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The quantum state cannot be interpreted statistically?

by inflector
Tags: interpreted, quantum, state, statistically
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Demystifier
#487
Feb1-12, 03:56 AM
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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
#488
Feb1-12, 12:15 PM
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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
#489
Feb5-12, 07:51 PM
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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/0/10456918...73656413/posts
bohm2
#490
Feb26-12, 08:56 PM
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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/newslet...d/vol6num3.pdf

Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/qu...e-pbr-theorem/
Fredrik
#491
Feb26-12, 10:04 PM
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Anyone know if the PBR paper has been published, or at least accepted for publication yet?
ThomasT
#492
Feb27-12, 03:02 AM
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Quote Quote by bohm2
... 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?

Quote Quote by John Bell
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
#493
Mar12-12, 09:26 PM
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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
#494
Mar13-12, 02:34 AM
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Quote Quote by Fredrik View Post
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
#495
Mar13-12, 03:34 AM
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Quote Quote by Demystifier View Post
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
#496
Mar16-12, 08:31 PM
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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/qu.../#comment-2618
Demystifier
#497
Mar22-12, 05:30 AM
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Another new paper on it:
http://lanl.arxiv.org/abs/1203.4779
bohm2
#498
Mar22-12, 08:06 PM
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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/...111.6597v1.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-t...dations-1.9392

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

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

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

Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/qu...e-pbr-theorem/

Philosophical papers:
Statistical-Realism versus Wave-Realism in the Foundations of Quantum
Mechanics

http://philsci-archive.pitt.edu/9021..._Mechanics.pdf
Demystifier
#499
Mar23-12, 03:51 AM
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Bohm2, thank you for the very useful list!
ThomasT
#500
Mar24-12, 01:01 AM
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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
#501
Apr16-12, 03:03 AM
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One related paper (not on the list above) recently published in Physical Review Letters:
http://lanl.arxiv.org/abs/1111.6597
GravitatisVis
#502
Apr27-12, 02:38 PM
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tag.
bohm2
#503
May7-12, 10:25 PM
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Quote Quote by Fredrik View Post
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/...nphys2309.html
Demystifier
#504
May8-12, 02:02 AM
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Quote Quote by bohm2 View Post
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/...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


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