understanding bell's theorem: why hidden variables imply a linear relationship?

lugita15

I claim they can in principle, although they have not yet done so in practice, definitively rule out the possibility that this is a local deterministic universe (excluding superdeterminism).

ThomasT

I said that, wrt the OP, it's been demonstrated that the assumption of hidden variables doesn't imply a linear relationship between θ and rate of coincidental detection. So, unless you're saying that a nonlinear LR model of quantum entanglement hasn't been done, then it's been demonstrated.

Perfect positive correlation between detection attributes at identical polarizer settings is either observed or it isn't. In hashing out these philosophical and semantic problems, an ideal situation with 100% efficient detection and 100% efficient pairing is usually assumed (which entail perfect positive correlation between detection attributes at identical polarizer settings).

LR models of entanglement have two main features: 1) functions determining rate of individual detection are constructed based on the assumption that a detectable transmission by a polarizer is due to a value of a variable parameter of an underlying property of an incident disturbance interacting with a polarizer setting, and 2) a function determining rate of coincidental detection is constructed based on the assumptions of, i) the independence of events/interactions at the distantly separated polarizers, and ii) a probability distribution of the hidden variable (entailing, ie., that coincidental detection is determined, in the formalism, by the hidden variable that determines individual detection). 1) is compatible with QM and experiment, 2i) isn't.

Of course. Where have I ever said that I thought otherwise?

That doesn't seem very nuanced to me. I have a local deterministic explanation in terms of a relationship (not transmissions) between entangled entities that's produced by local common cause interactions/transmissions, and measured by a global parameter, which satisfies me. It's just that LR modelling possiblities are circumscribed by certain requirements/restrictions. In this view, the assumption of locality is preempted by the consequences of encoding the LR requirements. Which means that BI violation isn't informing wrt nature, but rather wrt the incompatibility between the experimental design/execution and the formalism. QM, in contrast, has no such difficulty because it's not required to be explicitly realistic, or local, or even mechanical.

I don't think that loopholes and practical flaws have anything to do with LR being incompatible with QM and experiment.

What would be different? Perfect, loophole-free Bell tests are already assumed. LR models of entanglement are incompatible with QM.

If perfect, loophole-free Bell tests were ever done, then would QM would suddenly become incorrect? Would QM suddenly become compatible with LR? If not, then you'd have the same situation that exists now with QM making some reasonable assumptions regarding detection and pairing efficiencies.

Apparently, the predictions of QM are correct, but it doesn't follow that nature is nonlocal.

It's definitively proven that the predictions of QM are incompatible with the predictions of LR models which encode certain LR requirements/constraints. It isn't fully understood, much less proven, what might be inferred about nature from this. (My guess is nothing.)

I'll go through your 4 steps, step by step, in my next post.

harrylin

That sentence reproduces the fundamental error that Herbert made as discussed in the thread on Herbert's proof: "the known behavior of light predicted by quantum mechanics" confounds the known behaviour of light (we only know what is observed) and predictions by quantum mechanics about unobserved (and possibly unobservable, and thus not knowable) behaviour of light.

As I now understand it (I'm still very much learning here!), hidden variables may imply a linear relationship for some hypothetical experiments, but do not necessarily imply a linear relationship for realistic experiments as performed until today.

lugita15

Yes, I concede your point. I was just being a bit loose with my wording.

harrylin

[QUOTE=San K;3842509]Agreed. [local hidden variables says that the polarizer angles the photons will and won't go through are agreed upon in advance]

I disagree: that sounds like determinism without any allowance for "randomness". However, that isn't how most people think that nature works, has nothing to do with realism, and as Bell admitted, was also not required by EPR.

harrylin

I guess that it depends on one's preexisting knowledge what one finds that the experiments suggest... For example, the kind of things that comes to my mind (e.g. Ehrenfest paradox, M-M's Lorentz contraction "loophole") suggest to me that most likely local realism is right and that perhaps QM (with a minimal set of claims) is also correct.

ThomasT

Before we nitpick your 4 steps, I'd like to address some other statements you made.
Because of the LR requirements/restrictions, which, in effect, preempt (and thereby render irrelevant wrt nature) the locality assumption, Bell tests, even loophole-free one's, can't ever be used to determine an underlying nonlocality.

As for the assumption of a fundamental deterministic evolution. It's, in principle, nontestable. It's an unfalsifiable assumption. Just as the assumption of a fundamental nondeterminism is.

This just seems to be 'clutching at straws', so to speak. Since the correlation is perfect at θ = 0° for the entangled pairs that are detected, then I see no reason to assume that it would be different if all entangled pairs could be detected.

You said that wrt certain recent Bell tests the LR predictions were correct. We know that LR and QM predictions must be different wrt entanglement setups. So, if the LR predictions were correct, then the QM predictions had to be wrong wrt the tests in question. But now you say that the test results suggest that QM was right? So, which is it?

As I said, the loopholes are irrelevant, imo.

I think that ease of communication would be much better served if we simply write local determinism when we're referring to the philosophical assumptions, and LR when we're referring to the circumscribed LR formalism.

Step 2. doesn't represent a local common cause, or locality (independence). The photons might be exchanging ftl transmissions sometime after their emission from a common source, but before interacting with the polarizers.

From step 1. we might assume that the value of λ, the variable determining whether a photon will go through a polarizer or not, is the same for photons 1 and 2 of any given pair when θ = 0° .

If the value of λ is the same for photons 1 and 2 of an entangled pair when θ = 0°, then is there any reason to suppose that λ would be different for photons 1 and 2 of an entangled pair wrt any other θ, such as 30°?

Before we deal with that, we might speculate about the nature of λ in these experiments involving light and polarizers. The intensity of the light they transmit is affected by the polarizer's orientation. In a polariscopic setup, the intensity of the light transmitted by the analyzing polarizer varies as cos²θ. If we think of the optical disturbances incident on the polarizers as rotating wave shells whose expansion is constrained and directed by the transmission lines, then we can visualize the relationship between the polarizer setting and the axis of rotation as determining the amplitude of the wavefront filtered by the polarizer. So, for our purposes, the assumption that the rotational axes of entangled photons is identical seems to fit with the experimental result noted in step 1.
This common rotational axis of entangled photons, represented by λ, is also compatible with the assumption that it's produced locally via a common emission source.

Back to the preceding question. If photons 1 and 2 of any entangled pair have the exact same rotational axis, then how would we expect the rate of coincidental detection to vary as θ varies?

Using another QM observation we note that rate of individual detection doesn't vary with polarizer orientation, so we assume that λ is varying randomly from entangled pair to entangled pair. We also note that rate of coincidental detection only varies with θ, and, most importantly, as cos²θ. Is this behavior compatible with our conceptualization of λ? It seems to be.

Start with a source emitting entangled photons with λ varying randomly. The emitter is flanked by two detectors A and B. Whatever the rate of coincidental detection is in this setup is normalized to 1. After putting identical polarizers in place, one between the emitter and A and one between the emitter and B, we note that the maximum rate of coincidental detection is .5 what it was without the polarizers, and that it varies from .5, at θ = 0° to 0 at θ = 90° as cos²θ.

Now visualize this setup without the emitter in the middle and with the polarizers aligned (θ = 0°). We note a common rotational axis extending between the polarizers. Now rotate one or both of the polarizers to create a θ of 30°. We note a common rotational axis extending between the polarizers. Now rotate one or both of the polarizers to create a θ of 60°. We note a common rotational axis extending between the polarizers.

It's just like a polariscope, except that the source emitting random λ's is in the middle rather than at one end or the other, so both polarizers are analyzers, and the rate of coincidental detection is a function of the same angular dependency, and analogous to the detected intensity, as in a regular polariscopic setup.

Thus, the nonlinear angular dependencies observed in Bell tests are intuitive, and compatible with a local deterministic view.

San K

why would a detector not detect even one such photon?

also this is somewhat verifiable via (patterns between) count of photons sent Vs detected

lugita15

I still maintain my claim that in a local deterministic universe in which there is perfect correlation at identical angle settings, Herbert's Bell inequality MUST be satisfied and thus the exact nonlinear correlation predicted by quantum mechanics can NOT be reproduced.
I agree, experimental loopholes like detector efficiency are irrelevant for the philosophical issues we're discussing concerning whether local determinism is compatible in principle with all the predictions of quantum mechanics. The only reason I brought it up is because you mentioned local deterministic theories that are consistent with the results of currently practical Bell tests, and I was explaining how that is possible. It is because those models exploit experimental loopholes in order to claim that some of the predictions of QM are wrong, but that current practical limitations prevent us from definitively testing those particular predictions. Remember, when I say "local hidden variables" I mean what you call "local determinism". Keeping that in mind, I assume you don't agree with me anymore.Loopholes have nothing to do with why local determinism is incompatible with the predictions of QM. But loopholes are relevant to the question of whether currently practical Bell tests definitively rule out local determinism, which is a question I'm not really interested in.Of course they're assumed in our philosophical discussion. I was just making a brief aside because you were making claims about what has and hasn't been demonstrated experimentally.I claim that a perfect, loophole-free Bell test could in principle either disprove QM or disprove local determinism.Well, if the predictions of QM are correct and nature is local, then I claim that my four steps show nature is nondeterministic.

lugita15

But my proof, which is about a perfect loophole-free Bell test, isn't talking about the formal model you call LR. It's talking about the philosophical stance that this is a local deterministic universe. But even if determinism by itself is not testable, I claim local determinism is, at least in principle.I agree that the view zonde advocates can be fairly described as "clutching at straws" (no offense), but I was just responding to your mention of local deterministic theories that are not absolutely ruled out by currently practical Bell tests.Bell tests performed to date have not been good enough to definitively test which is right, the predictions of QM or the predictions of local determinism. They strongly lean towards QM being right, but there are small loopholes from making this definitive, and it is these loopholes that local determinists like zonde cling to. I agree that the experimental loopholes are irrelevant to the philosophical issues.Yes, I'll try to avoid using at least the term "local realism". But just keep in mind that when I say "local hidden variables", I mean what you call "local determinism". (By the way, your usage of the term local realism is nonstandard, because most people use the term to refer to a philosophical stance). You're right, Step 2 applies not only to all local deterministic theories, but also to some nonlocal deterministic theories. Anyway, is step 2 where you disagree with my argument, and if not which step is it? But I'm not asking you to give a plausible justification for why you think the nonlinear correlation predicted by QM would make reasonable sense in a local deterministic universe. I'm asking you, what specific step in my reasoning do you dispute?

morrobay

It is understood that Malus's Law and QM were derived independently.
I = I_m cos² theta
cos² 30^o = .75
cos² 60^o = .25
cos² 120^o= .25
cos² 45^o = .5
And when polarizing plates are parallel , 0^o, 180^o
cos² = 1
For QM : 1/2Pi integral cos²(theta) d(theta) = same as above (1/2Pi)
How then can the mechanism in Malus's Law be discounted in having an effect
(not cause ) in the Bells Inequalities violation counts ?
http://www.physicsforums.com/showthr...lus+law&page=4

ThomasT

You said that nonlinear LR models haven't been demonstrated, implying that, wrt the OP and title question, hidden variables imply a linear relationship between θ and rate of coincidental detection. But, it's a matter of fact that hidden variables don't imply a linear relationship θ and rate of coincidental detection, because there are nonlinear LR models of quantum entanglement. So, the OP's question has been answered.

Your claim is, in part, that LR models can't reproduce the exact nonlinear correlation predicted by QM. I agree with this. Afaik, most everybody agrees with this.

But you want to extend that mathematical fact to a statement about nature. Namely, that the incompatibility between LR and QM proves that nature is nonlocal. There do seem to be a number of physicists who believe this, but there are also a number who don't. I don't know the numbers, but, in my experience, no working physicist, teacher, professor, experimentalist, or theorist that I've talked to about this stuff believes that nonlocality has been proven vis the incompatibility between LR and QM -- with the possible exception of dBB advocates, who, it bears noting, have a sort of vested interest in interpreting Bell's theorem as proof positive that nature is nonlocal.

The bottom line is that your n step proof(s) cannot possibly prove that nature is nonlocal, because the only thing that can possibly prove the empirical truth of such a statement would be the objective observance and recording of the ocurrence of ftl transmissions. Wrt which, afaik, there are none.

I offered, in post #75, a certain way of looking at optical Bell tests to show that wrt a slightly less pedestrian (but not much less) and non-anthropomorphic conceptualization of what's happening in the quantum realm underlying instrumental behavior it's possible to construct a view of quantum entanglement (at least wrt certain simplified and idealized setups) that's compatible with the philosophical assumption of local determinism. Of course, this conceptualization doesn't prove that nature is local any more than your arguments prove that it isn't.

It really is an open question, imho, as to whether nature is local or nonlocal. But modern physical science continues to assume (ie., proceed according to the working hypothesis) that nature, our universe, is evolving deterministically in accordance with the principle of locality, because these assumptions are the most reasonable given what's currently known.

The assumption that nature is exclusively local is a falsifiable assumption vis the production of just one nonlocal transmission. The assumption that nature is evolving deterministically isn't falsifiable.

With this, I think I should fade back into the peanut gallery wrt this thread. As far as I'm concerned the OP's question has been answered. If he wants more info he can find it via PF, Google, Yahoo, arxiv.org, etc. searches. If you still want to discuss your n step proof(s) that nature is nonlocal, then I think the appropriate place to do that would be in the philosophy forum.

ThomasT

Thanks for the link. Interesting thread. Regarding your question, Malus Law isn't discounted in the QM treatment of optical Bell tests. I wouldn't call Malus Law itself a mechanism. Not that you did that.

I suppose you're referring to some presumed underlying dynamics that result in the observations referred to collectively as supporting the Malus Law function. I would also suppose that virtually all optics texts have something to say about the mechanism underlying observations of Malus Law.

San K

Thanks Thomas. My question has been answered namely - laws of probabilities are additive and hence linear. Bells proof, proving existence of quantum entanglement, seems valid to me within the scope of this question. If one has to go beyond that then it requires much more research and thinking. I will go through your posts in detail later this week.

the hypothesis that I had in mind was that at various angles it would not be linear however I realized that in LHV the photons would not even know the angle between the polarizers. The hypothesis that I had in mind however fits with QM

ThomasT

Yes. Bell's proof is valid. But it doesn't prove the existence of quantum entanglement. Quantum entanglement refers to certain experimental results and the preparations that produce those results. It's just a convention. What Bell proved was that Bell LR models of entanglement are incompatible with QM. The larger question is how to interpret that, what it might entail wrt inferences about nature.

But don't waste any time on my posts. I'm as fascinated and confused about this stuff as anyone. A recommended path of inquiry would be to go back to Bell 1964 and work your way forward from there. When you have questions about a mathematical meaning or a conceptual line of reasoning, then present them at PF.

harrylin

I'm not sure about this, but it seems to me that here is again a partial misunderstanding, for there is a "twist" on this: the correlation may be perfect for those pairs that are called "entangled pairs".

To be clearer I'll give an example (however deeper discussion would need a new thread): in Weihs' experiment, many pairs were actually detected but rejected for analysis by means of a very small time window, while reanalysis by De Raedt et al yielded a very different result with a larger time window; this was all matched with a partly ad hoc local simulation model.

San K

agreed

good suggestion, thanks Tom.

a thought .....

50% of all photons pass through a polarizer at all angles .....

- are the 50% different from the 50% that don't pass through (just like the initial conditions of a coin toss which shows heads is different from a coin toss which shows tails)?
- are photon spins are partially malleable, by a polarizer, within limits?
- do the members of the 50% pass-through group keep changing with the polarizer angle?