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

[lugita15]

thanks lugita...can you respond to https://www.physicsforums.com/showthread.php?t=592401

Sure. The reason that your idea won't work is that if you just look at the results for one of the polarizers, then it will seem like the photon is going through or not going through the polarizer with 50-50 probability, regardless of the angle the polarizer is turned to. It is only when you compare the results of the two polarizers that you notice the correlation. That is why quantum entanglement does not allow you to do faster than light communication.

For a simple example of this, consider the case when you turn both polarizers to the same angle. Then, as you know, they'll either both go through or they'll both not go through. They have a 50 percent chance of both going through and a 50 percent chance of both not goon through. Of course, if you just looked at one of the polarizers it will just seem like the photon is just randomly going through or not going through. But if the experimenters recording the results of the two polarizers compare their data, they will find a remarkable phenomenon: the two photons always do the same thing!

 

[lugita15]

the short answer is: the hidden variables imply a linear relationship because the laws of probability are additive?...and not cosine, exponential etc

Yes, exactly. And the reason that the same logic does not apply to quantum mechanics itself is that in QM, when you turn the polarizers to -30 and 30, it makes no sense to talk about "the instruction at 0 degrees". So step 3 does not work for QM, only for hidden variable theories.

 

[San K]

It is only when you compare the results of the two polarizers that you notice the correlation. That is why quantum entanglement does not allow you to do faster than light communication.

oh yes...i missed that...ha ha...got it..thanks

this happens often with people...they come up with some way to do faster than light communication and then forgot they missed the fact that...both the "ends" need to be compared...:)

 

[lugita15]

oh yes...i missed that...ha ha...got it..thanks

OK, so you might want to delete the new thread you started.

 

[lostprophets]

I have no idea what you're talking about. All I said is that certain assumptions lead to correct conclusions about the world, and certain assumptions lead to incorrect conclusions about the world. Many arguments take the form of starting from an assumption and showing how it leads to a false conclusion about the world. For instance, Rayleigh-Jeans showed that the assumption that light is described by Maxwell's equation leads to the ultraviolet catastrophe, which does not occur in real life. Rayleigh-Jeans certainly wasn't ignoring the fact that there is no ultraviolet catastrophe for real-life blackbody radiation, but he was showing how a certain assumption led to that incorrect conclusion. Herbert's (and Bell's) proof works the same way. They are trying to show that the assumption of local hidden variables leads to a certain conclusion that is contrary to the experimental predictions of quantum mechanics, even though the predictions of QM are presumably correct.

i like assumptions.
provided there used as an awareness of what may or may not be and not the be all .there how we built the world

 

[ThomasT]

No, the local hidden variable models that successfully reproduce the results of current Bell tests do NOT agree with the quantum mechanical prediction of perfect correlation at identical polarizer settings.

Not sure what you're saying. Are you saying that there are recent Bell tests wrt which there are viable LR models? If so, then because any LR model of entanglement must disagree with QM, then that would mean that QM gets those Bell tests wrong.

I actually agree with you that Herbert's conclusion is stated a bit too boldly. He says that the proof definitively show that reality is not local, i.e. local hidden variable theories are decisively ruled out.

Showing that LR theories of entanglement are ruled out isn't showing that nature is nonlocal. It just means that entanglement can't be modeled in a certain way. There are more parsimonious ways of understanding why this is so than resorting to the assumption that nature is nonlocal.

But in my 4 steps, I am not discussing any formal model. I am starting with the premise that this is a local deterministic universe, and I am logically deducing the consequences of this premise.

It's still not clear to me how, from those 4 steps, it can be deduced that nature is nonlocal.

Maybe if you put your argument in a form like: 'If the universe is local deterministic, then ___ must be the case ...', and so on.

 

[ThomasT]

I agree that empirically this is still an open question, albeit open by a very slim margin. But logically, the only way local determinism would not be ruled out by an ideal loophole-free experiment would be if the predictions of QM were disproven.

The experiments can only rule out LR models of entanglement. They can't inform wrt whether or not nature is nonlocal. Both locality and nonlocality are assumptions. Locality is a generalization of all known experience. Nonlocality is, so far anyway, just a word for our ignorance. It has no physical referents.

 

[lugita15]

Not sure what you're saying. Are you saying that there are recent Bell tests wrt which there are viable LR models?

That is exactly what I'm saying, because currently there are various experimental loopholes that prevent the kind of ideal Bell test which would be able to definitively test whether this is a local deterministic universe. In particular, as zonde has pointed out, it is difficult to test the prediction that you get perfect correlation at identical polarizer settings, because you would have to "catch" literally all the photons that are emitted by the source, and that requires really efficient photon detectors. All we can say is that when the angles of the polarizers are the same, the correlation is perfect for the photon pairs we DO detect. But that leaves open the possibility, seized on by zonde and other local determinists, that the photon pairs we do detect are somehow special, because the detector is biased (in an unknown way) towards detecting photon pairs with certain (unspecified) characteristics, and that the photon pairs we do NOT detect would NOT display perfect correlation, and thus the predictions of QM would be incorrect.

If so, then because any LR model of entanglement must disagree with QM, then that would mean that QM gets those Bell tests wrong.

No, it just means that the experiments are not good enough to definitively answer which is right and which is wrong. They strongly suggest quantum mechanics is right, but due to practical loopholes they leave open a slim possibility for a local deterministic theory.

He says that the proof definitively show that reality is not local, i.e. local hidden variable theories are decisively ruled out.

Showing that LR theories of entanglement are ruled out isn't showing that nature is nonlocal. It just means that entanglement can't be modeled in a certain way. There are more parsimonious ways of understanding why this is so than resorting to the assumption that nature is nonlocal.

Sorry, there's a miscommunication. When I say "local hidden variables", I mean the philosophical stance you call "local determinism", not the formal model you call "local realism", so keep that in mind when reading my posts. I'm trying to show that a the predictions of QM cannot be absolutely correct in a local deterministic universe.

It's still not clear to me how, from those 4 steps, it can be deduced that nature is nonlocal.

As I said, the thing to be deduced from my four steps is not the claim that nature is nonlocal. Rather it is the claim that if the predictions of quantum mechanics are completely correct, than nature is nonlocal or nondeterministic.

Maybe if you put your argument in a form like: 'If the universe is local deterministic, then ___ must be the case ...', and so on.

Sure, I just need to change the wording of step 2 slightly.

1. Entangled photons behave identically at identical polarizer settings.
2. In a local deterministic universe, the polarizer angles the photons will and won't go through must be agreed upon in advance by the two entangled photons.
3. In order for the agreed-upon instructions (to go through or not go through) at -30 and 30 to be different, either the instructions at -30 and 0 are different or the instructions at 0 and 30 are different.
4. The probability for the instructions at -30 and 30 to be different is less than or equal to the probability for the instruction at -30 and 0 to be different plus the probability for the instructions at 0 and 30 to be different.

 

[lugita15]

The experiments can only rule out LR models of entanglement.

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]

No, it has not been demonstrated.

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.

I maintain that it is impossible for a local hidden variable theorist who believes in identical behavior at identical polarizer settings to not accept Herbert's Bell inequaity.

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.

Wait a minute, you agree with me that any possible local hidden variable theory must make predictions contrary to those of QM?

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

No, my conclusion is more nuanced: it is that if all the predictions of QM are right, then any possible hidden variable explanation MUST be nonlocal.

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 agree with you that the BI violations produced by current Bell tests, with their practical flaws, do not definitively prove that the universe is nonlocal or nondeterministic.

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

However, it would be a different story if BI violations were produced by perfect, loophole-free Bell tests.

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.

If the predictions of QM are correct, then the universe must be nonlocal or nondeterministic.

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

I'm interested in showing that in principle, the predictions of QM are incompatible with the assumptions of locality and determinism, and I claim to have done so in my four steps.

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]

[..] The proof shows that local hidden variable theories MUST make predictions contrary to the known behavior of light predicted by quantum mechanics. [..]

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]

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.

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

 

[harrylin]

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]

[..] the experiments are not good enough to definitively answer which is right and which is wrong. They strongly suggest quantum mechanics is right, but due to practical loopholes they leave open a slim possibility for a local deterministic theory.[..]

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.

... currently there are various experimental loopholes that prevent the kind of ideal Bell test which would be able to definitively test whether this is a local deterministic universe.

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.

In particular, as zonde has pointed out, it is difficult to test the prediction that you get perfect correlation at identical polarizer settings, because you would have to "catch" literally all the photons that are emitted by the source, and that requires really efficient photon detectors. All we can say is that when the angles of the polarizers are the same, the correlation is perfect for the photon pairs we DO detect. But that leaves open the possibility, seized on by zonde and other local determinists, that the photon pairs we do detect are somehow special, because the detector is biased (in an unknown way) towards detecting photon pairs with certain (unspecified) characteristics, and that the photon pairs we do NOT detect would NOT display perfect correlation, and thus the predictions of QM would be incorrect.

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.

No, it just means that the experiments are not good enough to definitively answer which is right and which is wrong. They strongly suggest quantum mechanics is right ...

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?

... but due to practical loopholes they leave open a slim possibility for a local deterministic theory.

As I said, the loopholes are irrelevant, imo.

Sorry, there's a miscommunication. When I say "local hidden variables", I mean the philosophical stance you call "local determinism", not the formal model you call "local realism", so keep that in mind when reading my posts.

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.

I'm trying to show that the predictions of QM cannot be absolutely correct in a local deterministic universe. As I said, the thing to be deduced from my four steps is not the claim that nature is nonlocal. Rather it is the claim that if the predictions of quantum mechanics are completely correct, than nature is nonlocal or nondeterministic.

1. Entangled photons behave identically at identical polarizer settings.
2. In a local deterministic universe, the polarizer angles the photons will and won't go through must be agreed upon in advance by the two entangled photons.
3. In order for the agreed-upon instructions (to go through or not go through) at -30 and 30 to be different, either the instructions at -30 and 0 are different or the instructions at 0 and 30 are different.
4. The probability for the instructions at -30 and 30 to be different is less than or equal to the probability for the instruction at -30 and 0 to be different plus the probability for the instructions at 0 and 30 to be different.

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]

because the detector is biased (in an unknown way) towards detecting photon pairs with certain (unspecified) characteristics, and that the photon pairs we do NOT detect would NOT display perfect correlation, and thus the predictions of QM would be incorrect.

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 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.

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.

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).

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.

Wait a minute, you agree with me that any possible local hidden variable theory must make predictions contrary to those of QM?

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

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.

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

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.

What would be different? Perfect, loophole-free Bell tests are already assumed.

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.

If perfect, loophole-free Bell tests were ever done, then would QM would suddenly become incorrect? Would QM suddenly become compatible with LR?

I claim that a perfect, loophole-free Bell test could in principle either disprove QM or disprove local determinism.

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

Well, if the predictions of QM are correct and nature is local, then I claim that my four steps show nature is nondeterministic.

 

[lugita15]

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.

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.

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.

But even if determinism by itself is not testable, I claim local determinism is, at least in principle.

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.

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.

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?

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.

As I said, the loopholes are irrelevant, imo.

I agree that the experimental loopholes are irrelevant to the philosophical issues.

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.

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).

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.

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?

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

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 ?
https://www.physicsforums.com/showthread.php?t=74806&highlight=malus+law&page=4

 

[ThomasT]

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.

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.

... even if determinism by itself is not testable, I claim local determinism is, at least in principle.

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]

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 ?
https://www.physicsforums.com/showthread.php?t=74806&highlight=malus+law&page=4

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]

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.

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]

[..]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.
[..]

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]

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.

agreed

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.

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?

 

[ThomasT]

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

My understanding is that, wrt Bell tests, there's a source emitting randomly polarized (or unpolarized) photons. Looking at just one side, without a polarizer between the emitter and detector, then there will be a certain rate of detection per unit time. When a polarizer is placed between the emitter and detector, then the rate of detection is cut by 50%, no matter how the polarizer is oriented.

- 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)?

I'm not sure what you're asking. A photon transmitted by the polarizer and registered by the detector is hypothesized, I think, to have the same polarization orientation, on interacting with the detector, as the orientation of the polarizer that transmitted it.

- are photon spins partially malleable, by a polarizer, within limits?

I think that's the mainstream hypothesis. But I don't know. There was a thread about this some time back. I forget the title of it.

 

[ThomasT]

I'm not sure about this ...

Neither am I. DrC is pretty familiar/fluent wrt the experiment and simulation you mentioned. I think he might agree with:

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.

But I don't know.

 

[lugita15]

zonde might be a good person to ask about this. He believes in models in which you would get dramatically different results if you detected all the entangled pairs. He thinks the polarizers are somehow biased towards only detecting the ones that display perfect correlation.

 

[ThomasT]

zonde might be a good person to ask about this. He believes in models in which you would get dramatically different results if you detected all the entangled pairs. He thinks the polarizers are somehow biased towards only detecting the ones that display perfect correlation.

This is one point that you and I agree on. Isn't it -- that there wouldn't be any difference if everything were perfect?

Looking at Aspect 1982 the setup is biased in the sense that the only photons that are, supposedly, considered (ie., interacting with the polarizers) are one's moving in exactly opposited directions and which are detected within a certain 19ns time interval, and thus presumably were emitted by the same atom during the same atomic transition. That is, the setup is designed so that the only photons which might possibly be detected are entangled photons. (I'm not exactly sure how it works, and it might be that disturbances of lower amplitude get randomly into the transmission lines and that this is one source of the inefficiencies.)

There's no particular reason to assume that anything else is biased or inefficient in any way that can't be accounted for with some reasonable assumptions. Identical polarizers placed in the transmission line path are used, and identical PMTs are used.

So, to me, the most reasonable assumption is that if you had 100% detection efficiency, and 100% pairing efficiency, then QM would still hold, and LR, being necessarily incompatible with QM, would not.

 

[Gordon Watson]

This is one point that you and I agree on. Isn't it -- that there wouldn't be any difference if everything were perfect?

Looking at Aspect 1982 the setup is biased in the sense that the only photons that are, supposedly, considered (ie., interacting with the polarizers) are one's moving in exactly opposited directions and which are detected within a certain 19ns time interval, and thus presumably were emitted by the same atom during the same atomic transition. That is, the setup is designed so that the only photons which might possibly be detected are entangled photons. (I'm not exactly sure how it works, and it might be that disturbances of lower amplitude get randomly into the transmission lines and that this is one source of the inefficiencies.)

There's no particular reason to assume that anything else is biased or inefficient in any way that can't be accounted for with some reasonable assumptions. Identical polarizers placed in the transmission line path are used, and identical PMTs are used.

So, to me, the most reasonable assumption is that if you had 100% detection efficiency, and 100% pairing efficiency, then QM would still hold, and LR, being necessarily incompatible with QM, would not.

Tom, Not wishing to hi-jack this thread, I wonder if this might help you in discussions elsewhere?

"I am certain that, if you had 100% detection-efficiency and 100% pairing-efficiency, then QM would hold, as would Einstein-locality. So that suggests to me the need to focus on the R in LR."

Regards, GW