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Kon
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PostPosted: Tue Nov 29, 2011 11:51 pm    Post subject: Quantum theorem shakes foundations Reply with quote

Quote:
Quantum states are the key mathematical objects in quantum theory. It is therefore surprising that physicists have been unable to agree on what a quantum state represents. There are at least two opposing schools of thought, each almost as old as quantum theory itself. One is that a pure state is a physical property of system, much like position and momentum in classical mechanics. Another is that even a pure state has only a statistical significance, akin to a probability distribution in statistical mechanics. Here we show that, given only very mild assumptions, the statistical interpretation of the quantum state is inconsistent with the predictions of quantum theory. This result holds even in the presence of small amounts of experimental noise, and is therefore amenable to experimental test using present or near-future technology. If the predictions of quantum theory are confirmed, such a test would show that distinct quantum states must correspond to physically distinct states of reality.


http://lanl.arxiv.org/abs/1111.3328
http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392

Quote:
The PBR theorem rules out psi-epistemic models within the standard Bell framework for ontological models. The remaining options are to adopt psi-ontology, remain psi-epistemic and abandon realism, or remain psi-epistemic and abandon the Bell framework.


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

Generalisations of the recent Pusey-Barrett-Rudolph theorem for statistical models of quantum phenomena
http://xxx.lanl.gov/abs/1111.6304
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Kail
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PostPosted: Wed Nov 30, 2011 6:23 am    Post subject: Reply with quote

Thank you Smile
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ruveyn
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PostPosted: Wed Nov 30, 2011 9:05 am    Post subject: Reply with quote

Way cool! Thank you for reference.

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Kon
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PostPosted: Thu Dec 01, 2011 12:05 am    Post subject: Reply with quote

I'm still trying to understand the last paper but here's a quoted comment from Matt Leifer (in another blog devoted to this paper) posted regarding this newest Hall paper that you guys might find interesting. If you guys come across anything on this topic, please post it on here as I'm extremely interested in this topic.

Quote:
As far as I can see, this paper is a fairly straightforward extension of PBR, but I only think that one of the weakened constraints is conceptually interesting. The original proof required a factorizability condition, i.e. for product states you have a Cartesian product of ontic state spaces and the distribution is independent over the factors. This can be replaced by a “local compatibility” condition, which is just the condition that if lambda is a possible ontic state for a single copy of a bunch of different states, then n copies of lambda is possible for any tensor product of n states chosen from that set. This drops the independence part of the assumption. Why this is true is very easy to see, since this is the only property of factorizability used in the original PBR result.

Hall also claims to have weakened this further to a condition of “compatibility”. This is supposed to go beyond reductionist models, which say that each system has its own individual ontic properties and the properties of composite systems are simply the collection of properties of all the parts. Hall tries to go beyond this by allowing the ontic state space of two systems to be arbitrarily different from the cartesian product of the ontic state spaces of the individual systems. I don’t think this has been achieved, since one still needs to know how the properties of the global system are related to the properties of the subsystems. Hall says that if we know that lambda is compatible with some states of one system, then we need only know that lambda is compatible with n-fold products of those states. However, since the state spaces are completely distinct, I don’t think that it makes sense to consider lambda as a possible ontic state for both a subsystem and the full composite system. This is not the case in the original theorem, or in the version with local compatibility, in which case the state on the global system is n copies of lambda rather than just one. Therefore, I don’t think that this part of the paper makes much sense.

Hall also points out that the probability distribution over the ontic state need not be independent of the choice of measurement, since only one measurement is considered for each pair of states. Whilst this is true, and perhaps interesting because it places a constraint on certain types of retrocausal theory, it does not allow the original PBR conclusion to be drawn. If another choice of measurement were made then the distributions could overlap and the quantum state would be epistemic. It is this loophole that I hope to exploit in developing an epistemic retrocausal theory. Perhaps this is worth saying, but it is certainly not groundbreaking.


http://www.scottaaronson.com/blog/?p=822
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Oodain
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PostPosted: Thu Dec 01, 2011 11:22 am    Post subject: Reply with quote

this goes so far beyond me at the moment Confused
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Kon
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PostPosted: Thu Dec 01, 2011 1:14 pm    Post subject: Reply with quote

Oodain wrote:
this goes so far beyond me at the moment Confused


The theorem basically limits the class of wavefunction interpretations:


Quote:
1.Wavefunctions are epistemic and there is some underlying ontic state. Quantum mechanics is the statistical theory of these ontic states in analogy with Liouville mechanics.
2.Wavefunctions are epistemic, but there is no deeper underlying reality.
3.Wavefunctions are ontic (there may also be additional ontic degrees of freedom, which is an important distinction but not relevant to the present discussion).


According to this theorem, class 1 interpretations are not possible, So one is left with either class 2 or class 3 interpretations. Anything that narrows down possible interpretations is a good thing, I think.
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Kon
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PostPosted: Thu Dec 01, 2011 4:12 pm    Post subject: Reply with quote

Wow! Another paper discussing this theorem:


Completeness of quantum theory implies that wave functions are physical properties

http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.6597v1.pdf

The Bohmians and Everett people must be smiling, I think.
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Apple_in_my_Eye
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PostPosted: Thu Dec 01, 2011 6:05 pm    Post subject: Reply with quote

Interesting. I thought "hidden variables" theories had been ruled out in the past, but in any case I guess this drives the final stake through it's heart. Einstein must be rolling in his grave.
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Oodain
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PostPosted: Thu Dec 01, 2011 6:06 pm    Post subject: Reply with quote

Kon wrote:
Oodain wrote:
this goes so far beyond me at the moment Confused


The theorem basically limits the class of wavefunction interpretations:


Quote:
1.Wavefunctions are epistemic and there is some underlying ontic state. Quantum mechanics is the statistical theory of these ontic states in analogy with Liouville mechanics.
2.Wavefunctions are epistemic, but there is no deeper underlying reality.
3.Wavefunctions are ontic (there may also be additional ontic degrees of freedom, which is an important distinction but not relevant to the present discussion).


According to this theorem, class 1 interpretations are not possible, So one is left with either class 2 or class 3 interpretations. Anything that narrows down possible interpretations is a good thing, I think.


thank you that actually gave me a reference sto start from Surprised
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ruveyn
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PostPosted: Thu Dec 01, 2011 7:37 pm    Post subject: Reply with quote

Oodain wrote:


thank you that actually gave me a reference sto start from Surprised



Try this:

http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.5057v1.pdf

ruveyn
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graywyvern
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PostPosted: Thu Dec 01, 2011 7:56 pm    Post subject: wavefunctions Reply with quote

"All that we see or seem/
Is but a dream within a dream."
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Kon
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PostPosted: Thu Dec 08, 2011 12:01 am    Post subject: Reply with quote

Talk about 2 different interpretations of PBR theorem:

Leifer:
Quote:
Pretty much all of the well-developed interpretations that take a realist stance fall under option 3, so they are in the psi-ontic camp. This includes the Everett/many-worlds interpretation, de Broglie-Bohm theory, and spontaneous collapse models. Advocates of these approaches are likely to rejoice at the PBR result, as it apparently rules out their only realist competition, and they are unlikely to regard anti-realist approaches as viable.


Oscar Dahlsten:
Quote:
Let me try to summarise their argument. They suppose a particular kind of PSI-epistemic model is possible and then show a contradiction with quantum statistics. The kind of model they consider is essentially a hidden-variable one. The idea is that at the time of preparation of a quantum system one also sets the value of some hidden variable q. This is *not* assumed to be local as far as I can tell....So the argument, modulo potential subtleties like hidden assumptions, puts another nail in the coffin for hidden variable theories, adding to the contributions by Bell and others. As it is quite clean and does not appear to assume the hidden variable is local, one can imagine it turning up in text-books at some point.
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Kon
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PostPosted: Wed Feb 01, 2012 1:33 pm    Post subject: Reply with quote

Another paper from 2 of those authors came out today. We debated this issue on a physics forum and one theoretical physicist had pointed out that the proof only holds true if one assumes non-contextuality. Well, it seems that the new paper by 2 of those authors take that assumption into consideration and reach a different conclusion:
Quote:
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
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Kon
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PostPosted: Thu May 10, 2012 1:27 am    Post subject: Reply with quote

Here's a compilation of all the papers to date on this recent no-go PBR theorem:

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

On the reality of the quantum state
http://lanl.arxiv.org/pdf/1111.3328.pdf (revised paper based on original PBR paper-May 2012)
http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys2309.html

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

Is a system's wave function in one-to-one correspondence with its elements of reality?
http://lanl.arxiv.org/pdf/1111.6597v2.pdf

Are quantum states real?
http://lanl.arxiv.org/pdf/1205.1439.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

Why I Am Not a Psi-ontologist
http://pirsa.org/displayFlash.php?id=12050021 (Video from Perimeter Institute-according to the author "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.)

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/9021/1/Statistical_Realism_Versus_Wave_Realism_in_the_Foundations_of_Quantum_Mechanics.pdf
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PostPosted: Thu May 10, 2012 5:11 am    Post subject: Reply with quote

The universe hates to think of itself as finite, and yet physicists love to try to make it finite Smile
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