Are quantum no-go theorems overrated/potentially counterproductive?

[bhobba]

Bohm2 quoted E.T. Jaynes:
'Our present quantum mechanical formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature-all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we think that this unscrambling is a pre-requisite for any further advance in basic physical theory'

I most emphatically do NOT agree with that at all. As Ballentine shows it follows from 2 axioms - and to a certain extent the second axiom follows from the first via Gleasons theorem so its really wrapped up in one axiom.

And that axiom has a reasonable justification that goes something like this:

Imagine we have a system and some observational apparatus that has n possible outcomes associated with values yi. This immediately suggests a vector and to bring this out I will write it as Ʃ yi |bi>. Now we have a problem - the |bi> are freely chosen - they are simply man made things that follow from a theorem on vector spaces - fundamental physics can not depend on that. To get around it QM replaces the |bi> by |bi><bi| to give the operator Ʃ yi |bi><bi| - which is basis independent. This is the foundational axiom of QM, and heuristically why its reasonable.

IMHO it is not a mismash of ideas, it is the consequence of one key and very fundamental idea.

What it means is another issue - and that is hotly debated.

But what the theory says, and even why it says it, is IMHO VERY well understood - what it MEANS is what's discussed.

This is what I mean by you really need to read the modern texts on QM like Ballentine that develops it correctly from the modern perspective, then make up your own mind - you will not get it from the commentary of those that may have a different view than what you would form, and may not have even been exposed to the modern approach detailed in Ballentine. I find it VERY hard to believe Jaynes could have a view like that after being exposed to a modern treatment - my understanding is he died in 1998 and his views were probably formed from the early textbooks like Dirac and Von Neumann - things have moved on considerably since then.

In my early exposure to QM I learned it from those two texts - the treatment of Ballentine a WAY WAY ahead of those - but that's only to be expected - we have had many decades of research separating them.

Thanks
Bill

 

[bohm2]

I most emphatically do NOT agree with that at all. As Ballentine shows it follows from 2 axioms - and to a certain extent the second axiom follows from the first via Gleasons theorem so its really wrapped up in one axiom.

The quote of Jaynes which you disagree with came from the original PBR paper (see first page):

On the reality of the quantum state
http://arxiv.org/pdf/1111.3328.pdf

If you don't favour realist interpretation of quantum states, then PBR has no implications. Epistemic interpretations of the quantum state can be divided into 2 types:

1. those that are epistemic with respect to underlying ontic states
2. those that are epistemic with respect to measurement outcomes

The PBR theorem (with the few assumptions noted below) would place serious constraints on 1. but not 2. As far as I understand it, Ballentine's view (I've read only a few chapters of his book but not all of it) is sympathetic to the ensemble interpretation. I don't know much about it, but PBR just rules out certain realist interpretations (e.g. Einstein's). The diagram attached (from The life of psi article) below nicely summarizes the 4 major positions:

But again the PBR no-go theorem makes the following assumptions:

1. a system has a "real physical state" not necessarily completely described by quantum theory, but objective and independent of the observer
2. systems that are prepared independently have independent physical states

If one's interpretation doesn't make those assumptions, PBR is irrelevant.

 

[bhobba]

If you don't favour realist interpretation of quantum states, then PBR has no implications. Epistemic interpretations of the quantum state can be divided into 2 types:

This has nothing to do with interpretation - it has to do with the formalism of QM - which is what the quote you gave referred to:

'Our present quantum mechanical formalism is not purely epistemological; it is a peculiar mixture describing in part realities of Nature, in part incomplete human information about Nature-all scrambled up by Heisenberg and Bohr into an omelette that nobody has seen how to unscramble. Yet we think that this unscrambling is a pre-requisite for any further advance in basic physical theory'

Every physicist agrees with the formalism. And while it may not have been true when the person that was quoted studied QM, nowadays we know that only two axioms are required to derive all of QM. And if you accept Gleason's theorem then you only need one. Most definitely the formalism of QM is NOT a mishmash of ideas - it is the logical development of a very fundamental idea. The exact idea depending on exactly what approach you use. In my approach its basis independence. Other approaches are based on reasonableness conditions imposed on generalized probability models eg:
http://arxiv.org/pdf/quant-ph/0101012.pdf

There are probably others as well. But the point remains the same. The formalism is well understood. Interpreting it is another matter.

Thanks
Bill

 

[Demystifier]

one of the most surprising no go theorem comes from Haag. He says that interaction picture does not exist.

The theorem is valid only for quantum field theory, which has an INFINITE number of degrees of freedom and thus leads to UV and IR divergences. If you regularize the theory such that UV and IR divergences are removed (which you always must do to make sense of interacting QFT), then the Haag theorem does not longer apply and the interaction picture exists.

For details, see also the book
A. Duncan, The Conceptual Framework of Quantum Field Theory (2012)

 

[bohm2]

This has nothing to do with interpretation - it has to do with the formalism of QM - which is what the quote you gave referred to...

Okay, but it is the latter part of that quote that I was referring to. We are discussing physical theories. On its own, the QM formalism is just a piece of mathematics. There is little agreement on interpretation and unscrambling and this is important. Whether no-go theorems have made any advance in this direction is what I'm questioning.

Zonde had argued (if I understand him) that one of the PBR assumptions should not be questioned (e.g. systems that are prepared independently have independent physical states), because without it, we would have to abandon the scientific method. But I'm still confused if that PBR assumption actually implies this? Some physicists suggest it does (e.g. T. Rudolph). Others (e.g. Spekkens) argue that it just hi-lites the necessary separability/contextuality of QM. What is confusing is that 2 recent experiments have been done questioning the ψ-epistemic interpretation but they do rely on the assumptions noted above:

If systems have real states, regardless of an experimenter or measurements performed, then a natural question is whether the quantum state is epistemic, i.e. corresponding merely to knowledge of these underlying real states. In the presented manuscript we tested for this specific possibility and ruled out the most natural class of such models to a high degree of confidence.

Can different quantum state vectors correspond to the same physical state? An experimental test
http://arxiv.org/pdf/1211.0942v1.pdf

Assuming a natural continuity assumption and a separability assumption, we show here that epistemic interpretations of the quantum state are in contradiction with quantum theory...Our experimental results are in agreement with the predictions of quantum theory and provide strong constraints on possible epistemic extensions of quantum mechanics..

Experimentally probing the reality of the quantum state
http://arxiv-web3.library.cornell.edu/pdf/1211.1179v1.pdf

 

[bhobba]

Okay, but it is the latter part of that quote that I was referring to. We are discussing physical theories. On its own, the QM formalism is just a piece of mathematics.

Sorry - but its not.

It makes statements about actual things out there called observations.

Euclidean geometry as presented by Euclid is more than math because it specifically maps to things out there - points and lines - and you draw actual diagrams.

Euclidean geometry as presented by Hilbert is a piece of abstract mathematics because it does not map to anything - everything is purely abstract

This is a really fundamental - its the difference between applied and pure math.

Take the foundational axiom in Ballentines treatment and my heuristic justification for it:

Imagine we have a system and some observational apparatus that has n possible outcomes associated with values yi. This immediately suggests a vector and to bring this out I will write it as Ʃ yi |bi>. Now we have a problem - the |bi> are freely chosen - they are simply man made things that follow from a theorem on vector spaces - fundamental physics can not depend on that. To get around it QM replaces the |bi> by |bi><bi| to give the operator Ʃ yi |bi><bi| - which is basis independent. This is the foundational axiom of QM, and heuristically why its reasonable.

I, and Ballentine, are talking about real things - a system and an observational apparatus with n distinct possible outcomes. This is not an abstract bit of math like Peanoes axioms etc - it is concrete.

All physicists agree on the formalism and without any interpretation can be used to solve problems and make predictions. In fact many, probably even most, couldn't give a hoot about interpretations and quite happily ignore it.

Zonde had argued (if I understand him) that one of the PBR assumptions should not be questioned (e.g. systems that are prepared independently have independent physical states), because without it, we would have to abandon the scientific method.

It can be questioned - its validity is purely an experimental matter. What we know from everyday experience is it seems true - but science has a different standard.

This is similar to Noether's Theorem. Everyone exposed to it immediately senses this is the correct basis for conservation laws because that the laws of nature should not depend on where, when, or what direction is very intuitive from everyday experience - but its validity is, strictly speaking, still an experimental matter.

Feynman discusses this somewhere - in the Feynman Lectures I think - but don't hold me to it. He points out some philosophers claim that science couldn't even be done if the laws of nature were not like that. Poppycock - science doesn't depend on that - its nice that so far it has proven true - but its not required. Same with similarly prepared systems.

Thanks
Bill

 

[bohm2]

Okay, the Jaynes quote may not have been best one to post, but I don't feel too bad because the PBR authors made the same error.

It makes statements about actual things out there called observations...

Observations of what?

All physicists agree on the formalism and without any interpretation can be used to solve problems and make predictions.

Predictions of what?

That's where the interpretation part comes in, I think.

In fact many, probably even most, couldn't give a hoot about interpretations and quite happily ignore it.

Do you any evidence for this? One can argue that even the 'shut up and calculate' approach is just another interpretation and from polls, I've seen, it's not the most popular one, although there's problems with these polls as pointed out by Matt Leifer:

Can anything be learned from surveys on the interpretations of quantum mechanics?
http://www.aps.org/units/gqi/newsletters/upload/vol7num2.pdf

 

[bhobba]

Observations about what?

Are you serious? Its irrelevant - we are considering observations in a general sense. See figure 1 of the following:
http://arxiv.org/pdf/quant-ph/0101012.pdf

One can argue that even the 'shut up and calculate' approach is just another interpretation

You can argue that - but shut up and calculate is usually considered a group of approaches that includes no interpretation to a very minimal interpretation.

The interpretation part of that group, if it contains an interpretation, usually centers around the interpretation of probability in the Born rule. Most applied mathematicians, and that would include physicists, have an intuitive view of probability and don't worry about what it is, and would be a bit annoyed if anyone harped on about it. However if pushed they would probably say as I do its as defined by the Kolmogerov axioms with specific realizations being frequentest and subjective - that is if they know the details of such things at all - I suspect most simply have an intuitive idea of probability. The frequentest view leads to the Ensemble interpretation, the subjective to Copenhagen, but those sticking to the formalism would probably leave it up in the air as the Born rule does.

The reason I say most couldn't give a hoot is its not part of a physicists, or applied mathematicians, usual training in QM. For example check out the physics program at the uni down the road from where I live:
https://www148.griffith.edu.au/prog...rements?programCode=1369&studentType=Domestic

It contains nothing on interpretations at all.

But that university has an active group into foundations - if it is what interests you then you will gravitate towards that - but I would say most couldn't give a hoot.

And polls I have seen are usually from things like conferences on interpretations - obviously people that attend those are interested.

Thanks
Bill

 

[bohm2]

Are you serious? Its irrelevant - we are considering observations in a general sense. See figure 1 of the following:
http://arxiv.org/pdf/quant-ph/0101012.pdf

I have previously read Hardy's article but I think we are talking past (misunderstanding) one another. I was trying to argue for the importance of interpretation in QM and the lack of progress/confusion in this area (hence the Jaynes quote-I interpreted his quote as suggesting that there are problems of interpretation and so did the PBR authors). I don't disagree with you that QM makes statement about observation. But I think physical theories are more than just that. Hence my questions: Observations of what? Predictions of what? Information of what? This is why interpretation is important. I mean, what is the status of the wave function? I have read papers arguing that interpretation is not important:

Quantum Theory Needs No ‘Interpretation’
http://www.phy.pku.edu.cn/~qhcao/resources/class/QM/PTO000070.pdf

But I don't find these arguments convincing. In fact, the author (Fuchs) himself didn't believe it as he professed in another more recent paper (see below). I tend to see interpretation as an important issue as noted in the latter part of the Jaynes quote. There are a number of reasons why interpretation is important (other than I just find it interesting). Some of the reasons are spelled out in these articles:

Quantum Theory: Interpretation Cannot be Avoided
http://arxiv.org/pdf/quant-ph/0408178v1.pdf

Shut up and let me think! Or why you should work on the foundations of quantum mechanics as much as you please
http://arxiv.org/pdf/1308.5619.pdf

Does Quantum Mechanics Need Interpretation?
http://arxiv.org/pdf/0902.3005v1.pdf

Interview with a Quantum Bayesian
http://arxiv.org/pdf/1207.2141v1.pdf

Why Physics Needs Quantum Foundations
http://arxiv.org/pdf/1003.5008.pdf

P.S. My university has a number of foundational/interpretational courses both at the graduate and undergraduate level: http://www.physics.utoronto.ca/students/undergraduate-courses/current/phy491h1 I enrolled or audited all such courses and they were among my favourite courses. It is the only part of physics that really interests me.

 

[bhobba]

But I don't find these arguments convincing.

Among those interested in foundations its quite likely many think those that profess to not have an interpretation are really applying a subconscious one. I am not one of those - so I guess on this point we will have to disagree.

Regarding what's taught at uni's - there are undoubtedly courses on interpretation available as electives - especially postgrad - but the issue is they are not required - most physicists seem to get by fine without it.

And of course foundational issues in QM is a perfectly legit area of study attracting physicists, philosophers and mathematicians. Its just I think many couldn't really care less. And no - I don't have any kind of definite proof of this.

Thanks
Bill

 

[bhobba]

But I think physical theories are more than just that. Hence my questions: Observations of what? Predictions of what? Information of what? This is why interpretation is important. I mean, what is the status of the wave function? I have read papers arguing that interpretation is not important

Mate that's because you are interested in the deep questions - I am as well BTW. But do you think, for example, a physicist employed say at Bell Labs that wants to apply it has that as their primary motivation?

Thanks
Bill

 

[bohm2]

I think it's incredible that one can evade many of these no-go theorem by questioning the probabilistic content of Bell's theorem. Khrennikov does this be developing a contextual probability theory:

Our main point was that any mathematical theorem (when formulated in rigorous mathematical terms) is based on a list of assumptions. If such a precise list is not provided, then one cannot call it a mathematical theorem, and should not make any definitive conclusions. It was pointed out on many occasions, both by Walter Philipp and his collaborator Karl Hess, see e.g. [10]–[13], as well as by Luigi Accardi, see e.g. [14, 15], and myself [16]–[19], that without a presentation of a precise probabilistic model for Bell’s framework, one cannot proceed in a rigorous way. If one uses the Kolmogorov measure-theoretic model then one should be aware that there is no reason, even in classical physics, to assume that statistical data that were obtained in different experiments should be described by a single Kolmogorov probability space, see e.g. [16] for details. Walter Philipp strongly supported this kind of counterarguments by finding a purely mathematical investigations in probability which were devoted to a similar problem, but without any relation to quantum physics. In particular, Walter found a theorem(proved by a Soviet mathematician Vorob’ev[20]) describing the conditions which are necessary and sufficient for the realization of a few random variables on a single Kolmogorov space.

A Mathematician’s Viewpoint to Bell’s theorem: In Memory of Walter Philipp
http://arxiv.org/pdf/quant-ph/0612153.pdf

I wonder if this is related with the arguments presented by Matt Leifer's first prize 2013 fqxi.org winning essay where he argues that:

For the subjective Bayesian, the main lesson of this is that, in general, only certain subsets of all possible bets are jointly resolvable. Define a betting context to be a set of events such that bets on all of them are jointly resolvable and to which no other event can be added without violating this condition. It is safe to assume that each betting context is a Boolean algebra, since, if we can find out whether E occurred at the same time as finding out whether F occurred, then we can also determine whether they both occurred, whether either one of them occurred, and whether they failed to occur, so we can define the usual logical notions of AND, OR and NOT. However, unlike in conventional probability theory, there need not be a common algebra on which all of the events that occur in different betting contexts are jointly defined.

“It from bit” and the quantum probability rule
http://arxiv.org/pdf/1311.0857v1.pdf

Then again, I might be messing this up but I still think it's interesting that one can have keep both locality and realism as in the Vaxjo interpretation (e.g. realism on the subquantum level with nonobjectivity of quantum observables).

 

[audioloop]

Observations of what?

Predictions of what?

right.

just concepts.

based on ?

who or what decides what is pertinent ?

.

 

[atyy]

Among those interested in foundations its quite likely many think those that profess to not have an interpretation are really applying a subconscious one. I am not one of those - so I guess on this point we will have to disagree.

No, they are in a superposition of interpretations, and don't have one until asked :p

 

[Demystifier]

No, they are in a superposition of interpretations, and don't have one until asked

 

[forcefield]

I am not against no-go theorems but I would argue that they are unscientific because they don't predict any observations that can be verified.

 

[Demystifier]

I am not against no-go theorems but I would argue that they are unscientific because they don't predict any observations that can be verified.

If so, then mathematics as such is also unscientific.
Besides, the Bell no-go theorem lead to an experimentally testable prediction.

 

[forcefield]

If so, then mathematics as such is also unscientific.

Good point.

Besides, the Bell no-go theorem lead to an experimentally testable prediction.

I meant observations that verify the conclusions. The observations related to the Bell experiment only directly verify that QM is correct. Sorry for being unclear.

 

[DrChinese]

The observations related to the Bell experiment only directly verify that QM is correct. Sorry for being unclear.

You are basically in circular territory here. The point of a no-go is to draw a line in the sand. The experiment then points to one side or the other. They operate in tandem. If it is a useful no-go, the line is clear and the result convincing. With Bell, the confirmation of QM also directly rules out EPR-like local realism.

 

[Jilang]

You are basically in circular territory here. The point of a no-go is to draw a line in the sand. The experiment then points to one side or the other. They operate in tandem. If it is a useful no-go, the line is clear and the result convincing. With Bell, the confirmation of QM also directly rules out EPR-like local realism.

I think there is some dissension on that
http://arxiv.org/pdf/quant-ph/0612153.pdf

See previous post.
I have always seen the logic of applying Bells Inequalities to the state (being a complete description of the system), but regard applying set theory to the state multiplied by its complex conjugate ( and claiming that in that way it rules out hidden variables) rather illogical.

 

[bohm2]

I think there is some dissension on that
http://arxiv.org/pdf/quant-ph/0612153.pdf

See previous post.
I have always seen the logic of applying Bells Inequalities to the state (being a complete description of the system), but regard applying set theory to the state multiplied by its complex conjugate ( and claiming that in that way it rules out hidden variables) rather illogical.

Thanks for bringing this up as I was really hoping that someone with a lot of math background in this area could shed light on the validity of Khrennivok's idea (e.g. non-Kolmogorov probability model) of questioning Bell's assumptions on his famous Bell inequality.

Non-Kolmogorov probability models and modified Bell’s inequality
http://arxiv.org/pdf/quant-ph/0003017.pdf

 

[DrChinese]

I think there is some dissension on that
http://arxiv.org/pdf/quant-ph/0612153.pdf

Not really. There are always a few dissenters, but this is a settled issue in the normal use of the word.

 

[Jilang]

Thanks for bringing this up as I was really hoping that someone with a lot of math background in this area could shed light on the validity of Khrennivok's idea (e.g. non-Kolmogorov probability model) of questioning Bell's assumptions on his famous Bell inequality.

Non-Kolmogorov probability models and modified Bell’s inequality
http://arxiv.org/pdf/quant-ph/0003017.pdf

Bless you, but you need to keep hoping as I don't have a huge maths background. That said I don't think it takes a maths genius to see where the incompatibility lies. For example if you take the 60 degree, 120 degree spin type experiment that is often quoted as an example of the Bells inequality you will find there is no inequality type issue up until the point you start squaring the wave function. I could not say if it applies to all situations but on this one applying it to the amplitudes does not lead to a discrepancy. (The maths is easy -do try it!). The interesting thing about the article was when it mentioned game theory and how even classically you cannot apply Bells inequalities to both the system and the measuring system together. Since quite Quantum probabilities are defined as much by the measurement process as the state of the thing being measured it is perhaps not surprising that Bells inequalities are violated.

 

[Jilang]

Not really. There are always a few dissenters, but this is a settled issue in the normal use of the word.

What would be the normal use of the word and who has settled this issue for good?

 

[DrChinese]

What would be the normal use of the word and who has settled this issue for good?

I settled it just now.

Around here, we follow "generally accepted" as a standard. So seriously, an arxiv entry won't do it and neither will 20 more (which I could give you as dissent). There are probably thousands of experiments being worked on this year around Bell, so I would say it has been hugely successful.

No one is stopping you from holding any opinion you like, but it is not appropriate to share your personal opinions as generally accepted on this forum.

 

[bohm2]

So seriously, an arxiv entry won't do it and neither will 20 more (which I could give you as dissent).

Can you provide any papers that critically discuss his contextual probability model. I've come across some stuff where he's discussing stuff with Fuchs but nothing substantial, even though, from my understanding, he has published a lot of stuff in peer-reviewed journals and organised international conferences with well-known researchers in QM/foundation in probability:

http://lnu.se/employee/andrei.khrennikov?l=en

But that means squat, if he is wrong about his views. So there's no misunderstanding, he doesn't question Bell's no-go theorem. Only its application.

 

[DrChinese]

Can you provide any papers that critically discuss his contextual probability model. I've come across some stuff where he's discussing stuff with Fuchs but nothing substantial, even though, from my understanding, he has published a lot of stuff in peer-reviewed journals and organised international conferences with well-known researchers in QM/foundation in probability:

http://lnu.se/employee/andrei.khrennikov?l=en

But that means squat, if he is wrong about his views. So there's no misunderstanding, he doesn't question Bell's no-go theorem. Only its application.

Sorry, about all I have on him is the "Vaxjo Interpretation of Wave Function" stuff which you already have. A lot of people just let some of these type assertions go without bothering to reign things in.

There is a lot of semantic debate in this area, and yet the upshot of the no-go theorems is that people don't look for local hidden variables in the usual spots anymore. So to me, that makes no-go's useful. You have to be creative just to grab a toehold anywhere.

 

[bohm2]

The Fuchs piece I cam across is below. He seems to agree with Khrennikov on some points but doesn't think Khrennikov accomplishes what he wants to:

The way I view the problem presently is that, indeed, quantum theory is a theory of contextual probabilities. This much we agree on: within each context, quantum probabilities are nothing more than standard Kolmogorovian probabilities. But the contexts are set by the structure of the Positive Operator-Valued Measures: one experimental context, one POVM. The glue that pastes the POVMs together into a unified Hilbert space is Gleason’s “noncontextuality assumption”: where two POVMs overlap, the probability assignments for those outcomes must not depend upon the context. Putting those two ideas together, one derives the structure of the quantum state. The quantum state (uniquely) specifies a compendium of probabilities, one for each context. And thus there are transformation rules for deriving probabilities in one context from another. This has the flavor of your program. But getting to that starting point from more general considerations—as you would like to do (I think)—is the challenge I haven’t yet seen fulfilled.

The Anti-Vaxjo Interpretation of Quantum Mechanics
http://perimeterinstitute.ca/personal/cfuchs/VaxjinationQPH.pdf

 

[bohm2]

Here's another recent no-go theorem based on a critical look at one of the assumptions ("preparation independence") of PBR theorem and is a follow-up paper to 2 previous papers by Schlosshauer and Fine:

Building on the Pusey–Barrett–Rudolph theorem, we derive a no-go theorem for a vast class of deterministic hidden-variables theories, including those consistent on their targeted domain. The strength of this result throws doubt on seemingly natural assumptions (like the “preparation independence” of the Pusey–Barrett–Rudolph theorem) about how “real states” of subsystems compose for joint systems in nonentangled states. This points to constraints in modeling tensor-product states, similar to constraints demonstrated for more complex states by the Bell and Bell–Kochen–Specker theorems.

A no-go theorem for the composition of quantum systems
http://arxiv.org/pdf/1306.5805v2.pdf

I'm still having difficulty understanding the merits of this criticism of the PBR assumption. It seems to me that if this criticism is valid for the PBR theorem, then one can also question the assumptions of Bell's theorem; that is, a good case can be made that this is really in line with Khrennikov/Pitovsky/Accardi/Kupczynski/Nieuwenhuizen/Hess/Philipp arguments where one cannot assume that statistical data that are obtained in different experiments should be described by a single Kolmogorov probability space:

Our point will be that Bell went wrong even before the issue of these loopholes has to be addressed, because of the contextuality loophole, that cannot be closed...In his opening address of the 2008 Växjö conference Foundations of Probability and Physics , Andrei Khrennikov took the position that violations of Bell inequalities occur in Nature, but do not rule out local realism, due to lack of contextuality: the measurements needed to test Bell inequalities (BI) such as the BCHSH inequality cannot be performed simultaneously . Therefore Kolmogorian probability theory starts and ends with having different probability spaces, and Bell inequality violation (BIV) just proves that there cannot be a reduction to one common probability space. This finally implies that no conclusion can be drawn on local realism, since incompatible information cannot be used to draw any conclusion.

Where Bell Went Wrong
http://arxiv.org/pdf/0812.3058.pdf

 

[Dale]

I think that everyone has had a chance to state their preferred interpretation by now.