The quantum state cannot be interpreted statistically?

[bohm2]

That's understandably and, imho, unacceptably, vague. Nonlocality is defined by some (most? ... I don't know) quantum physicists as referring to entangled quantum states, which might ultimately refer to ftl propagations or not.

With respect to the OP, I'm not sure what you are asking. If one buys Leifer's argument, it's pretty clear which models PBR scraps. With respect to non-locality, some physicists (e.g. Bell, Maudlin, Laudisa, Norsen, etc.) interpreted Bell's theorem as already implying non-locality (ftl) irrespective of "realism" issues. Others, however, did not interpret Bell's theorem in that way. I think it has to be vague (e.g. "influence") because some have argued that non-locality does not imply incompatibility with relativity since it may depend on which interpretation of relativity is true. A Lorentzian interpretation of relativity (single preferred frame) is compatible with non-locality. Does this mean just some finite v>c or instantaneous influence? I think it implies the latter. Here's what Bell wrote on non-locality implied by his theorem:

I think it’s a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. But I would say that the cheapest resolution is something like going back to relativity as it was before Einstein, when people like Lorentz and Poincare thought that there was an aether -a preferred frame of reference-but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether...that is certainly the cheapest solution. Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant...what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincar´e, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether - that is a perfectly coherent point of view...The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent, that also means that things can go backwards in time...[this] introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is a real causal sequence which is defined in the aether.”

More recently a number of "realist" spontaneous collapse and Bohmian interpretations that are Lorenz-invariant (and even narrative) have been developed:

http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.1425v1.pdf
http://arxiv.org/PS_cache/quant-ph/pdf/0406/0406094v2.pdf
http://xxx.lanl.gov/abs/1002.3226

But I have come across some criticisms about these models as well (for example, Valentini). From Towler's site:

Valentini’s Aristotelian spacetime: Galilean invariance not a fundamental symmetry of the standard low-energy pilot-wave theory. The search for a Lorentz-invariant extension thus seems misguided. In Valentini’s view, the difficulties encountered in such a search are no reflection on the plausibility of the pilot-wave theory. Rather, they show that the theory is not being interpreted correctly. Pilot-wave theory then has a remarkable internal logic - both structure of dynamics, and operational possibility of nonlocal signalling away from equilibrium (see later) independently point to existence of natural preferred state of rest.

http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm5.pdf

 

[ThomasT]

I'm not sure what you are asking.

I'm not really asking anything. Just stating my opinion wrt my admittedly limited take on the current state of affairs. Wrt which I welcome any criticisms you might be inclined to offer.

If one buys Leifer's argument, it's pretty clear which models PBR scraps.

Well, no, I don't buy Leifer's take on things.

With respect to non-locality, some physicists (e.g. Bell, Maudlin, Laudisa, Norsen, etc.) interpreted Bell's theorem as already implying non-locality (ftl) irrespective of "realism" issues.

Bell didn't speak of FTL, he spoke of instantaneous effects. Big difference, imo. Norsen is just wrong in his analysis, imho. Don't know about the others you mention.

Others, however, did not interpret Bell's theorem in that way.

Indeed, imo, the most sophisticated analyses of Bell's theorem interpret it as being applicable only to formalizations of quantum entanglement and not informing wrt nature.

I think it has to be vague (e.g. "influence") because some have argued that ftl does not imply incompatibility with relativity since it may depend on which interpretation of relativity is true.

SR is pretty clear imo. No matter what interpretation is assumed. It states that there's a limit on the propagational speed of material objects.

A Lorentzian interpretation of relativity (single preferred frame) is compatible with non-locality.

Not if nonlocality is taken to refer to acceleration to faster than light propagations of material entities. And if we're not talking about that, then we might as well be talking about pink unicorns or whatever.

Does this mean just some finite v>c or instantaneous influence? I think it implies the latter.

The problem is that "instantaneous influence" doesn't imply ftl progagation, it implies that event B is happening at the same time as event A. There's no propagation, ftl or whatever, involved.

 

[bohm2]

Well, no, I don't buy Leifer's take on things.

Why?

 

[ThomasT]

Why?

Because I don't think that Bell's theorem informs wrt physical reality -- but only wrt viable formalisms.

 

[bohm2]

A very interesting paper that came out today. Two of the authors are the same as per PBR in this thread:

Many quantum physicists have suggested that a quantum state does not represent reality directly, but rather the information available to some agent or experimenter. This view is attractive because if a quantum state represents only information, then the collapse of the quantum state on measurement is possibly no more mysterious than the Bayesian procedure of updating a probability distribution on the acquisition of new data. In order to explore the idea in a rigorous setting, we consider models for quantum systems with probabilities for measurement outcomes determined by some underlying physical state of the system, where the underlying state is not necessarily described by quantum theory. A quantum state corresponds to a probability distribution over the underlying physical states, in such a way that the Born rule is recovered. We show that models can be constructed such that more than one quantum state is consistent with a single underlying physical state-in other words the probability distributions corresponding to distinct quantum states overlap. A recent no-go theorem states that such models are impossible. The results of this paper do not contradict that theorem, since the models violate one of its assumptions: they do not have the property that product quantum states are associated with independent underlying physical states.

The quantum state can be interpreted statistically
http://lanl.arxiv.org/pdf/1201.6554.pdf

Edit: This sounds similar to Demystifier's criticism of PBR's assumptions? This is from Demystifier's earlier post (#95) from this thread:

In short, they try to show that there is no lambda satisfying certain properties. The problem is that the CRUCIAL property they assume is not even stated as being one of the properties, probably because they thought that property was "obvious". And that "obvious" property is today known as non-contextuality. Indeed, today it is well known that QM is NOT non-contextual. But long time ago, it was not known. A long time ago von Neumann has found a "proof" that hidden variables (i.e., lambda) were impossible, but later it was realized that he tacitly assumed non-contextuality, so today it is known that his theorem only shows that non-contextual hidden variables are impossible. It seems that essentially the same mistake made long time ago by von Neumann is now repeated by those guys here.

Let me explain what makes me arrive to that conclusion. They first talk about ONE system and try to prove that there is no adequate lambda for such a system. But to prove that, they actually consider the case of TWO such systems. Initially this is not a problem because initially the two systems are independent (see Fig. 1). But at the measurement, the two systems are brought together (Fig. 1), so the assumption of independence is no longer justified. Indeed, the states in Eq. (1) are ENTANGLED states, which correspond to not-independent systems. Even though the systems were independent before the measurement, they became dependent in a measurement. The properties of the system change by measurement, which, by definition, is contextuality. And yet, the authors seem to tacitly (but erroneously) assume that the two systems should remain independent even at the measurement. In a contextual theory, the lambda at the measurement is NOT merely the collection of lambda_1 and lambda_2 before the measurement, which the authors don't seem to realize.

 

[Ken G]

That helps put words to my earlier objection also, the reliance on the idea that "properties" determine outcomes. This I believe is the same idea as "non-contextuality", because we normally think of a "property" as something that exists in and of itself, independently of anything else. That's what I was imagining they meant by "properties", and I objected to their claim that it would be "radical" to reject that assumption. I think Demystifier put a more accurate word to it: non-contextual properties. Or another way to put it might be, reductionist properties rather than holistic elements of the system and its interactions.

 

[Demystifier]

Let me just note that I have sent an e-mail to the authors with a content similar to the above, but they have not mentioned me in the Acknowledgements of the new paper. (In fact, they don't have Acknowledgements at all.)

 

[bohm2]

Just in case anybody is interested, here's that exchange from Demystefier’s posts 123 + 124:

I had a brief exchange of e-mails with the authors of that paper. After that, now I am even more convinced that I am right and they are wrong. Here are some crucial parts of that exchange, so that you can draw a conclusion by yourself:

> Prof. Barrett:
> Briefly, the vectors in Eq.(1) are entangled, yes but they don't represent
> the state of the system. They are the Hilbert space vectors which
> correspond to the four possible outcomes of the measurement.

Me (H.N.): But in my view, the actual outcome of the measurement (i.e., one of those in Eq. (1) ) DOES represent the state of the system. Not the state before the measurement, but the state immediately after the measurement. At the measurement the wave function "collapses", either through a true von Neumann collapse, or through an effective collapse as in the many-world interpretation or Bohmian interpretation.
...

> Prof. Barrett:
> The assumption is that the probabilities for the different outcomes of
> this procedure depend only on the physical properties of the systems at a
> time just before the procedure begins (along with the physical properties
> of the measuring device).

Me (H.N.): Yes, I fully understand that if you take that assumption, you get the conclusion you get. (In fact, that conclusion is not even entirely new. For example, the Kochen-Specker theorem proves something very similar.) But it is precisely that assumption that I don't find justified. Any measurement involves an interaction, and any measurement takes some time (during which decoherence occurs), so I don't think it is justified to assume that the measurement does not affect the probabilities for the different outcomes.

In short, to make their results meaningfull, a correct title of their paper should be changed to "The quantum state cannot be interpreted non-contextually statistically" But that is definitely not new!

 

[bohm2]

Here's another post from Leifer talking about this more recent paper:

The issue of measurements causing a disturbance is not relevant here since we are only considering a simple prepare-and-measure experiment. If we were concerned with what happens after the measurement then it would be relevant, but this is not involved in the PBR scenario.

There is no assumption in the PBR paper that xi^k_p depends only on the projector. It may also depend on the other projectors in the measurement, i.e. it may be different for different measurements that share a common projector. However, the proof of the PBR theorem only makes use of a single measurement, so it doesn't get into trouble with the KS theorem in any case.

Since http://arxiv.org/abs/1201.6554 came out, we now know that psi-ontology and contextuality are definitely separate issues, since a psi-epistemic theory can be obtained for any Hilbert-space dimension, whereas a noncontextual theory cannot. This also shows that the factorization assumption is crucial in the PBR proof.

https://plus.google.com/u/0/104569184257973656413/up/#104569184257973656413/posts

 

[bohm2]

Another interesting paper by Leifer posted on his site and a newsletter but gives a bit more detail on the implications of PBR:

We have seen that the PBR result can be used to establish some known constraints on hidden variable theories in a very straightforward way. There is more to this story that I can possibly fit into this article, and I suspect that every major no-go result for hidden variable theories may fall under the rubric of PBR. Thus, even if you don’t care a fig about fancy distinctions between ontic and epistemic states, it is still worth devoting a few braincells to the PBR result. I predict that it will become viewed as the basic result about hidden variable theories, and that we will end up teaching it to our students even before such stalwarts as Bell’s theorem and Kochen-Specker.

PBR, EPR, and all that jazz
http://www.aps.org/units/gqi/newsletters/upload/vol6num3.pdf

Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/

 

[Fredrik]

Anyone know if the PBR paper has been published, or at least accepted for publication yet?

 

[ThomasT]

... some have argued that non-locality does not imply incompatibility with relativity since it may depend on which interpretation of relativity is true.

Or which definition of quantum nonlocality is used?

I think it’s a deep dilemma, and the resolution of it will not be trivial; it will require a substantial change in the way we look at things. But I would say that the cheapest resolution is something like going back to relativity as it was before Einstein, when people like Lorentz and Poincare thought that there was an aether -a preferred frame of reference-but that our measuring instruments were distorted by motion in such a way that we could not detect motion through the aether...that is certainly the cheapest solution. Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant...what is not sufficiently emphasized in textbooks, in my opinion, is that the pre-Einstein position of Lorentz and Poincar´e, Larmor and Fitzgerald was perfectly coherent, and is not inconsistent with relativity theory. The idea that there is an aether, and these Fitzgerald contractions and Larmor dilations occur, and that as a result the instruments do not detect motion through the aether - that is a perfectly coherent point of view...The reason I want to go back to the idea of an aether here is because in these EPR experiments there is the suggestion that behind the scenes something is going faster than light. Now if all Lorentz frames are equivalent, that also means that things can go backwards in time...[this] introduces great problems, paradoxes of causality, and so on. And so it is precisely to avoid these that I want to say there is a real causal sequence which is defined in the aether.”

Wrt the above, my current opinion is that John Bell's view was just wrong.

 

[bohm2]

Two more papers on this theorem. The first paper is difficult to understand. I don't understand what the author is trying to say.

Can quantum mechanics be considered as statistical? An analysis of the PBR theorem
http://lanl.arxiv.org/pdf/1203.2475.pdf

Alternative Experimental Protocol for a PBR-Like Result
http://lanl.arxiv.org/pdf/1202.6465.pdf

 

[Demystifier]

Anyone know if the PBR paper has been published, or at least accepted for publication yet?

This perhaps will never happen after the two of the authors in PBR has somewhat contradicted themselves in
http://xxx.lanl.gov/abs/1201.6554

See also posts #485 - #488.

 

[Fredrik]

This perhaps will never happen after the two of the authors in PBR has somewhat contradicted themselves in
http://xxx.lanl.gov/abs/1201.6554

This doesn't seem to be a reason to not publish it, since the abstract says that "The results of this paper do not contradict that theorem, since the models violate one of its assumptions". However, if it was up to me to decide if the PBR paper should be published or not, I would at least demand that they rewrite the paper. I think it's just a mess. There isn't even a clear statement of the theorem in the article, and the "proof" is extremely non-rigorous.

 

[bohm2]

The author of the last paper on PBR http://lanl.arxiv.org/pdf/1203.2475.pdf posted in Leifer's blog and Leifer doesn't seem to agree with his take on it:

I don’t really agree with your take on the PBR theorem. According to Harrgian and Spekkens, and also PBR, λ is supposed to be the full ontic state of the system. If the wavefunction is ontic in the model under consideration, then it is considered to be specified by λ and is not considered a separate variable. This is the reason why the term “ontic state” is used instead of “hidden variable state” because the latter is often interpreted to be variables in addition to the wavefunction. Most people would consider the wavefunction to be ontic in de Broglie-Bohm theory. I know there is some discussion of whether it should instead be regarded as nomological (lawlike) in the literature, but this is not really relevant here. The fact is, even if we know the exact values of the position variables in Bohm’s theory, we will still also need the wavefunction in addition to the position variables to compute the outcome probabilities for any experiment because it is needed to find the trajectories. Anything you need to compute the final outcome probabilities, over and above the primitive ontology (beables), is considered part of the ontic state by PBR by definition. You might not like that definition, but by using it we see that one feature of Bohmian theory is actually necessary for any hidden variable theory, namely that the wavefunction is ontic (in the sense of being required to compute the probabilities of any possible experiment). Therefore, Bohmians should be pretty happy about the PBR result as it vindicates one of their assumptions.

Also, I just wanted to note that I do not understand your discussion around eq. (10). Why do you think we can always replace a qubit state with one that has equal amplitudes up to a relative phase?

Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/q...-the-pbr-theorem/comment-page-1/#comment-2618

 

[Demystifier]

Another new paper on it:
http://lanl.arxiv.org/abs/1203.4779

 

[bohm2]

I thought I'd post these PBR-related papers here for reference:

Physics papers:
The quantum state cannot be interpreted statistically (original PBR paper)
http://lanl.arxiv.org/abs/1111.3328

Generalisations of the recent Pusey-Barrett-Rudolph theorem for statistical models of quantum phenomena
http://xxx.lanl.gov/abs/1111.6304

Completeness of quantum theory implies that wave functions are physical properties
http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.6597v1.pdf

The quantum state should be interpreted statistically
http://lanl.arxiv.org/pdf/1112.2446.pdf

Alternative Experimental Protocol for a PBR-Like Result
http://lanl.arxiv.org/pdf/1202.6465.pdf

The quantum state can be interpreted statistically
http://lanl.arxiv.org/pdf/1201.6554.pdf

Can quantum mechanics be considered as statistical? an analysis of the PBR theorem
http://lanl.arxiv.org/pdf/1203.2475.pdf

On a recent quantum no-go theorem
http://lanl.arxiv.org/pdf/1203.4779.pdf

Popular:
Quantum theorem shakes foundations
http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392

PBR, EPR, and all that jazz
http://www.aps.org/units/gqi/newsletters/upload/vol6num3.pdf

The PBR Argument - a simplified presentation
http://astairs.posterous.com/the-pbr-argument-a-simplified-presentation

Useful Blogs:
Can the quantum state be interpreted statistically?
http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/

Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/

Philosophical papers:
Statistical-Realism versus Wave-Realism in the Foundations of Quantum
Mechanics
http://philsci-archive.pitt.edu/902...m_in_the_Foundations_of_Quantum_Mechanics.pdf

 

[Demystifier]

Bohm2, thank you for the very useful list!

 

[ThomasT]

Thanks for the references/links bohm2. I think that quantum states can be interpreted statistically, ie., that quantum states don't necessarily represent real physical states. But if you think otherwise, then it would be interesting to read your opinion on that.

 

[Demystifier]

One related paper (not on the list above) recently published in Physical Review Letters:
http://lanl.arxiv.org/abs/1111.6597

 

[GravitatisVis]

tag.

 

[bohm2]

Anyone know if the PBR paper has been published, or at least accepted for publication yet?

There was an advance online publication in "Nature Physics" on May 6/12:

On the reality of the quantum state
http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys2309.html

 

[Demystifier]

There was an advance online publication in "Nature Physics" on May 6/12:

On the reality of the quantum state
http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys2309.html

See also their significantly revised arXiv preprint that appeared today:
http://lanl.arxiv.org/abs/1111.3328 v2


Hardy also uploaded a related paper today: Are quantum states real?
http://lanl.arxiv.org/abs/1205.1439

 

[bohm2]

That Hardy paper was really confusing. A video (May 8/12) from Perimeter Institute by Robert Spekkens discussing PBR but he doesn't seem persuaded to become a psi-ontologist:

This talk will address the question of whether the PBR theorem should be interpreted as lending evidence against the psi-epistemic research program. I will review the evidence in favour of the psi-epistemic approach and describe the pre-existing reasons for thinking that if a quantum state represents knowledge about reality then it is not reality as we know it, i.e., it is not the kind of reality that is posited in the standard hidden variable framework. I will argue that the PBR theorem provides additional clues for "what has to give" in the hidden variable framework rather than providing a reason to retreat from the psi-epistemic position... The connection between the PBR theorem and other no-go results will be discussed. In particular, I will point out how the second assumption of the theorem is an instance of preparation noncontextuality, a property that is known not to be achievable in any ontological model of quantum theory, regardless of the status of separability (though not in the form posited by PBR). I will also consider the connection of PBR to the failure of local causality by considering an experimental scenario which is in a sense a time-inversion of the PBR scenario.

Why I Am Not a Psi-ontologist
http://pirsa.org/displayFlash.php?id=12050021

 

[Demystifier]

Bohm2, thank you for this info. In particular, I would like to quote a part of a sentence by Spekkens above:
"... the second assumption of the theorem is an instance of preparation noncontextuality, a property that is known not to be achievable in any ontological model of quantum theory ..."
That was exactly my objection too in an early stage of this thread.

 

[bohm2]

An interesting PhD thesis arguing for state realism that also discusses the recent PBR theorem quite a bit. Interesting, that one of the examiners for this thesis is Robert Spekkens:

The case for quantum state realism
http://ir.lib.uwo.ca/cgi/viewcontent.cgi?filename=0&article=1657&context=etd&type=additional

 

[DrChinese]

An interesting PhD thesis arguing for state realism that also discusses the recent PBR theorem quite a bit. Interesting, that one of the examiners for this thesis is Robert Spekkens:

The case for quantum state realism
http://ir.lib.uwo.ca/cgi/viewcontent.cgi?filename=0&article=1657&context=etd&type=additional

As I interpret quantum state realism: I would say that ANY 2 particles with the same eigenstates are absolutely indistinguishable. They therefore have NO HIDDEN differences. If you accept that, then you would also conclude that the collapse upon measurement absolutely changes the state and does not reveal a pre-existing characteristic. Thus you would reject the idea that it is only our knowledge which is being updated, and this is not Bayesian conditionalization.

I am not saying this is actually the case, just that is how I understand the concept. The author of the cited paper (Tait) discusses some of these ideas in detail.

 

[yoda jedi]

Generalisations of the recent Pusey-Barrett-Rudolph theorem for statistical models of quantum phenomena
http://xxx.lanl.gov/abs/1111.6304

...For example, the ‘factorisability’ assumption used by PBR can be replaced by a far weaker ‘compatibility’ assumption for the preparations of uncorrelated quantum states...

in agreement with leifer.

 

[bohm2]

Another paper on PBR:

The analysis of Pusey, Barrett and Rudolph aims to show there can be no objective physical reality which underlies, and is more general than, the state vector. But there appears to be a gap in their reasoning. To show their result, they use entangled states of independent systems. However, no specific experimental arrangement to detect these entangled states has been proposed. Thus their argument as it stands does not fully show there is a detectable conflict between the predictions of quantum mechanics and the existence of an underlying reality. And it is not clear that one can devise the necessary measuring device.

A problem with the Pusey, Barrett, Rudolph analysis of the reality of the quantum state.
http://lanl.arxiv.org/ftp/arxiv/papers/1206/1206.6491.pdf