The quantum state cannot be interpreted statistically?

inflector
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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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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.
 
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!
 
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!
 
Normally I wouldn't bother to read an unpublished* article that makes claims that sound absurd to me, but at least it's a short article, and it's a topic I'm very interested in.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".
 
inflector said:
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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It's worth a read, indeed. Which interpretation do they use ? Copenhagen ?
 
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.[/color] 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
Inflector posted that link in post #6.
 
  • #12
I'm concerned over what they write under Figure 1. It sounds like before measurement, the quantum system was in a definite state.
 
  • #13
Fredrik said:
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
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
Fredrik said:
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
Thank you for that very nice summary:
Fredrik said:
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.[/color] 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
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
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
(I wrote this before reading anything after post #16).

martinbn said:
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.

alxm said:
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.

alxm said:
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
juanrga said:
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.

juanrga said:
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
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
Ken G said:
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.

Ken G said:
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
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
bohm2 said:
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.
 
  • #27
Terry (one of the authors) occasionally hangs out around here, although I haven't seen him lately. Looks like he has been very busy!

This is a pretty sophisticated argument, kinda reminds me of GHZ. Will need some time to look at this.
 
  • #28
Fredrik said:
...

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.

I am a definitely a proponent of the first view, that the wave function essentially corresponds to an element of reality. So I am definitely interested in their reasoning, and understanding whether it will stand. Rudolph hangs with a pretty strong crew, so I take the paper seriously.
 
  • #29
Ken G said:
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.
I think it's just proving something that has nothing to do with the statistical view. The argument relies on a statement that they seem to consider obviously true. I consider it almost obviously false. It's certainly not something that I can accept as true just like that.

I strongly object to the word "theorem" in the Nature article. This doesn't even look like a theorem to me. The main reason is that the "proof" assumes that there's an accurate theory in which there's an exact representation of all the properties of the system, without defining what that means. A theorem is something mathematical. Mathematics is based on set theory. So terms used in a theorem must have set-theoretic definitions.

You may be thinking that I meant that they should have defined it, but that's not where I was going with that. I don't think there is a meaningful definition. So they should leave it undefined, and call the main claim something like an "informal argument" rather than a theorem followed by a proof. Of course, even an informal argument is worthless if it relies on a crazy sounding completely unsupported claim.
 
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  • #30
DrChinese said:
I am a definitely a proponent of the first view, that the wave function essentially corresponds to an element of reality. So I am definitely interested in their reasoning, and understanding whether it will stand. Rudolph hangs with a pretty strong crew, so I take the paper seriously.
I think the first view is plausible, but I also think that it makes something "weird" unavoidable, like many worlds, or quantum logic replacing normal logic. I definitely prefer the second view, not only because of the "weirdness", but also because QM looks so much like a toy theory that someone invented just to show that there exists a theory where even the pure states are associated with non-trivial probability measures.
 
  • #31
This is an aside (and way too early) but if the "theorem" of that paper is correct would that imply that one is left with either the Everett or de Broglie/Bohmian versions?
 
  • #32
Fredrik said:
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.
The key issue here is whether we should regard quantum mechanics as incomplete compared to a physical theory that would be possible (Einstein's view), or simply incomplete compared to our naive preconceptions about what a physical theory ought to be (i.e., we should not expect to completely represent the properties of a system with a mathematical object, either because the properties can't be represented that way, or don't exist in the first place). The article appears to consider it a "mild assumption" to take the former view, so does so, and shows that the ensemble view is inconsistent with that view. But I see nothing inconsistent in the ensemble view with the latter stance, and to me, the key question is not ensemble vs. real state, it is that first issue. So if we must take a stance on the first issue to follow their proof, then we have already ducked the most important question.
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.
That is OK within the assumptions they are making to give their argument. They are saying that if there are "properties" of individual systems, then either knowledge of the properties suffices to specify the state vector, or it doesn't. If it does, then each state vector has a correspondence to its own unique possible collection of properties-- i.e., if there are properties of individual systems, then the state vector limits the possibilities for those properties, so it does convey information about individual systems. If knowledge of the properties doesn't uniquely specify the quantum state, then it must be possible for the same properties to be associated with two different state vectors. That's what they use to get a contradiction. I think they are saying that if two state vectors connect with all different properties, those vectors have to be orthogonal, but by assumption they have two states that are not orthogonal, so they must have properties that appear with both state vectors-- unless the state vectors are themselves properties.

But if I was a proponent of the ensemble interpretation, I would simply claim that the whole reason I need an ensemble interpretation is that individual systems don't have properties like that! The "true state" of a system is not just a collection of eigenvalues for experiments we can think to do on it. (Whereas if I thought they did have properties like that, I'd call them hidden variables, and take the deBroglie-Bohm approach rather than the ensemble interpretation anyway.)
 
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  • #33
Ken, please check your PM , maybe something of an interest to you, related to this material.
 
  • #34
Ken G said:
The key issue here is...
I'm not sure I understood what you consider the key issue. Is it the existence (vs. non-existence) of that theory in which a mathematical object λ represents all the properties of the system? That's an interesting issue, but (as you know) it's not what the article is about.

Ken G said:
If knowledge of the properties doesn't uniquely specify the quantum state, then it must be possible for the same properties to be associated with two different state vectors. That's what they use to get a contradiction.
Right. That's the part of the argument that I summarized as "If properties do not determine probabilities, then we're screwed. Therefore, properties determine probabilities." I have no problem with that part of it. In fact, I consider "properties do not determine probabilities" to be an absurd statement on its own. They didn't even have to derive a contradiction from it. (If λ doesn't determine all the probabilities (and then some), then why would anyone call it "all the properties of the system"). To me, their argument is very much like proving that 1≠1 implies that 2≠2, and then concluding that "Sons of Anarchy" isn't the best thing on TV right now.

I have always been thinking that the statistical view (ensemble interpretation) and "properties determine probabilities" are both true. It has never even occurred to me to consider that a complete specification of all the system's properties would be insufficient to determine the probabilities. Where did they get the idea that the statistical view implies that properties are insufficient to determine probabilities? I don't think it implies anything like that. What it says is that a complete specification of the preparation procedure determines the probabilities, but is insufficient to determine the properties (if it makes sense to talk about properties at all).
 
  • #35
Fredrik said:
I'm not sure I understood what you consider the key issue. Is it the existence (vs. non-existence) of that theory in which a mathematical object λ represents all the properties of the system? That's an interesting issue, but (as you know) it's not what the article is about.


Right. That's the part of the argument that I summarized as "If properties do not determine probabilities, then we're screwed. Therefore, properties determine probabilities." I have no problem with that part of it. In fact, I consider "properties do not determine probabilities" to be an absurd statement on its own. They didn't even have to derive a contradiction from it. (If λ doesn't determine all the probabilities (and then some), then why would anyone call it "all the properties of the system"). To me, their argument is very much like proving that 1≠1 implies that 2≠2, and then concluding that "Sons of Anarchy" isn't the best thing on TV right now.

I have always been thinking that the statistical view (ensemble interpretation) and "properties determine probabilities" are both true. It has never even occurred to me to consider that a complete specification of all the system's properties would be insufficient to determine the probabilities. Where did they get the idea that the statistical view implies that properties are insufficient to determine probabilities? I don't think it implies anything like that. What it says is that a complete specification of the preparation procedure determines the probabilities, but is insufficient to determine the properties (if it makes sense to talk about properties at all).

I have a problem with ensemble interpretation, it is as if the equations know how we are going to study QM i.e. by doing experiments on prepared systems.
 
  • #36
OK, new summary. Simplified.
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 view 2 above is the correct one. Then λ doesn't determine the probabilities of all possible results of measurements.[/color] Yada-yada-yada. Contradiction! Therefore view 2 is false.​
I say that
  • The entire article rests on the validity on the statement in brown, which says that view 2 somehow implies that "all the properties" are insufficient to determine the probabilities. (If that's true, then why would anyone call them "all the properties"?)
  • The brown statement is a non sequitur. (A conclusion that doesn't follow from the premise).
  • The only argument the article offers in support of the brown claim, doesn't support the brown claim at all.
Am I wrong about something?
 
  • #37
Fredrik said:
OK, new summary. Simplified.
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 view 2 above is the correct one. Then λ doesn't determine the probabilities of all possible results of measurements.[/color] Yada-yada-yada. Contradiction! Therefore view 2 is false.​
I say that
  • The entire article rests on the validity on the statement in brown, which says that view 2 somehow implies that "all the properties" are insufficient to determine the probabilities. (If that's true, then why would anyone call them "all the properties"?)
  • The brown statement is a non sequitur. (A conclusion that doesn't follow from the premise).
  • The only argument the article offers in support of the brown claim, doesn't support the brown claim at all.
Am I wrong about something?

I am probably missing something, but isn't the statement in brown what the difference between the two schools of thought is?
 
  • #38
martinbn said:
I am probably missing something, but isn't the statement in brown what the difference between the two schools of thought is?
That's what the authors of the article are saying. To me it seems like a completely unrelated assumption. Maybe I'm missing something.

I would say that the difference is that the second school of thought asserts that a complete specification of the preparation procedure determines the probabilities, but is insufficient to determine the properties (if it makes sense to talk about properties at all).
 
  • #39
They are comparing two different schools of thought:

A state vector represents the properties of the system.
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.

Isn't the bolded part the problem or am I missing something?
 
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  • #40
so they are going for the realist position, is that correct ?
 
  • #41
bohm2 said:
Isn't the bolded part the difference or am I missing something?
That's definitely the difference. :smile: So no, you're not missing anything. But since the article claims that this difference changes the truth value of the statement
"The properties determine the probabilities."​
from true to false, the story doesn't end with that observation.
 
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  • #42
Fredrik said:
Am I wrong about something?

I don’t know because I haven’t read the full paper yet (isn’t this just typical :smile:), but is this really about ensembles (and the Ensemble interpretation)? Isn’t it about "state-as-probability" vs. "state-as-physical"?

I’ve cheated, and consumed the 'condensed version' by David Wallace (thanks inflector) and it looks convincing to me:
http://blogs.discovermagazine.com/c...lace-on-the-physicality-of-the-quantum-state/

Why the quantum state isn’t (straightforwardly) probabilistic
...
Consider, for instance, a very simple interference experiment. We split a laser beam into two beams (Beam 1 and Beam 2, say) with a half-silvered mirror. We bring the beams back together at another such mirror and allow them to interfere. The resultant light ends up being split between (say) Output Path A and Output Path B, and we see how much light ends up at each. It’s well known that we can tune the two beams to get any result we like – all the light at A, all of it at B, or anything in between. It’s also well known that if we block one of the beams, we always get the same result – half the light at A, half the light at B. And finally, it’s well known that these results persist even if we turn the laser so far down that only one photon passes through at a time.

According to quantum mechanics, we should represent the state of each photon, as it passes through the system, as a superposition of “photon in Beam 1″ and “Photon in Beam 2″. According to the “state as physical” view, this is just a strange kind of non-local state a photon is. But on the “state as probability” view, it seems to be shorthand for “the photon is either in beam 1 or beam 2, with equal probability of each”. And that can’t be correct. For if the photon is in beam 1 (and so, according to quantum physics, described by a non-superposition state, or at least not by a superposition of beam states) we know we get result A half the time, result B half the time. And if the photon is in beam 2, we also know that we get result A half the time, result B half the time. So whichever beam it’s in, we should get result A half the time and result B half the time. And of course, we don’t. So, just by elementary reasoning – I haven’t even had to talk about probabilities – we seem to rule out the “state-as-probability” rule.

Indeed, we seem to be able to see, pretty directly, that something goes down each beam. If I insert an appropriate phase factor into one of the beams – either one of the beams – I can change things from “every photon ends up at A” to “every photon ends up at B”. In other words, things happening to either beam affect physical outcomes. It’s hard at best to see how to make sense of this unless both beams are being probed by physical “stuff” on every run of the experiment. That seems pretty definitively to support the idea that the superposition is somehow physical.
 
  • #43
DevilsAvocado said:
I don’t know because I haven’t read the full paper yet (isn’t this just typical :smile:), but is this really about ensembles (and the Ensemble interpretation)? Isn’t it about "state-as-probability" vs. "state-as-physical"?
That's the same thing.

"state-as-probability" = "ensemble interpretation" = "statistical interpretation" = "Copenhagen interpretation" (although some people will insist that the CI belongs on the "state-as-physical" side).

The stuff I'm talking about is covered on the first one and a half pages, so you don't have to read the whole thing. I haven't, and I'm not going to unless someone can convince me that I'm wrong.

Wallace said:
But on the “state as probability” view, it seems to be shorthand for “the photon is either in beam 1 or beam 2, with equal probability of each”.
Maybe it seems that way, but this is not implied by my definition of the second "school of thought" above.

This is however a point that different statistical/ensemble interpretations disagree about. Ballentine's 1970 article "The statistical interpretation of quantum mechanics" explicitly made the assumption that all particles have well-defined positions, even when their wavefunctions are spread out. That assumption is notably absent from Ballentine's recent textbook, so maybe even he has abandoned that view.
 
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  • #44
I'll try again..
Fredrik said:
The entire article rests on the validity on the statement in brown, which says that view 2 somehow implies that "all the properties" are insufficient to determine the probabilities. (If that's true, then why would anyone call them "all the properties"?)

The way I read it, what they mean by "all the properties" is some set of hidden variables or similar that are sufficient to determine the outcome of any measurement. The "real" state is represented by lambda, and the quantum state is just a classical statistical distribution over the various "lambda states". It's not a classical analogy, it is classical. Although whatever goes into putting the system into a particular lambda state is not necessarily deterministic or local or whatever; only point is that QM tells us that certain processes will allow us to prepare states with certain distributions.

So knowing lambda doesn't tell you how you got there. A coin's 'real' states could be 'heads' or 'tails' but measuring 'heads' doesn't tell you if you got it there by putting it in heads (process 1) or a coin-toss (process 2). All you know from QM is that process 1 will always cause you to measure 'heads' and process 2 results in either 'heads' or 'tails' with some associated probabilities.

By extension the main result here is that for two identical systems prepared in isolation from each other, the result predicted by quantum mechanics for a joint measurement cannot be enforced merely by knowing lambda1 and lambda2, since it doesn't tell you how you got it there, which has importance for what you measure.

But if lambda is actually the wave-function (or can tell you it), then obviously there's no problem.

I didn't really think it was that complicated? Maybe I'm the one under-thinking it.
 
  • #45
Fredrik said:
That's the same thing.

"state-as-probability" = "ensemble interpretation" = "statistical interpretation" = "Copenhagen interpretation" (although some people will insist that the CI belongs on the "state-as-physical" side).

The stuff I'm talking about is covered on the first one and a half pages, so you don't have to read the whole thing. I haven't, and I'm not going to unless someone can convince me that I'm wrong.

I’ll do that tomorrow. It’s 3:32 AM here so my brain is in an upside-down-superposition...

Fredrik said:
Maybe it seems that way, but this is not implied by my definition of the second "school of thought" above.

This is however a point that different statistical/ensemble interpretations disagree about. Ballentine's 1970 article "The statistical interpretation of quantum mechanics" explicitly made the assumption that all particles have well-defined positions, even when their wavefunctions are spread out. That assumption is notably absent from Ballentine's recent textbook, so maybe even he has abandoned that view.

Okay thanks. I have to reconnect tomorrow, I’m really... :zzz:
 
  • #46
What I gathered from reading the article at work:
1. they're assigning a definite state to the system after preparation
2. QM would then NOT be appropriate for describing the system - it is not in a pure state.
3. and the first experiment they show us gives a prediction different to QM, yet they're using it as refuting the statistical interpretation of QM - but I don't get that. They're practically saying QM is wrong.
4. on page 4, they use the conclusion as an assumption (a premise) in their argument.
 
  • #47
Fredrik said:
I'm not sure I understood what you consider the key issue. Is it the existence (vs. non-existence) of that theory in which a mathematical object λ represents all the properties of the system? That's an interesting issue, but (as you know) it's not what the article is about.
Right, I'm saying that to me, that's the real issue here. So I don't find the conclusions in the article to be particularly important, because they require making assumptions that I doubt are reliable. It seems to me that people who make those assumptions have already chosen a specific approach to interpreting quantum mechanics, so whether or not the ensemble interpretation is consistent with that specific approach is only interesting to people inclined to choose both the ensemble interpretation and that specific approach (and I don't count myself in either of those groups). But we can still analyze whether the paper reaches valid conclusions that people in both those groups should worry about.
Right. That's the part of the argument that I summarized as "If properties do not determine probabilities, then we're screwed."
But we aren't screwed in that case, we're just fine. If someone writes an article tomorrow that proves that quantum mechanics is not consistent with the attitude that properties determine probabilities, does quantum mechanics suddenly not work to predict our experiments? Nothing that we use quantum mechanics for requires that properties determine probabilities, instead what we need is for state vectors to determine probabilities, because that's how quantum mechanics works. Properties are completely irrelevant to doing physics, they are purely philosophical, and somewhat naive philosophy at that. That's my primary objection-- the fixation on the importance of "properties" is a very specific interpretation choice, but physics only requires that "properties" be a useful organizational principle, it never requires that we take this concept seriously, and certainly doesn't need us to make any mathematical proofs based on the notion. I doubt that systems actually have properties at all, that's just how we like to think about them.

The whole issue reminds me of Hume's lucid critique of taking the cause and effect relationship too seriously. He makes the point that even young children quickly develop a useful concept of cause and effect, but even the greatest philosophers cannot demonstrate any logical relationship there that you could use to prove anything, it is nothing but a practical correlation that we use to make actionable predictions. I think the concept of a "property" is just exactly like that too. So if someone hands me a physics proof that starts with "assume that the cause and effect relationship is a deterministic connection whereby some element of the cause leads, not by experience but by logical necessity, to some element of the effect", and goes on to say that interpretation X of theory Y can't be right, it is no kind of knock on interpretation X. Indeed, it makes me see interpretation X in a better light, that it failed to pass a test that it probably should fail!

In fact, I consider "properties do not determine probabilities" to be an absurd statement on its own.
It's not absurd if the whole concept of properties is already viewed as absurd. I agree it would be absurd to believe in properties that do not determine probabilities, for what would be the point in believing in properties like that, but the rational alternative is to view the whole "property" concept as an effective notion we create to make progress, like all the other effective notions we make in physics and should certainly have learned by now not to take so seriously as to prove things based on them as axioms. Or put differently, when we use them as assumptions and prove things, we should do it from the point of view of showing why we shouldn't have assumed that thing in the first place-- it forces us to imagine we are dictating to nature.
I have always been thinking that the statistical view (ensemble interpretation) and "properties determine probabilities" are both true. It has never even occurred to me to consider that a complete specification of all the system's properties would be insufficient to determine the probabilities. Where did they get the idea that the statistical view implies that properties are insufficient to determine probabilities?
This is an important question, and demands closer scrutiny. They seem to be saying they have proven that your position is internally inconsistent-- you cannot maintain both that a state vector is only a claim on the properties of an ensemble, not a claim on the properties of an individual system, and that properties of individual systems determine the probabilities for that system. I'm not sure exactly what they think the statistical interpretation is, but the one you expound sounds like a standard version, so they must feel that they have proven it to be internally inconsistent.

What it says is that a complete specification of the preparation procedure determines the probabilities, but is insufficient to determine the properties (if it makes sense to talk about properties at all).
That's my point too, because quantum mechanics (and physics) only involves a connection between a preparation procedure and probabilities. That's it, that's all the physics that's in there. There aren't any "properties" in the physics, that's some kind of added philosophical baggage that can be used to prove things but doesn't convince me it belongs there at all, so why should we care what can be proven from it?
 
  • #48
Ken G said:
That's my point too, because quantum mechanics (and physics) only involves a connection between a preparation procedure and probabilities. That's it, that's all the physics that's in there. There aren't any "properties" in the physics, that's some kind of added philosophical baggage that can be used to prove things but doesn't convince me it belongs there at all, so why should we care what can be proven from it?

I finally read the paper and I'm still lost. It seems to me that in this quote below the authors are conceding that if one takes that perspective you are suggesting (e.g. Fuchian) then their conclusions don't hold. If that's true then what does their theory suggest?

For these reasons and others, many will continue to hold that the quantum state is not a real object. We have shown that this is only possible if one or more of the assumptions above is dropped. More radical approaches (e.g. Fuchs) are careful to avoid associating quantum systems with any physical properties at all.


Their assumptions:

1. If a quantum system is prepared in isolation from the rest of the universe, such that quantum theory assigns a pure state, then after preparation, the system has a well defined set of physical properties.

2. It is possible to prepare multiple systems such that their physical properties are uncorrelated.

3. Measuring devices respond solely to the physical properties of the systems they measure.
 
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  • #49
bohm2 said:
Their assumptions:

1. If a quantum system is prepared in isolation from the rest of the universe, such that quantum theory assigns a pure state, then after preparation, the system has a well defined set of physical properties.

I am assuming that by a 'well defined set of physical properties' that the system is in a definite state? That is the impression I'm getting from what they wrote under Figure 1, that the system is in either |0> or |1>.

You CANNOT use QM to predict the outcomes, clearly. QM doesn't deal with definite states. In the first experiment, they produce results different to what QM predicts.

And just looking at some of what they wrote, where do they get |-> from?
 
  • #50
I have to go to bed, so my answers to the stuff aimed at me will have to wait until tomorrow. Alxm's post gave me something to think about. It looks like I have misunderstood at least one important thing, so I will have to think everything through again.

StevieTNZ said:
I am assuming that by a 'well defined set of physical properties' that the system is in a definite state? That is the impression I'm getting from what they wrote under Figure 1, that the system is in either |0> or |1>.
No, either |0> or |+>. The latter is a superposition of |0> and |1>. |0> and |1> are the eigenstates of some operator, like a spin component operator. But they have one preparation device that always leaves the system in state |0> and another that always leaves the system in state |+>.
 

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