why is superdeterminism not the universally accepted explanation of nonlocality?

ThomasT

Yes. But wrt a local realistic view, the independent variables, the input, are not just the polarizer orientation, but also the polarization of the incident optical disturbance ... which are continuous within proscribed limits. The output is either the registration of a detection (usually denoted as 1), or a nondetection (usually denoted as 0), wrt any particular coincidence interval (ie., wrt paired detection attributes).

As I mentioned, maybe it's wrt this step that your particular LR line of reasoning necessitates the conclusion that the correlation between θ and rate of coincidental detection is linear.

Though I thought it was Step 5. But I could be mistaken.

I don't see how the inference of a linear correlation follows from Step 4. ...

... because all Step 4. says is that the correlation between θ and rate of coincidental detection is a function of θ. Which leaves open the question of whether or not this is a linear or a nonlinear correlation.

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.

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 - λ_a), or in the same way for the B side.

-------------------------------

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?

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?

lugita15

You still haven't told me how any of this determines whether a particular photon goes through the polarizer or not.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.

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).

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.

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 - λ_a)


Wrt your points this would be:

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).

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.

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.

ThomasT

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.

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.

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.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.

lugita15

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?

ThomasT

The function, cos²(a - λ_a), does determine whether a given photon goes through a given polarizer at a given angle. At least that's the assumption. But λ_a can't be controlled.

ThomasT

I'm not sure that's the case.

How, exactly, does that work? What do you think is the conceptual basis for that assumption?

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.

This seems to me to be compatible with QM. Why do you think it isn't?

ThomasT

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).

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.

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.

Which says:

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?

lugita15

So how do you get from cos²(a - λ_a) to a 0 or a 1?

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 a common wavefunction that stretches across space, and that any changes in the wavefunction propagate instantaneously.Where has this been demonstrated? 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.

lugita15

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.
No, QM doesn't.