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

[JesseM]

Factorability of the joint probability. The product of the probabilities of A and B. Isn't that the definition of statistical independence?

Again, you're ignoring the issue of whether the joint probability is conditioned on some other variable λ. 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?

 

[billschnieder]

Again, you're ignoring the issue of whether the joint probability is conditioned on some other variable λ. 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?

1) Is Bell's equation (2) specifying a conditional, or a marginal probability?
2) According to Bell's equation (2), is logical dependence between outcomes A and B allowed or not ?

The answers to the above two questions should shatter the smokescreen in the above response.

 

[zonde]

Theta is simply a polarizer setting relative to any arbitrary coordinate system. However, it only leads to valid counterfactual (after the fact) comparisons to route statistics at a 0 setting, but it makes no difference which coordinate choice you use, so long as the photon polarizations are uniformly distributed across the coordinate system.

Please do not escape my question.
Question is about the case when we do not have uniform distribution of polarization across the coordinate system but rather when we have only two orthogonal polarizations H and V.
That was the case you were describing with your formulas.

I will repeat my question. What theta represents physically when we talk about orientation of polarizer and photon beam consisting of photons with two orthogonal polarizations (H and V)?

 

[zonde]

Imagine that for a Bell Inequality, you look at some group of observations. The local realistic expectation is different from the QM expectation by a few %. Perhaps 30% versus 25% or something like that.

On the other hand, GHZ essentially makes a prediction of Heads for LR, and Tails for QM every time. You essentially NEVER get a Heads in an actual experiment, every event is Tails. So you don't have to ask whether the sample is fair. There can be no bias - unless Heads events are per se not detectible, but how could that be? There are no Tails events ever predicted according to Realism.

This is incorrect interpretations of GHZ theorem.
What Bell basically says is that cos(a-b) is not factorizable for all angles (even if it's factorizable when a-b=0,Pi and some other cases).
What GHZ says is that cos(a+b+c+d) is not factorizable even when a+b+c+d=0,Pi.
So there is no prediction at all in GHZ for (non-contextual) local realism.

So using a different attack on Local Realism, you get the same results: Local Realism is ruled out. Now again, there is a slight split here are there are scientists who conclude from GHZ that Realism (non-contextuality) is excluded in all forms. And there are others who restrict this conclusion only to Local Realism.

No it is not Local Realism that is ruled out but only non-contextual Local Realism that is ruled out.
And there is no need to put non-contextuality in parentheses after Realism because Realism is not restricted to non-contextuality only. Even more Realism is always more or less contextual and non-contextuality is only approximation of reality.

 

[JesseM]

1) Is Bell's equation (2) specifying a conditional, or a marginal probability?

Conditional.

2) According to Bell's equation (2), is logical dependence between outcomes A and B allowed or not ?

There can be a logical dependence in their marginal probabilities, but not in conditional probabilities conditioned on λ.

The answers to the above two questions should shatter the smokescreen in the above response.

No smokescreen, distinguishing the two is relevant to my discussion with ThomasT because he seems to be conflating the two, pointing to the example where two variables are correlated in their marginal probabilities due to a common cause in their past, and talking as though Bell's equation (2) was somehow saying this is impossible.

 

[DrChinese]

So there is no prediction at all in GHZ for (non-contextual) local realism.

No it is not Local Realism that is ruled out but only non-contextual Local Realism that is ruled out. ... And there is no need to put non-contextuality in parentheses after Realism because Realism is not restricted to non-contextuality only. Even more Realism is always more or less contextual and non-contextuality is only approximation of reality.

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."

In other words: You do not need to demonstrate that the elements of reality are SIMULTANEOUSLY predictable, in their view of a reasonable definition. Therefore, they only need to be predictable one at a time. All counterfactual observables are in fact elements of reality under THIS definition. That is because they can be individually predicted with certainty. So EPR is asserting the simultaneous realism of counterfactual observables as long as those observables qualify as "elements of reality". That is also the definition Bell used for his a, b and c. These qualify as being "real" by the EPR definition above. Bell introduces the counterfactual c as being on an equal basis with the observable a and b after his (14). See EPR and Bell as references.

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.

 

[DevilsAvocado]

... A local common cause is sufficient to explain the statistical dependencies that are observed. Period. If you think that Bell's theorem proves that there is no local common cause to the correlations, then you're just not thinking about this like a physicist. ...

A friendly advice: Hold on a couple of days with this kind of statements. I can guarantee you that you will regret this, as much as some other posts, and make you feel even worse than in https://www.physicsforums.com/showpost.php?p=2764087&postcount=750".

I’m currently working on compiling "new" (never discussed on PF) material from John Bell himself. If you should decide to continue along this line, you’re left with a catastrophic choice; John Bell’s own mathematical conclusion on Bell’s theorem is wrong, and ThomasT has on his own obtained the correct mathematical conclusion on Bell’s theorem - or the other way around.

If you make the wrong choice, your "sophisticated status" will be considered as hurt as the "Norwegian Blue Parrot" by all, from the casual reader to a real professor. I’m sorry, but this will be a fact.

After I’ve finished and posted this work, I’ll answer any posts from #727 and forward.

 

[billschnieder]

1) Is Bell's equation (2) specifying a conditional, or a marginal probability?

Conditional.

Have you ever heard of marginalization? If you marginalize a probability distribution with respect to λ, the resulting probability is no longer dependent on λ. It is a marginal probability. So Let me ask you the question again, so that you have an opportunity to correct yourself. Maybe you mispoke.

1) Is Bell's equation(2) specifying a conditional or a margnial probability?

If you insist it is conditional, please tell us on what it is conditioned. λ?

2) According to Bell's equation (2), is logical dependence between outcomes A and B allowed or not ?

There can be a logical dependence in their marginal probabilities, but not in conditional probabilities conditioned on λ.

You answered above that Bell's equation (2) specifies a conditional probability. The question is, in that "conditional probability" specified by Bell's equation (2) (according to you), is logical dependence between outcomes A and B allowed or not. From the part of your answer underlined above, I can surmise that you are saying logical dependence is not allowed between outcomes A and B in the probability expressed in Bell's equation (2), since you have already answered above that Bell's equation(2) specifies a conditional probability.

So then as a follow up question.

3) Is logical dependence between outcomes A and B allowed in Bell's inequalities which are derived from equation (2).


Your answers so far:

1: Bell's equation(2) expresses a conditional probability
2: Logical dependence between A and B is not allowed in the probability expressed in Bells equation (2)
3: ? -- waiting for an answer ---

You are free to go back and revise any of your previous answers. My intention here is not to trap you but to make you understand the issue being discussed here. ThomasT, correct me if I'm misrepresenting your position, but isn't this relevant to the question you asked?

 

[billschnieder]

Non-contextual = Realistic

Not according to EPR, it isn't.

All counterfactual observables are in fact elements of reality under THIS definition.

Contextual observables are also elements of reality under THIS definition

Can you see the moon if you are not looking at it? Just because you can not see the moon when you are not looking at it, does not mean the moon does not exist when no one is looking at it.

 

[JesseM]

Have you ever heard of marginalization?

Hadn't heard that particular term, no. Wikipedia defines it in the second paragraph here, it's just finding the marginal probability of one variable by summing over the joint probabilities for all possible values of another variable (so if B can take two values B₁ and B₂, we could find the marginal probability of A by calculating P(A)=P(A, B₁) + P(A, B₂)).

If you marginalize a probability distribution with respect to λ, the resulting probability is no longer dependent on λ. It is a marginal probability.

Yes, I wasn't familiar with the terminology but I'm familiar with the concept, in fact I referred to the same idea in many previous posts addressed to you, that we could find the marginal probabilities of A and B by summing over all possible values of the hidden variable (the last section of this post, for example).

So Let me ask you the question again, so that you have an opportunity to correct yourself. Maybe you mispoke.

1) Is Bell's equation(2) specifying a conditional or a margnial probability?

Bell's equation (2) involves such a sum, so the summation itself (on the right side of the equation) is a sum over various conditional probabilities, but result of the sum (on the left side of the equation) is a marginal probability. In case you want to quibble with this, 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), but this is just a special case of a conditional probability where the probability of any specific outcome for A will always be 0 or 1 (and in later proofs he did write it explicitly as a sum over conditional probabilities, as with equation (13) on p. 244 of Speakable and Unspeakable in Quantum Mechanics which plays the same role as equation (2) in his original paper)

You answered above that Bell's equation (2) specifies a conditional probability. The question is, in that "conditional probability" specified by Bell's equation (2) (according to you), is logical dependence between outcomes A and B allowed or not. From the part of your answer underlined above, I can surmise that you are saying logical dependence is not allowed between outcomes A and B in the probability expressed in Bell's equation (2), since you have already answered above that Bell's equation(2) specifies a conditional probability.

I'll amend that to say that on the right side there can be no logical dependence since this side deals with A and B conditioned on λ, but on the left side there can. Remember, ThomasT's original argument concerned whether or not Bell was justified in treating the joint probability as the product of two individual probabilities, which doesn't even involve marginalization, it just involves the sort of equation that you disputed in your first thread on this subject, P(AB|H)=P(A|H)*P(B|H) (or equation (10) on p. 243 of Speakable and Unspeakable).

So then as a follow up question.

3) Is logical dependence between outcomes A and B allowed in Bell's inequalities which are derived from equation (2).

When A and B are not conditioned on λ, as on the left side of (2) or in the Bell inequalities themselves, then yes there can be a logical dependence between them according to Bell's argument. Do you disagree?

 

[GeorgCantor]

Can you see the moon if you are not looking at it? Just because you can not see the moon when you are not looking at it, does not mean the moon does not exist when no one is looking at it.

Can you see the fullerene molecule when you are not looking at it? Or if i shoot c60 molecules in a quantum eraser experiment and 'erase' the information about the which-path i have obtained, would the resultant interference pattern mean the complex-structure 60-atom molecule was there?

 

[DevilsAvocado]

Sorry for bumping in, I have other "things" to complete, but this is a basic no-brainer, thus to avoid extensive discussions whether the moon is real or not:

So then as a follow up question.

3) Is logical dependence between outcomes A and B allowed in Bell's inequalities which are derived from equation (2).

Yes and No, according to QM predictions and experiments. It depends on the relative angle. If measured parallel or perpendicular, the outcome is strongly logical correlated. In any other case, it’s statistically correlated thru QM predictions cos²(A-B).

Every outcome on every angle is perfectly random, with exception for parallel and perpendicular, where the outcome for A must be perfectly correlated to B.

That’s it. Don’t make things harder than they are by "probability enigmas"...


"Everything should be made as simple as possible, but not simpler" -- Albert Einstein

Edit: Ops, Jesse has already answered...

 

[DrChinese]

1. Not according to EPR, it isn't.


2. Contextual observables are also elements of reality under THIS definition

3. Can you see the moon if you are not looking at it? Just because you can not see the moon when you are not looking at it, does not mean the moon does not exist when no one is looking at it.

1. I gave you the quote from EPR. Perhaps you have a quote that says something different that you might post. Oh, I mean from EPR.

2. The definition from EPR is that it can be predicted with certainty. If it is contextual and can be predicted with certainty, that would make it real per EPR.

3. You must be kidding, since that was the title of the Mermin piece. The conclusion is that the moon is most definitely NOT there when you are not looking at it. Of course, the existence of the moon is just an analogy. We are actually discussing elements of reality.

 

[billschnieder]

1. I gave you the quote from EPR. Perhaps you have a quote that says something different that you might post. Oh, I mean from EPR.

2. The definition from EPR is that it can be predicted with certainty. If it is contextual and can be predicted with certainty, that would make it real per EPR.

3. You must be kidding, since that was the title of the Mermin piece. The conclusion is that the moon is most definitely NOT there when you are not looking at it. Of course, the existence of the moon is just an analogy. We are actually discussing elements of reality.

1) I don't need any other quote. The quote you presented is consistent with what I said. If you think it is not, explain why it is not.

2) Again if you think a contextual element of reality can not be predicted with certainty, explain why you would believe such a ridiculous thing.

3) So what Mermin if said it? What matters is whether it is true or not. It is impossible to see the moon when you are not looking at it. Seeing the moon is contextual. It involves your eyes and the moon. Are you going to tell me next that "seeing the moon" is not real unless it is independent of any eyes? Are you going to tell me next that because it is impossible to see the moon without looking at it, there are no elements of reality which underlie that observation? Are you going to tell me that given all complete knowledge of all those hidden elements of reality, it will be impossible to predict if a hypothetical person in that same situation will see the moon or not?

Certainly you do not ascribe such a naive definiton of realism to EPR since they meant no such thing.

If without in any way disturbing a system, we can predict with certainty the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity

Please show me where EPR says contextual observables can not be predicted with certainty. In fact they argue aganist this mindset when they say:

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 either one or the other, but not both simultaneously, of the quantities P and Q can be predicted, they are not simultaneously 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.

 

[DrChinese]

1) I don't need any other quote. The quote you presented is consistent with what I said. If you think it is not, explain why it is not.

2) Again if you think a contextual element of reality can not be predicted with certainty, explain why you would believe such a ridiculous thing.

3) So what Mermin if said it? What matters is whether it is true or not. It is impossible to see the moon when you are not looking at it. Seeing the moon is contextual. It involves your eyes and the moon. Are you going to tell me next that "seeing the moon" is not real unless it is independent of any eyes? Are you going to tell me next that because it is impossible to see the moon without looking at it, there are no elements of reality which underlie that observation? Are you going to tell me that given all complete knowledge of all those hidden elements of reality, it will be impossible to predict if a hypothetical person in that same situation will see the moon or not?

Certainly you do not ascribe such a naive definiton of realism to EPR since they meant no such thing.

1) I gave it because it supports my position. Nice that you can turn that around with the wave of a... nothing!

2) Well of course it can be. For example, I measure Alice at 0 degrees. I know Bob's result at 0 degrees with certainty. That is an element of reality, and it is contextual (observer dependent). Duh. Perhaps you might read what I say next time.

3) The moon is NOT there when we are not looking, and of course this is an analogy as I keep saying. How many ways can I say it, and how many famous people need to say it before you accept it as a legitimate position (regardless of whether you agree with it)? There is no hypothetical observer, unless we live in a non-local universe. Which perhaps we do.

As to EPR not meaning it that way: Einstein SPECIFICALLY said he meant it that way. Do I need to produce the quote? That is why Mermin titled his article as he did.

You know, on a side note: It really makes me laff to see folks like you dismiss towering figures of modern science without so much as one iota of support for your position, other than YOU say it. I can't recall a single useful reference or quote from you.

 

[ThomasT]

In this situation do you think there is a single correct answer to whether A and B are "statistically independent" or not?

Ok, here's the way I'm thinking about it today. Wrt the experimental situation, there's a single correct answer, the data sets A and B are not independent. This is because of the data matching via time stamping. Matching the data in this way is based on the assumption of a local common cause. The fact that data matching via time stamping does produce (or reveal) entanglement correlations would, then, seem to support the idea that a locally produced relationship between counter-propagating disturbances is a necessary condition and the root cause of the correlations between joint detection and angular difference of the polarizers.

Wrt the form of Bell's (2), wasn't it demonstrated that it can be reduced to, or is analogous to, a statement of the independence of the two data sets?

 

[ThomasT]

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.

DrC, if you would clarify this for me it would be most appreciated.

 

[JesseM]

Ok, here's the way I'm thinking about it today. Wrt the experimental situation, there's a single correct answer, the data sets A and B are not independent. This is because of the data matching via time stamping. Matching the data in this way is based on the assumption of a local common cause.

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

The fact that data matching via time stamping does produce (or reveal) entanglement correlations would, then, seem to support the idea that a locally produced relationship between counter-propagating disturbances is a necessary condition and the root cause of the correlations between joint detection and angular difference of the polarizers.

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.

Wrt the form of Bell's (2), wasn't it demonstrated that it can be reduced to, or is analogous to, a statement of the independence of the two data sets?

Again, you can't just use words like "independence" without being more specific. 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 λ, but the equation is consistent with the idea that P(AB) can be different from P(A)*P(B).

 

[billschnieder]

2) Well of course it can be. For example, I measure Alice at 0 degrees. I know Bob's result at 0 degrees with certainty. That is an element of reality, and it is contextual (observer dependent). Duh. Perhaps you might read what I say next time.

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.

3) The moon is NOT there when we are not looking, and of course this is an analogy as I keep saying.

Keep deluding yourself.

How many ways can I say it, and how many famous people need to say it before you accept it as a legitimate position (regardless of whether you agree with it)?

You can not find enough famous people to make me believe a lie.

As to EPR not meaning it that way: Einstein SPECIFICALLY said he meant it that way. Do I need to produce the quote? That is why Mermin titled his article as he did.

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

You know, on a side note: It really makes me laff to see folks like you dismiss towering figures of modern science without so much as one iota of support for your position, other than YOU say it. I can't recall a single useful reference or quote from you.

Appeal to authority is a fallacy of reasoning. I don't think I'm the first one to point it out to you recently. Feel free to make a shrine of these "towering figures" but don't expect us to join you.

 

[billschnieder]

I'll amend that to say that on the right side there can be no logical dependence since this side deals with A and B conditioned on λ, but on the left side there can.

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

When A and B are not conditioned on λ, as on the left side of (2) or in the Bell inequalities themselves, then yes there can be a logical dependence between them according to Bell's argument. Do you disagree?

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. 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.


So then since you amended your answers, let me also amend my summary of your responses:

Your responses so far are now:
1: Bell's equation(2) expresses a [strike]conditional[/strike] marginal probability
2: Logical dependence between A and B is [strike]not[/strike] allowed in the probability expressed in Bells equation (2)
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)

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? Please look at it again carefully and if you decide to stick to this answer, let me know. I don't want to carry on an argument in which the opposing position is shifting based on argumentation tactics so I want to be sure I have given you enough opportunity to express your position before I proceed.

 

[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...