Local realism ruled out? (was: Photon entanglement and )

[SpectraCat]

I will try a bit differently. I understand that analogy is not the best argument but let me use one this time.

Let's consider an experiment.
You and I each take ten pebbles. We arrange them so that we can later identify pairs from our pebbles (say we number them from 1 to 10 and my n-th pebble makes pair with your's n-th pebble).
Now each of us picks one pebble and we compare them and identify if they are from the same pair. If they do not make pair we discard them. If they make a pair then we record whether your pebble is bigger than mine or not.
After that we repeat from start - you and I each take ten pebbles ...
When we have collected some amount of data we find out that your pebble is bigger in almost all cases (or more precisely there is on average one exclusion for every 200 000 successful runs).
Now there are two observers that analyze this data.
Observer A says that this result indicates that your pebbles are bigger than mine.
Observer B says that this result does not indicate anything particular about our pebbles but it shows that I am picking smallest pebble out of my ten but you are picking biggest pebble out of yours.
However observer A insists that he is correct because as he speculates if we modify the experiment so that we take only one pebble instead of ten then we will observe the same result.

Now do you agree with observer A?

What does this prove, other than that one can construct a random example where the free sampling assumption is not valid (in this case because choices of conscious beings are involved, which is hardly apropos of anything in the physical example we are discussing)?

Most significantly, what does it have to do with the Bell theorem? Analogies are only useful to the extent that they draw *clear* parallels between the elements of the physical systems they are created to explain/clarify.

 

[Frame Dragger]

What does this prove, other than that one can construct a random example where the free sampling assumption is not valid (in this case because choices of conscious beings are involved, which is hardly apropos of anything in the physical example we are discussing)?

Most significantly, what does it have to do with the Bell theorem? Analogies are only useful to the extent that they draw *clear* parallels between the elements of the physical systems they are created to explain/clarify.

Thank god you said that. I thought I was just being dense and missing some deep point. I agree with DrChinese (you're out beers Cat, sorry), but this metaphor seems... odd.

I think the issue here is that there is a cos^2Theta statistical relationship between photons that never "met" each other (I'm convinced of this via another thread). I can see the holes in it, I just think it's a "preponderance of the evidence" in favour of LR being out. I remain to be convinced "beyond a reasonable doubt".

I'd like to get back to the nuts and bolts of whether or not two entangled photons (really one photon), can be generated from separate sources. The implications are really disturbing if you accept them on their face.

 

[zonde]

Unfortunately, that doesn't make your point a whole lot clearer (at least not to me). In the "normal" interpretation of the experiment we are discussing (i.e. the one put forward by the authors of the paper), photons A1 and A2 (in your notation) become entangled when they interfere at the fiber beam splitter. This entanglement is then teleported to the "non-interacting" pair B1 and B2, as confirmed by violation of a Bell inequality.

Are you proposing an alternative explanation of the experiment, whereby A1 and A2 do not become entangled at the beamsplitter, or are you saying that their entanglement is not required for observation of a Bell violation for B1 and B2? Or are you saying something else entirely?

A1 and A2 photon interfere at beam splitter provides information about B1 and B2.
You have to determine this information by detections after beam splitter. If this wouldn't be so you wouldn't need any detections after BS.

 

[zonde]

What does this prove, other than that one can construct a random example where the free sampling assumption is not valid (in this case because choices of conscious beings are involved, which is hardly apropos of anything in the physical example we are discussing)?

Most significantly, what does it have to do with the Bell theorem? Analogies are only useful to the extent that they draw *clear* parallels between the elements of the physical systems they are created to explain/clarify.

Yes I agree that parallels should be clear between analogy and topic in question.
So the parallel is that if QM observable comes from this type of measurement described in this analogy then it might turn out that the thing you measure is actually workings of your measurement equipment and in no way your supposed measurement object.
In this case observable becomes more and more uncertain with increase of detection efficiency while becomes completely uncertain at 100% efficiency. And this is not tested experimentally so you can't exclude this (quite classical) possibility.

About fair or unfair sampling assumption - yes this is unfair sampling demonstration. But then what did you expected? About the choices of conscious beings I would say that they are quite mechanical so nothing unphysical here.

And what does it have to do with Bell is that fair sampling comes into the argument right at the start motivated by questionable interpretation of QM.

 

[DrChinese]

I will try a bit differently. I understand that analogy is not the best argument but let me use one this time.

Let's consider an experiment.
You and I each take ten pebbles. We arrange them so that we can later identify pairs from our pebbles (say we number them from 1 to 10 and my n-th pebble makes pair with your's n-th pebble).
Now each of us picks one pebble and we compare them and identify if they are from the same pair. If they do not make pair we discard them. If they make a pair then we record whether your pebble is bigger than mine or not.
After that we repeat from start - you and I each take ten pebbles ...
When we have collected some amount of data we find out that your pebble is bigger in almost all cases (or more precisely there is on average one exclusion for every 200 000 successful runs).
Now there are two observers that analyze this data.
Observer A says that this result indicates that your pebbles are bigger than mine.
Observer B says that this result does not indicate anything particular about our pebbles but it shows that I am picking smallest pebble out of my ten but you are picking biggest pebble out of yours.
However observer A insists that he is correct because as he speculates if we modify the experiment so that we take only one pebble instead of ten then we will observe the same result.

Now do you agree with observer A?

The problem with this argument is that it actually does not work! Designing an analogy that meets this criteria is not so simple as you imply, and the reason is as follows:

You must choose the larger pebble in some cases and the smaller one in others! How do you know which to do? You must communicate classically!

The De Raedt group attempted the same with their computer simulation. At first it appears that such a simulation can be constructed. However, the requirements of matching the QM predictions are so difficult that this turns out to be impossible.

It is NOT enough to say you can do it - without actually doing it!

 

[DrChinese]

In this case observable becomes more and more uncertain with increase of detection efficiency while becomes completely uncertain at 100% efficiency. And this is not tested experimentally so you can't exclude this (quite classical) possibility.

Except that when the full sample is counted, the results still match the QM prediction. That experiment has already been performed.

 

[SpectraCat]

Yes I agree that parallels should be clear between analogy and topic in question.
So the parallel is that if QM observable comes from this type of measurement described in this analogy then it might turn out that the thing you measure is actually workings of your measurement equipment and in no way your supposed measurement object.
In this case observable becomes more and more uncertain with increase of detection efficiency while becomes completely uncertain at 100% efficiency. And this is not tested experimentally so you can't exclude this (quite classical) possibility.

About fair or unfair sampling assumption - yes this is unfair sampling demonstration. But then what did you expected? About the choices of conscious beings I would say that they are quite mechanical so nothing unphysical here.

And what does it have to do with Bell is that fair sampling comes into the argument right at the start motivated by questionable interpretation of QM.

No, you seem to be missing the point. The Bell theorem has nothing to do with QM per se, only the test case for which it was initially devised has to do with QM. So any flaw in predictions or interpretation of QM is not transferred to the Bell theorem, all it does it cast some doubt on the proper interpretation of an experiment where an apparent Bell inequality violation is observed.

Second, I had not thought of this before, but it seems unfair sampling is covered within the context of the Bell theorem, as far as I can see. Bell uses $$\rho\left(\lambda\right)$$ to represent the probability distribution of the hidden variable parameter lambda, and the only assumption he makes about it is that it is normalized to 1. So, in the case of unfair sampling, the assumption is that the actual experiment only samples a subset, call it $$\rho'\left(\lambda\right)$$ of the "real" probability distribution, correct? If so, this should make *no difference* on the predictions of the Bell theorem, because it is valid for any probability distribution. All that is required is a "renormalization" of the $$\rho'$$ distribution to 1, which certainly seems valid, since that distribution now represents all of the possible measurement results for A and B.

Am I missing something with the above analysis? If not, what is the big deal about "unfair sampling"?

 

[DrChinese]

Second, I had not thought of this before, but it seems unfair sampling is covered within the context of the Bell theorem, as far as I can see. Bell uses $$\rho\left(\lambda\right)$$ to represent the probability distribution of the hidden variable parameter lambda, and the only assumption he makes about it is that it is normalized to 1. So, in the case of unfair sampling, the assumption is that the actual experiment only samples a subset, call it $$\rho'\left(\lambda\right)$$ of the "real" probability distribution, correct? If so, this should make *no difference* on the predictions of the Bell theorem, because it is valid for any probability distribution. All that is required is a "renormalization" of the $$\rho'$$ distribution to 1, which certainly seems valid, since that distribution now represents all of the possible measurement results for A and B.

Am I missing something with the above analysis? If not, what is the big deal about "unfair sampling"?

Preaching to the choir here... :)

The issue of unfair sampling seems to revolve around an idea which changes every time you ask anyone to be specific. Sometimes it relates to the coincidence time window. Sometimes it is that actual entire pairs go undetected (which would be bizarre given detector efficiencies).

I simply challenge anyone who asserts the fair sampling assumption is a valid loophole to provide a dataset in which the full universe differs suitably from the sample. Then tell me by what rule data items are included or excluded. Then we can see if that hypothesis can be physically viable. So far, there have been no takers. But there have been a lot of hand wavers - because the constraints are quite severe when you actually run the exercise.

So yes, I think the Bell Inequality applies, and this becomes clear during the exercise when you try to think up a universe in which the QM predictions are wrong.

 

[ThomasT]

Awww, I just knew there was a catch. I'd say the thread has improved

There's always a catch. I'm betting that there's one regarding the standard interpretation of Bell's theorem.

... I've made my views clear in this thread ...

You haven't commented on any specific aspect of the formal incompatibility between Bell's ansatz and Bell tests. I gather that you think that nonlocality can be inferred from Bell test results. This requires that something in Bell's generalized LHV formulation represents locality. What exactly do you think that is?

... I'd say the thread has improved ...

At least they're not talking about superdeterminism and free will any more.

I've learned some things from the thread, and, as always, these discussions get me thinking about this stuff again -- and, yes, I'm still confused.

The OP's (akhmeteli) main points are not supported.

Bell test results do not imply nonlocality.

Bell's general LR formulation doesn't represent locality.

LR is not definitively ruled out (but it doesn't look promising for the LRists).

Ruling out LR doesn't entail that Nature is nonlocal.

A more reasonable viewpoint is that our lack of a detailed qualitative understanding of quantum level reality (and other technical problems which prohibit the accurate prediction of individual results) is what prohibits a viable LR description.

Is it possible to say that LR is ruled out experimentally and ignore all arguments about internal problems in QM?

Yes. The ruling out, or not, of LR has nothing to do with QM. It has to do with the problem of formalizing locality. Bell expresses locality as the factorability of the joint probability. Do you see a problem with that? If not, you should.

Hm
Imagine that QM is not discovered yet (but SR is discovered)
However, there are many EPR Alice/Bob experiments and tons of data
I was thinking that in that case it would be possible to rule out local theories, even without QM, just based on the experiments. AM I wrong?

No. Let's go further and say that you've got tons of data from biphoton Bell-type experiments, and there's no Bell's theorem, no QM, and no consideration of nonlocality.

You're producing pairs of counter-propagating optical disturbances via atomic cascades, with each pair randomly polarized (and members of each pair identically polarized via emission by the same atom), and you're analyzing each pair with 2 crossed polarizers.

From classical optics, which is all you've got to refer to, What sort of correlation would you expect to see between rate of joint detection, P(A,B), and the angular difference (|a-b|, or θ) between the polarizer's transmission axes?

You would expect to see P(A,B) = cos²θ . Why? Because when you put two polarizers between a source of randomly polarized light and a detector, then the measured intensity (the rate of coincidental detection) varies as cos²θ.

Intuitively, from the above, this seems like a local common cause scenario, right? Now formalize it.

If you can't construct a viable and explicitly local model for joint detection, then does that mean that joint detection is determined nonlocally? No.

But suppose that you are able to construct a viable and explicitly nonlocal model, then does that mean that joint detection is determined nonlocally? No.

 

[SpectraCat]

Bell expresses locality as the factorability of the joint probability. Do you see a problem with that? If not, you should.

You keep saying that, but I went back to the original Bell paper again recently to check something else, and I really don't think your statement is correct.

The passage from Bell's paper addressing locality is from section II:

"The result A of measuring $$\vec{\sigma_{1}}\cdot\vec{a}$$ is then determined by $$\vec{a}$$ and $$\lambda$$, and the result B of measuring $$\vec{\sigma_{2}}\cdot\vec{b}$$ in the same instance is determined by $$\vec{b}$$ and $$\lambda$$, and
$$A\left(\vec{a},\lambda\right)=\pm1, B(\vec{b},\lambda)=\pm1$$.
The vital assumption [here he references Einstein's definition of locality from an earlier text] is that the result B for particle 2 does not depend on the setting $$\vec{a}$$, of the magnet for particle 1, nor A on $$\vec{b}$$."

Just to be clear, the definitions of the terms are: $$\sigma$$ refers to the spin of one member of an entangled pair, a and b are the settings of the detectors (Stern-Gerlach magnets in his example), and $$\lambda$$ is the parameter introduced to account for any and all hidden variables.

So, at this point, he is just using the definition of locality put forth by Einstein, summarized in the last sentence of the quote above. That seems a good definition of locality to me, do you find fault with it?

He then goes on to say,

"If $$\rho\left(\lambda\right)$$ is the probability distribution of $$\lambda$$ then the expectation value of the product of the two components $$\vec{\sigma_{1}}\cdot\vec{a}$$ and $$\vec{\sigma_{2}}\cdot\vec{b}$$ is
$$P(\vec{a},\vec{b})=\int d\lambda\rho(\lambda)A(\vec{a},\lambda)B(\vec{b},\lambda)$$

So, what is the problem with that? Where is the contradictory assumption that you keep asserting exists? I have reproduced it all here in Bell's words so that you can point it out, because I cannot find it.

I also don't think this is simply the "factorability of the joint probability" ... the integration is significant there, and as far as I can see prevents any factorization as you suggest.

In past posts, you have written that Bell locality is *defined as* P(A,B)=P(A)P(B) ... that certainly looks different to me from what is actually written in his paper.

 

[Dmitry67]

Yes. The ruling out, or not, of LR has nothing to do with QM. It has to do with the problem of formalizing locality. Bell expresses locality as the factorability of the joint probability. Do you see a problem with that? If not, you should.

Got it.

But let's approach it from another side: if we take QM and assume any Interpretation where wavefunction is "real/objective" (whatever it means :) ) we automatically assume that Nature is nonlocal?

So Local Realists have a shorter list of Interpretations to be used?

 

[zonde]

No, you seem to be missing the point. The Bell theorem has nothing to do with QM per se, only the test case for which it was initially devised has to do with QM. So any flaw in predictions or interpretation of QM is not transferred to the Bell theorem, all it does it cast some doubt on the proper interpretation of an experiment where an apparent Bell inequality violation is observed.

The goal of Bell's theorem is to compare QM prediction with something else. You can not compare apples with oranges so you have to make similar formulation to QM formulation. If QM formulation is misleading you would replicate the same flaw in alternate formulation.
Look you can see this here:
"If $$\rho\left(\lambda\right)$$ is the probability distribution of $$\lambda$$ then the expectation value of the product of the two components $$\vec{\sigma_{1}}\cdot\vec{a}$$ and $$\vec{\sigma_{2}}\cdot\vec{b}$$ is
$$P(\vec{a},\vec{b})=\int d\lambda\rho(\lambda)A(\vec{a},\lambda)B(\vec{b},\lambda)$$
This should equal the quantum mechanical expectation value, which for the singlet state is
$$<\vec{\sigma_{1}}\cdot\vec{a}\,\vec{\sigma_{2}}\cdot\vec{b}>=-\vec{a}\cdot\vec{b}$$"

It all comes from interpretation of QM that QM probability should look something like that:
$$P(\vec{a},\vec{b})=\int d\lambda\rho(\lambda)A(\vec{a},\vec{b},\lambda)B(\vec{b},\vec{a},\lambda)$$

Second, I had not thought of this before, but it seems unfair sampling is covered within the context of the Bell theorem, as far as I can see. Bell uses $$\rho(\lambda)$$ to represent the probability distribution of the hidden variable parameter lambda, and the only assumption he makes about it is that it is normalized to 1. So, in the case of unfair sampling, the assumption is that the actual experiment only samples a subset, call it $$\rho'(\lambda)$$ of the "real" probability distribution, correct? If so, this should make *no difference* on the predictions of the Bell theorem, because it is valid for any probability distribution. All that is required is a "renormalization" of the $$\rho'$$ distribution to 1, which certainly seems valid, since that distribution now represents all of the possible measurement results for A and B.

Am I missing something with the above analysis? If not, what is the big deal about "unfair sampling"?

Yes you are missing that you have $$\rho'_{a}(\lambda)$$ and $$\rho'_{b}(\lambda)$$ and you can't both of them normalize to 1 at the same time.
So you will have something like that:
$$P(\vec{a},\vec{b})=\int d\lambda\rho'_{a}(\lambda)\rho'_{b}(\lambda)A(\vec{a},\lambda)B(\vec{b},\lambda)$$

Or alternatively you can look at counter example that I have posted here in attachment:
https://www.physicsforums.com/showthread.php?p=2538611#post2538611"

 

[Eye_in_the_Sky]

Zonde_on_the_Ground

And how you define "PC"?

For a photon ("twin-state") pair emitted in opposite directions, we can define the "PC" feature as follows:

Whenever Alice and Bob set their polarizers to the same angle, they get the same result.

"PC" is essential for Bell's argument but is it essential for local realism?

I think "PC" would be an essential ingredient of any theory which incorporates in it the notion of "angular momentum" as construed in conventional terms. Up here in_the_Sky all theories are formulated with respect to ideal detectors.

Say if light is linearly polarized and then it goes through polarizer with the same orientation of polarization axis as for light. All light is passing through polarizer - perfect measurement.
Now polarizator is oriented at different angle and measurement becomes probabilistic. Are you saying that local realism requires that probability for individual photon can depend only from properties of photon and in no way from context?

Of course it depends on the context – the polarizer orientation, for example. But you mean something else. (Does it have something to do with non-ideal detection?)
________________

Let's go back to Stapp's definition of "CFD":

For each particle on which a measurement is performed, a definite value would have been found if a different spin component had been measured on it instead (although we cannot know what the specific value would have been) and, furthermore, the complete set of such values (measured and unmeasured together) can be meaningfully discussed.

That's clear.

Is it?

But does it mean that deterministic chaos is completely excluded by this definition?

Not at all. This definition has no conflict with deterministic theories, be they of the "controllable" or "chaotic" genre. "CFD" is only in (apparent) conflict with irreducibly stochastic theories of the "fuzzy ontology" genre.

It's hard to accept that [local] deterministic chaos somehow contradicts local realism.

There is no contradiction.
________________

Now if we have chaotic context that determines probability and say we include some controllable factor that contributes to context. Now the the outcome will become predictable but only marginally. We can not eliminate chaotic context we can only override it with controllable factors to some extent.

Okay.

Therefore I say "PC" are not realistic.

Zonde_on_the_Ground, you have done it again. ... I have no idea what you mean.

 

[Eye_in_the_Sky]

... I had not thought of this before, but it seems unfair sampling is covered within the context of the Bell theorem, as far as I can see. Bell uses $$\rho\left(\lambda\right)$$ to represent the probability distribution of the hidden variable parameter lambda, and the only assumption he makes about it is that it is normalized to 1. So, in the case of unfair sampling, the assumption is that the actual experiment only samples a subset, call it $$\rho'\left(\lambda\right)$$ of the "real" probability distribution, correct? If so, this should make *no difference* on the predictions of the Bell theorem, because it is valid for any probability distribution. All that is required is a "renormalization" of the $$\rho'$$ distribution to 1, which certainly seems valid, since that distribution now represents all of the possible measurement results for A and B.

Am I missing something with the above analysis? If not, what is the big deal about "unfair sampling"?

My reply is essentially the same as zonde's.

Let p(a,λ) denote:

the probability that a particle incident on the detector will be registered as a detection event when the measuring device is set to a and the incident particle is in the state λ.

Sampling is unfair iff p(a,λ)≠const.

In the case of (nontrivial) functional dependence on a, Bell's equation (2) needs to be replaced with

P(a,b) = [1/N(a,b)] ∫dλ ρ(λ) p(a,λ) p(b,λ) A(a,λ) B(b,λ) ,

where

N(a,b) = ∫dλ ρ(λ) p(a,λ) p(b,λ) .

 

[Frame Dragger]

For a photon ("twin-state") pair emitted in opposite directions, we can define the "PC" feature as follows:

Whenever Alice and Bob set their polarizers to the same angle, they get the same result.
I think "PC" would be an essential ingredient of any theory which incorporates in it the notion of "angular momentum" as construed in conventional terms. Up here in_the_Sky all theories are formulated with respect to ideal detectors.
Of course it depends on the context – the polarizer orientation, for example. But you mean something else. (Does it have something to do with non-ideal detection?)
________________

Let's go back to Stapp's definition of "CFD":

For each particle on which a measurement is performed, a definite value would have been found if a different spin component had been measured on it instead (although we cannot know what the specific value would have been) and, furthermore, the complete set of such values (measured and unmeasured together) can be meaningfully discussed.
Is it?
Not at all. This definition has no conflict with deterministic theories, be they of the "controllable" or "chaotic" genre. "CFD" is only in (apparent) conflict with irreducibly stochastic theories of the "fuzzy ontology" genre.
There is no contradiction.
________________

Okay.

Zonde_on_the_Ground, you have done it again. ... I have no idea what you mean.

Wow... talk about reaching back in the discussion. I had to go back to page 22 (post 343, thanks for that information) to pick up the thread of just what the hell you were saying.

Oh, and what the hell is this "in the sky" and "on the ground" nonsense? Either it's a joke about your nickname that falls flat, or it's arrogant as hell and laughably unwarrented. Either way, if you're going to ignore the last 5 pages and take things up as though they hadn't happened, how about a little "head up, this is from post #..." ok?

EDIT: You've posted again I see. Are you proposing a revision of Bell's Theorem, or just that there is the famous "loophole" *grits teeth* ? How do you arrive at your "corrections", without piggybacking Zonde's argument which you "basically" have in common?

 

[Eye_in_the_Sky]

Wow... talk about reaching back in the discussion. I had to go back to page 22 (post 343, thanks for that information) to pick up the thread of just what the hell you were saying.

All you needed to do was click on the little blue arrow-thing where it says "Originally Posted by zonde".

Oh, and what the hell is this "in the sky" and "on the ground" nonsense? Either it's a joke about your nickname that falls flat, or it's arrogant as hell and laughably unwarrented.

It's me joking.

Either way, if you're going to ignore the last 5 pages and take things up as though they hadn't happened, how about a little "head up, this is from post #..." ok?

Again, click on the little blue arrow-thing.

EDIT: You've posted again I see. Are you proposing a revision of Bell's Theorem, or just that there is the famous "loophole" *grits teeth* ?

Neither. I was just responding to SpectraCat's query in terms which I thought were absolutely clear.

How do you arrive at your "corrections", without piggybacking Zonde's argument which you "basically" have in common?

I don't know what you mean by this.

 

[SpectraCat]

The goal of Bell's theorem is to compare QM prediction with something else. You can not compare apples with oranges so you have to make similar formulation to QM formulation. If QM formulation is misleading you would replicate the same flaw in alternate formulation.

Again, look at what is written carefully, and you will see that equation 2 in his text is completely unrelated to any postulates of quantum mechanics. It is phenomenologically based, with each term carefully defined, and makes no unstated assumptions, except perhaps that the properties of the entangled particles can somehow be measured in the lab. His "formulation" is not in any way quantum mechanical that I can see.

Bell's theorem is a completely general theorem concerning the joint probability of obtaining particular values from two independent events, that may or may not share a connection through hidden variables.

Look you can see this here:
"If $$\rho\left(\lambda\right)$$ is the probability distribution of $$\lambda$$ then the expectation value of the product of the two components $$\vec{\sigma_{1}}\cdot\vec{a}$$ and $$\vec{\sigma_{2}}\cdot\vec{b}$$ is
$$P(\vec{a},\vec{b})=\int d\lambda\rho(\lambda)A(\vec{a},\lambda)B(\vec{b},\lambda)$$
This should equal the quantum mechanical expectation value, which for the singlet state is
$$<\vec{\sigma_{1}}\cdot\vec{a}\,\vec{\sigma_{2}}\cdot\vec{b}>=-\vec{a}\cdot\vec{b}$$"

It all comes from interpretation of QM that QM probability should look something like that:
$$P(\vec{a},\vec{b})=\int d\lambda\rho(\lambda)A(\vec{a},\vec{b},\lambda)B(\vec{b},\vec{a},\lambda)$$

I do not think it says what you imply, I think you are reading it backward, and inserting a sense that is not there. Bell is just stating what QM predicts for P(a,b), assuming QM is correct. He is establishing his "test case", against which the hidden variable probability expression in equation 2 will be compared, as I have said before. Also, you will have to show me where he makes the statement that:

QM probability should look something like that:
$$P(\vec{a},\vec{b})=\int d\lambda\rho(\lambda)A(\vec{a},\vec{b},\lambda)B(\vec{b},\vec{a},\lambda)$$

as you claim. What he says is (paraphrasing section III), *if* the results at A and B are allowed to depend on the settings at *both* detectors, then a hidden variables description can be formed that is consistent with the predictions of QM, but you are inherently sacrificing locality to do this.

Yes you are missing that you have $$\rho'_{a}(\lambda)$$ and $$\rho'_{b}(\lambda)$$ and you can't both of them normalize to 1 at the same time.
So you will have something like that:
$$P(\vec{a},\vec{b})=\int d\lambda\rho'_{a}(\lambda)\rho'_{b}(\lambda)A(\vec{a},\lambda)B(\vec{b},\lambda)$$

You have not defined what you mean by $$\rho'_{a}(\lambda)$$ and $$\rho'_b{b}(\lambda)$$, and it is not clear what they are supposed to be from context. Bell's $$\rho(\lambda)$$ and my $$\rho'(\lambda)$$ are probability distributions for lambda. Presumably your expressions are intended to reflect that the behavior at a given detector, or for a given setting may depend on lambda in a way that is different from other detectors or settings? But that is already accounted for in Bell's definition of the measurements A and B .. in fact, I cannot see any possible definition for your "probability sub-distributions" that is not already accounted for in the definitions of $$A(\vec{a},\lambda)$$ and $$B(\vec{a},\lambda)$$ in Bell's paper.

Or alternatively you can look at counter example that I have posted here in attachment:
https://www.physicsforums.com/showthread.php?p=2538611#post2538611"

The link in the last post is broken ... I will read through the thread when I have more time .. it seems like there is a lot there to absorb.

 

[SpectraCat]

My reply is essentially the same as zonde's.

Let p(a,λ) denote:

the probability that a particle incident on the detector will be registered as a detection event when the measuring device is set to a and the incident particle is in the state λ.

Sampling is unfair iff p(a,λ)≠const.

In the case of (nontrivial) functional dependence on a, Bell's equation (2) needs to be replaced with

P(a,b) = [1/N(a,b)] ∫dλ ρ(λ) p(a,λ) p(b,λ) A(a,λ) B(b,λ) ,

where

N(a,b) = ∫dλ ρ(λ) p(a,λ) p(b,λ) .

Ok, if that is what zonde was trying to say, then I missed it, but I see your point, and it is basically that unfair sampling is inherently only a problem when the detection efficiency is less than 100%. Since Bell did not account for that, it seems that his formulation does not account for all forms of unfair sampling, as I had thought. I'm not sure I agree with your "iff" above though, because it seems that there could be other ways of introducing a bias through the hidden variables. But in any case, I think those *are* taken care of in Bell's theorem, based on my earlier analysis.

So, would you then agree that a Bell test with 100% detector efficiencies and a spacelike separation between the detectors would be loophole free?

 

[zonde]

I do not think it says what you imply, I think you are reading it backward, and inserting a sense that is not there. Bell is just stating what QM predicts for P(a,b), assuming QM is correct.

And what I imply?
Yes, Bell is just stating what QM predicts for P(a,b), assuming QM is correct.
What I imply is that Bell have to make comparable prediction for local realism. That is what he does in (2) prior to (3).

He is establishing his "test case", against which the hidden variable probability expression in equation 2 will be compared, as I have said before.

Yes and you are saying that this test case can be viewed independently from QM predictions and I kind of disagree with that.

Also, you will have to show me where he makes the statement that:
...
as you claim.

I am not claiming that. Read carefully. I am saying that this is implied QM context for the test case.

You have not defined what you mean by $$\rho'_{a}(\lambda)$$ and $$\rho'_b{b}(\lambda)$$, and it is not clear what they are supposed to be from context. Bell's $$\rho(\lambda)$$ and my $$\rho'(\lambda)$$ are probability distributions for lambda. Presumably your expressions are intended to reflect that the behavior at a given detector, or for a given setting may depend on lambda in a way that is different from other detectors or settings? But that is already accounted for in Bell's definition of the measurements A and B .. in fact, I cannot see any possible definition for your "probability sub-distributions" that is not already accounted for in the definitions of $$A(\vec{a},\lambda)$$ and $$B(\vec{a},\lambda)$$ in Bell's paper.

Sorry for that.
$$\rho'_{a}(\lambda)$$ and $$\rho'_b{b}(\lambda)$$ are probability distributions for measurements of Alice and Bob respectively.
And what I say is that your proposed $$\rho'(\lambda)$$ describes subsample of pairs and therefore it incorporates fair sampling too. In general case you make two subsamples for measurement of Alice and Bob. Then you join them but in case of unfair sampling you get something like that for joined distribution $$\rho'(\lambda,\vec{a},\vec{b})$$.

The link in the last post is broken ... I will read through the thread when I have more time .. it seems like there is a lot there to absorb.

Ok, I attached it here. In this file you have to fill rows up to 10001 except in first sheet. That's so to keep file small.

 

[DrChinese]

So, would you then agree that a Bell test with 100% detector efficiencies and a spacelike separation between the detectors would be loophole free?

Just to be clear about the state of things:

a) Bell tests with 100% detection support QM and rule out LR.
b) Bell tests with spacelike separation support QM and rule out LR.

So far, there is NO LR candidate that can account for Fair Sampling loophole. As I have previously demonstrated, for example, the De Raedt model does not qualify. So I am really curious as to HOW any loopholes are supposed to yield a) and b) separately (supporting QM) but together work to give results consistent with LR. Because I don't think that is possible.

 

[yoda jedi]

However, his definition of the word "covariant" is, mildly speaking, quite unusual.

...Quantum measurements applied to systems composed of several distant subsystems, as those used in Bell inequality tests, are at odds with special relativity. Indeed, quantum measurements "collapse" the wavefunction of the system in a non-covariant way. This is true even if one doesn't strictly apply the projection postulate, as long as one admits that (at least some) measurements have defnite classical results secured in a fnite time. Consequently, the usual wavefunction (or equivalently the state vector) is not a covariant object. This led many authors to conclude that only the probabilities that appear in quantum physics can be described in a covariant way, not the state...Should one conclude that the real stuf in quantum physics is not the state, but the probabilities? Or in more dramatic words, that the real stuf are the probabilities, not the probability amplitudes? In this little note I would like to plunge into quantum ontology and ask what is the real stuf in quantum physics and what are these covariant quantum probabilities...

(and beyond that, ontic vs epistemic vs complete (STATE))





...lies in very different understanding of what a “covariant quantum process” is......Covariant dynamics refers to events that are related to each other through only covariant or Lorentz invariant links. If these events are locally deterministic one has a covariant deterministic model, and if they are locally random a covariant stochastic one.....

maybe the REALITY is poly-ordered or omni-ordered, can coexist (in principle or possibily) past, present and the future.


[STRIKE]irrespective of locality, have to be seen if the CPC negates CTCs[/STRIKE].

better yet, establishes order without time (no determinism or a convoluted determinism, non chronological determinism).

(nonlocal determinism requires nonlocal influences in time ordered manner).

[STRIKE]Ruling out LR[/STRIKE] doesn't entail that Nature is nonlocal.

A more reasonable viewpoint is that our lack of a detailed qualitative understanding of quantum level reality (and other technical problems which prohibit the accurate prediction of individual results) is what prohibits a viable LR description.

maybe order come outside space-time.

REALITY is more.

 

[Eye_in_the_Sky]

I'm not sure I agree with your "iff" above though, ...

As far as I know "unfair sampling" is synonymous with "variable detection probability". If that is correct, then it seems to me that the double "f" of my "iff" is appropriate:

Sampling is unfair iff p(a,λ)≠const.

And then you say:

... it seems that there could be other ways of introducing a bias through the hidden variables. But in any case, I think those *are* taken care of in Bell's theorem, based on my earlier analysis.

It sounds like you are talking about the case where p(a,λ) has no functional dependence on a, so it depends on λ alone. If that is what you mean, then yes I agree: redefine "ρ(λ)" as "ρ(λ)p(λ)² normalized".

So, would you then agree that a Bell test with 100% detector efficiencies and a spacelike separation between the detectors would be loophole free?

I do not know much about the experimental side of things, and I have not been following this issue of "loopholes" closely at all. Albeit, I have known about the "light-cone" loophole for quite some time, it was only after reading your remarks concerning ρ(λ) and ρ'(λ) that I decided to start reading a little bit about just what the "fair-sampling" assumption is supposed be. Since then, I have gone on to read a little more about some of the various "loophole" concerns which are being raised.

With regard to practical loopholes, the only ones that seem readily understandable to me are the "fair-sampling" and "light-cone" loopholes. These two, it seems, are considered to be the most serious. Of course, "100% detector efficiencies" and "spacelike separation" would rule them both out. But with regard to any of the other (alleged) practical loopholes, I just do not know enough about them to formulate an opinion.

... But there will always be the "superdeterminism" loophole. (My only reason for ever entertaining it, however, is for it to entertain me. )

 

[Eye_in_the_Sky]

The Bell theorem has nothing to do with QM per se, only the test case for which it was initially devised has to do with QM. So any flaw in predictions or interpretation of QM is not transferred to the Bell theorem, all it does it cast some doubt on the proper interpretation of an experiment where an apparent Bell inequality violation is observed.

The goal of Bell's theorem is to compare QM prediction with something else. You can not compare apples with oranges so you have to make similar formulation to QM formulation. If QM formulation is misleading you would replicate the same flaw in alternate formulation. ...

Again, look at what is written carefully, and you will see that equation 2 in his text is completely unrelated to any postulates of quantum mechanics. It is phenomenologically based, with each term carefully defined, and makes no unstated assumptions, except perhaps that the properties of the entangled particles can somehow be measured in the lab. His "formulation" is not in any way quantum mechanical that I can see.

In section IV, "Contradiction", of Bell's paper, the argument presented there can be formally written as:

local determinism Λ QM → CONTRADICTION .

What we need to do is CORRECTLY split this proposition up into two parts. In my discussions with akhmeteli, unfortunately, I did not do it right! (Sorry, akhmeteli!) There I wrote:

local determinism → D

and

QM → ~D ,

where D is a certain condition

The correct way to do the split is:

local determinism Λ [P(a,a) = <σ₁∙a σ₂∙a> , for any a] → D

and

QM → ~D .

You can see this from Bell's words centered around equation (13). There he argues that the minimum value of P(a,b) [where P(a,b) is the LHV expectation value as defined in equation (2)] is -1. This follows from relations (1), (2), and (12). So far nothing from QM has been invoked. And then he writes:

It can reach -1 at a = b only if

A(a,λ) = - B(a,λ)

except at a set of points λ of zero probability. Assuming this ...

What is the "this" in the "Assuming this"? It is the condition:

P(a,b) = -1 , for a = b .

And why is he assuming this? ... Because he is assuming:

P(a,a) = <σ₁∙a σ₂∙a> , for any a .
_____________________

SpectraCat, me thinks this is what zonde is getting at.

(... once again, zonde, thanks for helping to open me-Eye)

 

[Demystifier]

...Quantum measurements applied to systems composed of several distant subsystems, as those used in Bell inequality tests, are at odds with special relativity. Indeed, quantum measurements "collapse" the wavefunction of the system in a non-covariant way. This is true even if one doesn't strictly apply the projection postulate, as long as one admits that (at least some) measurements have defnite classical results secured in a fnite time. Consequently, the usual wavefunction (or equivalently the state vector) is not a covariant object.

What do YOU mean by the word "covariant"?
Anyway, with the usual definition of that word, there is a way to make the wave function covariant:
http://xxx.lanl.gov/abs/1002.3226

 

[zonde]

For a photon ("twin-state") pair emitted in opposite directions, we can define the "PC" feature as follows:
Whenever Alice and Bob set their polarizers to the same angle, they get the same result.

I would use "entangled state" instead of "twin-state" because that way you imply certain things that might not be very appropriate.
But otherwise I think we are on the same line here with addition that instead of the same result (maximally similar) there might be maximally opposite result as well depending from setup.

I think "PC" would be an essential ingredient of any theory which incorporates in it the notion of "angular momentum" as construed in conventional terms. Up here in_the_Sky all theories are formulated with respect to ideal detectors.

I would say that I do not quite understand how do you incorporate "angular momentum" in this context. If you associate "angular momentum" with polarization of individual photon then allowing the idea that individual photon is quantized interaction of individual photon with polarizer does not conserve "angular momentum".
If you however take the whole ensemble then yes it seems like you conserve "angular momentum". But then if we will correlate entangled ensembles as a whole we would find out that independent from angle half of both ensembles is passing polarizer. So nothing useful here.
But entanglement is measured by correlating individual photons from entangled ensembles and here it is not obvious that your point about "angular momentum" holds.

And let me even say that it does not hold. Let's take equation that describes entangled state:
$$P_{VV}(\alpha,\beta) = sin^{2}\alpha\, sin^{2}\beta\, cos^{2}\theta_{l} + cos^{2}\alpha\, cos^{2}\beta\, sin^{2}\theta_{l} + \frac{1}{4}sin 2\alpha\, sin 2\beta\, sin 2\theta_{l}\, cos \phi$$
Allow for a moment the possibility that interference (third) term in this equation describes unfair sampling effect. Then by manipulating $$\phi$$ (phase between polarization components) we can reduce interference term to 0.
Resulting equation is completely factorizable and easily explained classically. However if I understand your point correctly it is excluded by your hypothetical classical theory.

 

[zonde]

Just to be clear about the state of things:

a) Bell tests with 100% detection support QM and rule out LR.
b) Bell tests with spacelike separation support QM and rule out LR.

Just to be clear. Your position is that QM without involving Bell inequalities can not stand on it's own complete or incomplete, right?

Btw would you care to scrutinize any particular Bell test with 100% detection?

 

[DrChinese]

1. Just to be clear. Your position is that QM without involving Bell inequalities can not stand on it's own complete or incomplete, right?

2. Btw would you care to scrutinize any particular Bell test with 100% detection?

1. I do not follow this statement. My stand is that the predictions of QM are well supported by experiment. Also that QM does not need to be accurate for Bell's Theorem to be meaningful, as Bell points out that QM and LR are incompatible.

2. Sure:

"Experimental violation of a Bell's inequality with efficient detection" (2001) Rowe et al.

http://www.nature.com/nature/journal/v409/n6822/full/409791a0.html

Not actually 100% detection but high enough. This uses Be ions rather than photons.

"Our measured value of the appropriate Bell's 'signal' is 2.25+/- 0.03, whereas a value of 2 is the maximum allowed by local realistic theories of nature. In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements. Moreover, the high detection efficiency of our apparatus eliminates the so-called 'detection' loophole."

 

[DrChinese]

..And why is he assuming this? ... Because he is assuming:

P(a,a) = <σ₁∙a σ₂∙a> , for any a .

This comment is intended for zonde as much as anyone:

Please, don't forget the historical background. EPR considered that perfect correlations could be explained by a Local Realistic theory. So this must always be considered as well for any candidate theory. Of course, it could be a bad assumption but the evidence says it is not.

 

[ytuab]

1. I do not follow this statement. My stand is that the predictions of QM are well supported by experiment. Also that QM does not need to be accurate for Bell's Theorem to be meaningful, as Bell points out that QM and LR are incompatible.

2. Sure:

"Experimental violation of a Bell's inequality with efficient detection" (2001) Rowe et al.

http://www.nature.com/nature/journal/v409/n6822/full/409791a0.html

Not actually 100% detection but high enough. This uses Be ions rather than photons.

"Our measured value of the appropriate Bell's 'signal' is 2.25+/- 0.03, whereas a value of 2 is the maximum allowed by local realistic theories of nature. In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements. Moreover, the high detection efficiency of our apparatus eliminates the so-called 'detection' loophole."

Actually, Be ion is a "more real" thing than a photon, so the detection efficiency becomes high.

This experiment uses the Paul trap (like the Penning trap?).
This trap probably uses the "external magnetic field and electronic field" to trap the ion correctly.
In page 792(of this paper), " After making the state $$\psi_{2}$$, we again Raman beams for a pulse of short duraion(~400ns) so that the state of each ion j is transformed in the interaction picture as,...

This means the "manipulation" is a laser wave in this experiment?
I have a question about this.
Is it possible that the paul trap influence on the ions is so "strong" that this manipulation of a laser is meaningless?

 

[SpectraCat]

Actually, Be ion is a "more real" thing than a photon, so the detection efficiency becomes high.

This experiment uses the Paul trap (like the Penning trap?).
This trap probably uses the "external magnetic field and electronic field" to trap the ion correctly.
In page 792(of this paper), " After making the state $$\psi_{2}$$, we again Raman beams for a pulse of short duraion(~400ns) so that the state of each ion j is transformed in the interaction picture as,...

This means the "manipulation" is a laser wave in this experiment?
I have a question about this.
Is it possible that the paul trap influence on the ions is so "strong" that this manipulation of a laser is meaningless?

No ... if that were that case, the states giving rise to the spectroscopic transitions would be perturbed by the Stark effect, shifting the transition out of resonance with the laser. The lasers are not being used to "manipulate" the ions in the sense of changing their positions ... they are being used to prepare quantum states in those atoms. The electric fields used in these experiments to confine the ions in the Paul trap are not nearly strong enough to measurably affect the energies of these states.

 

[Eye_in_the_Sky]

... I who harbours a misconception

Previously, I began a discussion with akhmeteli saying:

Hello, akhmeteli. It appears to me there may be some misconception in the way you are thinking about Bell's theorem.

At the conclusion of our discussion, I said:

Thank you, akhmeteli, for answering my questions. Originally, it appeared to me that there may have been some misconception in the way you were thinking about Bell's Theorem. But from the answers you have given, I do not detect any such misconception.

Indeed ...

local determinism → D

and

QM → ~D ,

where D is a certain condition.

Now I see it has been I who harbours a misconception. The first proposition in the above is INCORRECT. The correct statement is:

local determinism Λ PC → D ;

this is the weak version of deriving a Bell inequality.

The strong version reads like this:

locality Λ CF Λ PC → D .

The first is only a corollary of the second, because

local determinism → locality Λ CF ,

but not conversely.
____________________

In case anyone is wondering:

PC ≡ perfect (anti-) correlation ,

CF ≡ counterfactuality ,

D ≡ a Bell inequality .
------------------------------------------------------
------------------------------------------------------
Oh Mom … there it is again!

... So, there are two 'theorems', a weak one and a strong one:

Weak Theorem: local determinism → D ;

Strong Theorem: locality Λ PC Λ CF → D .

... whoops!

 

[Eye_in_the_Sky]

Bell expresses locality as the factorability of the joint probability.

You keep saying that, but I went back to the original Bell paper again recently to check something else, and I really don't think your statement is correct.

The passage from Bell's paper addressing locality is from section II ...

SpectraCat, ThomasT's claim does not apply to the part of Bell's paper that you quoted. The part you quoted is the beginning of "stage 2" in Bell's two-stage argument. At that spot, at the beginning of "stage 2", all outcomes are assumed to be predetermined (yet unknown). ThomasT's claim applies to "stage 1", not "stage 2".

So where then in Bell's paper is "stage 1" to be found? It is to be found in the first paragraph of section II as follows:

Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions. Measurements can be made, say by Stern-Gerlach magnets, on selected components of the spins σ₁ and σ₂. If measurement of the component σ₁∙a, where a is some unit vector, yields the value +1 then, according to quantum mechanics, measurement of σ₂∙a must yield the value -1 and vice versa. Now we make the hypothesis [2], and it seems one at least worth considering, that if the two measurements are made at places remote from one another the orientation of one magnet does not influence the result obtained with the other. Since we can predict in advance the result of measuring any chosen component of σ₂, by previously measuring the same component of σ₁, it follows that the result of any such measurement must actually be predetermined.
-------------------------------------------------------------------------
[2] "But on one supposition we should, in my opinion, absolutely hold fast: the real factual situation of the system S₂ is independent of what is done with the system S₁, which is spatially separated from the former."

Note, however, that ThomasT's claim can only be applied to the above argument after that argument has been reformulated in terms of the joint-probability-function of the particle pair as calculated at the level of a physical theory. At this level, Einstein's locality statement [2] is transferred over to a mathematical condition which the joint-probability-function must then satisfy. That mathematical condition has come to be called "Bell Locality".

ThomasT's claim, then, boils down to the following:

"Bell Locality" is not a faithful representation of a principle of "Local Causality".
___________________________

Way back in post #239, I posted a diagram and two quotes on Bell's "Local Causality Criterion", thinking it might stimulate some discussion. When I saw that it did not do so, I decided I had better follow up on it with some more information on the matter. Thereafter, I decided I ought to attempt to present a 'clean presentation' of the entire matter. So far, this has proved to be exceedingly difficult for me.

Unfortunately, my time is running out, and by next week I will definitely have to stop posting here in the forum for quite some time.

So maybe I will have to compromise in some way.

 

[Eye_in_the_Sky]

I would use "entangled state" instead of "twin-state" because that way you imply certain things that might not be very appropriate.
But otherwise I think we are on the same line here with addition that instead of the same result (maximally similar) there might be maximally opposite result as well depending from setup.

Yes we are 'on the same line' here. "Twin-state" is idiomatic for

(|x>|x> + |y>|y>) / √2 .

I would say that I do not quite understand how do you incorporate "angular momentum" in this context. If you associate "angular momentum" with polarization of individual photon then ...

For the moment, let us restrict our considerations to the singlet spin-½ pair with Stern-Gerlach magnets. In this context, would you say that the following statement is true?

"PC" is an essential ingredient of any theory which incorporates in it the notion of "angular momentum" as construed in conventional terms.

If the statement is true in the spin-½ context, then it might be possible (... at this stage I do not quite see how) to construct an argument for its truth in the optical context. On the other hand, if even in the spin-½ context the statement is false, then surely it is also false in the optical context.

 

[zonde]

"Experimental violation of a Bell's inequality with efficient detection" (2001) Rowe et al.

http://www.nature.com/nature/journal/v409/n6822/full/409791a0.html

Not actually 100% detection but high enough. This uses Be ions rather than photons.

"Our measured value of the appropriate Bell's 'signal' is 2.25+/- 0.03, whereas a value of 2 is the maximum allowed by local realistic theories of nature. In contrast to previous measurements with massive particles, this violation of Bell's inequality was obtained by use of a complete set of measurements. Moreover, the high detection efficiency of our apparatus eliminates the so-called 'detection' loophole."

This experiment makes joined detection for photons scattered from both ions. It can be picked out here:
"The state of an ion, |down> or |up>, is determined by probing the ion with circularly polarized light from a 'detection' laser beam. During this detection pulse, ions in the |down> or bright state scatter many photons, and on average about 64 of these are detected with a photomultiplier tube, while ions in the |up> or dark state scatter very few photons. For two ions, three cases can occur: zero ions bright, one ion bright, or two ions bright. In the one-ion-bright case it is not necessary to know which ion is bright because the Bell's measurement requires only knowledge of whether or not the ions' states are different. Figure 2 shows histograms, each with 20,000 detection measurements. The three cases are distinguished from each other with simple discriminator levels in the number of photons collected with the phototube."

So the photon interference happens and result of measurement is not discrete sum of two photon ensembles but result of interference of two photon ensembles.
For easier visualization I can suggest to compare this experiment with double slit experiment where two ions play the role of slits. Difference is that each ion separately produces sharp bands but presence of other ion shifts the bands to one side.

So my point is that you don't even need any specific LR theory to account for results of this experiment in local realistic fashion.

 

[Frame Dragger]

So my point is that you don't even need any specific LR theory to account for results of this experiment in local realistic fashion.

As long as you realize that you're in a terribly small minority. Frankly, I'd make your point from the outset and seek to justify it, not the other way around.

Bell is a test for LR matching QM's predictions, and there is a REASON why dBB is the only HV theory to be left after Bell (that is meaningful in any way, which is debatable)

You're seeming to advocate the notion of ensembles of particles creating apparent interference patterns, but that it is not a property of a single photon (or particle). If you're formulating this through LHVs, just say it so we can all go on our way.