The quantum state cannot be interpreted statistically?

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  • #1
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Any comments on the Pusey, Barret, Rudolph paper of Nov 11th?

I didn't find any references to it via search here in the forum yet.

http://lanl.arxiv.org/abs/1111.3328"

ABSTRACT: 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.
 
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  • #2
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Two systems are prepared independently. The quantum
state of each, determined by the preparation method, is
either j0i or j+i.
Ah, then they've defined a definite state BEFORE measurement.

Don't get any of the article.
 
  • #3
Ken G
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It looks like a pretty interesting article, but I haven't had time to digest it. Whomever does so first should share their analysis with the rest of us!
 
  • #4
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Oh that's brilliant.. hmm my university's name is cited as well. I am definitely going to read it up thoroughly tomorrow.
Thanks for the share!
 
  • #5
Fredrik
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Normally I wouldn't bother to read an unpublished* article that makes claims that sound absurd to me, but at least it's a short article, and it's a topic I'm very interested in. I'll have a look at it tomorrow.

*) Articles posted at arxiv.org that have also been published in a peer reviewed journal will usually have a "journal reference" after "comments" and "subjects".
 
  • #7
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Any comments on the Pusey, Barret, Rudolph paper of Nov 11th?

I didn't find any references to it via search here in the forum yet.

http://lanl.arxiv.org/abs/1111.3328"

ABSTRACT: 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.
Quantum state represents the state of a quantum system, not of an ensemble.
 
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  • #8
dextercioby
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It's worth a read, indeed. Which interpretation do they use ? Copenhagen ?
 
  • #9
Fredrik
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I have started reading it now. It seems to me that the argument is fundamentally flawed right at the start, so I would like to discuss this before I continue to read. If I'm wrong, I'd like to find out as soon as possible, and if I'm not, I don't want to read the rest. You only have to read the second column on page 1 and about 2/3 of the first column on page 2 to be able to discuss this with me.

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.
Their argument against the second view goes roughly like this:

Suppose that there's a theory that's at least as good as QM, in which a mathematical object λ represents all the properties of the system. Suppose that a system has been subjected to one of two different preparation procedures, that are inequivalent in the sense that they are associated with two different state vectors. Suppose that these state vectors are neither equal nor orthogonal. The preparation procedure will have left the system with some set of properties λ. If view 1 is correct, then the state vector is determined by λ, i.e. if you could know λ, you would also know the state vector. Suppose that view 2 is correct. Then either of the two inequivalent preparation procedures could have given the system the properties represented by λ. Yada-yada-yada. Contradiction!

I haven't tried to understand the yada-yada-yada part yet, because the statement I colored brown seems very wrong to me. This is what I'd like to discuss. Is it correct? Did I misunderstand what they meant? (It's possible. I didn't find their explanation very clear).

Their only explanation of the brown statement is a classical analogy: Consider two different methods to prepare a coin that give the result "heads" different non-zero probabilities. Then observing the result "heads" (only once) will not tell us how the coin was prepared.

This doesn't seem to have anything to do with the brown claim. The state vector determines the probabilities of all possible results. The brown claim says that the properties of the system do not determine those probabilities. You can't support that claim by mentioning that a single measurement result will not tell us all the probabilities.
 
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  • #11
Fredrik
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Inflector posted that link in post #6.
 
  • #12
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I'm concerned over what they write under Figure 1. It sounds like before measurement, the quantum system was in a definite state.
 
  • #13
martinbn
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This doesn't seem to have anything to do with the brown claim. The state vector determines the probabilities of all possible results. The brown claim says that the properties of the system do not determine those probabilities. You can't support that claim by mentioning that a single measurement result will not tell us all the probabilities.
I don't think they say anything about a single measurement. They say that if the properties of the system do determine all probabilities then the QM state does represent the properties of the system.
 
  • #14
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Like most of my great thinking, I thought about this article a bit more in the shower before. I'm going to print it off and read it while I walk to work soon. Then after work I'll come back and share my comments.
 
  • #15
alxm
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if you could know λ, you would also know the state vector
Huh? It appears to say quite the opposite: "If the quantum state is statistical in nature (the second view), then a full specification of λ need not determine the quantum state uniquely."

Then either of the two inequivalent preparation procedures could have given the system the properties represented by λ.
Yes, since λ does not uniquely determine the state vector. If the quantum state is a (non-unique) representation of the statistical probabilities of different sets of λ, then it's assumed that two non-orthogonal states may contain some of the same λ, because it's these 'underlying' properties that determine what you actually measure, whereas the state vector is merely an expression of our lack of knowledge.
 
  • #17
Ken G
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Thank you for that very nice summary:
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.
It seems this is an important step right away. We need to understand what they have in mind by the "properties of a system" versus the "statistical properties of an ensemble." What if the "properties of a system" are nothing but statistical tendencies? In that case, I cannot see how any logical argument or experimental test could ever distinguish #1 and #2. So they must be arguing that if "properties" and "statistical tendencies defined by ensembles" are the same thing, then we should still reject the ensemble interpretation! I'm immediately skeptical they could pull that off without some subtle circularity in their argument, but let's see how they proceed.

Suppose that there's a theory that's at least as good as QM, in which a mathematical object λ represents all the properties of the system. Suppose that a system has been subjected to one of two different preparation procedures, that are inequivalent in the sense that they are associated with two different state vectors. Suppose that these state vectors are neither equal nor orthogonal. The preparation procedure will have left the system with some set of properties λ. If view 1 is correct, then the state vector is determined by λ, i.e. if you could know λ, you would also know the state vector. Suppose that view 2 is correct. Then either of the two inequivalent preparation procedures could have given the system the properties represented by λ. Yada-yada-yada. Contradiction!
Yeah, no way does that brown statement make any sense to me either. It sounds to me like they have assumed that there exists some theory that has the properties they would like quantum mechanics to have-- a one-to-one association between real properties of a single system that statistically determine experimental outcomes on that system and states in the theory. Then they ask, is quantum mechanics that theory? Then they conclude, quantum mechanics must be that theory, assuming such a theory exists and QM is true. That's circular-- if they assume the truth has property A, and they assume quantum mechanics is true, then they can prove that quantum mechanics must have property A-- regardless of what property A actually asserts.

We can expose the circularity with counterexamples.

Counterexample #1: Let's assume that real systems don't actually have "properties", but rather that properties are a mode of analysis used by our intelligence to try and understand them. Then we cannot even get past the first assumption in their logic.

Counterexample #2: Let's assume that systems really do have "properties", but no theory exists in which some mathematical object can represent all the properties of an individual system. That is, the universe is fundamentally property-oriented, but is not fundamentally mathematical, so there is no one-to-one correspondence between any mathematical object and all the "properties" that system possesses. Again, we cannot even get past their first assumption. But let's give them a pass on these two points, because they do say "given only very mild assumptions." Personally, I don't find either of those two assumptions to be "mild", I expect them both to be wrong (as a skeptic), but let's see if there are any other objections if we do buy off on those assumptions.

Counterexample #3: The universe is property-based, and is mathematical, so there does exist some mathematical object that represents all of the properties of a single system. However, the only "properties" that a system has is its statistical tendencies, like the "properties" of the dice in a craps game. Here we run afoul of a third assumption in the authors' logic, that possibility #1 and possibility #2 must be disjoint-- such that for possibility #2 to be true, possibility #1 must be false. In this counterexample, we find a case where both #1 and #2 can be true since they are indistinguishable, leaving the issue up to the preference of the physicist. Indeed, if the universe really were such that the only "properties" that any system has are its statistical tendencies, then any mathematical object that represents those properties is going to look a heck of a lot like an ensemble interpretation, because "statistical tendencies" require an ensemble picture to have meaning-- even if we choose to associate it with properties of a single system. In my view, in such a situation, the entire dispute between possibility #1 and possibility #2 becomes moot, but that does not adjudicate the question in favor of possibility #1.

So where does that leave us? The logic of their argument only holds if we make two assumptions about our reality:
1) systems have properties that determine their statistical behavior (we can't say their complete behavior or we are doing hidden-variables approaches like deBroglie-Bohm)
2) these properties can be represented completely by some mathematical object.
Then it follows immediately that the QM state must be that mathematical object if it makes all the correct predictions about that statistical behavior, since that is the meaning of "represent completely". Framed like this, I'd say their argument suffers from two flaws:
1) its "mild assumptions" are not mild at all, they are at the heart of what we wonder about our reality and its relation to quantum mechanics, and
2) it is circular, as the italicized part shows. If we assume QM is the correct theory, and we make other assumptions that force the correct theory to be a theory of properties of individual systems, then sure enough, QM must be a theory of the properties of individual systems. This tells me nothing of what I want to know about how to interpret quantum mechanics, but can be viewed as a clear way to lay out the assumptions required for quantum mechanics to be interpreted as a complete theory about the properties of individual systems.

However, they go on to talk about experimental ways to distinguish their possibilities #1 and #2, and I haven't read that through yet. So maybe there is something more going on than the way Fredrik and I have framed their argument, this is just my initial reaction.
 
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  • #18
stevendaryl
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The way that I understood what they were saying was in terms of the relationship between the quantum state ψ and a hypothetical physical state λ. The quantum state reflects how the system was prepared, while the physical state represents the physically relevant information about the state of the system. If you perform an experiment, the results of the experiment can only depend on λ.

The two views that the authors were talking about were whether (1) ψ is determined by λ, so different values of ψ necessarily imply different values for λ, or (2) ψ determines the probability distribution on values of λ, but it is not possible to recover ψ from λ (because multiple values of ψ are consistent with the same value of λ). They give coin flips as an example of view 2; there can be multiple ways of flipping a coin, resulting in different probabilities of heads or tails, but knowing that the coin is heads cannot tell you which flipping procedure was used.

On the other hand, if an experiment can tell you which preparation procedure was used (what value of ψ), then that means that λ uniquely determines ψ, which is view (1). An experimental result can only depend on λ, so if tells you anything about ψ, it has to be because λ determines ψ. (They're talking here about single experiments, not performing many experiments and computing statistical results.)
 
  • #19
Ken G
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Right, I think that is a very nice summary (though note the argument you present requires that experiments be able to tell us everything about the preparation, not just "anything" about the preparation). That raises a fourth objection-- we know this isn't true because physics works! Our experiments had better not be able to tell us everything about the preparation, because physics assumes that quite a lot of what went into the preparation was irrelevant to the outcome. So the quantum mechanical state is focusing on certain salient elements of the preparation, it does not represent the entire preparation.

But my three objections still apply when their argument is framed your way:
1) they must assume that the preparation of a system leads to some set of properties, rather than the preparation just being the preparation and that's all,
2) they must assume that if the preparation does lead to properties, then those properties are describable by a mathematical object (a mathematical means of generating the probability distribution on all the kinds of experiments we have used to build quantum mechanics), and
3) even if both of those hold, they must still assume that the properties of an individual system must be somehow distinguishable from the statistical tendencies of an ensemble of such systems. Yet we can imagine that the "properties" are the statistical tendencies. So then the means of preparation (like flipping a coin) does completely specify the probability distribution of getting heads on any individual flip, but the meaning of that probability is an inherently ensemble-based concept. So in this case, we have a moot relationship between the alternatives they attempt to distinguish, which is pretty much what I think of as the relationship between all the quantum mechanics interpretations.

I think much of my objection boils down to this: I reject their fundamental separation of what is a "preparation" and what is a "property" of a system. I think that distinction is fundamentally artificial-- both of what we call preparation, and what we call properties, represent significant idealizations of the actual reality, so little can be inferred about the actual relationship of quantum mechanics to reality if we take those idealizations too seriously. I think the whole reason we need to struggle to interpret quantum mechanics is we tend to want to take our idealizations too seriously, and imagine that what we are doing is closer to the reality than we have any right to expect-- we are beguiled by the remarkable precision of many of our predictions. Every scientific generation has fallen for that one.
 
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  • #20
Fredrik
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(I wrote this before reading anything after post #16).

I don't think they say anything about a single measurement. They say that if the properties of the system do determine all probabilities then the QM state does represent the properties of the system.
Yes, one of their statements is equivalent to that. However, this is not something they prove. They seem to consider it so obvious that they can let the entire argument rest on the truth of this claim. I believe that the claim is false. The burden of proof is on them, not me.

Huh? It appears to say quite the opposite: "If the quantum state is statistical in nature (the second view), then a full specification of λ need not determine the quantum state uniquely."
The words you quoted were part of a statement about the first view, not the second.

Yes, since λ does not uniquely determine the state vector. If the quantum state is a (non-unique) representation of the statistical probabilities of different sets of λ, then it's assumed that two non-orthogonal states may contain some of the same λ, because it's these 'underlying' properties that determine what you actually measure, whereas the state vector is merely an expression of our lack of knowledge.
In the first sentence, you're expressing the brown statement in different words. I'm not sure what you're arguing for after that, but it doesn't seem to explain how the brown statement is implied by the statistical view.

Here's an even shorter summary of their argument: If properties do not determine probabilities, then we're screwed. Therefore, properties determine probabilities. Therefore the statistical view is false.

My objection is against the last "therefore" in this summary. I would say that what they're proving has nothing at all to do with the statistical view.
 
  • #21
Fredrik
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Quantum state represents the state of a quantum system, not of an ensemble.
This is wrong, and it's also a very different claim from the one made by this article. A state vector is certainly an accurate representation of the properties of an ensemble of identically prepared systems. It's conceivable that it's also an accurate representation of the properties of a single system. The article claims to be proving that it's wrong to say that it's not a representation of the properties of a single system.

Maybe it is time to cite again why the so-called «statistical interpretation of QM» is not QM but another thing
This is even more wrong. Also, if you want to discuss these things, please keep them to the other thread where you brought this up.
 
  • #22
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Just to add some other links/ideas to this debate. I'm not sure what all this means but here's a few interesting quotes including one from another physicist (Valentini):

“I don't like to sound hyperbolic, but I think the word 'seismic' is likely to apply to this paper,” says Antony Valentini, a theoretical physicist specializing in quantum foundations at Clemson University in South Carolina.

Valentini believes that this result may be the most important general theorem relating to the foundations of quantum mechanics since Bell’s theorem, the 1964 result in which Northern Irish physicist John Stewart Bell proved that if quantum mechanics describes real entities, it has to include mysterious “action at a distance” ...

The Copenhagen interpretation later fell out of popularity, but the idea that the wavefunction reflects what we can know about the world, rather than physical reality, has come back into vogue in the past 15 years with the rise of quantum information theory, Valentini says.
Rudolph and his colleagues may put a stop to that trend. Their theorem effectively says that individual quantum systems must “know” exactly what state they have been prepared in, or the results of measurements on them would lead to results at odds with quantum mechanics. They declined to comment while their preprint is undergoing the journal-submission process, but say in their paper that their finding is similar to the notion that an individual coin being flipped in a biased way — for example, so that it comes up 'heads' six out of ten times — has the intrinsic, physical property of being biased, in contrast to the idea that the bias is simply a statistical property of many coin-flip outcomes.
http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392
 
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  • #23
Fredrik
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Yeah, no way does that brown statement make any sense to me either. It sounds to me like they have assumed that there exists some theory that has the properties they would like quantum mechanics to have-- a one-to-one association between real properties of a single system that statistically determine experimental outcomes on that system and states in the theory.
I don't really have a problem with that. If I thought the rest of the argument was sound, I would be pointing out that it's not obvious that such a theory exists, but I would still find their result interesting.

Then they ask, is quantum mechanics that theory?
Not quite. They're saying "maybe it is, maybe it isn't". If it is, the state vector will be equal to λ (if the first view of QM is correct), and if it's not, it will still be completely determined by λ. This doesn't bother me. What bothers me is that they're saying that if the second view of QM (the statistical one) is correct, i.e. if a state vector doesn't accurately represent the properties of a single system, then the state vector isn't determined by λ.
 
  • #24
Ken G
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To follow up bohm2, this quote is also from that Nature blurb:
Robert Spekkens, a physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, who has favoured a statistical interpretation of the wavefunction, says that Pusey's theorem is correct and a “fantastic” result, but that he disagrees about what conclusion should be drawn from it. He favours an interpretation in which all quantum states, including non-entangled ones, are related after all.

Spekkens adds that he does expect the theorem to have broader consequences for physics, as have Bell’s and other fundamental theorems. No one foresaw in 1964 that Bell’s theorem would sow the seeds for quantum information theory and quantum cryptography — both of which rely on phenomena that aren’t possible in classical physics. Spekkens thinks this theorem may ultimately have a similar impact. “It’s very important and beautiful in its simplicity,” he says.
So I should not be too quick to object, this clearly calls for a careful study. A lot of people think it's a pretty important theorem, I'm just wondering if it isn't subtly assuming what it is claiming to show.
 
  • #25
Fredrik
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Just to add some other links/ideas to this debate. I'm not sure what all this means but here's a few interesting quotes including one from another physicist (Valentini):
This is the third time someone has linked to that article in this thread.
 
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