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

[ThomasT]

1) You say: "Your argument here does not follow regarding vectors. So what if it is or is not true?", but the claim about this aspect of vectors is factually true. Read this carefully:
http://www.vias.org/physics/bk1_09_05.html
Note: Multiplying vectors from a pool ball collision under 2 different coordinate systems don't just lead to the same answer expressed in a different coordinate system, but an entirely different answer altogether. For this reason such vector operations are generally avoided, using scalar multiplication instead. Yet the Born rule and cos^2(theta) do just that.
2) You say: "I think you are trying to say that if vectors don't commute, then by definition local realism is ruled out.", but they don't commute for pool balls either, when used this way. That doesn't make pool balls not real. Thus the formalism has issues in this respect, not the reality of the pool balls. I even explained why: because given only the product of a vector, there exist no way of -uniquely- defining the particular vectors that went into defining it.

Again, I am missing your point. So what? How does this relate to Bell's Theorem or local realism?

I think that my-wan's point might be related to Christian's formulation of his (Christian's) LR model. Christian's point being that you need an algebra that can suitably represent the rotational invariance of the local beables -- which, in his estimation, Bell didn't represent adequately. According to Christian, Bell's ansatz misrepresents the topology of the experimental situation. Christian has produced 5, or so, papers (for anyone interested, go to arxiv.org and search on Joy Christian) that I know of trying to explain his idea(s). I don't fully understand what he's saying. That is, presently, I'm having difficulty incorporating what Christian is saying into my own 'intuitive' understanding of what I currently regard as the lack of depth in Bell's 'logical' analysis. Although, intuitively, I see a connection. I've read his papers and the discussions on sci.physics.research that Christian participated in a couple of years ago, and the impression I got was that he became frustrated with the lack of knowledge and preparation of those involved. Since then, I've seen nothing about his stuff and don't know if it's still under consideration for publication or not. Maybe he just abandoned it. Maybe someone should send him an email or something to find out what's what. (No, not me!) After all, the guy is a bona fide mathematical physicist who got his PhD under Shimony -- and he has published some respected peer reviewed stuff. It's very curious to me.) If he came to the conclusion that he was wrong, then wouldn't he be obligated, as a scientist, to say so? I assume that there are physicists and mathematicians here at PF qualified to critique his stuff. So, maybe they will contribute their synopses and critiques.

Anyway, I think my_wan's considerations about vectors are related to this. If I'm wrong, then please let me know why.

 

[ThomasT]

If this is a local theory in which any correlations between the two disturbances are explained by properties given to them by the common source, with the disturbances just carrying the same properties along with them as they travel, then this is exactly the sort of theory that Bell examined, and showed that such theories imply certain conclusions about the statistics we find when we measure the "disturbances", the Bell inequalities. Since these inequalities are violated experimentally, this is taken as a falsification of any such local theory which explains correlations in terms of common properties given to the particles by the source.

Bell's ansatz depicts the data sets A and B as being statistically independent. And yet we know that separately accumulated data sets produced by a common cause can be statistically dependent -- even when there is no causal dependence between the spacelike separated events that comprise the separate data sets -- precisely because the spacelike separated events have a common cause.

Bell has assumed that statistical dependence implies causal dependence. But we know that it doesn't. So, I ask you, is Bell's purported locality condition, in fact, a locality condition?

Virtually all physicists would agree that the violation of Bell inequalities constitutes a falsification of the kind of theory you describe, assuming you're talking about a purely local theory.

But that isn't what I asked.

What I asked was:

... given a situation in which two disturbances are emitted via a common source and subsequently measured, or a situation in which two disturbances interact and are subsequently measured, then the subsequent measurement of one will allow deductions regarding certain motional properties of the other.

Assuming the conservation laws are correct, then are these sorts of deductions allowable?

 

[ThomasT]

The EPR conclusion is most certainly not the view which is currently accepted.

The EPR conclusion was that qm is not a complete description of the physical reality underlying instrumental phenomena. Are you telling me that this isn't the view of a majority of physicists? If so, how do you know that? Every single physicist that I've talked to personally about this, whether they're familiar with EPR and Bell etc. or not, has said to me that they regard qm, in the sense of a description of the physical reality underlying instrumental phenomena, to be incomplete. This doesn't speak to why it's incomplete, or whether it must be incomplete, but just that it is incomplete. I conjecture that this is the view of a majority of working physicists. Now you can do a representative survey to prove that that conjecture is incorrect. But in the absence of such a survey, then a conjecture to the contrary is also just a conjecture.

That is because the EPR view has been theoretically (Bell) and experimentally (Aspect) rejected. But that was not the case in 1935. At that time, the jury was still out.

The EPR view stands as well today as it did in 1935. Either a real physical disturbance with real physical attributes is being emitted by the emitter or it isn't. If it isn't, then, according to a strict, realistic interpretation of the qm formalism, then the reality of B depends on a detection at A, and vice versa. Pretty silly, eh?

What is wrong with this view is that it violates the Heisenberg Uncertainty Principle. Nature does not allow that.

There's nothing in the EPR view that violates the uncertainty relations.

EPR says that two particles emitted from a common source are related wrt an applicable conservation law. So that, if the position of particle A is measured, then the position of particle B can be deduced, and if the momentum of particle A is measured, then the momentum of particle B can be deduced.

The uncertainty relations say that for a large number of similar preparations, the deviation from the statistical mean value of the position measurements will be related to the deviation from the statistical mean value of the momentum measurements by the following inequality: (delta q) . (delta p) >= h (where h is Planck's constant, the quantum of action).

As Bohr so eloquently, and yet so, er, cryptically, expressed, the uncertainty relations have no bearing on the relationship between a measurement that WAS made at A and a measurement that WAS NOT made at B.

Bottom line, the EPR argument has nothing to do with the uncertainty relations.

But it has everything to do with the, I conjecture, virtually universal acceptance that qm is an incomplete description of the physical reality underlying instrumental phenomena.

However, just so you don't take what I'm saying the wrong way. I don't see that an unassailably more complete description is possible. Even though there are LR models of entanglement that reproduce the qm predictions, there's absolutely no way to ascertain whether or not they're accurate depictions of an underlying reality. This was Bohr and Heisenberg's, et al., meeting of the minds, so to speak. Qm is, as a probability calculus of instrumental phenomena, as complete as it needs to be, and as complete as it can be without unnecessary and ultimately frustrating speculation regarding what does or doesn't exist or what is or isn't happening in the deep reality underlying instrumental phenomena. The point is that qm, as a mathematical probability calculus, can continue to be progressively developed, and technologically applicable, without any consensus regarding the constituents or behavior of proposed underlying 'elements of reality'.

 

[my_wan]

Do you just mean that local properties of the particle are affected by local properties of the detector it comes into contact with? If so, no, this cannot lead to any violations of the Bell inequalities.

I'll go through the computer model (virtual detectors) I used in your question below. I'll also explain the empirical based assumptions used.

Suppose the experimenters each have a choice of three detector settings, and they find that on any trial where they both chose the same detector setting they always got the same measurement outcome.

Naturally you get consistency between experiments, at least statistically. It really would be weird otherwise. But real experiments are limited to 2 setting choices at a time. The 3rd setting is a counterfactual from previous experiments. I doubt you've read the unfair coin example, an unfair coin with a tiny adjuster to set so it match a second 85% of the time, but by defining a 3rd simultaneous setting you are putting very severe non-random constraints on how it relates to 2 other settings. Both completely correlated with 1 and totally uncorrelated with the other, yet expecting this nonrandom choice to match stochastically with both based on statistical profiles pulled from previous experiments without such constraints. Neither classical nor QM mechanism allows this. Only QM is not explicitly time dependent so it's much harder to see the mechanism counterfactually in QM.

Then in a local hidden variables model where you have some variables associated with the particle and some with the detector, the only way to explain this is to suppose the variables associated with the two particles predetermined the result they would give for each of the three detector settings; if there was any probabilistic element to how the variables of the particles interacted with the state of the detector to produce a measurement outcome, then there would be a finite probability that the two experimenters could both choose the same detector setting and get different outcomes. Do you disagree?

Finite, maybe. Though there's at least some reason to believe nature is not finite. But assuming finite, I can also calculate the odds that all the air in the half of the room you are in spontaneously ends up in the other half of the room. The odds of it happening are indeed finite, but I'm not holding my breath just in case.

What do you mean by "assigning" coordinate systems? Coordinate systems are not associated with physical objects, they are just aspects of how we analyze a physical situation by assigning space and time coordinates to different events. Any physical situation can be analyzed using any coordinate system you like, the choice of coordinate system cannot affect your predictions about coordinate-invariant physical facts.

Quiet simple cases exist were quantities are not coordinate-invariant, and a very important one involves basic vector products. Consider:
http://www.vias.org/physics/bk1_09_05.html

The[/PLAIN] operation's result depends on what coordinate system we use, and since the two versions of R have different lengths (one being zero and the other nonzero), they don't just represent the same answer expressed in two different coordinate systems. Such an operation will never be useful in physics, because experiments show physics works the same regardless of which way we orient the laboratory building! The useful vector operations, such as addition and scalar multiplication, are rotationally invariant, i.e., come out the same regardless of the orientation of the coordinate system.

It states it "will never be useful in physics", yet both the Born rule and Malus Law involve just such a vector product if you presume there is some underlying mechanism. Given just a single vector magnitude it's not even possible to uniquely identify the vectors that it was derived from.

Anyway, your description isn't at all clear, could you come up with a mathematical description of the type of "hv model" you're imagining, rather than a verbal one?

My model is based on a computer model, virtual emitters and detectors.

Assumptions (I'll use photons and polarizations for simplicity):
1) A photon has a single unique default polarization, which is only unique in that upon meeting a polarizer at the same polarization it effectively has a 100% chance of passing that polarizer.
2) The odds that a photon will pass through a polarizer that is offset from that photon default polarization is defined by cos^2(theta), Malus Law.
3) A bit field is set to predefine passage through a polarizer it meats at various settings, with the odds of a bit being predefined as 1 (for passage) determined by a random number generator with a min/max of 0/1 that rolls less than cos^2(theta) when created at the emitter.
4) A random number with a min/max of 0/359.5, rounded to half degree increments, predefines the default polarization at the emitter. These can be rotated with impunity.

For computer modeling a default polarization and a bit field is set. I used 180 bit field, which predefines passage or not for each 1/2 degree over 90 degrees, reversed for every other 90 degrees. The odds that a 10 degree bit, for instance, will be predefined 1 is cos^2(10). Anticorrelated photons are simply flipped 180 degrees, with the same bit field. The photons can be randomly generated and written to a text file. I have lots of improvements to try, but haven't got to it yet.

The formula, when a photon meets a detector is simply (polarizer1 - photon1) and (polarizer2 - photon2) at the other end. Then simply count that many bits into the bit field to see if a detection occurs. No Malus Law used here because it's built into the statistics of the bit field. Detections are returned before comparisons are made between polarizer1 and polarizer2.

This only works to match QM predictions if 1 of the polarizer settings is defined to be 0. Yet you can rotate the photons coming from the emitter with impunity, without effecting the coincidence statistics. So there exist no unique physical state at certain rotations. Neither polarizer directly references the setting of the other polarizer. Only the difference between the photons default polarization and the polarizer setting it actually comes in contact with is used to define detections.

The 0 angle is the biggest issue. You could also add another 719 180 bit fields, for 1/2 degree increments, to undo the 0 degree requirement on one of the detector. This would blow up into a huge, possibly infinite, number of variables in real world conditions, but if quantum computers work as well as expected this shouldn't be an issue.

I'm not happy with this, and have a lot of improvements to try, when I get to it. Including using predefined ranges instead of bit fields, and non-commutative vector rotations in an attempt to remove the coordinate rotations as I change a certain detector setting. I have my doubts about these.

 

[my_wan]

Please tell me what theta represents physically.

As I asked already:
How you define theta? Is it angle between polarization axis of polarizer (PBS) and photon so that we have theta1 for H and theta2 for V with condition that theta1=theta2-90?
Or it's something else?

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.

 

[JesseM]

Bell's ansatz depicts the data sets A and B as being statistically independent.

Only when conditioned on the appropriate hidden variables represented by the value of λ. When not conditioned on λ, Bell's argument says there can certainly be a statistical dependence between A and B, i.e. P(A|B) may be different than P(A). Do you disagree?

And yet we know that separately accumulated data sets produced by a common cause can be statistically dependent -- even when there is no causal dependence between the spacelike separated events that comprise the separate data sets -- precisely because the spacelike separated events have a common cause.

Yes, and this was exactly the possibility that Bell was considering! If you don't see this, then you are misunderstanding something very basic about Bell's reasoning. If A and B have a statistical dependence, so P(A|B) is different than P(A), but this dependence is fully explained by a common cause λ, then that implies that P(A|λ) = P(A|λ,B), i.e. there is no statistical dependence when conditioned on λ. That's the very meaning of equation (2) in Bell's original paper, that the statistical dependence which does exist between A and B is completely determined by the state of the hidden variables λ, and so the statistical dependence disappears when conditioned on λ. Again, please tell me if you disagree with this.

Bell has assumed that statistical dependence implies causal dependence.

No, he didn't. He was explicitly considering a case where there is a statistical dependence between A and B but not a causal dependence because the dependence is fully explained by λ. In the simplest type of hidden-variables theory, λ would just represent some set of hidden variables assigned to each particle by the source when the two particles were created, which remained unchanged as they traveled to the detector and which determined their responses to various detector settings.

It would really help if you looked over my lotto card analogy in post #2 here! Your comments suggest you may be confused about the most basic aspects of Bell's proof, so instead of trying to understand the abstract equations in his original paper, I think it would definitely help to look over a concrete model of a situation where we propose a simple hidden-variables theory (involving a common cause, namely the cards being assigned identical 'hidden fruits' by the source) to explain a statistical dependence in observed measurements (the fact that whenever Alice and Bob choose the same box on their respective cards to scratch, they always find the same fruit behind it).

So, I ask you, is Bell's purported locality condition, in fact, a locality condition?

Properly understood, yes it most certainly is.

Virtually all physicists would agree that the violation of Bell inequalities constitutes a falsification of the kind of theory you describe, assuming you're talking about a purely local theory.

But that isn't what I asked.

What I asked was:

given a situation in which two disturbances are emitted via a common source and subsequently measured, or a situation in which two disturbances interact and are subsequently measured, then the subsequent measurement of one will allow deductions regarding certain motional properties of the other.

That paragraph is not even a question, so I would say that's not what you asked. My comment above was in response to your question (which I quoted in my post), "Do you doubt that this is the view of virtually all physicists?" And I understood "this is the view" to refer to your earlier comment "The EPR view was that the element of reality at B determined by a measurement at A wasn't reasonably explained by spooky action at a distance", i.e. specifically the view that correlations in quantum physics could be explained by this sort of common cause, in which case this is not the view of virtually all physicists. On the other hand, if you were just asking whether all physicists would agree there are some situations (outside of QM) where correlations between separated measurements can be explained in terms of common causes, then of course the answer is yes.

Assuming the conservation laws are correct, then are these sorts of deductions allowable?

Here you seem to be asking a new question, and my answer is "yes, in cases where two disturbances are emitted by a common source, observations of one may allow for deductions about the other". And of course, the whole point of Bell's argument was to consider whether or not the observed correlations between measurements on entangled particles could be explained in terms of this sort of "common cause" explanation in a local realist theory. The conclusion he reached was that any such explanation would imply certain Bell inequalities, which are experimentally observed to be violated in quantum experiments.

 

[ThomasT]

Only when conditioned on the appropriate hidden variables represented by the value of ?. When not conditioned on λ, Bell's argument says there can certainly be a statistical dependence between A and B, i.e. P(A|B) may be different than P(A). Do you disagree?

Does the form, Bell's (2), denote statistical indepencence or doesn't it?

Yes, and this was exactly the possibility that Bell was considering! If you don't see this, then you are misunderstanding something very basic about Bell's reasoning. If A and B have a statistical dependence, so P(A|B) is different than P(A), but this dependence is fully explained by a common cause λ, then that implies that P(A|λ) = P(A|λ,B), i.e. there is no statistical dependence when conditioned on λ. That's the very meaning of equation (2) in Bell's original paper, that the statistical dependence which does exist between A and B is completely determined by the state of the hidden variables λ, and so the statistical dependence disappears when conditioned on λ. Again, please tell me if you disagree with this.

It seems that you're saying that if the disturbances incident on a and b have a common cause, then the results, A and B, can't be statistically dependent. Is that what you're saying?

... the whole point of Bell's argument was to consider whether or not the observed correlations between measurements on entangled particles could be explained in terms of this sort of "common cause" explanation in a local realist theory. The conclusion he reached was that any such explanation would imply certain Bell inequalities, which are experimentally observed to be violated in quantum experiments.

Yes, well, we disagree then on the depth of Bell's analysis, or simply on the way his analysis and result is communicated. The problem is that viable LR models of entanglement exist. Would you care to look at one and refute it -- either wrt to its purported locality or reality or agreement with qm predictions?

 

[DrChinese]

Quiet simple cases exist were quantities are not coordinate-invariant, and a very important one involves basic vector products. Consider:
http://www.vias.org/physics/bk1_09_05.html

We are not discussing whether 2 measurements commute or not. Or two vector operations. We are discussing whether 2 measurements on separated particles have various attributes. So this statement and the related example are completely meaningless in the context of this discussion. I really wish you would stop mentioning it as it leads us nowhere useful.

We understand that your model lacks rotational invariance in that it works with a reference angle of 0 and not at others. And no, it is not OK that you can define any angle as 0 to make it appear to work. Your "trick" works because you are effectively communicating Alice's setting to Bob or vice versa. Whether or not vectors add in all coordinate systems does not change this point in any way.

 

[ThomasT]

JesseM, do you think that most physicists equate EPR's spooky action at a distance with quantum correlations?

 

[JesseM]

Does the form, Bell's (2), denote statistical indepencence or doesn't it?

You haven't defined what you mean by "statistical independence". I think I made clear already that two variables can be statistically dependent in their marginal probabilities but statistically independent when conditioned on other variables.

Could you please answer the questions I ask you in my posts, like this one?

When not conditioned on λ, Bell's argument says there can certainly be a statistical dependence between A and B, i.e. P(A|B) may be different than P(A). Do you disagree?

It seems that you're saying that if the disturbances incident on a and b have a common cause, then the results, A and B, can't be statistically dependent. Is that what you're saying?

If the common cause is the complete explanation for the statistical dependence in the marginal probabilities, then when conditioned on the common cause they wouldn't be statistically dependent (i.e. if you already know precisely what properties were given to system A by the common cause which also gave some related properties to system B, then learning about a later measurement on system B will tell you nothing new about what you are likely to see when you measure system A). Do you disagree with that? If you do disagree, can you think of any classical examples where we have correlations that are completely explained by a common cause, yet where the above would not be true?

Of course you could have a more complicated situation where there were multiple common causes, and perhaps also some direct causal influences between A and B. But then the given common cause wouldn't be the complete explanation for the correlation observed between measurements on A and B.

Yes, well, we disagree then on the depth of Bell's analysis.

OK, but do you want to engage in an actual substantive discussion about the details of his analysis and whether his assumptions are justified? If so then I would ask that you please answer my direct questions to you, and also address the examples and arguments I present like the lotto card analogy in post #2 here or the argument I made about conditioning on complete past light cones, and what this would imply in both deterministic and probabilistic theories, in this post. Of course there's no need to respond to all of this immediately, but if you are intellectually serious about exploring the truth and not just trying to engage in rhetorical denunciations, then I'd like some assurances that you do plan to address my questions and arguments seriously if we're going to keep discussing this stuff.

 

[DrChinese]

Does the form, Bell's (2), denote statistical indepencence or doesn't it?

It seems that you're saying that if the disturbances incident on a and b have a common cause, then the results, A and B, can't be statistically dependent. Is that what you're saying?

A common cause is assumed. Statistical correlation of A and B is assumed as well. Even perfect correlations can be explained, all within Bell (2). There is no problem with any of this. This is simply a restatement of what EPR was trying to say.

The problem is getting this to agree to the QM expectation values. There are a variety of constraints in this as my_wan has discovered. Under scenario a), the Malus relationship does not hold except at privileged angle settings. Under scenario b), an infinite or at least very large amount of data must be encoded. And both of these scenarios are BEFORE we come to terms with a Bell Inequality.

So my point is that for everyone attacking Bell (2), you are coming at it backwards. It is a generic statement, and does not provide any particular insight into the EPR issue at all. Any way you want to express the statement "The result A does not depend on setting b, and vice versa" would work here. Bell calls this requirement essential because it is his version of locality. (Or call it "local causality" if that is a preferable label.) Bell assumed his version would not cause anybody to have a cow, that it would be accepted as a mathematical version of the "...A not dependent on b..." statement. So whether or not there is a statistical connection, that really makes no difference. Since this is assumed by everyone. So Bell (2) is not an expression of the independence of statistical correlations A and B. It has to do with the independence of A and b, and B and a. If your model has A dependent on b, then it fails test #1. Because it is not local.

 

[ThomasT]

You haven't defined what you mean by "statistical independence".

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

 

[DrChinese]

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

a and b are different than A and B. A and B do not need to be independent.

 

[ThomasT]

a and b are different than A and B. A and B do not need to be independent.

Exactly. But that's how Bell's model denotes them. In Bell's model, the data sets A and B are independent.

 

[ThomasT]

So Bell (2) is not an expression of the independence of statistical correlations A and B.

Are you sure about that? I think it's been demonstrated that Bell's ansatz reduces to the probability definition of statistical independence. If you think otherwise then maybe you should revisit the posts in this and other threads dealing with that.

 

[ThomasT]

DrC, the view of many physicists, including past discussions I've had here at PF, indicate that Bell's idea was that if the data sets A and B were statistically dependent, then they must be causally dependent. Of course, we know this is wrong.

 

[DrChinese]

Are you sure about that? I think it's been demonstrated that Bell's ansatz reduces to the probability definition of statistical independence. If you think otherwise then maybe you should revisit the posts in this and other threads dealing with that.

I have stated many times: A and b, not A and B. The result A is definitely correlates with B. The question is: does A change with b? It shouldn't in a local world. In other words: if Alice's result changes when spacelike separated Bob moves his measurement dial, then there is spooky action at a distance. I know you will agree with that statement.

From the EPR conclusion: "This makes the reality of P and Q depend upon the process of measurement carried out on the first system in any way. No reasonable definition of reality could be expected to permit this." They are saying the same thing as Bell (2).

And in Bell's words: "The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b." Which he then presents in his form (2). There is no restriction on the correlation of A and B in this.

So the data points for A with setting a come out the same regardless of the value of b. Of course the correlation of A and B may change with a change in a or b. Bell (2) is not saying anything about that. If you doubt this, just re-read what Bell said above. Or what EPR said.

 

[DrChinese]

DrC, the view of many physicists, including past discussions I've had here at PF, indicate that Bell's idea was that if the data sets A and B were statistically dependent, then they must be causally dependent. Of course, we know this is wrong.

There is nothing wrong with causality in this situation. I mean, the entire point is that the pairs are clones (or anti-clones) of each other because they were created at the same time. The question is whether there is observer independence in the outcomes. Whether the reality of P and Q are independent of what goes on elsewhere. Whether the result A is dependent on setting b.

And as far as anyone knows, this is "possible" within constraints when you consider Bell (2) by itself. This has been demonstrated by who knows how many local realistic papers. But of course all this falls apart when you add the realism requirement. EPR said that it was possible to constrain reality to just the number of observables that could be predicted simultaneously (1), but that was too restrictive (in their opinion). So by then applying the less restrictive definition of reality which they claim as reasonable (2 or more), Bell obtains his famous result.

 

[DrChinese]

Exactly. But that's how Bell's model denotes them. In Bell's model, the data sets A and B are independent.

No, that is my point. You have misinterpreted Bell (2). How many times must I repeat Bell:

"The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b."

"The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b."

"The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b."

Yes, I am pretty good with ^V. And there can be a connection between A and B. In fact, there has to be to have an element of reality according to EPR. It was assumed that A and B would be perfectly correlated when a=b. That is how you predict the outcome of one without first disturbing it.

 

[ThomasT]

I have stated many times: A and b, not A and B. The result A is definitely correlates with B. The question is: does A change with b? It shouldn't in a local world. In other words: if Alice's result changes when spacelike separated Bob moves his measurement dial, then there is spooky action at a distance. I know you will agree with that statement.

From the EPR conclusion: "This makes the reality of P and Q depend upon the process of measurement carried out on the first system in any way. No reasonable definition of reality could be expected to permit this." They are saying the same thing as Bell (2).

And in Bell's words: "The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b." Which he then presents in his form (2). There is no restriction on the correlation of A and B in this.

So the data points for A with setting a come out the same regardless of the value of b. Of course the correlation of A and B may change with a change in a or b. Bell (2) is not saying anything about that. If you doubt this, just re-read what Bell said above. Or what EPR said.

You miss the point. Bell's ansatz denotes that the data sets A and B are statistically independent.

 

[DrChinese]

You miss the point. Bell's ansatz denotes that the data sets A and B are statistically independent.

No. They aren't independent. Bell never mentions that point.

 

[ThomasT]

No, that is my point. You have misinterpreted Bell (2). How many times must I repeat Bell:

"The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b."

"The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b."

"The vital assumption is that the result B for particle 2 does not depend on the setting a, of the magnet for particle 1, nor A on b."

Yes, I am pretty good with ^V. And there can be a connection between A and B. In fact, there has to be to have an element of reality according to EPR. It was assumed that A and B would be perfectly correlated when a=b. That is how you predict the outcome of one without first disturbing it.

You can repeat anything you want as much as you want. The fact is that Bell's model says that the data sets A and B are independent.

This point is important, so if you dispute it, then you'll have to demonstrate why.

And yet we know from the experimental designs that the data sets, A and B, aren't independent. And we also know that this statistical dependence doesn't have to have anything to do with a causal connection between A and B or A and b or B and a or B and A. 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. In fact, I'll submit this: many physicists, maybe even most, having neither the time nor the inclination to delve very deeply into Bell's theorem, have accepted the common view that all local realistic theories of entanglement are impossible. What do they care. It has nothing to do with their research or their experiments or their grants. Period.

Of course, imo, they're wrong. But so what? It doesn't affect their programs one bit. So I reject your appeals to 'a majority of physicists' think this or that. I've issued you a challenge and asked you to clarify what you mean by your 'requirement'. Please address that issue. It's most difficult to learn anything from obfuscations.

 

[ThomasT]

No. They aren't independent. Bell never mentions that point.

It doesn't matter if he 'mentions' it. It's there, in the model.

On the one hand, in some posts, you say that it doesn't matter if Bell says this or that. And on the other hand, when it suits your purpose, you appeal to what Bell did or didn't say.

Well, I'm telling you now, the arguments that have been presented have nothing to do with what Bell did or didn't say about any of his formal presentations. All we're concerned with are the formalisms. Period.

So, you'd better forget about what 'most' physicists say or believe, and what Bell said or believed, and just look at what he presented as a model of a certain experimental situation. It happens to be wrong. And we're trying to determine exactly what's wrong with it.

 

[DrChinese]

It doesn't matter if he 'mentions' it. It's there, in the model.

On the one hand, in some posts, you say that it doesn't matter if Bell says this or that. And on the other hand, when it suits your purpose, you appeal to what Bell did or didn't say.

Well, I'm telling you now, the arguments that have been presented have nothing to do with what Bell did or didn't say about any of his formal presentations. All we're concerned with are the formalisms. Period.

So, you'd better forget about what 'most' physicists say or believe, and what Bell said or believed, and just look at what he presented as a model of a certain experimental situation. It happens to be wrong. And we're trying to determine exactly what's wrong with it.

It would be nice if you would mention that it is the 1965 paper which I quote, not his later writings. And it is that same paper which is usually referenced by authors, not his later writings. There has never been much question about the respect I give that paper.

Now, after saying the words, Bell presents the mathematical form which is the SAME as the words. There is no question about this to most anyone. But I see that for many, this can be a bit confusing. So I will point out EXACTLY what his (2) says:

There is a result function for Alice, A(a, lambda), which has no dependence on b. There is a result function for Bob, B(b, lambda), which has no dependence on a. These share a common dependence on a set of hidden variables or hidden functions. I believe you can see this point for yourself. And there is the correlation function, P(a, b) which we would expect to match the quantum expectation value, which is Bell's (3). For a=b, the result is -1 for the singlet state. I believe you can plainly see this point.

Now, where is the above any different than what I have told you: Bob's result B is independent of Alice's setting a. But there is definitely a correlation between A and B, which is in fact -1 when a=b.

I really don't know how to make it much clearer. Show me any respected author who says that Bell (2) is a requirement that outcomes A and B are statistically unrelated. Or if the author is not respected, at least give me a funny quote.

 

[DrChinese]

And yet we know from the experimental designs that the data sets, A and B, aren't independent. And we also know that this statistical dependence doesn't have to have anything to do with a causal connection between A and B or A and b or B and a or B and A. 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. In fact, I'll submit this: many physicists, maybe even most, having neither the time nor the inclination to delve very deeply into Bell's theorem, have accepted the common view that all local realistic theories of entanglement are impossible. What do they care. It has nothing to do with their research or their experiments or their grants. Period.

Of course, imo, they're wrong. But so what? It doesn't affect their programs one bit. So I reject your appeals to 'a majority of physicists' think this or that. I've issued you a challenge and asked you to clarify what you mean by your 'requirement'. Please address that issue. It's most difficult to learn anything from obfuscations.

OK, you are going off the deep end again. There are a lot of physicists out there who DO follow Bell tests very closely, and it is these that I generally quote. Zeilinger and Aspect being just 2, but there are a lot of very well respected scientists out there - Gisin, Weihs, Mermin, Greenberger, many many more. I am not invoking the authority of those who don't know the field. So I would recommend you cease your diatribe, it really reflects poorly. These guys know their stuff, theory and history. And every day they are dreaming up and running experiments that would be impossible in a local realistic world. So please, don't speak like a fool.

Second, as I have repeatedly told you, there IS a statistical relationship between the results of Alice and Bob. And that IS effectively due to a common cause or whatever you want to call it. I call it a conservation law. Also, a local connection MIGHT be able to follow the requirements of Bell (2) and Bell (3) but cannot survive the Bell final result (which rules out all local realistic theories).

And third, it is not my requirements which are in question here. It is the requirement of EPR, as I quoted you earlier, that there be 2 or more simultaneous elements of reality. In Bell's case, there are 3: a, b and c.

 

[ThomasT]

It would be nice if you would mention that it is the 1965 paper which I quote, not his later writings. And it is that same paper which is usually referenced by authors, not his later writings. There has never been much question about the respect I give that paper.

Now, after saying the words, Bell presents the mathematical form which is the SAME as the words. There is no question about this to most anyone. But I see that for many, this can be a bit confusing. So I will point out EXACTLY what his (2) says:

There is a result function for Alice, A(a, lambda), which has no dependence on b. There is a result function for Bob, B(b, lambda), which has no dependence on a. These share a common dependence on a set of hidden variables or hidden functions. I believe you can see this point for yourself. And there is the correlation function, P(a, b) which we would expect to match the quantum expectation value, which is Bell's (3). For a=b, the result is -1 for the singlet state. I believe you can plainly see this point.

Now, where is the above any different than what I have told you: Bob's result B is independent of Alice's setting a. But there is definitely a correlation between A and B, which is in fact -1 when a=b.

I really don't know how to make it much clearer. Show me any respected author who says that Bell (2) is a requirement that outcomes A and B are statistically unrelated. Or if the author is not respected, at least give me a funny quote.

The 'form' of Bell's (2) says, explicitly, that the data sets A and B are independent.

Look, I don't care about this right now. I already understand it. I want you to tell me what your LR 'requirement" means. Please do that. Thank you.

 

[ThomasT]

I'm waiting ...

 

[ThomasT]

Look, I have some other stuff to do soon. I want the 'casual reader' to understand that you're unable to refute a simple LR model of entanglement.

There's no need to be alarmed. It will only hurt for a second or two.

 

[DrChinese]

I want the 'casual reader' to understand that you're unable to refute a simple LR model of entanglement.

You are proof of the existence of many worlds.

ThomasT, you are really messing yourself up with this one. I appreciate that you have convinced yourself that you have brilliantly deduced the "flaws" in Bell that no one else has had the keen insight to spot. But I don't need to prove Bell, that has already been done X times over. And you have not put forth ANYTHING, much less a candidate to refute.

Any casual reader who mistakenly takes you as an authority on this subject will end up disappointed in the end. But please, continue your idle boasting if it makes you feel better.

 

[DrChinese]

I'm waiting ...

And if you are holding your breath, you will eventually turn blue. I am pretty certain of that.

 

[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.