Is action at a distance possible as envisaged by the EPR Paradox.

[JesseM]

Bell's equation (2) is an equation, which means the LHS is equal to the RHS, how can one side of an equation be conditioned on λ when the other is not?

Because a sum of probabilities conditioned on λ can be equal to a probability that isn't conditioned on λ. That's essentially what's meant by "marginalization" according to wikipedia--you agree that if some variable B can take two values B₁ and B₂, then marginalization says P(A) = P(A, B₁) + P(A, B₂) right? Well, by the definition of conditional probability, P(A, B₁) = P(A|B₁)*P(B₁), and likewise for B₂, so the marginalization equation reduces to P(A) = P(A|B₁)*P(B₁) + P(A|B₂)*P(B₂). Here, the left side is not conditioned on B, while the right side is a sum of terms conditioned on every possible specific value of B.

Don't you mean the term under the integral sign is conditioned on a specific λ?

Sure, and the integral represents the idea that you are summing over every possible specific value of λ, just as in my simpler equation above.

We have discussed this before and apparently you did not get anything out of it. Each λ on the RHS represents a specific value, so you can not say the LHS is conditioned on λ.

I remember our previous discussion, which consisted of you making a big deal out of a mere semantic quibble. I already explained in posts like this one and this one (towards the end of each) that what I mean when I say "conditioned on λ" is just "conditioned on each specific value of λ", so construing me as saying anything else would suggest you either forgot the entire previous discussion, or that you are using a semantic quibble as an excuse for a strawman argument about what I actually mean. And as far as semantics go, in those posts I also pointed you to section 13.1 of this book which is titled "conditioning on a random variable"--do you think the book is using terminology incorrectly?

Each term under the integral is dependent on a specific value of λ, not the vague concept of λ as we have already discussed at length.

Yes, and when I talk about conditioning on λ I just mean conditioning on each specific value of λ, as you should already know if you'd been paying attention. If you understand what I mean but don't like my terminology, tough, I think it's correct and I've given a reference to support my use of terminology, you'll have to point me to an actual reference rather than just assert your authority if you want to convince me to change it.

Your responses so far are now:
1: Bell's equation(2) expresses a [strike]conditional[/strike] marginal probability

Conditional probabilities in the integral on the right side of the equation, a marginal probability on the left.

2: Logical dependence between A and B is [strike]not[/strike] allowed in the probability expressed in Bells equation (2)

Allowed for the term on the left side of the equation.

2b: Logical dependence between A and B is not allowed for the probability dependent on a specific λ under the integral on the RHS of Bell's equation (2)

Yes.

Does this reflect your view accurately? Are you sure Bell's equation (2) is not a conditional probability, conditioned on the pair of detector settings a and b?

Well, now you're quibbling again, the main idea being discussed with ThomasT was the idea that there could be a dependence between A and B when not conditioned on the hidden variables which disappeared when they were conditioned on the hidden variables. It's true that you can interpret the left side as a conditional probability conditioned on a and b, but the only point relevant to the argument is whether it's conditioned on the hidden variables. And Bell doesn't clearly use the conditional probability notation in (2), so you could think of the a and b that appear in the equation as just denoting the idea that we are considering a sample space which consists only of trials where the detectors were set to a and b, in which case A would be defined as a variable that represents the measurement outcome with detector setting a and B is a variable that represents the measurement outcome with detector setting b. So under this interpretation the left side is really a marginal probability...it just depends how you interpret the equation, and in any case the choice of interpretation is irrelevant to the actual discussion with ThomasT. So, if you try to do a "gotcha" based on the fact that I said the left side was a marginal probability as it's not conditioned on λ, which you say is wrong because it is conditioned on a and b, I'll consider you to be playing pointless one-upmanship games again. It's irrelevant to the actual argument whether or not the left side is conditioned on variables other than λ, the argument is just about how A and B are statistically independent when conditioned on λ but statistically dependent when not. It simplifies the discussion to call the "when not" case the marginal correlation between A and B, and as I said you're free to interpret the left side of the equation so that it is a marginal probability and a and b merely tell us which settings are to be considered in the sample space.

 

[zonde]

Non-contextual = Realistic

Now some folks quibble about the difference, but the difference is mostly a matter of your exact definition - which does vary a bit from author to author. So I acknowledge that. However, I think EPR covers the definition in a manner most accept:

"One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted... No reasonable definition of reality could be expected to permit this."

Not sure but I think you misquoted EPR.
Full quote goes like that:
"One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since aither one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simulataneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this."
To me it seems that last sentence speaks about previous sentence i.e. EPR says that first measurement can not "create" reality of second measurement.
So it is like even with that definition of reality their argument as it is outlined in their paper still holds.

As to GHZ:

"Surprisingly, in 1989 it was shown by Greenberger, Horne and Zeilinger
(GHZ) that for certain three- and four-particle states a conflict with
local realism arises even for perfect correlations. That is, even for those cases
where, based on the measurement on N −1 of the particles, the result of the
measurement on particle N can be predicted with certainty. Local realism
and quantum mechanics here both make definite but completely opposite
predictions.

"To show how the quantum predictions of GHZ states are in stronger conflict
with local realism than the conflict for two-particle states as implied by Bell’s
inequalities, let us consider the following three-photon GHZ state:

"We now analyze the implications of these predictions from the point of
view of local realism. First, note that the predictions are independent of the
spatial separation of the photons and independent of the relative time order
of the measurements. Let us thus consider the experiment to be performed
such that the three measurements are performed simultaneously in a given
reference frame, say, for conceptual simplicity, in the reference frame of the
source. Thus we can employ the notion of Einstein locality, which implies
that no information can travel faster than the speed of light. Hence the
specific measurement result obtained for any photon must not depend on
which specific measurement is performed simultaneously on the other two
or on the outcome of these measurements. The only way then to explain
from a local realistic point of view the perfect correlations discussed above
is to assume that each photon carries elements of reality for both x and y
measurements considered and that these elements of reality determine the
specific individual measurement result. Calling these elements of reality...

"In the case of Bell’s inequalities for two photons the conflict between local
realism and quantum physics arises for statistical predictions of the theory;
but for three entangled particles the conflict arises even for the definite predictions."

Zeilinger talking about GHZ in:
http://www.drchinese.com/David/Bell-MultiPhotonGHZ.pdf

So GHZ does show that Local Realism makes specific predictions which are flat out contradicted by both QM and experiment.

Hmm, I will need to investigate a bit more.
I looked at this paper where they speak about 4 particle GHZ and here it is clear that they can not produce prediction for local realism at all.
http://arxiv.org/abs/0712.0921"
On the other hand in the paper from your site they make some prediction for local realism when tree-photon GHZ is considered. I will look at four-photon GHZ experiment from the same paper.

 

[unusualname]

4 Particle GHZ violations of local realism were demonstrated back in 2003:

Violation of Local Realism by Four-Photon
Greenberger-Horne-Zeilinger Entanglement Phys. Rev. Lett. 91, 180401 (2003) [4 pages] [/url]

We report the first experimental violation of local realism by four-photon Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the nonstatistical GHZ conflicts between quantum mechanics and local realism are confirmed, within the experimental accuracy, by four specific measurements of polarization correlations between four photons. In addition, our experimental results also demonstrate a strong violation of Mermin-Ardehali-Belinskii-Klyshko inequality by 76 standard deviations. Such a violation can only be attributed to genuine four-photon entanglement.

There are several results like this:

Greenberger-Horne-Zeilinger-type violation of local realism by mixed states (2008)
Bell Theorem without Inequality for Some Generalized GHZ and W States (2007)

local realism is dead, live with it :)

We're (obviously) just observing a 3-dimensional subset of reality restricted to a 3-brane or similar.

 

[DrChinese]

1. So you have changed your mind that Realism means non-contextual? You are not making a lot of sense. One minute you are arguing that realism means non-contextual, the next you are arguing that it means contextual also.


2. Keep deluding yourself... You can not find enough famous people to make me believe a lie.


3. I just gave you a quote in which EPR said such a view as unreasonable. What about that quote did you not understand?

1. The realism requirement is essentially equivalent to non-contextuality, no change in my view on that.

Apparently, you do not understand: accepting that there exists an inidividual "element of reality" per EPR - which can be demonstrated experimentally - is not the same thing as accepting that all "elements of reality" are simultaneously real. The belief that elements of reality simultaneously exist - that the moon is there even when you are not looking - is EPR realism.


2. All I am asking is that you accept a different point of view as legitimate. I have never said I expect you to accept the position of Zeilinger or whoever as your own. I appreciate that you think any opinion different than your own as being a "lie" but that is basically borderline moronic.


3. I wish you would read what you quote. Yes, EPR says that it is unreasonable to assert that the moon is not there when no one is looking. That would mean they believe the moon IS there when no one is looking. And Einstein said precisely that: "...an electron has spin, location and so forth even when it is not being measured. I like to think that the moon is there even if I am not looking at it..."


Come on, Bill, I think you can do better. Don't you have anything USEFUL to add? Other than being a craggly contrarian?

 

[DrChinese]

Not sure but I think you misquoted EPR.
Full quote goes like that:
"One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted. On this point of view, since aither one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simulataneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this."
To me it seems that last sentence speaks about previous sentence i.e. EPR says that first measurement can not "create" reality of second measurement.
So it is like even with that definition of reality their argument as it is outlined in their paper still holds.

Yes, that is the full quote. My point is that EPR sets up a definition of realism which is NOT limited to what can be experimentally demonstrated. That 2 or more elements of reality - a, b and c were used by Bell - should be reasonably expected to exist simultaneously. Bell and Aspect have shown us that this view (EPR realism) is theorically and experimentally invalid.

 

[DevilsAvocado]

General Warning - billschnieder

I’ve found "the source" for billschnieder’s weirdness, and it’s some of the worse crackpots I ever seen. His name is A. F. Kracklauer:

(Please note! This is NOT a joke: Krack-lauer / Crack-pot )

He’s an "independent researcher" and on his homepage http://www.nonloco-physics.000freehosting.com/" that he is real "independent"...

billschnieder’s crazy arguments is a raw copy of Crackpot Kracklauer’s NOT peer reviewed paper - http://arxiv.org/abs/quant-ph/0602080" . After rambling on for 9 pages of completely meaningless words (familiar!?), Crackpot Kracklauer draws this breathtaking conclusion:

IX. CONCLUSIONS
The points made above offer several explanations for the observation noted in the introduction, that BELL’s Ansatz, Eq. (1), cannot be found in treatises on statistics and probability. To begin, there is misleading notation; BELL used a COMMA to separate the independent arguments, whereas ‘hidden’ variables, by definition would be conditioning parameters, and, as such, in the notation customary in works on probability, are separated from independent variables by a VERTICAL BAR. This malapropos TURN OF THE PEN appears to have been an important facilitating element in the general misconstrual of BELL’s analysis. Once this defect is corrected, it is a short leap to the understanding of the necessity for applying BAYES’ formula; a leap apparently made first by JAYNES.

WOW! Now we know why Bell is wrong! He used a comma instead of vertical bar! THIS IS GROUNDBREAKING NEWS! Why hasn’t anyone thought of this BEFORE !?!?!?

Laughing out loud? Wait, next part in this story of Crackpot Kracklauer is a strong competitor to Monty Python's Flying Circus!

I’ve found this very amusing video (23:46), where Crackpot Kracklauer makes a hilarious "analysis" of Bell inequalities violation, and finally presents his own very functional solution to the problem:

"[URL - EPR Experiments: Analysis of Bell Inequalities Violation[/B]

[/URL]

I’m pretty impressed by his vocabulary. He frequently uses the scientifically sophisticated term – "Blah Blah Blah" and sometimes even "Ops!".

Crackpot Kracklauer is a brave man, not afraid to challenge the establishment:

"There is NO quantum mechanics in 'Qubit Space'!"​

(He also sees a real possibility to run quantum computing on vacuum tubes! !)

Crackpot Kracklauer therefore rejects that a http://en.wikipedia.org/wiki/Qubit" , which is breaking news and deserves a Nobel!

Crackpot Kracklauer rambles on and makes scandalous insinuations on John Bell’s death ("knocked over" by his theorem), and gets the year wrong.

Finally, at 16:25 he presents his "solution" and his equations for a few sec, and says:

"Now once again, it takes a little patient and thought to see exactly how these equations work." (you bet! )​

But he really scores at 16:30, where he gets to the "punch line". Here he shows real data from his own computer simulation (using his "solution"), and states:

"This simulation exceeds the limit of 2, in fact it’s 2 times the square of 2, what’s exactly what a Bell inequality shows you!"​

The only problem with this revolutionary news is that Crackpot Kracklauer apparently has forgotten that he one year earlier "proved" that Bell inequalities are WRONG! And now he is using Bell inequalities to prove the he is RIGHT? Pure madness!


After this, there’s absolutely NO reason to "Trying to Understand billschnieder’s reasoning". He’s inspired by a complete lunatic, and he’s thereby polluting PF with cranky speculations. Completely meaningless words and argumentation from billschnieder in thread https://www.physicsforums.com/showthread.php?t=399795" generated 111 posts, to absolutely NO use at all, polluted PF, and has stolen valuable time.

Please, ignore all new post along this line from billschnieder. It will make us all happier!

 

[DrChinese]

I’ve found "the source" for billschnieder’s weirdness, and it’s some of the worse crackpots I ever seen. His name is A. F. Kracklauer:
...

I have this one of his in my list of local realists, a paper from 2009:

http://arxiv.org/abs/0903.0733

Hmmm.

By the way, the sirens are a nice effect. And you always have the best.

 

[ajw1]

The man seems to have quite an impressive list of what I suppose to be peer reviewed articles. So why call him crackpot?

 

[DevilsAvocado]

I have this one of his in my list of local realists, a paper from 2009:

http://arxiv.org/abs/0903.0733

Hmmm.

By the way, the sirens are a nice effect. And you always have the best.

Thanks DrC. Yes, Crackpot Kracklauer is a real heavy borderliner. He’s apparently fairly productive and has skills in mathematics and physics, but the overall picture says only one thing – crackpot.

Here’s http://arxiv.org/find/all/1/all:+Kracklauer/0/1/0/all/0/1" on arXiv.org.

 

[DevilsAvocado]

The man seems to have quite an impressive list of what I suppose to be peer reviewed articles. So why call him crackpot?

Do you mean his 21 papers on arXiv.org? There is no obligation for http://en.wikipedia.org/wiki/ArXiv#Peer_review", and only 2 are peer reviewed, and that was more than 10 years ago, and I can’t tell about the legitimacy of these two:

http://arxiv.org/abs/quant-ph/0008121"
Journal reference: Physics Essays 5(2) 226-234 (1992)

http://arxiv.org/abs/quant-ph/9711013"
Journal reference: Found. Phys. Lett. 12(5) 441-453 (1999)

But if you watch the whole video, you don’t need to be a professor to draw the conclusion I did, and I’m 100% - he IS a crackpot.

Do you really think a serious scientist would have a homepage named Non-loco Physics (loco means crazy in Spanish) = Non-crazy Physics. This can only be interpreted two ways; either Kracklauer thinks physics in general should be considered "loco" – or he acting preemptive to his own wild ideas. None is appealing...

How big is the chance that a great and healthy scientist has links to papers titled "Complementarity or Schizophrenia: is Probability in Quantum Mechanics Information or Onta?" ... ??

The man is a BIG joke, watch the video and have fun...

 

[RUTA]

Do you mean his 21 papers on arXiv.org? There is no obligation for http://en.wikipedia.org/wiki/ArXiv#Peer_review", and only 2 are peer reviewed, and that was more than 10 years ago, and I can’t tell about the legitimacy of these two:

http://arxiv.org/abs/quant-ph/0008121"
Journal reference: Physics Essays 5(2) 226-234 (1992)

http://arxiv.org/abs/quant-ph/9711013"
Journal reference: Found. Phys. Lett. 12(5) 441-453 (1999)

But if you watch the whole video, you don’t need to be a professor to draw the conclusion I did, and I’m 100% - he IS a crackpot.

Do you really think a serious scientist would have a homepage named Non-loco Physics (loco means crazy in Spanish) = Non-crazy Physics. This can only be interpreted two ways; either Kracklauer thinks physics in general should be considered "loco" – or he acting preemptive to his own wild ideas. None is appealing...

How big is the chance that a great a healthy scientist has links to papers titled "Complementarity or Schizophrenia: is Probability in Quantum Mechanics Information or Onta?" ... ??

The man is a BIG joke, watch the video and have fun...

Are you talking about A.F. Kracklauer, "Is 'entanglement' always entangled?" J. Opt. B: Quantum Semiclass. Opt. 4 (2002), S121-S126? I met him at a conference some years ago and he presented what he claimed was the "proper" statistics for QM. In his approach, there was no need for non-locality or non-separability. After the conference, I found the faulty assumption in his approach -- his statistics assumes that knowledge of detector settings is available at both detection sites. I wrote him a detailed email explaining that experiments change polarization settings at very high frequencies precisely so info about Alice's detector settings is not available to Bob and vice versa. He became very upset and told me I didn't know what I was talking about. I don't know what else to do to help him and we haven't been in contact since.

 

[DevilsAvocado]

Are you talking about A.F. Kracklauer, "Is 'entanglement' always entangled?" J. Opt. B: Quantum Semiclass. Opt. 4 (2002), S121-S126? I met him at a conference some years ago and he presented what he claimed was the "proper" statistics for QM. In his approach, there was no need for non-locality or non-separability. After the conference, I found the faulty assumption in his approach -- his statistics assumes that knowledge of detector settings is available at both detection sites. I wrote him a detailed email explaining that experiments change polarization settings at very high frequencies precisely so info about Alice's detector settings is not available to Bob and vice versa. He became very upset and told me I didn't know what I was talking about. I don't know what else to do to help him and we haven't been in contact since.

Hehe! Sounds very much like "my" Crackpot Kracklauer!

This is getting better and better. The world is full of weird surprises. One thing that’s baffles me – how can a man with this much mathematical skill still draw completely illogical conclusions...? The only reasonable conclusion is that he knows what he’s doing – and he does it on purpose... You can’t be completely mad and solve this kind of equations, can you??

(Did you see https://www.physicsforums.com/showthread.php?p=2766674#2766674"?)


P.S. I will be surprised if billschnieder ever shows up in this thread again.

 

[RUTA]

(Did you see https://www.physicsforums.com/showthread.php?p=2766674#2766674"?)

No, that's the first I've seen it. That is the guy I met and tried to educate. I haven't seen any of his recent stuff, but given my past experience with him, it's probably not worth the time.

 

[DevilsAvocado]

... it's probably not worth the time.

Okay, I understand you completely.

RUTA, I think it would be of value (for any 'doubtful' reader) if you, as legitimate professor in physics, could confirm my conclusion that; Kracklauer cannot be using Bell inequalities to prove that he has found a working classical local realistic solution to EPR-Bell – and at the same time publish a paper where he claims to have proven that Bell inequalities are wrong from the very first assumption.

I’m only a layman, but even I understand that this is a complete crazy Catch-22, that it cannot be regarded as serious in any way.

 

[billschnieder]

Conditional probabilities in the integral on the right side of the equation, a marginal probability on the left.
...
It's true that you can interpret the left side as a conditional probability conditioned on a and b

So then your answer is that the left hand side of Bell's equation (2) is conditional with respect to (a,b) but marginal with respect to λ. And that outcome dependence between A and B exists when conditioned only on (a,b) but does not exist when conditioned on λ.

So then the expression P(AB|a,b) will accurately reflect what the probability Bell is calculating in equation (2) on the LHS? Yes or no.

And according to the chain rule of probability theory, the following expression is also true according to Bell's equation (2).

P(AB|a,b) = P(A|a,b)P(A|a,b,B)

Yes or no.

Please, note I am trying to engage in a precise discussions so don't assume you know where I am going with this and give me a preemptive response. A simple yes or no is sufficient here.

 

[DevilsAvocado]

billschnieder, please stop polluting this thread with CRACKPOT THEORIES, read https://www.physicsforums.com/showthread.php?p=2766674#post2766674".

 

[ajw1]

Do you mean his 21 papers on arXiv.org? There is no obligation for http://en.wikipedia.org/wiki/ArXiv#Peer_review", and only 2 are peer reviewed, and that was more than 10 years ago, and I can’t tell about the legitimacy of these two:

On the http://www.nonloco-physics.000freehosting.com/#personalia"I see about 25 publications in peer reviewed magazines (not counting the ones planned to be published), the last few being in 2007. I would say a little modesty would be in place.

 

[DevilsAvocado]

I see about 25 publications in peer reviewed magazines

Please, show me one paper from Kracklauer published outside Non-loco Physics and peer reviewed in a reputable scientific magazine after 1999?

 

[billschnieder]

Please, show me one paper from Kracklauer published outside Non-loco Physics and peer reviewed in a reputable scientific magazine after 1999?

Devil,
I was surprised not so see flashing and blinking animation reminiscent of 1995's internet in the above post of yours, check your calendar, it is 2010 not 1999. It is now possible to just type a name in scholar.google.com and verify what awj1 said above. BTW, you could have simply asked I would have given you the list of people who have influenced my approach to Bell.

Initially I thought I would just ignore you but then again by directly challenging you, you might benefit something from it and grow up from the dated distracting gifs and animations your posts are so infamous for.

Oh by the way, do you esteem yourself more wise and knowledgeable than the folks here, to the extent that you think they are unable to think for themselves, and need your advice on when to pay attention to what I say or not?

 

[ThomasT]

One thing that’s baffles me – how can a man with this much mathematical skill still draw completely illogical conclusions...?

Maybe they're not illogical. Maybe his premises are wrong. Or maybe some of his conclusions are illogical. Or maybe not. Since I haven't read his papers it's, as they say, too early (for me) to tell.

In any case, thanks for the resource. He has peer reviewed publications in several well respected journals. Even if his approach or conclusions turn out to be wrong, there is the benefit of his, from what I've seen so far, clear writing style. And of course there are his translations of some real classics in the physics literature. Definitely recommended reading.

So far, he doesn't seem like a crackpot. But I'll grant you that in the video he did seem a bit, er, scattered (but considering the obvious time constraint, his behavior didn't seem weird or anything). Nevertheless, his credentials appear to exceed any of the contributors to this thread.

So, again, thank you DA.

Edit:

Please, show me one paper from Kracklauer published outside Non-loco Physics and peer reviewed in a reputable scientific magazine after 1999?

There appear to be several.

 

[ThomasT]

... his statistics assumes that knowledge of detector settings is available at both detection sites.

This 'global' knowledge is available via the data processing and analysis. Isn't it?

I wrote him a detailed email explaining that experiments change polarization settings at very high frequencies precisely so info about Alice's detector settings is not available to Bob and vice versa.

While it's true that the settings are changed rapidly and randomly, it's also true that for any given time-matched pair of detection attributes there's an associated pair of polarizer settings. The statistics associated with any given run would include all of that. Wouldn't they?

I've only just glanced at the paper so far. If you can point out where his error appears, that would be appreciated.

 

[ThomasT]

It's {the data matching} based on the assumption from quantum mechanics that entangled particles are both created at the same position and time ...

Ok.

... but that doesn't mean that it's assumed that correlations in measurements of the two particles can be explained by local hidden variables given to them by the source.

I agree. The relationship between the two particles isn't, strictly speaking, a 'local' hidden variable. It's a parameter that emerges, and is only relevant, in the joint context. It doesn't determine individual measurement probabilities. And yet, isn't Bell's (2) requiring that the joint probability be modeled as the product of the two individual probabilities?

If by "a locally produced relationship" you mean local hidden variables, then no, the fact that the statistics violate Bell's inequalities show that this cannot be the explanation.

I agree, per above. But the root cause of the relationship can be assumed to be a local common source.

The local hidden variable in any trial is the randomly varying (from trial to trial) polarization angle that, presumably, would, if known, allow precise predictions of individual results. Qm says, in effect, that this local hidden variable is irrelevant wrt determining joint results -- that it is, rather, the unvarying relationship between counter-propagating disturbances emitted during the same atomic transition due to the conservation of angular momentum that determines joint results (re, eg., Clauser-Aspect type setups). This is just an interpretation of course, but it doesn't contradict anything in the qm treatment. And it's suggested that the attribution of, and subsequent projection along, a 'principle' axis given a qualitative result at one end or the other is compatible with the assumptions of locality and predetermination (albeit not separable) regarding the jointly measured underlying parameter. Why does the cos^2 theta rule following the attribution of the principle axis wrt a detection attribute work? Because the local hidden variable (as differentiated from the global parameter) can be any polarization angle. There are three vectors involved, call them, V1, V2, and V3, an optical vector and two unit vectors. They can be ordered in any way. One, the optical vector, is undetermined but assumed to be continuous between the two unit vectors. So, it seems logical to me, and compatible with the idea that everything is evolving according to the principle of locality, that the joint detection rate would be described by the cos^2 of the angular difference between the two unit vectors. As, I've said before, it's just accepted optics. And, because it's accepted optics, this is why the qm treatment for these types of setups is evaluated using Malus Law. I don't think that Bell's analysis rules this out, but rather that it's saying something about how this situation can be modeled. And, wrt that, Bell was correct.

The equation (2) was based on the assumption of causal independence between the two particles (i.e measuring one does not affect the other), which was expressed as a condition saying they're statistically independent conditioned on the hidden variables L ...

I agree. The equation says that the two particles (ie., the sets of detection attributes denoted by A and B) are statistically independent. In which case, the locality condition (separability of the joint state) is clearly formulated, but simply doesn't fit the experimental situation which, per se, doesn't require, or indicate in its evolution, the presence of nonlocal or ftl 'communication' between anything. So, we have a situation in which the purported independence between A and B is violated by the experimental design and realization which are entirely compatible with the assumption of locality. In other words, the fact that Bell's lhv form models statistical independence supercedes it's purported modelling of locality.

... but the equation is consistent with the idea that P(AB) can be different from P(A)*P(B).

Not sure what you mean.

 

[ThomasT]

DrC, you might have missed this. So, I'm posting it again. You've been asked to look at and comment on some LR models, and have refused to do so because they reproduce the qm predictions. This doesn't make sense to me, so if you would clarify the following, then maybe we might proceed. Thanks.

Here is the issue: I demand of any realist that a suitable dataset of values at three simultaneous settings (a b c) be presented for examination. That is in fact the realism requirement, and fully follows EPR's definition regarding elements of reality. Failure to do this with a dataset which matches QM expectation values constitutes the Bell program. Clearly, Bell (2) has only a and b, and lacks c. Therefore Bell (2) is insufficient to achieve the Bell result.

 

[DrChinese]

DrC, you might have missed this. So, I'm posting it again. You've been asked to look at and comment on some LR models, and have refused to do so because they reproduce the qm predictions. This doesn't make sense to me, so if you would clarify the following, then maybe we might proceed. Thanks.

I stated:

i) I demand of any realist that a suitable dataset of values at three simultaneous settings (a b c) be presented for examination. That is in fact the realism requirement, and fully follows EPR's definition regarding elements of reality. Failure to do this with a dataset which matches QM expectation values constitutes the Bell program.

ii) Clearly, Bell (2) has only a and b, and lacks c. Therefore Bell (2) is insufficient to achieve the Bell result.

------------------
So to expand on these:

i) There are a number of papers that "purport" to provide local realistic models. But they do not provide datasets (with 3 angle settings) which match the QM expectation values. That is to be expected, because Bell discovered that there are no such datasets. Why is a dataset important? Because it was known already that datasets with 2 angle settings were possible. In fact, that was more or less one of the EPR conclusions although they did not really specify that single point. What they did specify was that the existing (at that time) QM program could be made "more complete" with additional parameters, yet to be discovered.

So local realistic theories with 2 simultaneous settings are missing the boat, precisely because they describe something which is not prohibited by Bell. And if they did offer the ability to provide a 3 setting dataset, they would simply provide it and Bell would be overturned. So I don't really need to read and de-bunk each purported solution until and unless a dataset can be provided.

In the case of the De Raedt local realistic computer simulation, on the other hand, such a dataset is provided. So naturally I DO take it seriously and am actively involved in working with a respected member of their team to understand their model and its characteristics. Keep in mind that it is a simulation, not a true physical model. However, the success of their model would open the door to a physical model - if it can survive questions that are inevitable.

ii) One of the recent questions on this board concerns whether Bell (2) is a sufficient assumption to achive the main result. You can see for yourself - as can anyone who will simply look - that it does not involve 3 settings, but instead only 2. The Bell program requires the assumption of at least existence of 3 simultaneous "elements of reality". In the EPR program, there was only 1 (let's call it a), because that was all that could be predicted with certainty. But they said in their closing papragraphs that it was reasonable to consider that any element of reality individually should reasonably be considered to exist independent of actual observation. So this is the counterfactual case: b, c... etc. They needed this because it was essential to their claim that QM was incomplete. Bell accepted the "challenge" and considered a, b and c, achieving his now famous result. But you cannot get it - as far as I have seen - with just (2). You need after (14) too.

 

[billschnieder]

DrC,
Take a look at my last post in the thread "Understanding Bell's logic (post #113)" in which I presented a simplified version of JesseM's scratch-lotto card example, which is essentially a copy of Mermin's example.

Is it still your believe that an instruction set explanation of it is impossible? Will an instruction-set explanation of that example qualify as a "dataset" that you keep asking for?

 

[DrChinese]

DrC,
Take a look at my last post in the thread "Understanding Bell's logic (post #113)" in which I presented a simplified version of JesseM's scratch-lotto card example, which is essentially a copy of Mermin's example.

Is it still your believe that an instruction set explanation of it is impossible? Will an instruction-set explanation of that example qualify as a "dataset" that you keep asking for?

Yes, Bill, I think that works for me. I looked over the example and it looks pretty good. That is definitely the kind of example that clarifies so that definitions are not standing in the way of finding a common ground.

 

[DevilsAvocado]

He has peer reviewed publications in several well respected journals.

Could you please show me one title, link, or paper-id?

So far, he doesn't seem like a crackpot. But I'll grant you that in the video he did seem a bit, er, scattered (but considering the obvious time constraint, his behavior didn't seem weird or anything). Nevertheless, his credentials appear to exceed any of the contributors to this thread.

ThomasT, please tell me you are joking, right? A bit "scattered"?? This is some of the worst cranky stuff I have ever seen. The first 4 min of the video Crackpot Kracklauer dismisses QM and states that the Heisenberg uncertainty principle is wrong! According to Crackpot Kracklauer at 03:20.

"The reason they don’t commute is not because someone has imposed the Heisenberg uncertainty relationship on them. In fact, the reason they don’t commute is purely geometry. The ah eh the the the structure of 'Qubit Space' in terms of polarization was worked out by... by... what’s his name... an Englishman ...in 1856... Stokes's! Fifty years before Pauli was born even!"​

Crackpot Kracklauer is now talking about one of the pioneers of quantum physics and a Nobel laureate in Physics http://en.wikipedia.org/wiki/Wolfgang_Pauli" was a QM pioneer and a Nobel laureate in Physics.

Don’t you see the pure madness in this!? Crackpot Kracklauer tries to give picture that QM is completely wrong, and the big questions were already solved fifty years before anyone has ever heard the word quantum theory?? This is insane. He runs his own private mad war against QM.

And to be perfectly clear to the "casual reader"; IF Crackpot Kracklauer is right and QM is wrong, then right now your hard disk drive in your own computer will have 3 times lesser capacity! Since QM http://en.wikipedia.org/wiki/Giant_magnetoresistance" is used by ALL manufacturers to increase HDD capacity.

Furthermore, there’s a whole bunch of gadgets you use every day that will stop working if Crackpot Kracklauer is anywhere near right. But don’t worry, Crackpot Kracklauer dead wrong and QM is the most precise theory we got. Period.

So, Crackpot Kracklauer is just too much, and I will never back off from this, never. Supporting Crackpot Kracklauer must be against all and everything in https://www.physicsforums.com/showthread.php?t=5374" (my emphasis):

Overly Speculative Posts:
One of the main goals of PF is to help students learn the current status of physics as practiced by the scientific community; accordingly, Physicsforums.com strives to maintain high standards of academic integrity. There are many open questions in physics, and we welcome discussion on those subjects provided the discussion remains intellectually sound. It is against our Posting Guidelines to discuss, in most of the PF forums or in blogs, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional mainstream scientific discussion. Personal theories/Independent Research may be submitted to our Independent Research Forum, provided they meet our Independent Research Guidelines; Personal theories posted elsewhere will be deleted. Poorly formulated personal theories, unfounded challenges of mainstream science, and overt crackpottery will not be tolerated anywhere on the site. Linking to obviously "crank" or "crackpot" sites is prohibited.

In any case, thanks for the resource.

You are welcome.

 

[DevilsAvocado]

... BTW, you could have simply asked I would have given you the list of people who have influenced my approach to Bell.

So I’m asking you very friendly now: Please show me one reputable scientist who speculates around the possibilities that John Stewart Bell made a terrible mistake when he used a comma instead of vertical bar, in equation (2), and therefore Bell's Theorem is all wrong from start. Please, just one trustworthy scientist.

I will apologize sincerely if you prove me wrong.

 

[billschnieder]

So I’m asking you very friendly now: Please show me one reputable scientist who speculates around the possibilities that John Stewart Bell made a terrible mistake when he used a comma instead of vertical bar, in equation (2), and therefore Bell's Theorem is all wrong from start. Please, just one trustworthy scientist.

I will apologize sincerely if you prove me wrong.

Provide a quote from the article where you think Kracklauer made such a statement, and I will use the same quote to prove to the whole world just why it is you who has issues understanding simple English. So the the ball is in your court. I hope you will keep your honor by appologizing sincerely when this is all over.

I'm waiting!

 

[DevilsAvocado]

Provide a quote from the article where you think Kracklauer made such a statement

I hope there’s nothing wrong with your glasses? Because it’s right in front of your nose in https://www.physicsforums.com/showpost.php?p=2766674&postcount=806":

(I’ll make it a little bigger for you this time)

IX. CONCLUSIONS
The points made above offer several explanations for the observation noted in the introduction, that BELL’s Ansatz, Eq. (1), cannot be found in treatises on statistics and probability. To begin, there is misleading notation; BELL USED A COMMA to separate the independent arguments, whereas ‘hidden’ variables, by definition would be conditioning parameters, and, as such, in the notation customary in works on probability, are separated from independent variables by a VERTICAL BAR. This malapropos TURN OF THE PEN appears to have been an important facilitating element in the general MISCONSTRUAL OF BELL’S ANALYSIS. Once this defect is corrected, it is a short leap to the understanding of the necessity for applying BAYES’ formula; a leap apparently made first by JAYNES.

The pure fact that you are continually supporting Crackpot Kracklauer proves, without any doubt, that I was perfectly correct from the start. I gave you a fair chance to solve this in a civilized manner – you didn’t take it.

If you continue to promote Crackpot Kracklauer’s completely crazy theories, I will report you. I don’t even have to "prove" anything – Crackpot Kracklauer is, by his very own definition, an independent researcher. His crazy "stuff" is only allowed in the Independent Research Forum, provided he meets the Independent Research Guidelines, which he will never do. End of story.

I do hope you are capable of reading and understanding the https://www.physicsforums.com/showthread.php?t=5374"?

Make your choice.

 

[billschnieder]

Remember, the phrases you are trying to prove against Kracklauer are the following, in your own words:

WOW! Now we know why Bell is wrong! He used a comma instead of vertical bar! THIS IS GROUNDBREAKING NEWS!

John Stewart Bell made a terrible mistake when he used a comma instead of vertical bar, in equation (2), and therefore Bell's Theorem is all wrong from start.

You said twice, that Kracklauer claims Bell's Theorem is all wrong because he used a comma instead of a vertical bar. So let us examine your so-called proof.

IX. CONCLUSIONS
The points made above offer several explanations for the observation noted in the introduction, that Bell’s Ansatz, Eq. (1), cannot be found in treatises on statistics and probability.
To begin, there is misleading notation; Bell used a comma to separate the independent arguments, whereas ‘hidden’ variables, by definition would be conditioning parameters, and, as such, in the notation customary in works on probability, are separated from independent variables by a vertical bar.
This malapropos turn of the pen appears to have been an important facilitating element in the general misconstrual of Bell's analysis. Once this defect is corrected, it is a short leap to the understanding of the necessity for applying bayes’ formula; a leap apparently made first by Jaynes.

Clearly, from the above, any layman capable of understanding English can figure out that according to Kracklauer, the non-standard notation used by Bell, has facilitated a general misunderstanding of Bell's analysis. Was this quote supposed to prove that Kracklauer claims Bell's inequalities are wrong because he used a comma instead of a vertical bar?

1) Did Bell use non-standard notation? Yes
2) Does standard notation use a vertical bar instead of a comma when expressing conditional probability? Yes
3) Is it reasonable to suggest that the use of non-standard notation leads to misunderstanding? Yes.

I do hope you are capable of reading and understanding the https://www.physicsforums.com/showthread.php?t=5374"?

Let us see what the document you linked to says:

When posting a new topic do not use the CAPS lock (all-CAPS), bold, oversized, or brightly colored fonts, or any combination thereof. They are hard to read and are considered yelling. When replying in an existing topic it is fine to use CAPS or bold to highlight main points.

So keep looking and produce the quote where Kracklauer claims Bell's inequalities are wrong because he used a comma instead of a vertical bar.

 

[DevilsAvocado]

Remember, the phrases you are trying to prove against Kracklauer are the following

Hahahah! I’m laughing my pants off! (<-- Note: BOLD! )

billschnieder, you must be the most "peculiar" guy I’ve ever seen on PF. Don’t you understand that you are helping me to prove beyond any doubts – that your one and only source for all this extensive cranky-probability-mess, that you have practiced all over the place, is Crackpot Kracklauer!

Don’t you understand this?? Is this really so hard??

And this strategic blunder is nothing more than laughable (and I do feel sorry for you):

1) Did Bell use non-standard notation? Yes
2) Does standard notation use a vertical bar instead of a comma when expressing conditional probability? Yes
3) Is it reasonable to suggest that the use of non-standard notation leads to misunderstanding? Yes.

Here you are actually verifying that all my claims were correct from the very start.

I don’t care if you spend 1000 "probability-enigma-posts" in threads like "Trying to understand this and that", but if you continue in this thread, I will report you, guaranteed.

By the way: Why don’t you report me for using CAPS lock (all-CAPS) + bold + oversized?? It’ll be fun! Ever heard of the boomerang??

Thanks for the laughs, take care.

 

[billschnieder]

DevilsAvocado,
Did you find the quote yet where you say Kracklauer claims Bell's inequalities are wrong because he used a comma instead of a vertical bar? Or was it just as untrue as the claim that Kracklauer has only two peer reviewed articles published before 1999 and none after.

 

[billschnieder]

Yes, that is the full quote. My point is that EPR sets up a definition of realism which is NOT limited to what can be experimentally demonstrated. That 2 or more elements of reality - a, b and c were used by Bell - should be reasonably expected to exist simultaneously. Bell and Aspect have shown us that this view (EPR realism) is theorically and experimentally invalid.

DrC,
I disagree with your interpretation of the EPR quote, which I parse below. Not only is theEPR definition not limited to what can be experimentally demonstrated, but it is also not limited to what can be predicted as explained below.

"
1) One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive.
2) Indeed, one would not arrive at our conclusion if one insisted that two or more physical quantities can be regarded as simultaneous elements of reality only when they can be simultaneously measured or predicted.
3) On this point of view, since either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simulataneously real. This makes the reality of P and Q depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way.
4) No reasonable definition of reality could be expected to permit this."

1) Here they lay out a possible objection to their criterion for reality, the one that they should have restricted it more as outlined in point (2).
2) EPR argue that, if we insist that "simultaneous elements of reality" is taken to mean elements of reality must be simultaneously measured or predicted, then their conclusion can not be reached. Therefore, according to EPR, their definition of "simultaneous elements of reality" does not mean they must be simultaneously measured or predicted.
3) In support of the above, EPR lay out a situation in which it is not possible to simultaneously measure or predict P and Q, and use it to show that if we insist that "simultaneous elements of reality" means they must simultaneously be measurable or predictable, then under this more restrictive definition (which is not the one they are proposing), the reality of a remote station can be changed by a measurement on a local station.
4) They then conclude that such a more restrictive definition is therefore not reasonable. According to EPR, therefore, any definition of reality which insists that elements of reality are only simultaneously real if they can be simultaneously measured, is a different definition from the EPR definition.

 

[DrChinese]

Did you find the quote yet where you say Kracklauer claims Bell's inequalities are wrong because he used a comma instead of a vertical bar?

And I will tell you again, as I have said many times before, that trying to read Bell on a literal or character for character basis is absurd. You don't need Bell (2) to get to his result, there are other ways too. That is simply a single way to express one of the assumptions of local realism. If you substitute your own, you will still arrive at his conclusion. Ergo, attacking the specific form is a waste of time.

The correct way to read Bell is to consider his audience. He knew they would follow his thinking in their own manner. The key was that any reasonable set of local realistic assumptions - again supply your own - leads right back to the Bell conclusion: QM and LR are not compatible.

I have to tell you that Devil's quote about the "misleading" notation is pretty funny. I don't think I have EVER heard an attack like that from a professional about another professional. And as I say, it is ridiculous to boot!

 

[DrChinese]

...

1) Here they lay out a possible objection to their criterion for reality, the one that they should have restricted it more as outlined in point (2).
2) EPR argue that, if we insist that "simultaneous elements of reality" is taken to mean elements of reality must be simultaneously measured or predicted, then their conclusion can not be reached. Therefore, according to EPR, their definition of "simultaneous elements of reality" does not mean they must be simultaneously measured or predicted.
3) In support of the above, EPR lay out a situation in which it is not possible to simultaneously measure or predict P and Q, and use it to show that if we insist that "simultaneous elements of reality" means they must simultaneously be measurable or predictable, then under this more restrictive definition (which is not the one they are proposing), the reality of a remote station can be changed by a measurement on a local station.
4) They then conclude that such a more restrictive definition is therefore not reasonable. According to EPR, therefore, any definition of reality which insists that elements of reality are only simultaneously real if they can be simultaneously measured, is a different definition from the EPR definition.

Yes, I quite agree with your parsing of EPR (as I said previously). And as I said, they assert that for their elements of reality to stand - a, b and c for example - they do not need to be simultaneously predictable with certainty. Bell accepted this definition, and I do too.

So then Bell went to work on a, b and c, and discovered that IF they existed simultaneously - as EPR asserts - then they could NOT match the QM expectation values. Ergo, either the EPR assertion is wrong OR there is spooky action at a distance. Take your pick!

 

[billschnieder]

So then Bell went to work on a, b and c, and discovered that IF they existed simultaneously - as EPR asserts - then they could NOT match the QM expectation values. Ergo, either the EPR assertion is wrong OR there is spooky action at a distance. Take your pick!

But you are drawing the wrong conclusion. EPR did not say Bell's a, b, c must be simultaneous elements of reality. So I do not see which EPR assertion is claimed to be wrong here?

 

[DevilsAvocado]

And I will tell you again, as I have said many times before, that trying to read Bell on a literal or character for character basis is absurd. You don't need Bell (2) to get to his result, there are other ways too. That is simply a single way to express one of the assumptions of local realism. If you substitute your own, you will still arrive at his conclusion. Ergo, attacking the specific form is a waste of time.

Thanks DrC, very well formulated words.

 

[my_wan]

Yes, I quite agree with your parsing of EPR (as I said previously). And as I said, they assert that for their elements of reality to stand - a, b and c for example - they do not need to be simultaneously predictable with certainty. Bell accepted this definition, and I do too.

So then Bell went to work on a, b and c, and discovered that IF they existed simultaneously - as EPR asserts - then they could NOT match the QM expectation values. Ergo, either the EPR assertion is wrong OR there is spooky action at a distance. Take your pick!

Put this way I have to agree. The operational definition of realism as provided by EPR is fatally flawed beyond any reasonable doubt. I see this as an indication that observables are not non-degenerate. As such, the observables likely do, in a sense, lack a reality independent of the measurement. I don't see the generalization of this as a refutation of realism in general, nor that determinism is refuted. Though this, and other considerations, indicates that if elements of reality exist they are not directly accessible empirically and also most likely transfinite.

 

[zonde]

As to GHZ:

"Surprisingly, in 1989 it was shown by Greenberger, Horne and Zeilinger
(GHZ) that for certain three- and four-particle states a conflict with
local realism arises even for perfect correlations. That is, even for those cases
where, based on the measurement on N −1 of the particles, the result of the
measurement on particle N can be predicted with certainty. Local realism
and quantum mechanics here both make definite but completely opposite
predictions.

"To show how the quantum predictions of GHZ states are in stronger conflict
with local realism than the conflict for two-particle states as implied by Bell’s
inequalities, let us consider the following three-photon GHZ state:

"We now analyze the implications of these predictions from the point of
view of local realism. First, note that the predictions are independent of the
spatial separation of the photons and independent of the relative time order
of the measurements. Let us thus consider the experiment to be performed
such that the three measurements are performed simultaneously in a given
reference frame, say, for conceptual simplicity, in the reference frame of the
source. Thus we can employ the notion of Einstein locality, which implies
that no information can travel faster than the speed of light. Hence the
specific measurement result obtained for any photon must not depend on
which specific measurement is performed simultaneously on the other two
or on the outcome of these measurements. The only way then to explain
from a local realistic point of view the perfect correlations discussed above
is to assume that each photon carries elements of reality for both x and y
measurements considered and that these elements of reality determine the
specific individual measurement result. Calling these elements of reality...

"In the case of Bell’s inequalities for two photons the conflict between local
realism and quantum physics arises for statistical predictions of the theory;
but for three entangled particles the conflict arises even for the definite predictions."

Zeilinger talking about GHZ in:
http://www.drchinese.com/David/Bell-MultiPhotonGHZ.pdf

So GHZ does show that Local Realism makes specific predictions which are flat out contradicted by both QM and experiment.

I looked into experiments. Have to say that the one provided by unusualname was very helpful:

4 Particle GHZ violations of local realism were demonstrated back in 2003:
Violation of Local Realism by Four-Photon
Greenberger-Horne-Zeilinger Entanglement Phys. Rev. Lett. 91, 180401 (2003) [4 pages] [/url]

So as to what it demonstrates.
First of all it uses four modifications of experiment to demonstrate the point about LR.
Three experiments are used to make LR prediction for the fourth experiment.
That way you can't say that contradiction is achieved in single run.

Another thing is that as in any real experiment you don't have perfect result. So if you say that every single (4-fold coincidence) detection confirms QM and contradicts LR then in experiment we have situation like that:
"The experimental results in (f) are in agreement with the QM predictions (d) while in conflict with LR (e), with a visibility of 0.789+-0.012."
That means we have 90 detections out of every 100 that without any doubt confirm QM and 10 detections that without any doubt confirm LR.

That of course is not very serious interpretation of experimental results.

Next if we look at this sentence (from the quote you already provided):
"The only way then to explain from a local realistic point of view the perfect correlations discussed above is to assume that each photon carries elements of reality for both x and y measurements considered and that these elements of reality determine the specific individual measurement result."
First of all correlations are not perfect. If we compare visibility of HVVH and VHHV results they had around 0.98 visibility. Switching to L/R and H'/V' (+45°/-45°) base considerably reduced visibility i.e. around 0.80. So measurements in base that is incompatible with the base photons where created in are far from prefect correlations.
Second a local realistic point of view is not restricted to the point that each photon should carry all the relevant information.
For example, two photon combination can carry more information than simple sum of information from two single photons. That's because there is additional information in possible two photon configurations relative to each other.
So the point about "the only way" is not very serious.

 

[JesseM]

So then your answer is that the left hand side of Bell's equation (2) is conditional with respect to (a,b) but marginal with respect to λ. And that outcome dependence between A and B exists when conditioned only on (a,b) but does not exist when conditioned on λ.

Yes.

So then the expression P(AB|a,b) will accurately reflect what the probability Bell is calculating in equation (2) on the LHS? Yes or no.

Yes.

And according to the chain rule of probability theory, the following expression is also true according to Bell's equation (2).

P(AB|a,b) = P(A|a,b)P(A|a,b,B)

Yes or no.

No, but if you meant to write P(AB|a,b) = P(B|a,b)P(A|a,b,B) then yes. This would actually be derived from the chain rule plus a few substitutions...the chain rule of probability would tell us this:

P(A,B,a,b)=P(A|B,a,b)P(B|a,b)P(a|b)P(b)

And from the definition of conditional probability we know P(a|b)*P(b)=P(a,b), and P(A,B,a,b)=P(AB|a,b)*P(a,b), so substitute these in the above equation, divide both sides by P(a,b) and we get P(AB|a,b)=P(A|B,a,b)P(B|a,b).

 

[JesseM]

but that doesn't mean that it's assumed that correlations in measurements of the two particles can be explained by local hidden variables given to them by the source.

I agree. The relationship between the two particles isn't, strictly speaking, a 'local' hidden variable. It's a parameter that emerges, and is only relevant, in the joint context. It doesn't determine individual measurement probabilities.

But are you saying that this relationship is completely explained by some parameters that each particle got at the moment they were created at a common location by the source (like each starting out with the same 'polarization vector'), and where the parameter for each particle is itself a local variable that's carried around by the particle as it travels, either unchanging (like if each particle's own polarization vector continues to point in the same direction as the particle travels, at least until the particle is measured by a polarizer) or changing in a way that isn't causally affected by anything outside the particle's past light cone? If so this would be a local hidden variables explanation for the relationship between the particles.

And yet, isn't Bell's (2) requiring that the joint probability be modeled as the product of the two individual probabilities?

Only when conditioned on the hidden variables. In other words, P(AB|λ) is equal to the product of the two individual probabilities P(A|λ)*P(B|λ), but P(AB) is not equal to the product of the two individual probabilities P(A)*P(B). Do you understand the distinction?

If by "a locally produced relationship" you mean local hidden variables, then no, the fact that the statistics violate Bell's inequalities show that this cannot be the explanation.

I agree, per above. But the root cause of the relationship can be assumed to be a local common source.

I think you misunderstand, if the "root cause of the relationship" can be explained in terms of correlated local hidden variables assigned to each particle by the source, then is exactly what a "local hidden variables explanation" means, and this sort of explanation is ruled out if the statistics violate Bell's inequality.

The local hidden variable in any trial is the randomly varying (from trial to trial) polarization angle that, presumably, would, if known, allow precise predictions of individual results.

Can you explain how the "polarization angle" would interact with the detector angle to give the results? I've asked you this before and you haven't answered my question. Suppose the particle's polarization angle were 90 degrees while the detector angle was set to 60 degrees...what would this imply about the results? Would it mean the probability the particle passes through the detector is cos²(90-60), for example?

And it's suggested that the attribution of, and subsequent projection along, a 'principle' axis given a qualitative result at one end or the other is compatible with the assumptions of locality and predetermination (albeit not separable) regarding the jointly measured underlying parameter.

"suggested" by who? You? It certainly isn't suggested by orthodox QM or by anyone who agrees with Bell's analysis.

Why does the cos^2 theta rule following the attribution of the principle axis wrt a detection attribute work? Because the local hidden variable (as differentiated from the global parameter) can be any polarization angle. There are three vectors involved, call them, V1, V2, and V3, an optical vector and two unit vectors. They can be ordered in any way. One, the optical vector, is undetermined but assumed to be continuous between the two unit vectors.

I don't understand, what do these vectors represent physically in the problem? Is the optical vector supposed to be the hidden polarization angle, and the unit vectors are the angles of the two detectors? If not, what?

So, it seems logical to me, and compatible with the idea that everything is evolving according to the principle of locality, that the joint detection rate would be described by the cos^2 of the angular difference between the two unit vectors. As, I've said before, it's just accepted optics. And, because it's accepted optics, this is why the qm treatment for these types of setups is evaluated using Malus Law. I don't think that Bell's analysis rules this out, but rather that it's saying something about how this situation can be modeled.

Again, if you're just saying that each particle received the same "polarization vector" when they were created by the source, and that the polarization vectors are local properties of the particles that travel along with them and determine their response to the detectors, then this is definitely ruled out by Bell's analysis.

The equation (2) was based on the assumption of causal independence between the two particles (i.e measuring one does not affect the other), which was expressed as a condition saying they're statistically independent conditioned on the hidden variables L ...

I agree. The equation says that the two particles (ie., the sets of detection attributes denoted by A and B) are statistically independent.

No it doesn't. P(AB) can be different than P(A)P(B), meaning that they are statistically dependent in their probabilities when not conditioned on the hidden variables λ. For example, if A and B represent measurement results when both detectors are set to the same angle (say, 60 degrees), then if we know B, that automatically tells us the value of A with probability 1. Do you disagree?

It would really help if you would answer my question from post 781:

Do you agree it's possible to have a situation where P(AB) is not equal to P(A)*P(B), and yet P(AB|λ)=P(A|λ)*P(B|λ)? (and that this situation was exactly the type considered by Bell?) In this situation do you think there is a single correct answer to whether A and B are "statistically independent" or not? If so, what is that answer?

Can you address this please?

... but the equation is consistent with the idea that P(AB) can be different from P(A)*P(B).

Not sure what you mean.

Do you understand that if P(AB)=P(A)*P(B), that means A and B are statistically independent in their marginal probabilities (i.e. probabilities not conditioned on another variable like λ)? If so, my point is that if P(AB) is different from P(A)*P(B), that models a situation where A and B are statistically dependent in their marginal probabilities, equivalent to saying that P(A|B) is different from P(A) (i.e. learning the outcome B causes you to modify your estimate of the probability of A). Bell's equation certainly allows for this--it had better do so, because he was trying to explain the perfect correlation (the highest degree of statistical dependence possible) between A and B when both detectors were set to the same angle.

 

[DrChinese]

But you are drawing the wrong conclusion. EPR did not say Bell's a, b, c must be simultaneous elements of reality. So I do not see which EPR assertion is claimed to be wrong here?

Yes, EPR says this. Of course they do not say a, b and c. Bell said that.

What EPR gives is a definition of an element of reality. By that definition, any angle setting measuring particle spin qualifies as an element of reality because it can be predicted with certainty. They then discuss whether 2 or more such elements of reality stand if they cannot be predicted with certainty simultaneously. They assert that such requirement is unreasonable. You are then left with the EPR definition of realism being that any observable which can be predicted with certainly maps to an element of reality.

That would include Bell's a, b and c, which qualify as elements of reality.

 

[DrChinese]

Put this way I have to agree. The operational definition of realism as provided by EPR is fatally flawed beyond any reasonable doubt. I see this as an indication that observables are not non-degenerate. As such, the observables likely do, in a sense, lack a reality independent of the measurement. I don't see the generalization of this as a refutation of realism in general, nor that determinism is refuted. Though this, and other considerations, indicates that if elements of reality exist they are not directly accessible empirically and also most likely transfinite.

You could be correct, to a certain degree it is in fact a function of your definition of reality. I choose to believe that observables of a particle do not have simultaneous reality in the EPR sense of being elements of reality. In other words, I believe their reality is a function of the act of observation.

 

[DrChinese]

Another thing is that as in any real experiment you don't have perfect result. So if you say that every single (4-fold coincidence) detection confirms QM and contradicts LR then in experiment we have situation like that:
"The experimental results in (f) are in agreement with the QM predictions (d) while in conflict with LR (e), with a visibility of 0.789+-0.012."
That means we have 90 detections out of every 100 that without any doubt confirm QM and 10 detections that without any doubt confirm LR.

That of course is not very serious interpretation of experimental results.

Hmmm, I am not sure how you get this because that is quite different than the actual conclusion. Visibility means the number that are detected. So that is 78.9% +/-1.2%. The actual result was a value of 4.433+/-0.032. This was greater than the Local Realistic max of 4 by 76 standard deviations.

So, no this was not a contest where 90% of events say one thing, and 10% say the opposite. 76 SD is overwhelming. 5 SD was enough for the 1982 Aspect experiment.

 

[DevilsAvocado]

P(A,B,a,b)=P(A|B,a,b)P(B|a,b)P(a|b)P(b)

JesseM, you are PF Science Advisor with +6,000 posts, I beg you to read https://www.physicsforums.com/showthread.php?p=2766674#post2766674" to get information about the source for billschnieder’s search for "knowledge and clarity".

Also read the following posts between billschnieder and me, and you will see beyond any doubt that the one and only source for billschnieder’s reasoning is Crackpot Kracklauer.

It may look like billschnieder is here to learn more about professional mainstream science, while billschnieder and Crackpot Kracklauer are in fact trying to dismiss Bell’s Theorem by cranky argumentation around the notation in Bell (2).

This is the cranky "truth", that you are currently engaged in:

http://arxiv.org/abs/quant-ph/0602080"
Authors: A. F. Kracklauer
...
IX. CONCLUSIONS
...
And, once it is clear that Bell Inequalities cannot be derived using BAYES’ formula, the issue of nonlocality is rendered moot. This, in turn, resolves one conflict between two fundamental theories of modern physics—a conflict that on the face of it has the character typical of small, technical misunderstandings. This is only reinforced by the observation that there is no empirical evidence for nonlocality; that which has been taken as such, is in fact just an interpretation imposed indirectly on statistics derived from non kinematic data, but as argued herein, incorrectly.

I sincerely hope you realize the madness in continuing this kind of discussion, spread out all over PF.

 

[my_wan]

You could be correct, to a certain degree it is in fact a function of your definition of reality. I choose to believe that observables of a particle do not have simultaneous reality in the EPR sense of being elements of reality. In other words, I believe their reality is a function of the act of observation.

Put this way I can respect such a position. I'm accustomed to thinking of observables as degenerate, since even before my teens or any notion of what QM was. The reasoning very closely followed your argument on the unobservability of independent variables I like to quote. I didn't know about the correspondence between statistical mechanics and classical thermodynamics at the time either, but the same basic reasoning was embedded in my thinking.

I'll give up what notions I must, but my feeling is that, in some sense, defining what ideas must go requires a comparison to various notions of realism, not just the one operationally defined by EPR. Much like what inspired Bell to derive his inequality. However, I must admit science has made astounding progress without it, and the crackpots that want to claim QM is not science are easy to lose patients with. That's enough to prove my feelings about it are not strictly true, but I still think comparing different notions of realism has value, even if only to define exactly where and how they break. I guess you could call it a minimalist approach to weirdness.

 

[DrChinese]

I have started a new thread in Independent Research:

https://www.physicsforums.com/showthread.php?t=408231

This is on another subject off-topic to this thread. I wanted to invite my friends here to come over and give me your thoughts on a paper I have written on a proposed experiment. Thanks!

 

[billschnieder]

No, but if you meant to write P(AB|a,b) = P(B|a,b)P(A|a,b,B) then yes.

That is what I meant, thanks for spotting the typo.

So then according to Bell, the P on the LHS ie equivalent to P(AB|a,b) in standard notation, where as we have agreed before a and b are place-holders for a specific value of the "random variables" a and b.

Now on age 405 of Bell's paper, just after equation (12) he writes the following:

P in (2) can not be less than -1. It can reach -1 at a = b, only when when
A(a,λ) = -B(b,λ)

How can a probability reach -1? Clearly then, according to Bell, P can not be a probability, since probabilities are only defined from 0 to 1. Do you agree? Yes or no?

 

[JesseM]

How can a probability reach -1? Clearly then, according to Bell, P can not be a probability, since probabilities are only defined from 0 to 1. Do you agree? Yes or no?

OK, this is another minor quibble, the left side is actually an expectation value. I noted earlier in post #790 that A and B in (2) were just written as functions rather than probabilities:

I suppose I should point out that strictly speaking, in equation (2) Bell actually assumes the measurement outcomes are determined with probability 1 by the value of λ, so instead of writing P(A|a,λ) he just writes A(a,λ)

I neglected to note there that he allows the function A(a,λ) (and likewise B(b,λ)) to take values +1 or -1 depending on the measurement result (+1 for spin-up when measured with setting a and -1 for spin-down when measured with setting a, for example). So the notation P(a,b) on the left side of the equation is the expectation value for the product of A and B, which would be equivalent to a weighted sum of four different probabilities: P(A=+1, B=+1|ab)*(+1*+1) + P(A=+1, B=-1|ab)*(+1*-1) + P(A=-1, B=+1|ab)*(-1*+1) + P(A=-1, B=-1|ab)*(-1*-1)

This can be simplified to [P(A=+1, B=+1|ab) + P(A=-1, B=-1|ab)] - [P(A=+1, B=-1|ab) + P(A=-1, B=+1|ab)], and if you wish to do the substitution P(AB|a,b) = P(B|a,b)P(A|a,b,B), then it becomes:

[P(B=+1|a,b)P(A=+1|a,b,B=+1) + P(B=-1|a,b)P(A=-1|a,b,B=-1)] -
[(P(B=-1|a,b)P(A=+1|a,b,B=-1) + P(B=+1|a,b)P(A=-1|a,b,B=+1)]