they've made a definite decision about what angles are "good" and what angles are "bad". And it is just this information that I am calling P(θ).
Ok, and what I'm saying is that this "information" which determines the rate of individual detection is irrelevant wrt determining the rate of coincidental detection. Wrt the Aspect experiments the creation of an entangled pair imparts a relationship between them. They have a particular common or identical polarization which determines the rate of individual detection, and they have a relationship which, obviously, does not determine the rate of individual detection.

As I mentioned, the usual way of thinking about this is that, wrt say the Aspect experiments, λ refers to an underlying common polarization orientation ... which is, as far as I can tell, an acceptable inference given the experimental results.

From that inference one can construct a model of individual detection that's compatible with QM.

But if one tries to model coincidental detection in terms of that underlying parameter (the parameter that determines individual detection), then such a model will not be able to reproduce all the predictions of QM.

Now, go back to the visualization I suggested. You'll see that the parameter that determines individual detection, λ, the polarization of polarizer-incident photons, has nothing to do with, ie., is irrelevant wrt, coincidental detection.

What might we conclude from this? The assumption of identical underlying (and locally produced via emission process) polarization seems supported by experimental results. But, as we've seen, the polarization orientation has nothing to do with the rate of coincidental detection, and, additionally, the underlying parameter determining the rate of coincidental detection cannot be varying from pair to pair. Hence, the only logical conclusion is that the underlying parameters determining individual detection and coincidental detection are different underlying parameters.

 Quote by lugita15 I think if you do not believe that the particles have chosen the good and bad angles in advance, but you believe in identical behavior at identical polarizer settings, you cannot sensibly call yourself a local determinist.
I do believe that there is an underlying parameter that determines rate of individual detection. And it's an experimental fact that when θ = 0° then coincidental detection attributes will be either (0,0) or (1,1).

And, I also believe that rate of coincidental detection is not determined by λ. It can be anything. Doesn't matter. Coincidental detection is only determined by θ.
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 Quote by ThomasT Afaik, there's no way to determine that. But, in one way of modelling it, the rate of individual detection (ie., the photon flux), per unit time, is, cos2(a - λa)
It's not good enough to determine the rate of individual detection. The hidden variable must determine whether a given photon goes through a given polarizer at a given angle. Otherwise you don't have a deterministic theory.
 Quote by ThomasT Wrt, say, Aspect 1982, the QM treatment is that the polarizer-incident optical disturbances are related wrt the conservation of angular momentum. The net effect of this assumption is that wrt θ = 0° coincidental detection attributes will be (1,1) or (0,0). This isn't in conflict with LR predictions, and doesn't necessitate a linear correlation between θ and rate of coincidental detection.
First of all, stick to the idealized setup please, because that's what my steps are designed for. Second of all, we've hit on a crucial point here: while it's true that both the quantum mechanics guy and the local determinist agree that at identical angles you only get (1,1) or (0,0), they disagree as to the interpretation of this fact. Quantum mechanics says that you have a wave function for the two particle system which gets collapsed, nonlocally of course, as soon as one of the particles is measured, and that is how the other particle knows to do the same thing as the first particle, even though they're separated by a great distance. In contrast, the local determinist would say that it's not some nonlocal collapse that is correlating their behaviors, but rather their past interaction in which they determined *in advance* what angles they would go through and what angles they would not go through. It is because of this difference that step 3 must hold for local deterministic theories but does not hold for quantum mechanics.
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 Quote by ThomasT I do believe that there is an underlying parameter that determines rate of individual detection.
That's not good enough. You have to believe that not just the rate of individual detection is predetermined, but also each and every individual detection result. You have to believe that for each individual entangled pair, the two particles in the pair decide in advance the pair's "good" angles and "bad" angles, meaning exactly which angles the photon will go through and which it won't. Without all that, how can you call yourself a local determinist?
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 Quote by lugita15 It's not good enough to determine the rate of individual detection. The hidden variable must determine whether a given photon goes through a given polarizer at a given angle. Otherwise you don't have a deterministic theory.
The function, cos2(a - λa), does determine whether a given photon goes through a given polarizer at a given angle. At least that's the assumption. But λa can't be controlled.
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 Quote by lugita15 ... we've hit on a crucial point here: while it's true that both the quantum mechanics guy and the local determinist agree that at identical angles you only get (1,1) or (0,0), they disagree as to the interpretation of this fact.
I'm not sure that's the case.

 Quote by lugita15 Quantum mechanics says that you have a wave function for the two particle system which gets collapsed, nonlocally of course, as soon as one of the particles is measured, and that is how the other particle knows to do the same thing as the first particle, even though they're separated by a great distance.
How, exactly, does that work? What do you think is the conceptual basis for that assumption?

 Quote by lugita15 In contrast, the local determinist would say that it's not some nonlocal collapse that is correlating their behaviors, but rather their past interaction in which they determined *in advance* what angles they would go through and what angles they would not go through.
I'm curious. This is based on a knowledge of the historically documented behavior of light. What makes you think that the standard QM treatment isn't based on that very same knowledge, and associated inferences/assumptions?

It's already been demonstrated that the function correlating individual detection to λ and individual polarizer setting is compatible with QM.

 Quote by lugita15 It is because of this difference that step 3 must hold for local deterministic theories but does not hold for quantum mechanics.
 Quote by lugita15 3. From this you conclude that both photons are consulting the same function P(θ). If P(θ)=1, then the photon goes through the polarizer, and if it equals zero the photon does not go through.
This seems to me to be compatible with QM. Why do you think it isn't?
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 Quote by lugita15 You have to believe that not just the rate of individual detection is predetermined, but also each and every individual detection result.
I believe that. And that belief is compatible with the QM formalism regarding individual results. It's just that λ can't be controlled. At least that's the assumption (based on extant experimental preparation).

 Quote by lugita15 You have to believe that for each individual entangled pair, the two particles in the pair decide in advance the pair's "good" angles and "bad" angles, meaning exactly which angles the photon will go through and which it won't. Without all that, how can you call yourself a local determinist?
I do believe something akin to that, just not in those terms. And so does QM. But QM recognizes that what's determining coincidental detection is the relationship between entangled photons. And that that's a parameter that individual measurements aren't measuring. Hence, the nonseparability of the parameters relevant to the coincidental measurement of entangled particles, and the nonseparability/nonlocality of the associated QM formalism.
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I asked you: which of your steps would a more comprehensive local deterministic view disagree with?

Stating that, it's the step (in your steps) from which a linear correlation between θ and rate of coincidental detection is necessitated.

Which says:

 Quote by lugita15 2. One of these [QM] experimental predictions is that entangled photons are perfectly correlated when sent through polarizers oriented at the same angle ...
And I pointed out that it's clearly evident (ie., obvious) that this observation, this step, doesn't imply a linear correlation between θ and rate of coincidental detection.

So, which of your steps does imply such a correlation?
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 Quote by ThomasT The function, cos2(a - λa), does determine whether a given photon goes through a given polarizer at a given angle. At least that's the assumption. But λa can't be controlled.
So how do you get from cos2(a - λa) to a 0 or a 1?
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 Quote by ThomasT How, exactly, does that work? What do you think is the conceptual basis for that assumption?
Wavefunction collapse has an illustrious history going back to Max Born and John von Neumann. They saw collapse as the most natural explanation for the fact the wavefunction could be calculated deterministically using the Schrodinger equation, but the results of quantum mechanical experiments could only be predicted probabilistically. And I think it was Schrodinger himself who came up with the idea that entangled particles are described a common wavefunction that stretches across space, and that any changes in the wavefunction propagate instantaneously.
 It's already been demonstrated that the function correlating individual detection to λ and individual polarizer setting is compatible with QM.
Where has this been demonstrated?
 This seems to me to be compatible with QM. Why do you think it isn't?
According to the conventional interpretation of quantum mechanics, you have a nonlocal wavefunction collapse that determines on the spot whether the particles should go through or not. Whereas a local determinist believes that the particles have agreed in advance what angles to go through or not go through.
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 Quote by ThomasT I believe that. And that belief is compatible with the QM formalism regarding individual results.
No, it's not. In the QM formalism, the question of what angles the photons goes through and what angles it doesn't go through is not predetermined in advanced, but is rather determined on the spot in a random manner when the wavefunction collapse occurs.
 I do believe something akin to that, just not in those terms. And so does QM.
No, QM doesn't.
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 Quote by ThomasT I asked you: which of your steps would a more comprehensive local deterministic view disagree with? Stating that, it's the step (in your steps) from which a linear correlation between θ and rate of coincidental detection is necessitated. Then I asked: which step, in your opinion, is that? And you answered that it's your Step 2.
No, I answered that it's my step 3, which says that the particles determine in advance what angles to go through and what angles not to go through. From there, it is my claim that logical deduction will get you to the conclusion that local determinism is incompatible with the notion that all the predictions of QM are correct.
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 Quote by lugita15 So how do you get from cos2(a - λa) to a 0 or a 1?
Since λa is presumably varying randomly from photon to photon, then individual detection attributes (0 or 1) can't be predicted.

We're concerned with the rate of detection at A, which can be denoted as the function R(A).
Since λa is varying randomly, then the angular difference argument of R(A) is also varying randomly. So, averaging over that, you get R(A) = .5 (the rate of detection, or photon flux per unit time, without the polarizer, a, in place).

That is, R(A) predicts a random sequence of 0's and 1's for a run ... half 0's and half 1's.

Which is the same thing that QM predicts.
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 Quote by ThomasT Since λa is presumably varying randomly from photon to photon, then individual detection attributes (0 or 1) can't be predicted.
OK, but given λa for a particular photon pair, how do you get a 0 or a 1 out of that?
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 Quote by lugita15 Wavefunction collapse has an illustrious history going back to Max Born and John von Neumann. They saw collapse as the most natural explanation for the fact the wavefunction could be calculated deterministically using the Schrodinger equation, but the results of quantum mechanical experiments could only be predicted probabilistically. And I think it was Schrodinger himself who came up with the idea that entangled particles are described by a common wavefunction that stretches across space, and that any changes in the wavefunction propagate instantaneously.
I don't think that's the most natural, or logical, way of looking at the experimental situation or interpreting the QM formalism. Instantaneous propagation seems to be a contradiction in terms. Reification of ψ carries some unnecessary baggage with it, and I doubt that most working physicists think in those terms.

Both LR and QM have coincidental detection determined by the incident photons consulting a common function. Ie., there's a common cause which produces the relationship between entangled photons that the polarizers are jointly measuring. The difference is that QM doesn't use λ (which refers to the polarization orientation of the polarizer-incident photons), presumably recognizing that the value of λ is irrelevant wrt determining rate of coincidental detection.

 Quote by lugita15 Where has this been demonstrated?
In my previous post. Or you can go back to Bell 1964.
 Quote by J. S. Bell So in this simple case there is no difficulty in the view that the result of every measurement is determined by the value of an extra variable, and that the statistical features of quantum mechanics arise because the value of this variable is unknown in individual instances.
Wrt,
 3. From this you conclude that both photons are consulting the same function P(θ). If P(θ)=1, then the photon goes through the polarizer, and if it equals zero the photon does not go through.
I said,
 Quote by ThomasT This seems to me to be compatible with QM. Why do you think it isn't?
To which you replied,
 Quote by lugita15 According to the conventional interpretation of quantum mechanics, you have a nonlocal wavefunction collapse that determines on the spot whether the particles should go through or not. Whereas a local determinist believes that the particles have agreed in advance what angles to go through or not go through.
Both QM and LR have entangled photons consulting the same function. This is because they both assume a common cause. The stuff about nonlocal wavefunction collapse is just unwarranted and unnecessary, imo. The fact is that QM is acausal and (to paraphrase Bohm) nonmechanical wrt entanglement.

Why is the QM formalism the way it is? I'm not sure about that, but I think it does have to do with the assumption of a common cause. Also, as I think I've shown, the value of λ is irrelevant wrt determining rate of coincidental detection. And, anyway, QM doesn't have to be causal, since it's just calculating measurement probabilities.

Why can one still assume local determinism given the QM formalism? Because the QM formalism is acausal wrt entanglement. So, one might interpret entanglement as being due to nonlocal transmissions between entangled photons, or not. No way to know, afaik. Ultimately, the QM treatment wrt optical Bell tests is evaluated wrt the known behavior of light. And of course so should be any LR treatment of entanglement ... which is something that your line of reasoning seems to ignore.

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