The quantum state cannot be interpreted statistically?

[Fredrik]

Very nice Fredrik! Keep up the good work and tell us what the heck this is all about!

Thanks. I hope I will be able to do that soon, but I'm still pretty confused about what's going on.

I think he went into a dead end when trying to 'refute' QM.

I would say that he made valuable contributions to QM, and never tried to refute it.

It doesn’t make sense? QM can’t say anything useful about one single electron in the Double-slit experiment? Is this really true??

To me that quote doesn't seem to say anything like that. Regardless of interpretation, QM assigns very accurate probabilities to positions where the particle might be detected. This assignment is certainly useful to someone who's forced to bet all his money on where the first dot will appear. If you can imagine one person that it's useful to, then how can you say that it's useless?

I don't want to spend too much time talking about the ensemble interpretation in this thread. This thread is about ψ-epistemic hidden variable theories*, not about the ensemble interpretation.

*) The terminology is explained in the article I linked to in my previous post.

 

[bohm2]

Some of you might find it entertaining to read the blog post by Lubos Motl (the angriest man in physics) about the topic. It will not help you understand anything, but it's mildly amusing to see how aggressively he attacks everything. It has a calming effect on me actually. I'm thinking about how I expressed some irritation earlier, and I'm thinking "I hope I don't sound like that".

I have performance/social/generalized anxiety among other things so the way Lubos Motl sounds to you is the way every human being on the planet sounds to me. Lubos is beyond scary for me. I would never dare to question his posts even if his posts sounded like they were coming from an anti-quantum-mechanical crackpot/lunatic. And I'm not implying they are...in case he drops by.

 

[my_wan]

The quantum state cannot be interpreted as something other than a quantum state

http://www.scottaaronson.com/blog/?p=822

Scott Aaronson made an observation that I find meaningful here:

I expect the rebuttal to prove a contrary theorem, using a definition of the word “statistical” that subtly differs from PBRs. I expect the difference between the two definitions to get buried somewhere in the body of the paper.

I expect the rebuttal to get blogged and Slashdotted. I expect the Slashdot entry to get hundreds of comments taking strong sides, not one of which will acknowledge that the entire dispute hinges on the two camps’ differing definitions.

Now consider what Fredrik has pointed out:

They are comparing two different schools of thought:

1. A state vector represents the properties of the system.
2. A state vector represents the statistical properties of an ensemble of identically prepared systems, and does not also represent the properties of a single system.

[...]Then either of the two inequivalent preparation procedures could have given the system the properties represented by λ. Yada-yada-yada. Contradiction![...]

What does "and does not also represent the properties of a single system" actually entail? In fact it entails:

1. That the law of the excluded middle applies to 'properties'.
2. That physical 'properties' are defined non-contextually, i.e., value definiteness.

In effect this particular definition of 'properties' simply brings the debate full circle into known debate territory. By this preprint hinging their argument the particular qualifier: "not also properties of a single system", it merely reaches the same conclusions as the Kochen-Specker Theorem. That being that either quantum properties are not value definite (contextual), or that they are not 'real' properties by whatever definition of 'real' some author chooses to define it to be. Whatever definition is chosen is not going to be satisfactory for every point of view.

The irony here is that the same contextuality issues used to argue non-real in the EPR and Kochen-Specker cases are used to argue quantum states are real. To compound that irony this preprint has taken certain non-realist approach to defining "statistical interpretation" to argue this. Yet to a very high degree much of the debate hinges on semantics, and which definition of semantics is a priori the academically valid one. Meanwhile both sides astutely avoid recognizing that the semantic variances in the respective definitions are anything more than an choice of perspective and continue to impose definitions on each others words that are not applicable in the context they were intended.

Given these semantic variances in how individual scientist internalize these definitions I do not know how to formulate and argument that would even be generally comprehensible to everybody. It's possible to make the exact same argument twice, working off of incongruent choices of definitions or semantic choices, and simply be accused of contradicting myself. Yet these semantic choices are as truth independent as a coordinate choice.

So my take on this paper is that it is valid in the context of the semantic choices it made and leads me to the same conclusions about QM as EPR, Kochen-Specker, and other theoretical issues have. If by academic definition "real" properties must a priori be value definite and non-contextual then that makes me a non-realist by definition, yet I am in the realist camp.

 

[TJ Radcliffe1]

I've found the discussion here quite useful. My "thinking out loud" take on the question can be found here: http://www.tjradcliffe.com/?p=621 and can be summed up as follows:

“'Preparing a photon in the same quantum state will sometimes result in photons in different physical states' does not imply 'Preparing a photon in different quantum states will sometimes result in photons that are in the same physical state'. The former proposition is the statistical interpretation. The latter is the assumption that the author’s argument depends on."

There really is no basis for assuming their primary assumption, and if you don't grant them that assumption that argument just fails. The statistical interpretation (which I do not cleave to myself) does not in any wise imply that individual photons must be ignorant of the means used to prepare them. That's just an arbitrary imposition.

 

[Fredrik]

Scott Aaronson made an observation that I find meaningful here:

Yes, that quote is my favorite part of his blog post.

In effect this particular definition of 'properties'
...
By this preprint hinging their argument the particular qualifier: "not also properties of a single system"

That qualifier is a part of how I characterized the difference between the two views.

The article doesn't define the term "property". The definition I posted is one I came up with on my own (inspired by the probability-1 definition in Isham's QM book) when I was trying to guess what Pusey, Barrett and Rudolph (PBR) meant. Now that I've read a big enough part of the article by Harrigan & Spekkens (HS) (link) that defines the terminology used by people who deal with hidden-variable theories, I no longer think that my guess was correct.

In the PBR article, the difference between the two views that is actually used in the argument is that in one of them, λ determines the state vector, and in the other it doesn't. This is exactly how HS defines the difference between ψ-ontic and ψ-epistemic hidden variable theories. So it appears that the title and the abstract of the PBR paper are extremely misleading. The paper argues against ψ-epistemic hidden variable theories, not against the idea that QM is just a set of rules that tells us how to calculate probabilities of possible results of experiments.

By the way, HS doesn't define "property" either, but they certainly don't mean that if you know all of them, you know the result of every experiment with certainty. So if PBR are using similar terminology, my guess was way off.

 

[Fredrik]

I have performance/social/generalized anxiety among other things so the way Lubos Motl sounds to you is the way every human being on the planet sounds to me. Lubos is beyond scary for me. I would never dare to question his posts even if his posts sounded like they were coming from an anti-quantum-mechanical crackpot/lunatic. And I'm not implying they are...in case he drops by.

In that case, I apologize for pointing out that others had posted the same link before. I assumed that you would just think "D'oh" (like Homer Simpson), and be completely over it a few seconds later. I certainly didn't mean to cause any anxiety.

Lubos is definitely not "an anti-quantum-mechanical crackpot/lunatic", but he thinks everyone else is.

 

[Fredrik]

Just a quick comment about hidden-variable theories...

One thing I realized when I read HS is that hidden-variable theories can be used to give precise definitions of statements like

• QM doesn't describe reality.
• A state vector represents the observer's knowledge of the system.

The former is made precise by the concept of ψ-incomplete hidden-variable theories, and the latter by the concept of ψ-epistemic hidden-variable theories. Now, I'm sure that some of you (in particular Ken G) will find these definitions unsatisfactory. But I didn't bring this up because I think these definitions describe exactly what a person who uses one of these statements has in mind. I'm bringing it up because until now I thought that statements like these can't be defined in terms of operational concepts like preparation procedures and measurement procedures, and I think it's pretty cool that there are meaningful definitions that can be expressed in scientific terms.

The HS article defines two classes of hidden-variable theories: ψ-ontic and ψ-epistemic. The first class can be further divided into ψ-complete and ψ-supplemented. The criteria that define the three classes are precisely the ones used on page 1 of the PBR article. The PBR article is arguing against the ψ-epistemic class of hidden-variable theories. It's interesting to note that the HS article is arguing that a local hidden-variable theory that can reproduce the predictions of QM is necessarily ψ-epistemic. So if these arguments all hold, they have ruled out all hidden-variable theories except the non-local ψ-ontic ones. (Bohmian mechanics is a non-local ψ-supplemented (and therefore ψ-ontic) hidden-variable theory).

 

[Fredrik]

These are a few good quotes from the comments section of Scott Aaronson's blog. (The one bohm2 linked to in #66).

Scott:

As I said, I would’ve strongly preferred if PBR had given a careful discussion of what they mean by “statistical” and what they don’t mean (and for which meanings the “statistical interpretation” can be trivially ruled out even without their theorem, etc. etc.), rather than breezing past these issues in a few sentences.
...
Let me put it this way: if what the epistemic camp believed is overturned by the PBR theorem, then what they believed is so obviously wrong that they shouldn’t have needed such a theorem to set them straight! And therefore, being charitable, I’m going to proceed on the assumption that they meant something else.​

Matt Leifer:

The psi-epistemicist response to PBR is quite straightforward. Basically, the result does not rule out any proposal that we were taking seriously in the first place. For the neo-Copenhagenists (e.g. Quantum Bayesians, Zeilinger’s, etc.) there is no underlying state of reality beyond the quantum predictions, so the result is irrelevant to their program and they can continue as before. Those of us who are realist, e.g. Rob Spekkens and myself, have more of a problem and we must deny one of the assumptions of the theorem. However, Bell’s theorem, Kochen-Specker, Hardy’s Ontological Excess Baggage theorem, and a host of results by Alberto Montina have already given us enough problems with the usual framework for ontological models that we had already abandoned it as a serious proposal a long time ago. Spekkens thinks that the ultimate theory will have an ontology consisting of relational degrees of freedom, i.e. systems do not have properties in isolation, but only relative to other systems. Personally, I can’t make much sense of that beyond a rephrasing of many worlds, so I favor a theory with retrocausal influences instead. Neither of these proposals is ruled out by the PBR theorem.

That said, I do think the PBR result is the most significant result in quantum foundations for several years. It was an important open question as to whether psi-epistemicism was possible within the standard framework for ontological theories and that has now been answered in the negative. However, as I said, this only confirms intuitions that we (both psi-ontologists and psi-epistemicists) already had.​

Gene:

Here is video of Lubos singing Queen’s Bohemian Rhapsody:

​

 

[DevilsAvocado]

The layman’s take on PBR – feel free to laugh

To begin with, this helped me not to fully understand what this is all about:

http://arxiv.org/abs/1111.3328][/PLAIN] The[/URL] statistical view of the quantum state is that it merely encodes an experimenter's information about the properties of a system. We will describe a particular measurement and show that the quantum predictions for this measurement are incompatible with this view.

Then I got somewhat confused:

http://arxiv.org/abs/1111.3328][/PLAIN]
If the quantum state is a physical property of the system (the first view), then either λ is identical with |ø0> or |ø1>, or λ consists of |ø0> or |ø1>, supplemented with values for additional variables not described by quantum theory. Either way, the quantum state is uniquely determined by λ.

If the quantum state is statistical in nature (the second view), then a full specification of λ need not determine the quantum state uniquely. Some values of λ may e compatible with the quantum state being either |ø0> or |ø1>. This can be understood via a classical analogy. Suppose there are two different methods of flipping a coin, each of which is biased. Method 1 gives heads with probability p0 > 0 and method 2 with probability 0 < p0 ≠ p1. If the coin is flipped only once, there is no way to determine by observing only the coin which method was used. The outcome heads is compatible with both. The statistical view says something similar about the quantum system after preparation. The preparation method determines either |ø0> or |ø1> just as the flipping method determines probabilities for the coin. But a complete list of physical properties λ is analogous to a list of coin properties, such as position, momentum, etc. Just as “heads” up is compatible with either flipping method, a particular value of λ might be compatible with either preparation method.

We will show that the statistical view is not compatible with the predictions of quantum theory.

And I after this sentence... well, it’s no use to pretend – I was completely lost.

But, I continue to read (stubborn ) and this paragraph helped me to form an 'illusion' that there might be something to understand after all:

http://arxiv.org/abs/1111.3328][/PLAIN] Finally, the argument so far uses the fact that quantum probabilities are sometimes exactly zero. The argument has not taken any account of the experimental errors that will occur in any real laboratory. It is very important to have a version of the argument which is robust against small amounts of noise. Otherwise the conclusion – that the quantum state is a physical property of a quantum system – would be an artificial feature of the exact theory, but irrelevant to the real world. Experimental test would be impossible.

Add this to the measurement apparatus in FIG 1:

They are measuring NOT values!

... This is a completely *WILD GUESS* but to me it looks like the logic goes like this:

Quantum probabilities are sometimes exactly zero, and when they are – we should not be able to measure 'this outcome'. If we manage to set up a system (I have no idea how they do that) where it is possible to indeed measure 'zero probabilities', well then these 'probabilities' are not probabilities, but real!​

Showtime! Boos/Applause/LOL – anything goes!

 

[Fredrik]

The title and the abstract of this paper are like newspaper headlines. They aren't meant to be honest, or even close to the truth. They are only meant to get your attention. But the article's argument against ψ-epistemic hidden-variable theories may still be correct.

I have examined the argument now. Let $|0\rangle$ and $|1\rangle$ be the eigenvectors of some operator on a two-dimensional Hilbert space (like a spin component operator for a spin-1/2 particle). Define
$$\begin{align} |+\rangle &=\frac{1}{\sqrt{2}} \left(|0\rangle+|1\rangle\right)\\ |-\rangle &=\frac{1}{\sqrt{2}} \left(|0\rangle-|1\rangle\right). \end{align}$$ These vectors form another orthonormal basis for the same Hilbert space. Suppose that there's one preparation procedure that puts the system in the $|0\rangle$ state, and another that puts the system in the $|1\rangle$ state. Each time we perform one of these procedures, the particle ends up having some set of properties. We are assuming that there's a λ (a "state" in the hidden-variable theory, i.e. a complete list of all the particle's properties) such that regardless of which of these two procedures we use, there's a probability ≥q>0 that the properties of the particle will be λ.

Suppose that we prepare two particles in isolation, both in the state $|0\rangle$. This puts the two-particle system in the state $|0\rangle\otimes|0\rangle$. There is a probability $\geq q^2>0$ that both particles will have properties λ.

Now suppose that we measure an operator (on the four-dimensional two-particle Hilbert space) with the following eigenvectors.
$$\begin{align} |\xi_1\rangle &=\frac{1}{\sqrt{2}} \left(|0\rangle\otimes|1\rangle +|1\rangle\otimes|0\rangle\right)\\ |\xi_2\rangle &=\frac{1}{\sqrt{2}} \left(|0\rangle\otimes|-\rangle +|1\rangle\otimes|+\rangle\right)\\ |\xi_3\rangle &=\frac{1}{\sqrt{2}} \left(|+\rangle\otimes|1\rangle +|-\rangle\otimes|0\rangle\right)\\ |\xi_4\rangle &=\frac{1}{\sqrt{2}} \left(|+\rangle\otimes|-\rangle +|-\rangle\otimes|+\rangle\right) \end{align}$$ The first one is orthogonal to $|0\rangle\otimes|0\rangle$, so QM assigns probability 0 to the result corresponding to that eigenvector. But at least a fraction $q^2>0$ of the time, the system has properties that it could have gotten from the preparation procedure that puts the system in state $|0\rangle\otimes|0\rangle$.

Right now I'm not sure why the above should be considered a contradiction. I have to go to a grocery store before it closes, so I don't have time to think it through right now. Is it that if you know the state vector, you know which of the four eigenvectors represents an impossible result, but if you just know λ, you don't?

 

[bohm2]

Is it that if you know the state vector, you know which of the four eigenvectors represents an impossible result, but if you just know λ, you don't?

How does that match up with what Scott Aaronson interprets PBR where he writes:

Basically, PBR call something “statistical” if two people, who live in the same universe but have different information, could rationally disagree about it. (They put it differently, but I’m pretty sure that’s what they mean.) As for what “rational” means, all we’ll need to know is that a rational person can never assign a probability of 0 to something that will actually happen.

 

[Fredrik]

Aaronson's blog helped me understand at least one detail in the PBR argument, but I think I understand less of his argument than of the PBR argument right now. He seems to be saying that QM is statistical if two people could assign different wavefunctions to the same system, and both be right. PBR are saying that QM is statistical if two preparation procedures that QM considers inequivalent might actually give the system the same properties. This doesn't sound like the same thing to me.

 

[DevilsAvocado]

How does that match up with what Scott Aaronson interprets PBR where he writes:

a rational person can never assign a probability of 0 to something that will actually happen.

[Again, wild guessing]
This sounds logical, but maybe the 'trick' is:

http://arxiv.org/abs/1111.3328]Finally,[/PLAIN] the argument so far uses the fact that quantum probabilities are sometimes exactly zero.

And you do find a clever way to measure that zero probability... that should give a completely new meaning to "probability", right...?

 

[bohm2]

Just to add more input (and confuse me even more) concerning the implications of this paper is another blog (Matt Leifer) just posted:

First up, I would like to say that I find the use of the word “Statistically” in the title to be a rather unfortunate choice. It is liable to make people think that the authors are arguing against the Born rule (Lubos Motl has fallen into this trap in particular), whereas in fact the opposite is true. The result is all about reproducing the Born rule within a realist theory. The question is whether a scientific realist can interpret the quantum state as an epistemic state (state of knowledge) or whether it must be an ontic state (state of reality). It seems to show that only the ontic interpretation is viable, but, in my view, this is a bit too quick.

Various contemporary neo-Copenhagen approaches also fall under this option, e.g. the Quantum Bayesianism of Carlton Caves, Chris Fuchs and Ruediger Schack; Anton Zeilinger’s idea that quantum physics is only about information; and the view presently advocated by the philosopher Jeff Bub. These views are safe from refutation by the PBR theorem, although one may debate whether they are desirable on other grounds, e.g. the accusation of instrumentalism. 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.

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. One of the things that a good interpretation of a physical theory should have is explanatory power. For me, the epistemic view of quantum states is so explanatory that it is worth trying to preserve it. Realism too is something that we should not abandon too hastily. Therefore, it seems to me that we should be questioning the assumptions of the Bell framework by allowing more general ontologies, perhaps involving relational or retrocausal degrees of freedom. At the very least, this option is the path less travelled, so we might learn something by exploring it more thoroughly.

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

Edit: I just read all of it. Matt wrote a great piece.

 

[Fredrik]

Just to add more input (and confuse me even more) concerning the implications of this paper is another blog just posted:

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

Thanks. I liked what that guy said in the comments section of Aaronson's blog, so I'm looking forward to reading what he says in his own.

 

[DevilsAvocado]

I would say that he made valuable contributions to QM, and never tried to refute it.

Absolutely, as I said he’s my hero, but even the Sun has spots. When the EPR-Bell loopholes are finally closed Local Realism is forever dead, and I guess that would have been some kind of a 'blow' to Einstein... I know 'refute' is a quite 'incomplete' description, but I did use single quotes...

Is there any person on this planet who clearly can describe what went on between Einstein & Bohr for 20+ years?? All we know for sure is that Einstein, after the 1927 Solvay Conference, was not completely happy with the state of affairs. The quote in the paper is quite telling:

... I incline to the opinion that the wave function does not (completely) describe what is real, but only a (to us) empirically accessible maximal knowledge regarding that which really exists [...] This is what I mean when I advance the view that quantum mechanics gives an incomplete description of the real state of affairs. -- A. Einstein​

To me that quote doesn't seem to say anything like that. Regardless of interpretation, QM assigns very accurate probabilities to positions where the particle might be detected. This assignment is certainly useful to someone who's forced to bet all his money on where the first dot will appear. If you can imagine one person that it's useful to, then how can you say that it's useless?

I don't want to spend too much time talking about the ensemble interpretation in this thread.

But I don’t get it? EI is no different than any other interpretation when comes to individual particles? What’s it good for then??

But you’re right, this thread is not about EI.

 

[my_wan]

@Fredrik
As much as I have learned to respect and often concur with your input here I was strongly at odds with your earlier take in this thread. Though I didn't know how to properly articulate it without moving well off topic, so I did the best I could with generalities. However, it seems you did comprehend quiet well

I remain interested in how to better articulate these ontic and epistemic variances in peoples perceptions but am at a complete loss. Namely because there are a number of arguments I would like to make but these perceptual variances invariably lead to an almost universal misunderstanding of the perceived consequences. For me it makes no difference which set of definitions I work under to make a point, so long as the point is understood in the context intended. That just doesn't seem possible under the present state of affairs. I can't even fully grok the full range of other peoples internal perspectives on these ontic and epistemic issues. Thanks for the http://arxiv.org/abs/0706.2661" , it does make many of the issues I struggle with a lot clearer. It fails to fully articulate a distinction between ontic locality verses epistemic locality, which I find pertinent, but was as clear an articulation of the basic issues as I have ever seen.

In particular I like the fact that this HS paper explicitly points out why Einstein would not have been swayed by the modern EPR experiments. In fact, not only did he reject the original EPR paper as representative of his view, his preferred form of the argument explicitly depended on the validity of modern EPR experiments and implicitly on the inequalities outlined by Bell. I'll keep this paper in mind in the event I get another debate involving opinions as to what Einstein would have been convinced of as a result of modern experiments.

In regards to post #77 I to was impressed with the rigor with which the authors made precise these confounding definitional issues, not perfect but impressive. However, your characterization of the PBR article as anti ψ-epistemic, though not explicitly wrong, is more nuanced than you seemed to imply when you noted the comparison with the HS article. A clue to this may be in your post #78 when you noted an inability to make sense of Spekkens view unless it was somehow related to many worlds. Spekkens toy model notwithstanding (it was a "toy" model after all) his views are not too far from mine, and many worlds has nothing to do with it. When the PBR article argues that the quantum state cannot be interpreted "statistically" it does not explicitly imply a one to one correspondence between |ψ|^2 and an ontic specification of ψ. Only that ψ refers to an actual ontic construct in a manner that may or may not involve a ψ-complete specification, at least as defined by the HS article to qualify as ψ-complete. In this respect it is a weaker argument than some may attempt to make it out to be but is somewhat more attuned to the type of argument Einstein made, the EPR paper notwithstanding as Einstein distanced himself from that article immediately upon publication. In the sense that the HS article defined ψ-epistemic the PBR article made no specific claims. To us realist this may seem anti-climatic, but that under-values a range of opinions and perspectives not shared by many realist.

I would be interested in a discussion about Spekkens views, particularly the concept of relational degrees of freedom, (lack of) properties in isolation, and relativistic (emergent) properties in general. It may help clear up some issues with Spekkens views. Some familiarity with Relational QM (RQM) would be useful, but would almost certainly exceed the scope of this thread. Personally I can't see any way to escape the non-realist views without an understanding of RQM or related concepts.

 

[DevilsAvocado]

Hey my_wan! Long time no see!

 

[DevilsAvocado]

Just to add more input (and confuse me even more) concerning the implications of this paper is another blog (Matt Leifer) just posted:

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

Edit: I just read all of it. Matt wrote a great piece.

Many thanks. Finally it’s possible to get a chance to understand what this is all about:

epistemic state = state of knowledge
ontic state = state of reality

1. ψ-epistemic: Wavefunctions are epistemic and there is some underlying ontic state.
   
   
2. ψ-epistemic: Wavefunctions are epistemic, but there is no deeper underlying reality.
   
   
3. ψ-ontic: Wavefunctions are ontic.

Conclusions
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. One of the things that a good interpretation of a physical theory should have is explanatory power. For me, the epistemic view of quantum states is so explanatory that it is worth trying to preserve it. Realism too is something that we should not abandon too hastily. Therefore, it seems to me that we should be questioning the assumptions of the Bell framework by allowing more general ontologies, perhaps involving relational or retrocausal degrees of freedom. At the very least, this option is the path less travelled, so we might learn something by exploring it more thoroughly.​

What’s left is to understand the proof, that seems to involve the Born rule and a 0 result which contradicts the normalization assumption of 1, and an argument that there can be no overlap in the probability distributions representing |0⟩ and |+⟩ in the model.

But I don’t understand it and are hoping that someone can 'translate'...

 

[DevilsAvocado]

... a local hidden-variable theory that can reproduce the predictions of QM is necessarily ψ-epistemic.

What am I missing?? A local hidden-variable theory that can reproduce the predictions of QM...?

This has been quite dead for awhile, hasn’t it??

 

[bohm2]

Many thanks. Finally it’s possible to get a chance to understand what this is all about:

epistemic state = state of knowledge
ontic state = state of reality

1. ψ-epistemic: Wavefunctions are epistemic and there is some underlying ontic state.
   
   
2. ψ-epistemic: Wavefunctions are epistemic, but there is no deeper underlying reality.
   
   
3. ψ-ontic: Wavefunctions are ontic.

Many realists have trouble understanding the purely epistemic stance. As Ghirardi writes in discussing Bell's view:

Bell has considered this position and he has made clear that he was inclined to reject any reference to information unless one would, first of all, answer to the following basic questions: Whose information?, Information about what?

So if one takes that pure epistemic/instrumentalist stance it seems to me one is almost forced to treat QT as "a science of meter readings". That view seems unattractive to me. It has the same stench/smell that held back progress in the cognitive sciences (e.g. behaviourism). But then, I could be mistaken?

But if one treats the wave function as a real "field"-like entity it is very much different than the typical fields we are accustomed to. The wave function evolves in 3N-dimensional configuration space, there's the contextuality/non-separability also and stuff like that make it a very strange kind of "causal" agent. If one takes the Bohmian perspective (at least one Bohmian version), how do the 2 (pilot wave and particle) "interact"? It can't be via the usual contact-mechanical stuff we are accustomed to because of the non-locality that is required in any realist interpretation.

http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.0958v1.pdf

Furthermore, if one wishes to scrap Bohm's dualistic ontology but remain a realist so that the wave function is everything then, there's another problem:

Since the proposal is to take the wave function to represent physical objects, it seem natural to take configuration space as the true physical space. But clearly, we do not seem to live in confguration space. Rather, it seems obvious to us that we live in 3 dimensions. Therefore, a proponent of this view has to provide an account of why it seems as if we live in a 3-dimensional space even though we do not. Connected to that problem, we should explain how to "recover the appearances" of macroscopic objects in terms of the wave function.

http://www.niu.edu/~vallori/AlloriWfoPaper-Jul19.pdf​

 

[Fredrik]

@Fredrik
As much as I have learned to respect and often concur with your input here I was strongly at odds with your earlier take in this thread. Though I didn't know how to properly articulate it without moving well off topic, so I did the best I could with generalities. However, it seems you did comprehend quiet well

There were a few things that I failed to understand, but I think I got the main point right: What they are attempting to disprove isn't what people who claim to prefer a statistical view actually believe in.

I must admit that I had a rather strong emotional reaction when I read the title and the abstract. They made me expect a bunch of crackpot nonsense, and I think this made it harder for me to understand some of the details correctly. For example, when they got to the condition that defines the ψ-epistemic theories, I thought they were saying that this was implied by the statistical view, but all they did was to consider a definition that makes an idea precise.

I also had no idea that there is a definition that makes that idea precise. This is why I said that the argument doesn't even look like a theorem. At the time, I thought about saying that a person who calls this a theorem doesn't know what a theorem is, but I decided that this was too strong a statement about something that I knew that I didn't fully understand.

I still think the title and the abstract makes the article look like crackpot nonsense, so I'm surprised that it didn't get dismissed as such by more people. I still don't fully understand the argument in the article, but now at least it looks like a theorem and a proof.

Thanks for the http://arxiv.org/abs/0706.2661" , it does make many of the issues I struggle with a lot clearer. It fails to fully articulate a distinction between ontic locality verses epistemic locality, which I find pertinent, but was as clear an articulation of the basic issues as I have ever seen.

I read their definition of locality, but I didn't understand it. I'm going to have to give it another try later, because it's something I've always felt needs a definition.

However, your characterization of the PBR article as anti ψ-epistemic, though not explicitly wrong, is more nuanced than you seemed to imply when you noted the comparison with the HS article.

Matt Leifer's blog brought up a few nuances that are absent both from my posts and the PBR article (like how there could be a hidden-variable theory where properties are relative rather than objective). But I don't see how PBR can be interpreted as anything but an argument against what HS called ψ-epistemic theories. Note that when PBR said

We begin by describing more fully the difference between the two different views of the quantum state [11].​

reference 11 is HS. (I didn't realize this until later).

A clue to this may be in your post #78 when you noted an inability to make sense of Spekkens view unless it was somehow related to many worlds.

This was a quote from Matt Leifer's comments to Scott Aaronson's blog post. But I have actually had similar thoughts (about how relational stuff seems to be MWI ideas in disguise), and even mentioned them in the forum a couple of times. I have no idea what Spekkens' toy model is about though. But I'm probably going to take some time to read some of the articles that Leifer is referencing soon.

When the PBR article argues that the quantum state cannot be interpreted "statistically" it does not explicitly imply a one to one correspondence between |ψ|^2 and an ontic specification of ψ. Only that ψ refers to an actual ontic construct in a manner that may or may not involve a ψ-complete specification, at least as defined by the HS article to qualify as ψ-complete.

I understood this, but maybe I typed it up wrong.

I would be interested in a discussion about Spekkens views, particularly the concept of relational degrees of freedom, (lack of) properties in isolation, and relativistic (emergent) properties in general. It may help clear up some issues with Spekkens views. Some familiarity with Relational QM (RQM) would be useful, but would almost certainly exceed the scope of this thread. Personally I can't see any way to escape the non-realist views without an understanding of RQM or related concepts.

Sounds like a good topic for another thread. (But I have spent a lot of time on this PBR stuff the past few days, so I'm somewhat reluctant to get into a long discussion about a new topic).

 

[Fredrik]

What am I missing?? A local hidden-variable theory that can reproduce the predictions of QM...?

This has been quite dead for awhile, hasn’t it??

Yes, but you're probably thinking that it's been dead since 1963 (± a few) when Bell's theorem was published, but HS proves it using two of Einstein's arguments, from 1927 and 1935.

The reason why that result was worth mentioning is that the PBR theorem is a result of the same type, a theorem that rules out some class of hidden-variable theories.

 

[Fredrik]

an argument that there can be no overlap in the probability distributions representing |0⟩ and |+⟩ in the model.

This is part of the definition of "ψ-epistemic theory". I think there are two basic ideas involved:

• A probability distribution can be thought of as a representation of our knowledge of the system's properties.
• Something that's completely determined by the properties of the system can be thought of as another property of the system.

If there are no overlapping probability distributions in the theory, then each λ determines exactly one probability distribution. Now the two ideas are in conflict. You can think of the probability distribution as "knowledge", but you can also think of it as a "property". If there's at least one λ that's associated with two probability distributions, then the probability distributions can't all be considered properties of the system. So now we have to consider at least some of them representations of "knowledge.

This motivates the definition that says that only theories of the latter kind (the ones with at least two overlapping probability distributions in the theory) are considered ψ-epistemic. These are the theories that the PBR article apparently has refuted. The first argument in the article is a bit naive, because it assumes specifically that there's overlap between the probability distributions associated with $|0\rangle$ and $|+\rangle$.

 

[Demystifier]

I believe I have found a flaw in the paper.

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.

 

[dextercioby]

Excellent post, Demystifier ! Very well and clearly written.

 

[Demystifier]

Thanks dextercioby! Now I have sent also an e-mail to the authors, with a similar (but slightly more polite) content. If they answer to me, I will let you know.

 

[dextercioby]

Just to be sure, are they assuming collapse, that is what they're taking for granted is essentially the Copenhagen interpretation ?

 

[Demystifier]

Just to be sure, are they assuming collapse, that is what they're taking for granted is essentially the Copenhagen interpretation ?

As far as I can see, they don't assume collapse.

 

[Fredrik]

Just to be sure, are they assuming collapse, that is what they're taking for granted is essentially the Copenhagen interpretation ?

I doubt that there are even two people who mean the same thing by the term "Copenhagen interpretation", so I try to avoid it. The informal version of the assumption they're making (in order to derive a contradiction) is that a state vector represents the experimenter's knowledge of the system. This is how some people describe "the CI". But nothing can be derived from an informal version of a statement, so the authors are choosing one specific way to give the statement a precise meaning. They are defining the claim that "a state vector represents knowledge of the system" as "there's a ψ-epistemic theory that makes the same predictions as QM".

In such theories, "collapse" is not a physical process. It's just a matter of changing your probability assignments when you have ruled out some of the possibilities.

 

[Ken G]

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.

I don't think this is something the authors don't realize, but it is essentially the objection I had from the start-- the assumption that an individual quantum system has "properties" that determine what happens to the system. I don't even think there is any such thing as an "individual quantum system", to me that is already an idealization that has left the building of any rigorous realism we should be using to prove theorems! But the authors do seem to associate that assumption with realism, all the same, so what they are doing is saying for all the people who want to be realists, they cannot believe in psi-epistemic interpretations. In other words, if there is a reality there that can be described completely by a mathematical structure, then the wave function is part of that structure (so is psi-ontic, even if incompletely so).

My objection was that this is a very narrow interpretation of realism, so I did not count it as a "mild" assumption, nor that it would be "radical" to reject it! You are giving more flesh to that objection-- you are talking about how a system could still be realistic but not be described completely by its own "properties"-- if realism must include contextuality. I believe this was also Spekkens' view, as summarized above in the Matt Leifer quote: "Spekkens thinks that the ultimate theory will have an ontology consisting of relational degrees of freedom, i.e. systems do not have properties in isolation, but only relative to other systems."

In other words, realists can retreat to a reality with a higher level of sophistication and reject the "individual system properties" concept, allowing them to maintain a psi-epistemic interpretation. I wasn't really counting that as realism at all, because I believe the "relational degrees of freedom" are not just between systems, they are between systems and observers, so I take a more Copenhagenesque spin. Whether or not that should count as some form of realism is highly debatable (remember Bohr said "there is no quantum world"). But I can certainly agree that it is not radical, so I concur with the bloggers who felt that the theorem eliminates a corner of interpretation space that was already largely unpopulated.

Personally, my main objection is with what I think is a rather naive claim: that most physicists want to hold to a form of realism that individual systems have properties that completely describe the system, they are not just attributes that we attach to the system ourselves, for some purpose. Indeed, I would argue that physics must be physics before it should be "realistic", and what physics is, by definition, is the intentional attachment of properties to systems to achieve some purpose. That's just exactly what any physics book does, we only need to look at it! So why on Earth is it now a "mild assumption" to say that physics should be something different from what physics books do, that physics should not be about attaching properties ourselves for certain specific purposes, it should be a study of the true properties of individual systems that nature really uses to control what happens? That's the radical claim, if you ask me-- the claim that nature "thinks just like we do." I'm a realist, but I think my mind, and my mathematical structures, are looking at the reality from the inside, so PBR's very first assumption has already left what I consider to be a true way to look at physics.

 

[Ken G]

One thing I realized when I read HS is that hidden-variable theories can be used to give precise definitions of statements like

• QM doesn't describe reality.
• A state vector represents the observer's knowledge of the system.

The former is made precise by the concept of ψ-incomplete hidden-variable theories, and the latter by the concept of ψ-epistemic hidden-variable theories. Now, I'm sure that some of you (in particular Ken G) will find these definitions unsatisfactory.

Actually I have no problem with those definitions, I think you have done an excellent job unearthing the idea that what PBR are fundamentally talking about are hidden-variable theories. My objection was always with the whole concept of hidden-variable theories, I believe they represent a form of pipe dream that physics should have figured out by now it just isn't! Hidden variables are nothing but the variables of the next theory that we haven't figured out yet, there's nothing ontological about them. Physics just makes theories, and they work very well, but none of that has anything do with the existence or non-existence of a "perfect theory" of a mathematical structure that completely describes the properties of a system. There is absolutely no reason to ever assume that such a structure exists, and any proof that starts there has entered into a kind of fantasy realm (and claimed it was a "mild assumption" to boot!). That's just never what physics was, so why should we keep pretending that's what it should be?

So if these arguments all hold, they have ruled out all hidden-variable theories except the non-local ψ-ontic ones.

Yes, that seems to be the key of the whole business. But that is also what I was saying before about the argument being circular-- I view the form of realism that they have assumed to be more or less (and now with this theorem, it's more the "more" than the "less") the same thing as the notion that psi is ontic in character, because if there is a true ontology there that can be described mathematically and have theorems proven about it, then it's not surprising that psi is saying something about it. That's what they proved, but man what a big "if." I think we intentionally retreat from reality when we place a mathematical template over it and start proving theorems about it, so to call that "realism" I think is way off, but that does seem to be how the term has been co-opted.

 

[DevilsAvocado]

Thanks B2, excellent. I can put my finger on it, but I just love every word you wrote in the last post... the 'openness'... it’s refreshing. More than often, there’s an "interpretational war" going on in this forum, and that’s maybe good, people learn how to sharpen their arguments and so on. But sometimes I wonder if "dogmatic interpretationalism" is really the thing that is going to take us to the "next level" in QM... I don’t know...

So if one takes that pure epistemic/instrumentalist stance it seems to me one is almost forced to treat QT as "a science of meter readings". That view seems unattractive to me.

I agree 100%. We humans are by nature 'curious creatures', we constantly strive make a coherent picture of the world around us. That’s just how our brains work. To just stare at "meter readings" and say:

– Well guys, this is it! This is the theory of everything, and we won’t get any further! ​

Is depressing...

Furthermore, I think Fredrik has put forward a quite powerful argument; if the measuring apparatus is not real, then how could we verify our theories? (or something like that)

It has the same stench/smell that held back progress in the cognitive sciences (e.g. behaviourism). But then, I could be mistaken?

I don’t think you are, and the "Fredrik argument" should be a quite powerful foundation for this stand.

I have just started to read about http://plato.stanford.edu/entries/structural-realism/#OntStrReaOSR"

But if one treats the wave function as a real "field"-like entity it is very much different than the typical fields we are accustomed to. The wave function evolves in 3N-dimensional configuration space, there's the contextuality/non-separability also and stuff like that make it a very strange kind of "causal" agent.

Exceptionally interesting... new ideas/perspectives that never crossed my crinkly little brain...

If we adopt the ψ-ontology (wavefunctions are states of reality) then the space where wavefunctions "live" must also be ontic, right? And this space is very different from 'our' normal 3D space... probably "unreal" to humans...??

Catch-22

Demystifier started a thread on this topic, but I don’t if there’s any answers (yet):

Configuration space vs physical space
https://www.physicsforums.com/showthread.php?t=285019

If one takes the Bohmian perspective (at least one Bohmian version), how do the 2 (pilot wave and particle) "interact"? It can't be via the usual contact-mechanical stuff we are accustomed to because of the non-locality that is required in any realist interpretation.

http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.0958v1.pdf

Extremely good question! How on Earth does a particle (ontic) interact with a pilot wave if causality and information is forbidden (by SR & No-communication theorem)??

Furthermore, if one wishes to scrap Bohm's dualistic ontology but remain a realist so that the wave function is everything then, there's another problem:

http://www.niu.edu/~vallori/AlloriWfoPaper-Jul19.pdf

Many thank for this link, I must read this paper and the others that you and Fredrik provided:

The interpretation of quantum mechanics: where do we stand?
http://arxiv.org/abs/0904.0958

Einstein, incompleteness, and the epistemic view of quantum states
http://arxiv.org/abs/0706.2661

 

[DevilsAvocado]

Yes, but you're probably thinking that it's been dead since 1963 (± a few) when Bell's theorem was published, but HS proves it using two of Einstein's arguments, from 1927 and 1935.

The reason why that result was worth mentioning is that the PBR theorem is a result of the same type, a theorem that rules out some class of hidden-variable theories.

Ops... I’m sorry Fredrik, my fault.

[I’ve acquire a sort of "brain damage" after years of debating "Bell Disclaimers"... everything goes RED when I see LHV... ]

 

[DevilsAvocado]

This is part of the definition of "ψ-epistemic theory". I think there are two basic ideas involved:

• A probability distribution can be thought of as a representation of our knowledge of the system's properties.
• Something that's completely determined by the properties of the system can be thought of as another property of the system.

If there are no overlapping probability distributions in the theory, then each λ determines exactly one probability distribution. Now the two ideas are in conflict. You can think of the probability distribution as "knowledge", but you can also think of it as a "property". If there's at least one λ that's associated with two probability distributions, then the probability distributions can't all be considered properties of the system. So now we have to consider at least some of them representations of "knowledge.

This motivates the definition that says that only theories of the latter kind (the ones with at least two overlapping probability distributions in the theory) are considered ψ-epistemic. These are the theories that the PBR article apparently has refuted. The first argument in the article is a bit naive, because it assumes specifically that there's overlap between the probability distributions associated with $|0\rangle$ and $|+\rangle$.

Many thanks!

I must digest this and reread everything again + the new papers + the blogs, and then get back on this.

Feels like the 'fog of ignorance' is slowly dissolving...