The quantum state cannot be interpreted statistically?

[Maui]

Actually it's a standard part of logic 101. The same logic that states that validity and truth are very different things. Theoretical constructs are predicated on validity, not truth. That's why they remain theories no matter how solidly the predicted consequences have been proven factual. Ken merely contextualized this logical fact in an unusual way.

The point to take from this is that we can theorize, opine, and ponder about how nature really is all we want, but at the end of the day all we have, that we can know, is the validity (not truth) of the matter as it has been empirically demonstrated. Too many people people, inside and outside of science, place too much truth value in the validity condition. The validity of a claim does not make it true.

What you just said is not only valid but quite true . Very pleasant thread to read and follow so far; love the depth of analysis and self-critique

 

[qsa]

what is the criteria for TRUTH then.

 

[Maui]

what is the criteria for TRUTH then.

This is slightly offtopic so i'll be very brief - Death.

Only death is absolutely certain(in the sense of cessastion of existence as we know it - billions of years of history, trillions of life forms, not a single exception). Please ask similar questions in the philosophy forum to keep this thread on topic. Thank you

 

[DevilsAvocado]

Can you explain where contextuality enters the picture in my version of their argument? (Post #155). I'm not saying that you're wrong. I just barely know what contextuality means, and I haven't really thought about whether you're right or wrong.

It’s absolutely safest if DM answers this question, but if you want to be 'prepared' I can give you a little something to 'chew on' in the meantime. It’s about HVT:

Value definiteness (VD) – All observables defined for a QM system have definite values at all times.​

And a second assumption of:

Non-contextuality (NC) – If a QM system possesses a property, then it does so independently of any measurement context (i.e. independently of how that value is eventually measured).​

The Kochen–Specker (KS) theorem establishes a contradiction between VD + NC and QM. Therefore, QM logically forces us to give up either VD or NC.

According to KS, it’s NC that has to be excluded in any HVT compatible with QM.

And I make the assumption that ψ-epistemic with an underlying ontic state is forced to 'deal' with a contextual HVT...


P.S. This paper could maybe be useful:

Hidden Variables, Non Contextuality and Einstein-Locality in Quantum Mechanics
http://arxiv.org/abs/quant-ph/0507182

 

[Fredrik]

I don't know what this means. I understand the distinction between ψ-ontic and ψ-epistemic ontological models for QM, but you seem to be taking the terms "ontic" and "epistemic" outside of the framework of ontological models for QM.

I would argue it is not I who is doing that-- the PBR proof does that. It asserts, as a central part of the logic of the theorem, that we must imagine there are properties that determine the outcomes, independently from the system preparation.

I really can't tell what you're thinking here. You seem to be saying that PBR are taking the terms "ontic" and "epistemic" outside of the framework of ontological models for QM, by talking about ontological models for QM. I'm sure you see the problem with that claim. They are certainly not going outside of the framework of ontological models for QM in the theorem or the proof.

We don't have to "imagine there are properties". We don't have to assume anything about what an ontic variable in an ontological model for QM really is. It's convenient to say that they represent all the properties of the system, but this doesn't actually mean anything. It's just a suggestion about how to think about it.

If we define "theory of physics" as I did in my previous post, the theorem says that state vectors in QM do not correspond bijectively to epistemic states in any theory of physics such that a) it makes the same predictions as QM, and b) some of the probability distributions are overlapping.

The crucial picture, associated with "realism", is that the preparation influences the properties, which in turn generate the outcomes. But if the preparation influences the properties, how are the properties not themselves just outcomes?

Because an outcome is something you can read off a measuring device.

What if a given preparation has a probability of creating a certain property, and another probability of creating a different property? They assume a very particular (and unlikely) relationship between the preparation and the properties, and then investigate two possible relationships between the preparation and the properties.

I don't understand why you think there's something weird here. Later in this post, you agreed that a theory of physics needs a rule that identifies preparations with probability measures on the set whose members determine the probabilities of measurement results. Now you seem to be dismissing that very thing, and it's very hard to tell why.

Thus, if I adopt the stance that "there are no properties, there is only preparations and outcomes", or equivalently, that whay they call properties is what I call outcomes, then their entire argument is about nothing-- yet I still retain all of quantum mechanics, every scrap.

I have really tried to make sense of this. Their argument is clearly not about nothing, and why would anyone want to call equivalence classes of preparations "outcomes" instead of "states"?

 

[Ken G]

The point to take from this is that we can theorize, opine, and ponder about how nature really is all we want, but at the end of the day all we have, that we can know, is the validity (not truth) of the matter as it has been empirically demonstrated.

That is very succinctly put, and very well. As you put it above, this is how one "rinses off the magic." Many people think a physics theory wouldn't survive such a rinsing, but the fact is, what the theory is used for, and tested with, survive just fine-- it merely ends up cleaner for it. It is all about helping us avoid pretending to know what we do not know. We don't always need this kind of caution-- very often, we can enter into such a pretense and it merely serves to streamline our language and allow greater parsimony in the process. But used to abandon, like when we don't even notice we are doing it, it just ends up slowing down progress because we don't recognize an opportunity if we aren't looking for one. A classical example of this (literally) is wave and particle mechanics-- it took a very long time to notice the need for the unification provided by wave/particle duality, because people were too willing to believe that waves and particles had different "hidden properties." They lived happily in a world of coins with "heads" on them, and coins with "tails" on them, and never realized they were all the same coins because they were thinking ontologically instead of epistemologically.

 

[my_wan]

So the two definitions correspond to:
Ontic if theory λ uniquely determines an outcome.
Epistemic if theory λ allows for multiple outcomes.

These are reasonable definitions IMO, but they're not consistent with the ones used by HS.

The only difference between these definitions and the ones provided by the HS article, which I gave just above where that quote was pulled from for comparative reasons, is the fact that I related the consistency condition HS specified to observable outcomes rather than the quantum state itself. The reason is quiet clear, it is in fact the observable outcomes provided by the quantum state that is used to empirically justify the theorem, not the quantum state itself. So when HS said:
ψ-ontic - Every complete physical or ontic state in the theory is consistent with only one pure quantum state.
The consistency condition specified is predicated in practice on the observed outcome $P(k|\lambda,\lambda,X)=0$. The zero probability is a uniquely specifies that observable for all cases. Hence, when I say:
Ontic if theory λ uniquely determines an outcome.
It is equivalent to:
Ontic if the complete physical or ontic state is consistent with only one pure quantum state.
Here the empirical outcomes, which was implicit in the HS version and explicitly given by PBR as $P(k|\lambda,\lambda,X)=0$, was merely made explicit in the definition itself. Otherwise the definitions are identical. If not then PBR can't claim to be using the definition given by PB.

So where would you say the consistency fails?

An ontological model for QM assigns a probability P(k|λ,M) to the result k, given an ontic state λ and a measurement procedure M. This probability isn't required to be 0 or 1. An ontological model for QM is ψ-ontic if an ontic state uniquely determines the state vector. Since a state vector doesn't uniquely determine an outcome, there's no reason to think that a λ from a ψ-ontic ontological model for QM determines a unique outcome.

You are mixing ontic and epistemic model conditions in a manner that makes it difficult to intuit the context in which you mean it. However, I did give an example of how a purely epistemic construct can give unique outcomes. A probabilistic model of classical thermodynamics is an epistemic construct. There is a distinction between characterizing a model of something and establishing certain characterizations of the thing it models. We can never know the thing it models in the same sense that we can know the empirical consequences.

Let's try this for an explanation of what the PBR theorem implies (removing the ontic and epistemic stuff):
What the PBR theorem seems to indicate is that in some sense the probability P(k|λ,M) more closely matches the actual state in certain empirical respects than the probabilistic language used seems to imply. In classical probability we speak of state A XOR B in probabilistic terms. Hence a mixed probability is not a mixture of state A and B classically, even when we mix them in the modeling. Many, what I consider naive realist, thought that QM probabilities could be completely interpreted in a similar manner. That being that given sufficient knowledge that the observables probabilistically defined by the state vector could be decomposed into either/or, A XOR B, heads XOR tails. What PBR seems to tell us is that in some respects A and B really are a mixture of properties. That classical probabilities entail A XOR B while quantum probabilities really can entail A OR (inclusive) B. Empirically this is predicated on the fact that certain mixes of A and B can sum into observable outcomes with non-random certainty that is defined by neither A XOR B alone. Hence the probability is not a probability per se (statistical interpretation), it is ostensibly the actual state in at least some empirical respects.

I personally find that explanation, free of all the ontological, epistemic, and other analogies, far better than any I have previously provided. If this is as clear as I think it should be perhaps we should discuss it in these terms rather than the ontological verses epistemic terms.

 

[bohm2]

I don't understand the question. Isn't what what PBR is supposed to do? Why would we want to attack Einstein's arguments, and what part are you talking about?


I don't understand what you're saying. What do you mean by "address the arguments"? Do you mean prove them wrong?


The article he refers to (section 4, starting on p. 10...read at least until eq. (28)), says that Einstein's 1927 argument shows that an ontological model for QM can't be both (ψ-)complete and local. So we don't need PBR for that. PBR argue against ψ-epistemic ontological models.

I read what I wrote and I don't understand what I was trying to say or thinking Maybe my ADD? I think I got to change my medication. Sorry about that.

 

[Ken G]

They are certainly not going outside of the framework of ontological models for QM in the theorem or the proof.

I don't see them as going outside the framework of ontological models, I see their position as largely circular-- they are embracing ontological models in their assumptions, then proving something about how ontological quantum mechanics needs to be. They have married ontology, in their assumptions right from the start, so we should not be surprised when they wake up in bed with it at the end of the proof! Indeed I would say they have married the most basic type of ontology, the ontology of individual systems with no "contextual", as per Demystifer, and no "relational", as per my_wan, elements to boot. It is only for those who would go along with that narrow concept of what realism requires that would even find relevance in their proof.

We don't have to "imagine there are properties".

Yet we do have to do that, or they have not proven anything. They state that themselves, and you summarized it, when they said "Our main assumption is that after preparation, the quantum system has some set of physical properties. These may be completely described by quantum theory, but in order to be as general as possible, we allow that they are described by some other, perhaps
undiscovered theory. Assume that a complete list of these physical properties corresponds to some mathematical object, lambda." (my bold).

So this is their main assumption, they are not claiming to have proven anything if this assumption is not taken as true, and true in the sense of mathematical logic, not merely a valid way (in my_wan's sense) to think about quantum mechanics in the physicist sense. Not only must we assume that the system "has" these properties, there are quite a few other implicit assumptions-- we must assume there really is such a thing as a quantum system (not just a treatment the physicist is choosing, which is actually how physics has always worked), and we must assume that the properties are expressible mathematically (so they cannot be some undefined concept of a property, they must be a property of a very specific type that ignores the distinctions between the map and the territory).

If we define "theory of physics" as I did in my previous post, the theorem says that state vectors in QM do not correspond bijectively to epistemic states in any theory of physics such that a) it makes the same predictions as QM, and b) some of the probability distributions are overlapping.

But that's only because the deck is already stacked against "epistemic states" by the assumption that ontological states actually mediate the connection between preparations and outcomes. Yet there is nothing in the meaning of a "theory of physics" that requires that "main assumption". I never make that assumption in any of the physics I conceptualize, I don't think that assumption has anything to do with physics at all in fact. Maybe they didn't really need to make that assumption, maybe they never needed to talk about the causal connection between properties and outcomes at all. But they appear to think they do-- if that is their main assumption! Why do they need that intermediary, that the preparation --> properties ---> predictions, instead of what physics demonstrably does, which is connect the preparation directly to the predicted outcomes via a mathematical object that "causes" the predictions, not the actual outcomes, to be what they are.

I don't understand why you think there's something weird here. Later in this post, you agreed that a theory of physics needs a rule that identifies preparations with probability measures on the set whose members determine the probabilities of measurement results. Now you seem to be dismissing that very thing, and it's very hard to tell why.

No, I don't have any issue with saying that the preparation leaves the system in a state, that's how the theory describes the preparation. I have no problem with saying that the theory takes that state and uses it to make predictions, that's just what the theory does. I don't even mind lending the name "properties" to the mathematical elements of the theory. But what I do object to is imagining that anything that happened in that series of sentences referred to anything other than the theory itself-- nowhere in that chain was there any attribution to something that the reality did, nowhere did the theory become subjugated to some physically real properties that actually caused the outcomes to occur. None of that is necessary in physics, and it's not even necessary in realism, which is more to the point. Yet it is their "main assumption." They cannot leave it at the chain of sentences I just gave, which referred only to the theory, they must create, as the foundation of their proof, a mechanism whereby ontological properties are actually responsible for what happens to the system. That's where they stacked the deck, in a way that is not a "mild assumption", and is not a requirement to apply realism (just not naive realism) to physics.

If you don't like my objection to talking about properties causing outcomes, then look at Demystifier's objection to treating the properties as if they were completely endemic to the system. The PBR approach requires that there be an ontic system in the first place, and it have its own properties, independent of its environment, and most importantly, independent of the physicist studying it. Those are huge assumptions, and actually leave rather little left for the actual proof, but the proof does proceed to completion from that point. Hence the proof should be characterized as a consequences for QM of a particular assumption about the universe, rather than something about QM by itself.

I have really tried to make sense of this. Their argument is clearly not about nothing, and why would anyone want to call equivalence classes of preparations "outcomes" instead of "states"?

I never suggested they should rename what a state is, such a renaming would not alter what they have proved-- and what they have not proved. Indeed I have no objection at all to characterizing states as equivalence classes of preparations, it is what they view as natural consequences of that characterization that I object to. A state is a decision to group together preparations in a certain way, with no requirement to enter into a certain kind of fantasy about reality (that preparations refer to properties in reality, not just properties of the theory).

 

[Fredrik]

Yet we do have to do that, or they have not proven anything. They state that themselves, and you summarized it, when they said "Our main assumption is that after preparation, the quantum system has some set of physical properties. These may be completely described by quantum theory, but in order to be as general as possible, we allow that they are described by some other, perhaps
undiscovered theory. Assume that a complete list of these physical properties corresponds to some mathematical object, lambda." (my bold).

So this is their main assumption, they are not claiming to have proven anything if this assumption is not taken as true,

You have to keep in mind that the article is very badly written. The part you're quoting is rather horrible, because the actual argument just proves that there are no ψ-epistemic ontological models for QM. That's it. The conclusion is true regardless of what you imagine about properties, and the argument is essentially correct* no matter what ontic states really are.

*) There seem to be some hidden assumptions about locality and non-contextuality. For the argument to be considered completely correct, these assumptions need to be stated explicitly.

and true in the sense of mathematical logic

Only a statement with a mathematical definition can be "true in the sense of mathematical logic" (unless we change the axioms of mathematics to include statements about these new terms). So if you bring "properties" into the mix without defining the term, it is impossible for the assumptions to be "true in the sense of mathematical logic".

Not only must we assume that the system "has" these properties, there are quite a few other implicit assumptions-- we must assume there really is such a thing as a quantum system (not just a treatment the physicist is choosing, which is actually how physics has always worked), and we must assume that the properties are expressible mathematically (so they cannot be some undefined concept of a property, they must be a property of a very specific type that ignores the distinctions between the map and the territory).

None of these assumptions make sense as the starting point of a mathematical proof.

 

[Fredrik]

Hence, when I say:
Ontic if theory λ uniquely determines an outcome.
It is equivalent to:
Ontic if the complete physical or ontic state is consistent with only one pure quantum state.
...
So where would you say the consistency fails?

You seem to have redefined "outcome" to mean "equivalence class of preparation procedures" instead of "measurement result". In a ψ-ontic ontological model for QM, λ uniquely identifies the class of preparation procedures that are equivalent in the sense that they correspond to the same epistemic state in the ontological model, and the same state vector in QM. λ does not however determine measurement results.

 

[Demystifier]

Can you explain where contextuality enters the picture in my version of their argument? (Post #155). I'm not saying that you're wrong. I just barely know what contextuality means, and I haven't really thought about whether you're right or wrong.

In the meantime, I have realized that contextuality is not really important here. My current understanding of the PBR theorem is best summarized in my later post #137. It is also interesting to see what the first author of the PBR paper said (via an e-mail communication) about my summary:

> Me (H.N.):
> In simple terms, it [the theorem] claims the following:
> If the true reality "lambda" is known (whatever it is), then from this
> knowledge one can calculate the wave function.

Matthew Pusey:
Yep.

> Me (H.N.):
> However, it does not imply that the wave function itself is real. Let me
> use a classical analogy. Here "lambda" is the position of the point-particle.
> The analogue of the wave function is a box, say one of the four boxes
> drawn at one of the Matt's nice pictures. From the position of the particle you
> know exactly which one of the boxes is filled with the particle. And yet,
> it does not imply that the box is real. The box can be a purely imagined
> thing, useful as an epistemic tool to characterize the region in which the
> particle is positioned. It is something attributed to a single particle (not to a
> statistical ensemble), but it is still only an epistemic tool.

Matthew Pusey:
I'm not sure a distinction between things that are "real" and things
that can be calculated from things that are "real" (which one might
call "derived quantities") is particularly meaningful. After all, one
can always re-label the lambda so that the labels include any "derived
quantity", and presumably the real world doesn't care about our labels
for it.
Such a distinction is probably only one of taste: we want the "real"
things to be as simple as possible. (In your example it would feel
unnecessarily complicated to specify the position of the
point-particle AND which box it is in.) It would be interesting if
somebody found something simpler than the quantum state that
nevertheless uniquely identifies it, thus permitting the relegation of
the quantum state to the status of a "derived quantity". Our theorem
doesn't rule out this possibility. But it does seem rather unlikely,
since Hilbert space is already a very elegant mathematical structure.
Yours,
Matt Pusey

 

[Fredrik]

My current understanding of the PBR theorem is best summarized in my later post #137. It is also interesting to see what the first author of the PBR paper said (via an e-mail communication) about my summary:

> Me (H.N.):
> In simple terms, it [the theorem] claims the following:
> If the true reality "lambda" is known (whatever it is), then from this
> knowledge one can calculate the wave function.

Matthew Pusey:
Yep.

The theorem implies that if there is such a thing as a "true reality lambda", then it determines the wavefunction. But what it actually says is just that if there's a lambda in a theory that makes the same predictions as QM, it determines the wavefunction. There's no need to talk about "true reality".

> Me (H.N.):
> However, it does not imply that the wave function itself is real. Let me
> use a classical analogy. Here "lambda" is the position of the point-particle.
> The analogue of the wave function is a box, say one of the four boxes
> drawn at one of the Matt's nice pictures. From the position of the particle you
> know exactly which one of the boxes is filled with the particle. And yet,
> it does not imply that the box is real. The box can be a purely imagined
> thing, useful as an epistemic tool to characterize the region in which the
> particle is positioned. It is something attributed to a single particle (not to a
> statistical ensemble), but it is still only an epistemic tool.

Matthew Pusey:
I'm not sure a distinction between things that are "real" and things
that can be calculated from things that are "real" (which one might
call "derived quantities") is particularly meaningful. After all, one
can always re-label the lambda so that the labels include any "derived
quantity", and presumably the real world doesn't care about our labels
for it.

Here he is simply defending the definition of "ψ-epistemic" from HS. My thoughts on that are in post #94. (I also argued that something that is determined by properties can be considered a property).

 

[my_wan]

You seem to have redefined "outcome" to mean "equivalence class of preparation procedures" instead of "measurement result".

No. Look at how the PBR paper defines λ:

Assume that a complete list of these physical properties corresponds to some mathematical object, λ.

Now to get the measurement results necessary to establish the theorem a pair of preparation procedures was chosen such that a comparison could be made, but the definition of λ is a far more general complete list of these physical properties. Yet it was ultimately not the preparation procedures, however important they may have been to the properties in question, that provides the empirical justification. It is in fact the outcome of the measurement results that provides that empirical justification. Assuming of course that the experiment is actually performed and the results are consistent with the predictions of QM, which nobody seriously doubts.

So when I replaced "consistent with" in the HS definition with "outcome", i.e. measurement result. Whereas PBR needed to specify the preparation procedures to make an explicit case pertinent to QM itself, I merely generalized over the details of the specific case to include theories in general. Yet even in the PBR case the evidence rest on the "outcome" of the proposed experiment itself.

In a ψ-ontic ontological model for QM, λ uniquely identifies the class of preparation procedures that are equivalent in the sense that they correspond to the same epistemic state in the ontological model, and the same state vector in QM.

It was the QM formalism, not λ, that imposed the class of preparation procedures needed to establish the theorem. λ is merely a complete specification of properties.

λ does not however determine measurement results.

If measurement results are not pertinent to the characterization of λ there is no empirical justification for the theorem, period.

_____
In correspondence with Demystifier, Pusey said something that made a lot of sense and implies a point that Ken G and myself has been trying to make wrt properties.

I'm not sure a distinction between things that are "real" and things that can be calculated from things that are "real" (which one might call "derived quantities") is particularly meaningful. After all, one can always re-label the lambda so that the labels include any "derived quantity", and presumably the real world doesn't care about our labels for it.

Though there are a lot of subtleties not mentioned here this, at least in principle, appears to me to obviate a lot of Ken G's issues. Though simply relabeling lambda may not be sufficient in the general case, as it still (seems to) implies that the property set in questioned is innate to the ontic parts.

 

[Fredrik]

No. Look at how the PBR paper defines λ:

That "definition" isn't used in the proof. It can't be used, because it's not a mathematical statement. The term "property" isn't even defined.

So when I replaced "consistent with" in the HS definition with "outcome", i.e. measurement result. Whereas PBR needed to specify the preparation procedures to make an explicit case pertinent to QM itself, I merely generalized over the details of the specific case to include theories in general. Yet even in the PBR case the evidence rest on the "outcome" of the proposed experiment itself.

I don't understand what you're saying here, but in an ontological model for QM, λ is just assumed to determine probabilities of measurement results. If, in addition to that, λ determines the epistemic state (probability distribution) corresponding to ψ, the model is said to be ψ-ontic. You said

Ontic if theory λ uniquely determines an outcome.​

That's not even close to the HS definition. In a ψ-ontic ontological model for QM, λ determines the state vector used by QM, which determines the probabilities of all measurement results. But it doesn't determine outcomes (=measurement results).

If measurement results are not pertinent to the characterization of λ there is no empirical justification for the theorem, period.

Right, but I never said that they're not pertinent. I said that λ doesn't determine measurement results (=outcomes). It determines probabilities of measurement results.

In correspondence with Demystifier, Pusey said something that made a lot of sense and implies a point that Ken G and myself has been trying to make wrt properties.

I made that point myself in #94. The idea that something that is uniquely determined by properties can be considered a property is a major part of the motivation for the definitions of "ψ-ontic" and "ψ-epistemic".

 

[qsa]

This is slightly offtopic so i'll be very brief - Death.

Only death is absolutely certain(in the sense of cessastion of existence as we know it - billions of years of history, trillions of life forms, not a single exception). Please ask similar questions in the philosophy forum to keep this thread on topic. Thank you

this was my response to mywan saying (which implied he new the exact difference)


that validity and truth are very different things

there seems to be no clear definition or an idea as to when a mathematical object is ontic or epistemic. maybe more thought should go into that.

 

[my_wan]

That "definition" isn't used in the proof. It can't be used, because it's not a mathematical statement. The term "property" isn't even defined.

It most certainly and absolutely was. Not only was it copied and pasted into the quote directly from the PBR article, it immediately and in the same context followed the specification that defined the pair of preparation methods for $|\phi_0\rangle$ and $|\phi_1\rangle$ as well as the specification for the "main assumption" ken g called you on. It was the first mention of λ, without which the statements immediately following, providing the definition "(the first view)" in the context of λ, has no defined meaning whatsoever. It was unambiguously central to defining the context under which the proof followed. In context, lacking that definition, it would be tantamount to saying assume ε without ever mentioning what ε is.

You can argue it's intended and/or effective meaning in the context of the proof, but to say that definition isn't used in the proof is factually and demonstrably false.

I don't understand what you're saying here, but in an ontological model for QM, λ is just assumed to determine probabilities of measurement results.

Whose ontological model are you presuming can be characterized this way? I went to great lengths to outline a lot of variability in the way different forms of such models can be characterized. Are you now presuming that your characterization of "ontological model" is a one size fits all universal characterization? If this is restricted to the particular characterization the PBR theorem took aim at, did you not just relate λ to "measurement results" (outcome) just as you just argued with me over me explicitly relating λ to outcomes in the definition?

If, in addition to that, λ determines the epistemic state (probability distribution) corresponding to ψ, the model is said to be ψ-ontic.

Is this another one size fits all characterization of all epistemic or ontic models? When you give these definitions you are apparently hinges these arguments on, I clarified why they didn't fit every situation. Yet without any further articulation you continue with this one size fits all in a manner I failed to get any clarification from you on. So I provided a context under which ontic and epistemic concepts could be avoided altogether, to give us a common language for discussing the PBR article. Again, no comment whatsoever on this ontic/epistemic free context. Meanwhile more ontic/epistemic claims lacking any clarification of the issues I had with the way you were using such concepts with a broad paintbrush. I even provided context outside of PBR and QM and asked how epistemic or ontological characterization would apply in those more concrete circumstances, again no reply.

So what's the point here? That you can poke whatever model specification you want into your one size fits all epistemic/ontological characterization and judge it based on those labels you put on it?

You said

Ontic if theory λ uniquely determines an outcome.​

That's not even close to the HS definition.

Why then did you say above:

I don't understand what you're saying here, but in an ontological model for QM, λ is just assumed to determine probabilities of measurement results.

(my bold)?

In a ψ-ontic ontological model for QM, λ determines the state vector used by QM, which determines the probabilities of all measurement results. But it doesn't determine outcomes (=measurement results).

I have read many ψ-ontic ontological model for QM in which the complete description, including hidden variables, attempted to give non-probabilistic explanations of measurement results. Many of which I consider rather naive. The PBR result hinged on $P(k|\lambda,\lambda,X)=0$, i.e., the non-random certainty of the result. Hence the "cannot be interpreted statistically" in the title.

Right, but I never said that they're not pertinent. I said that λ doesn't determine measurement results (=outcomes). It determines probabilities of measurement results.

Yet again, the PBR result hinged on $P(k|\lambda,\lambda,X)=0$. Note the 0? Hence there is no probability, but a certainty in the measurement results. Hence the "cannot be interpreted statistically" in the title.

I made that point myself in #94. The idea that something that is uniquely determined by properties can be considered a property is a major part of the motivation for the definitions of "ψ-ontic" and "ψ-epistemic".

Yes, what you said can be interpreted that way. However, I made the point that you can partition "epistemic" variables such that they have "ontic" properties. Then use those "ontic" properties to redefine a new set of emergent "epistemic" variables. Rinse repeat. same thing in reverse. So which variables are actually "epistemic" verses "ontic". Or is it strictly dependent on the context in which they are used? Address that issue rather than what seems to me to be a willy nilly that is "ψ-ontic" and that "ψ-epistemic" as if those designations say something about about what PBR entails or not.

Address those issues! Simply referring to "the definitions" is meaningless without addressing those issues. Simply labeling $P(k|\lambda,\lambda,X)=0$ by "the definitions" is meaningless without addressing those issues. Without addressing those issues stating "I made that point myself" is a moot claim, until those issues are addressed.

Or you can look at my epistemic/ontic free characterization of the PBR theorem and we can discuss it without the baggage of poorly defined characterization.

 

[billschnieder]

Would that it were so simple! But your stance involves making all kinds of assumptions about how reality works, assumptions that no theory in the history of physics has ever required, and no analysis of reality has ever supported. The fact is, no physics theory requires that there be any such thing as "complete physical properties", that is a complete fantasy in my view.

Your approach involves careless use of language which is just a recipe for confusion. All I did was define the terms clearly. Hopefully you have heard of the difference between "subject" and "object". The "subject" --physics studies the objects which are "physical properties". This is not a matter of worldviews, but a simple matter of definitions. Every "subject" by definition has an "object". We can debate legitimately the nature of the object, and how the subject relates to it. But to suggest that the subject exists without any object is a scary kind of intellectual laziness.

Also, no physical theory requires that it be true that probability must appear solely due to a lack of information. Information is something you can have, it never refers to anything that we cannot have. Thus, we can say that probabilities are affected and altered by our information, but we certainly have no idea "where probability comes from."

Look up the definition of "Probability" in any dictionary of your choice, and you will find that it is tightly coupled to "uncertainty". Now look up the meaning of "uncertainty". If you have no idea what probability is, or where it comes from, I will recommend the excellent book by ET Jaynes: (Probability Theory: The Logic of Science) or the shorter article which was cited in the topic article: http://bayes.wustl.edu/etj/articles/prob.in.qm.pdf

Imagining that we did leads to all kinds of absurd claims even in classical physics-- like the claim that butterflies "change the weather." The situation is even worse in quantum mechanics, where pretending that we understand what "causes probability" leads to all kinds of misconceptions about how the theory of quantum mechanics works, let alone how reality works.

You are right about one thing: Failure to understand "Probability" is one of the biggest problems facing theoretical physics today. Just because you don't know what causes probability theory, does not mean nobody else knows what causes it, nor does it mean nothing causes it. This approach is what Jaynes calls the "Mind Projection Fallacy" (see Jaynes, E. T., 1989, `Clearing up Mysteries - The Original Goal, ' in Maximum-Entropy and Bayesian Methods, J. Skilling (ed.), Kluwer, Dordrecht, p. 1, http://bayes.wustl.edu/etj/articles/cmystery.pdf)

THE MIND PROJECTION FALLACY
It is very difficult to get this point across to those who think that in doing probability calculations their equations are describing the real world. But that is claiming something that one could never know to be true; we call it the Mind Projection Fallacy. The analogy is to a movie projector, whereby things that exist only as marks on a tiny strip of film appear to be real objects moving across a large screen. Similarly, we are all under an ego-driven temptation to project our private thoughts out onto the real world, by supposing that the creations of one's own imagination are real properties of Nature, or that one's own ignorance signifies some kind of indecision on the part of Nature.
The current literature of quantum theory is saturated with the Mind Projection Fallacy. Many of us were first told, as undergraduates, about Bose and Fermi statistics by an argument like this: "You and I cannot distinguish between the particles; therefore the particles behave differently than if we could." Or the mysteries of the uncertainty principle were explained to us thus: "The momentum of the particle is unknown; therefore it has a high kinetic energy." A standard of logic that would be considered a psychiatric disorder in other fields, is the accepted norm in quantum theory. But this is really a form of arrogance, as if one were claiming to control Nature by psychokinesis.

Well, I'd say it's just obviously what a physics theory is, and quite demonstrably so. A little history is really all that is needed to establish this. Note that [no] one has the slightest idea if "the quantum particle may be completely specified", and there is certainly plenty of evidence that this is not the case.

Another example of "Mind Projection fallacy". Just because we are unable to completely "specify" the properties of a quantum particle does not mean a quantum particle does not "exist". A deficiency in your knowledge or our theories is not a deficiency of nature.

Even the very concept of "a quantum particle", when interpreted in the narrow way you interpret ontology, is quite a dubious notion.

I challenge you to define clearly what you mean by "particle" or even "ontology", then do a self re-examination to see if you have been using the terms in a manner consistent with your definitions.

 

[DevilsAvocado]

I still don’t understand that local vs non-local non-realism. According to the anti-realist position, there should be no issue as to the locality/non-locality because there is no quantum world for quantum mechanics to localy or non-localy describe. This makes no sense to me? I'm thinking here Bohr's thoughts that "there is no quantum world".

You’re right, this is confusing. I can only put forward what a PhD (involved the foundations community, talking to guys like Yakir Aharonov) told me; what’s left when we exclude local realism, is non-locality and/or non-realism:

• non-locality + realism
  
• locality + non-realism
  
• non-locality + non-realism

And to make it even more confusing, you could substitute non-realism for non-separability:

• non-locality + realism
  
• locality + non-separability
  
• non-locality + non-separability

What on Earth does non-locality + non-separability mean??

That’s why my "natural favorite" is non-local realism...

... but doesn’t address the arguments put forth by Einstein in 1927 that QM itself cannot be both complete and local. Isn't that the whole meaning of this quote by Matt Leifer:

I think this is the most common misconception about the Bohr–Einstein debates, which also has 'troubled' me for years... And I think one of the main reasons for this is that the EPR paper was written by Podolsky, by Einstein’s admission, but did not provide an accurate view of Einstein’s position. The title is telling:

Apparently also Niels Bohr was confused... ;)

What Einstein 'attacked' was not Quantum Mechanics as whole, but Niels Bohr’s interpretation that the quantum state alone constitutes a complete description of reality, the ψ-complete view.

And as we all know today, Einstein won this 'battle'...


(If you claim that you understand *exactly* what this is all about, then we could maybe talk ADD, but otherwise – you’re just fine! )

 

[my_wan]

this was my response to mywan saying (which implied he new the exact difference)


that validity and truth are very different things

there seems to be no clear definition or an idea as to when a mathematical object is ontic or epistemic. maybe more thought should go into that.

I'll try to articulate it. If you make a statement: If A then B, then we can access the validity of that statement. If B is a result of A then we can say the statement is valid. Yet even if B is true it could still be true for reasons other than A. Hence the fact that B is a valid result of A and A is true does not make the claim that B is because of A true.

Theoretical constructs take a different tact. Because if A then B is valid, and B is true, then we can say that this is evidence that B is because of A. The more independent variables that can be made dependent within the theoretical construct the stronger we say this evidence is. For instance we can ask A then B is valid and see that it is, and see that B is also true. We can then say if B is the result of A then C and verify its validity, and also verify that C is true. Hence the more these independent variables are compounded and made dependent the higher probability we attain in validity of the theoretical construct.

Some misconceptions:
On occasion people will make the claim X is only a theory. What they are generally implying is that B is false. In fact it is not the truth of B in question, which tends to have logical proofs in mathematical concepts and empirical verification in matter of science. It is only the causal attributes A that is not always absolute. Though the compound evidence can often be so strong that seriously questioning it is a waste of time.

Some pitfalls:
The strength of evidence can also be limited by retrodictions, though retrodictions still have some value as evidence. If you already know the fact B then inventing A, even when A then B is in fact valid, is not as strong as the evidence generated when A is not known or predicted and you reasons to suspect A and your able to make an unexpected prediction B as a result, and have b empirically verified. Hence many of the symmetries in physics, evolution, etc., are much more solid than say cosmology. Not picking on cosmology, nor belittling the evidence it provides, it's just a fact of the inherent limits only the available control the practitioners have in experimenting with the empirical data. Not as many opportunities for falsification, especially when the theoretical construct was explicitly formulated for known empirical data.

Some invalid logic (that can be sneaky):
The main one being circular logic. In well defined circumstances it is easy to recognize. This has even been brought up wrt the PBR theorem. If the main assumption entails A then it is no surprise that the result entails A. I'm not suggesting that the PBR theorem is guilty of this, but some of the interpretations of it might very well be. It basically says if A then A, if turkeys can walk then turkeys can walk. It's validity doesn't mean the turkey on my table can walk. You can read up on a whole lot of formal and informal fallacies that I will not go through. Most are actually subsets or slight variations of others. The main ones are well worth understanding.

All of these things and more are quiet easy to read about on the internet. Karl Popper is probably the most influential in science.

 

[DevilsAvocado]

I'm afraid you are falling into logical fallacy again.

Actually it's a standard part of logic 101.

my_wan & Ken G, I’m short on time, but I will answer these posts in a 'voluminous' way (in a day or two). Be prepared!


()

 

[my_wan]

my_wan & Ken G, I’m short on time, but I will answer these posts in a 'voluminous' way (in a day or two). Be prepared!


()

Can't speak for Ken G but I'll be watching. I am well aware that in some ways I differ from Ken G on some issues. I tend to consider ideas that are unfalsifiable in and of themselves more systematically, under the assumption that they can be useful in more falsifiable model constructions. These ideas are generally related to notions of reality as opposed to simply providing raw formalized symmetry relations. But a failure to recognize the epistemological limits of what we can "know" spells certain doom in such pondering. The target still remains those empirical valid symmetry relations.

 

[bohm2]

Yet again, the PBR result hinged on $P(k|\lambda,\lambda,X)=0$. Note the 0? Hence there is no probability, but a certainty in the measurement results. Hence the "cannot be interpreted statistically" in the title.

This is the most important argument that basically eliminates 1 of the 2 scientific "realist" positions out (if accurate). So now I see why Valentinil, Wallace, etc and others are so ecstatic because they really felt that (e.g. wavefunction is epistemic and there is an underlying ontic state) was the only rational alternative to their models?

An interesting paper discussing the difficulties with using "realism" is this paper by Norsen. He is one of the authors cited in the Harrigan/Spekkens article. He does a really good job of defining the different notions of realism (naive, scientific, perceptual, metaphysical) and argues that the word "realism" is flawed. His conclusion:

We thus suggest that the phrase ‘local realism’ should be banned from future discussions of these issues, and urge physicists to revisit the foundational questions behind Bell’s Theorem...With those preliminaries out of the way, we can finally raise the question of Locality, i.e., respect for relativity’s prohibition on superluminal causation. A natural first question would be: is orthodox quantum mechanics (OQM) a local theory? The answer is plainly “no”. (The collapse postulate is manifestly not Lorentz invariant, and this postulate is crucial to the theory’s ability to match experiment.) And so then: Might we construct a new theory which makes the same empirical predictions as orthodox quantum theory, but which restores Locality? (In other words, might we blame OQM’s apparent non-locality on the fact that it is dealing with wrong or incomplete state descriptions?) The answer – provided by Bell’s Theorem – turns out to be “no”. We are stuck with the non-locality, which emerges as a real fact of nature – one which ought to be of more concern to more physicists. And we are left with a freedom to decide among the various candidate theories (all of them nonlocal, e.g., OQM, Bohmian Mechanics, and GRW) using criteria that have nothing directly to do with EPR or Bell’s Theorem – e.g., the clarity and precision with which they can be formulated, to what extent they suffer from afflictions such as the measurement problem, and (looking forward) to what extent they continue to resolve old puzzles and give rise to new insights.

I'm guessing here that "a certainty in the measurement results. Hence the "cannot be interpreted statistically" in the title" goes against the hi-lited part? Which may be the reason why Valentini and others think PBR is so important? But then I'm confused because if Bell's already did this why is PBR seen as so important?

Against 'Realism'

http://arxiv.org/PS_cache/quant-ph/pdf/0607/0607057v2.pdf

 

[Fredrik]

It most certainly and absolutely was. Not only was it copied and pasted into the quote directly from the PBR article, it immediately and in the same context followed the specification that defined the pair of preparation methods for $|\phi_0\rangle$ and $|\phi_1\rangle$ as well as the specification for the "main assumption" ken g called you on. It was the first mention of λ, without which the statements immediately following, providing the definition "(the first view)" in the context of λ, has no defined meaning whatsoever. It was unambiguously central to defining the context under which the proof followed.

It's central to their interpretation of the result (the absurdities they put in the title and the abstract), but it's not used in the proof, and it's not needed to understand the statement of the theorem.

You can argue it's intended and/or effective meaning in the context of the proof, but to say that definition isn't used in the proof is factually and demonstrably false.

Not only is it demonstrably true, I have demonstrated it. See post #155, where I typed up the argument for a qubit without using any assumptions about "properties".

Whose ontological model are you presuming can be characterized this way?

It's the HS definition of ontological model. Yes, the person who thought of this definition probably had the concept of "complete list of properties" in mind when he wrote it down, but that idea just inspired the definition, it's not actually a part of it. It can't be, because you can't make something undefined a part of a definition. (Not if you're working within the framework of mathematics. If you're trying to define what you mean by "mathematics", that's another story).

If this is restricted to the particular characterization the PBR theorem took aim at, did you not just relate λ to "measurement results" (outcome) just as you just argued with me over me explicitly relating λ to outcomes in the definition?

I didn't object to the fact that you related λ to outcomes. I objected to the fact that you defined "ontic" as λ determines outcomes, and claimed that this is what HS did, when in fact they defined "ψ-ontic" as λ determines probabilities of outcomes.

Is this another one size fits all characterization of all epistemic or ontic models? When you give these definitions you are apparently hinges these arguments on, I clarified why they didn't fit every situation.

I'm not particularly interested in whether there are other definitions that would also make sense, and perhaps be more useful in a different context, because PBR indicated that they are using the HS definitions. They did this by referencing the HS article immediately after declaring that they are going to explain what they mean by the two views, and then proceeding to state criteria that perfectly match the HS definitions of ψ-ontic, ψ-complete, ψ-supplemented, and ψ-epistemic.

Yet without any further articulation you continue with this one size fits all in a manner I failed to get any clarification from you on. So I provided a context under which ontic and epistemic concepts could be avoided altogether, to give us a common language for discussing the PBR article. Again, no comment whatsoever on this ontic/epistemic free context.

I'm sorry about that, but I have spent most of this week on stuff related to this article, and I'd rather not expand the list of topics further by getting into a discussion about ways to avoid talking about the stuff the article is talking about.

Why then did you say above:

(my bold)?

The question only makes sense if you believe that "λ uniquely determines an outcome" means the same thing as "λ uniquely determines the probability of every outcome". An outcome is a measurement result. A specification of the probabilities of all the outcomes is a state, not an outcome.

I have read many ψ-ontic ontological model for QM in which the complete description, including hidden variables, attempted to give non-probabilistic explanations of measurement results. Many of which I consider rather naive. The PBR result hinged on $P(k|\lambda,\lambda,X)=0$, i.e., the non-random certainty of the result. Hence the "cannot be interpreted statistically" in the title.
...
Yet again, the PBR result hinged on $P(k|\lambda,\lambda,X)=0$. Note the 0? Hence there is no probability, but a certainty in the measurement results. Hence the "cannot be interpreted statistically" in the title.

$P(k|\lambda,\lambda,X)=0$ is the result that contradicts the assumption that we started with a ψ-epistemic ontological model for QM. It certainly doesn't mean that they assume that the ontological model only assigns probabilities 0 or 1 to measurement results. They do not make any such assumption. However, as I said in #141, I think the interesting part of the result is that it rules out ontological models that do satisfy that requirement. (It does so as a side effect of ruling out all ψ-epistemic ontological models for QM).

This is what I said in #141, in slightly different words:

Is it possible that quantum probabilities are classical probabilities in disguise? If the answer is yes, then there's a ψ-epistemic ontological model for QM that assigns probabilities 0 or 1 to each possible measurement result. We can prove that the answer is "no" by proving that no such model exists, but we have found a way to prove a stronger result: There is no ψ-epistemic ontological model for QM.​

So which variables are actually "epistemic" verses "ontic". Or is it strictly dependent on the context in which they are used?

Assuming that we're no longer talking about ψ-epistemic and ψ-ontic, and instead about whether a variable should be described as representing knowledge or reality, I would say that it depends on the context. The epistemic states of one theory might correspond to the ontic states of another, less accurate theory.

 

[Fredrik]

I would like to discuss two specific issues from (my version of) the PBR argument for a qubit.

For each $|\psi\rangle\in\mathcal H$ and each $\lambda\in\Lambda$, let $Q_\psi(\lambda)$ denote the probability that the qubit's ontic state is $\lambda$. The function $Q_\psi:\Lambda\to[0,1]$ is called the epistemic state corresponding to $|\psi\rangle$. Similarly, for each $|\psi\rangle\otimes|\psi'\rangle\in\mathcal H\otimes\mathcal H$ and each $(\lambda,\lambda')\in\Lambda\times\Lambda$, let $Q_{\psi\psi'}(\lambda,\lambda')$ denote the probability that the two-qubit system is in ontic state $(\lambda,\lambda')$. We assume that
$$Q_{\psi\psi'}(\lambda,\lambda') =Q_\psi(\lambda)Q_{\psi'}(\lambda')$$ for all values of the relevant variables.

PBR doesn't make this assumption explicit. I think it's implied by the fact that they're talking about "probability $q^2$". Matt Leifer made this assumption explicit in his presentation of the argument.

This is to assume locality, right? In that case, the theorem only rules out local ψ-epistemic ontological models for QM.

Let X be a self-adjoint operator on $\mathcal H\otimes\mathcal H$ with the eigenvectors
$$\begin{align} |\xi_1\rangle &=\frac{1}{\sqrt{2}} \left(|0\rangle\otimes|1\rangle +|1\rangle\otimes|0\rangle\right)\\ |\xi_2\rangle &=\frac{1}{\sqrt{2}} \left(|0\rangle\otimes|-\rangle +|1\rangle\otimes|+\rangle\right)\\ |\xi_3\rangle &=\frac{1}{\sqrt{2}} \left(|+\rangle\otimes|1\rangle +|-\rangle\otimes|0\rangle\right)\\ |\xi_4\rangle &=\frac{1}{\sqrt{2}} \left(|+\rangle\otimes|-\rangle +|-\rangle\otimes|+\rangle\right) \end{align}$$

How do you actually do this? Suppose that the qubit is a silver atom, and that the 0 and 1 kets are eigenstates of S_z, while the + and - states are eigenstates of S_x. What sort of measurement on two silver atoms has four possible results corresponding to the $|\xi_k\rangle$?

 

[Ken G]

All I did was define the terms clearly.

No, you went well beyond defining terms-- you made claims on how reality works. This is the point. I will point out every place you continue to do this.

Hopefully you have heard of the difference between "subject" and "object". The "subject" --physics studies the objects which are "physical properties". This is not a matter of worldviews, but a simple matter of definitions.

Well, it may be your definition, but to anyone else that is simply a claim on how reality works. You are claiming that you are defining "that which physics studies" to be "physical properties," but in more standard use of the term "physics", we would say that physics studies experimental outcomes, and invents physical properties as part of its theories. You think that physics is the study of its own theories, by your definition of a physical property, but to most people, the physical properties are just part of the theory that helps us understand the observations.

Every "subject" by definition has an "object".

I'm confused, just before you said that the subject was defined to be what physics studies, now you are saying that a subject is defined to have an object. Would you like to offer a complete definition of the terms "subject" an "object" please? I have absolutely no idea what you think those words mean, beyond a very naive kind of understanding that most high school students have. This is quantum mechanics, we can go deeper.

But to suggest that the subject exists without any object is a scary kind of intellectual laziness.

I can't tell if I'm suggesting that because I still have no idea what you mean by those poorly defined terms.

Look up the definition of "Probability" in any dictionary of your choice, and you will find that it is tightly coupled to "uncertainty".

That seems obvious, what does it have to do with anything I said or anything being discussed on this thread?

You are right about one thing: Failure to understand "Probability" is one of the biggest problems facing theoretical physics today. Just because you don't know what causes probability theory, does not mean nobody else knows what causes it, nor does it mean nothing causes it.

What "causes probability theory"? We might not know but someone else might know what causes probabilty theory? Your terms don't seem to make any sense.

This approach is what Jaynes calls the "Mind Projection Fallacy" (see Jaynes, E. T., 1989, `Clearing up Mysteries - The Original Goal, ' in Maximum-Entropy and Bayesian Methods, J. Skilling (ed.), Kluwer, Dordrecht, p. 1, http://bayes.wustl.edu/etj/articles/cmystery.pdf)

I don't think you understand the "mind projection fallacy", because frankly, I could have said Jaynes' words myself-- he seems to be making essentially exactly the same argument I made that you objected to: physics theories is all we have to describe nature, so language about what nature is doing that makes these theories work is fundamentally flawed. That is what I was also telling you.

Another example of "Mind Projection fallacy". Just because we are unable to completely "specify" the properties of a quantum particle does not mean a quantum particle does not "exist".

I think you should read Jaynes a little more closely.

I challenge you to define clearly what you mean by "particle" or even "ontology", then do a self re-examination to see if you have been using the terms in a manner consistent with your definitions.

Again I fear you miss the point. It was I who was pointing out the problems in these terms, so I certainly don't need to define them ontologically. I would simply say that "particle", like any other element of a physics theory, is an invention of the human intelligence that we use to try and help us formulate better approximate theories. Then I would say that "ontology" is a kind of pretense that we enter into because it affords us a sense of understanding and a useful degree of parsimony, but we should certainly never believe it is anything else.

 

[Ken G]

You have to keep in mind that the article is very badly written. The part you're quoting is rather horrible, because the actual argument just proves that there are no ψ-epistemic ontological models for QM. That's it. The conclusion is true regardless of what you imagine about properties, and the argument is essentially correct* no matter what ontic states really are.

This is the part I'm just not sure about. Both the proof, and Pusey's comments to Demystifier:
> Me (H.N.):
> In simple terms, it [the theorem] claims the following:
> If the true reality "lambda" is known (whatever it is), then from this
> knowledge one can calculate the wave function.

Matthew Pusey:
Yep.

...seem to suggest that the authors feel that the existence of a "complete set of properties" is an essential part of the proof (it's the "main assumption", and we get a "yep" that there is a "true reality" lambda). I can't tell if this is actually crucial to the proof, but it's in their, so I can only assume it is required to be there. If the proof can be reframed to not require that, so be it, but I don't see it. To me, the essential construct of the proof is that preparations don't determine outcomes, rather they select properties, and properties determine outcomes. If one assumes that the basic reality the physics is modeling must work that way, then one is assuming a strongly ontological structure right from the start. Then one concludes that the wavefunction is a strongly ontological structure. That just doesn't sound like an unnecessary coincidence.

 

[Fredrik]

This is the part I'm just not sure about. Both the proof, and Pusey's comments to Demystifier:
> Me (H.N.):
> In simple terms, it [the theorem] claims the following:
> If the true reality "lambda" is known (whatever it is), then from this
> knowledge one can calculate the wave function.

Matthew Pusey:
Yep.

...seem to suggest that the authors feel that the existence of a "complete set of properties" is an essential part of the proof (it's the "main assumption", and we get a "yep" that there is a "true reality" lambda). I can't tell if this is actually crucial to the proof, but it's in their, so I can only assume it is required to be there.

"In simple terms" means "I'm not going to bother to try to make this really accurate", and that gives Pusey a license to not be really accurate in his response. The article contains a mathematical argument that proves a theorem, which isn't clearly stated anywhere in the text. The correct statement of the theorem ("there is no local ψ-epistemic ontological model for QM") can be extracted from what they're saying, and from the precise definitions in HS. The article also contains an interpretation of the theorem. The interpretation consists of the absurdities in the title and the abstract, and most of the comments about "properties".

The authors have done a terrible job of separating the theorem (a mathematical statement supported by a mathematical argument) from the interpretation (words describing how they think about it). They don't seem to understand the difference between a theorem and a statement in plain English about a theorem. No wonder it's hard for their readers to understand what their assumptions are.

I think I answered the stuff about the "main assumption" better in my reply to my_wan than in my previous reply to you. This is what I said about it:

It's central to their interpretation of the result (the absurdities they put in the title and the abstract), but it's not used in the proof, and it's not needed to understand the statement of the theorem.​

If the proof can be reframed to not require that, so be it, but I don't see it.

As I said to my_wan,

See post #155, where I typed up the argument for a qubit without using any assumptions about "properties".​

There can't exist a version of the proof that involves their "main assumption", because their "main assumption" is a non-mathematical statement. An argument that relies on it is by definition not a proof of a theorem.

To me, the essential construct of the proof is that preparations don't determine outcomes, rather they select properties, and properties determine outcomes.

To be more precise, preparations determine probability measures on the set $\Lambda$ whose members are thought of as "complete lists of properties", and each member of $\Lambda$ determines the probabilities of all outcomes. But the validity of a mathematical proof can't depend on how you think of the members of $\Lambda$ .

 

[Ken G]

It's central to their interpretation of the result (the absurdities they put in the title and the abstract), but it's not used in the proof, and it's not needed to understand the statement of the theorem.

Ah, but this is a proof about interpretations. They are fundamentally trying to prove something about what quantum mechanics means, otherwise it doesn't have the same importance. So I don't think one can separate the interpretation from the proof without making the proof a lot less significant. That seems to be the way the authors have chosen to "sell" it, anyway. You might be quite correct that the formal proof does not require reference to properties, it is the ramifications of the proof that are more the issue however.

To be more precise, preparations determine probability measures on the set Λ whose members are thought of as "complete lists of properties", and each member of Λ determines the probabilities of all outcomes. But the validity of a mathematical proof can't depend on how you think of the members of Λ .

Yes but the interpretation of the significance of the proof can. The "buzz" around the proof is not its formal statement, it is its ramifications for what we imagine that quantum mechanics means (hence the paper's title). That's the part I'm objecting to. We can't just say the paper is written badly, or the title poorly chosen, we must evaluate the case they make for the conclusion they sell.

We can prove that the answer is "no" by proving that no such model exists, but we have found a way to prove a stronger result: There is no ψ-epistemic ontological model for QM.

Yes, I don't dispute this part, that was never my objection to the paper. If one assumes quantum mechanics needs an ontological intepretation, then the wave function is the way to go. That's a "big if", however. I've always felt that those who wish to give a statistical, or epistemic, interpretation to quantum mechanics should as their first step relax their tendency to believe in some absolute or underlying ontological description. They should relax their need to take ontological descriptions completely seriously, and to borrow my_wan's nice phrase, they should "rinse off the magic" from the interpretation.

 

[billschnieder]

No, you went well beyond defining terms-- you made claims on how reality works.

I made claims about how reasonable people use language and reason logically. Is that what you call "making claims about how the reality works"? Or are you utterly unable to appreciate the difference between pointing out poor use of language and illogical reasoning with proposing a particular flavor of ontology.

You think that physics is the study of its own theories, by your definition of a physical property, but to most people, the physical properties are just part of the theory that helps us understand the observations.

Physics is simply the study of nature. Nature is what exists. The object is nature (reality). We can legitimately debate what nature is and if you want to argue that only experimental outcomes exist, do that and we will examine the merits. What I'm arguing against right now is your suggestion that Nature is knowledge.

This is quantum mechanics, we can go deeper.

Attempting to go deeper without grasping the basics is folly.

I can't tell if I'm suggesting that because I still have no idea what you mean by those poorly defined terms.

OK let's examine one of your previous phrases from post #157:

Instead, I would like to offer a different definition of "realism". We start from the stance that everything we can say about nature is going to be a mental construct that is not an actual truth of nature, but rather, is an effective or useful truth, involving the way we have chosen to characterize nature.

As anyone with even one eye can see, the above statement makes the following assumptions:
- There is such a thing as an actual truth of nature.
- Something is being characterized.

Why don't you explain to us what you mean by "actual truth of nature", or explain the "thing" that is being characterized. Since you are quick to jump to judgement on others for suggesting that there is more to nature than what our theories can describe or what we can know. This is similar to suggesting that "Knowledge" can exist without "truth". The definition of "knowledge" involves "truth". Truth is the object of Knowledge. Throw out truth and out goes knowledge with it.

Let's look at another statement you made in post #158

And because that's exactly what we do, that is the realist stance-- ontology is epistemology. I say that to be a realist (not a naive realist), one merely needs to hold that there "actually is" a universe, but everything that we can say about that universe is epistemology, including the ontological claims we make on it for the purposes of advancing our conceptual understanding. I believe this is also what Bohr meant when he said that physics is not about nature, it is about what we can say about nature.

Here you are taking two words with completely different meanings and claiming them to mean the same thing. This is what I mean by lack of consistency about definitions. You also are implying here that all there is "knowledge". Appearing to dismiss the existence of "Truth" which is independent of knowledge. But had you known that the definition of "knowledge" is dependent on the existence of "truth" independent of it, you won't have made such a mistake. One only needs to ask you the question "Know what?" to burst the bubble.

The belief that nature is limited by what our small brains can know and understand is the mind projection fallacy and you are clearly demonstrating it here.

What "causes probability theory"? We might not know but someone else might know what causes probabilty theory? Your terms don't seem to make any sense.

That was a typo, But you knew that already didn't you?

I don't think you understand the "mind projection fallacy", because frankly, I could have said Jaynes' words myself-- he seems to be making essentially exactly the same argument I made that you objected to: physics theories is all we have to describe nature, so language about what nature is doing that makes these theories work is fundamentally flawed. That is what I was also telling you.
I think you should read Jaynes a little more closely.

I have. Have you? You are way off base on what he means. You are claiming that since physics theories is all we have to describe nature, there is therefore nothing more to nature than what physics theories describe. This IS the mind projection fallacy.

I would simply say that "particle", like any other element of a physics theory, is an invention of the human intelligence that we use to try and help us formulate better approximate theories.

When you say "better" you must have assumed that the current knowledge as represented by the current theory is not the complete truth. Which implies you secretly believe there is truth independent of what we currently know. If there is more truth that we know, how can it all be epistemology. Unless you really do not understand the difference between the meanings of the terms.

Then I would say that "ontology" is a kind of pretense that we enter into because it affords us a sense of understanding and a useful degree of parsimony, but we should certainly never believe it is anything else.

More evidence that you are not ready to go any deeper. You are still confused about the basics.

 

[bohm2]

That’s why my "natural favorite" is non-local realism...

Even that term "realism" seems difficult to pin-down. I always assumed that it meant "scientific realism" but now I'm not so sure?

 

[Ken G]

Physics is simply the study of nature. Nature is what exists.

As I said, your stance involves making relatively naive claims about how reality works. You don't seem to even be aware of the Einstein/Bohr debate. You might want to start your investigation with these quotes by Bohr, all found at http://en.wikiquote.org/wiki/Niels_Bohr :
"We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections.
Isolated material particles are abstractions, their properties being definable and observable only through their interaction with other systems.
Physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods of ordering and surveying human experience.
There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature..."

And so forth. Now, not everyone will agree with Bohr, but at least he has not bought off on simplistic concepts like the ones you are espousing.

Why don't you explain to us what you mean by "actual truth of nature", or explain the "thing" that is being characterized.

Bohr says it so much better.

Since you are quick to jump to judgement on others for suggesting that there is more to nature than what our theories can describe or what we can know.

You are not making sense. I would never "jump on anyone" for saying such a thing, that's the kind of thing I say.

You also are implying here that all there is "knowledge". Appearing to dismiss the existence of "Truth" which is independent of knowledge. But had you known that the definition of "knowledge" is dependent on the existence of "truth" independent of it, you won't have made such a mistake. One only needs to ask you the question "Know what?" to burst the bubble.

That's easy, know knowledge. You think the answer is "know truth", but that's because your views are quite simplistic. Maybe when I was first learning physics I thought that I was knowing truth when I was learning physics. Then I became able to handle more sophisticated notions about knowledge and truth, in particular the limitations on truth that stem from how truth must be predicated on knowledge of it. Consider for example a dog's knowledge of the truth of its master. Is a dog's conception of its master true? Is it the dog's truth, or a real truth? Can a dog know its master? Does it make a difference if we define "master" as the "relationship of the dog to its human overseer" versus if we define it as "the relationship of the human overseer to his/her dog"? There are many layers of complexity when dealing with "knowledge of the truth" in something as uncomplicated as a dog and its owner, so I hardly think we should expect to get very far into our investigations of physics with simplistic attitudes like "physics is the study of what exists."

The belief that nature is limited by what our small brains can know and understand is the mind projection fallacy and you are clearly demonstrating it here.

As I said, you have badly misinterpreted the mind projection fallacy. In actual fact, the mind projection fantasy that Jaynes is talking about is much closer to the opposite of what you think-- it is the belief that what we understand nature to be is not limited by what our small brains can know, it is mistaking what our small brains can know for nature. That's the whole point of the "movie as still frames" analogy, we create a concept of what is happening that is not the same as what is actually happening, but it serves us to do so. It is fine for us to do that, the "fallacy" is to not recognize that this is what we have done, and to think we did it because it is true (ontology) instead of simply because it serves our purposes (epistemology).

You are claiming that since physics theories is all we have to describe nature, there is therefore nothing more to nature than what physics theories describe.

You couldn't possibly be more wrong about what I said. What on Earth gave you the idea I said that? On the contrary, what I actually said, indeed what you quoted above, is that if one is take on a belief in actual truths of nature, then physics isn't them. That you could quote me, and then a few lines later claim I said something the opposite of what you just quoted, suggests there is a serious communication problem here.

When you say "better" you must have assumed that the current knowledge as represented by the current theory is not the complete truth. Which implies you secretly believe there is truth independent of what we currently know.

Not secretly, you may be assured that I quite openly believe this, although it depends on how naively you interpret your own word "independent" there. I would certainly not claim that what we currently know has no connection with what is true, if indeed there is something that is true. All my point requires is that there be a fundamental difference (called "epistemology") between what we know and what is actually true. Indeed, I cannot imagine how any thinking person with the least knowledge of physics history would not believe this.

If there is more truth that we know, how can it all be epistemology. Unless you really do not understand the difference between the meanings of the terms.

Actually, I understand the difference just fine, which is what makes it so easy to answer your question. How it can all be epistemology is simply that epistemology is all we get, we want truth and we get epistemology. Again, any other view of the situation seems downright bizarre. Note also that nothing I said requires there exist such a thing as absolute truth-- all I actually said is that physics isn't it, nor is any epistemology, but what epistemology is is a set of choices about what will be regarded as useful or effective truths, provisional truths that are predicated on what we are able to know and what we decide to regard as knowledge. Like physics, for example.

 

[Ken G]

Getting back to the more interesting stuff.

I would like to discuss two specific issues from (my version of) the PBR argument for a qubit.

I think there may be an important modification to the situation as you have presented it. You are talking about the probability that the qubit is in some given ontic state, but it is only the system itself, not its qubit, that can have such a probability (if we are even to assume that ontic states exist in the first place). The qubit is a choice, by a physicist, to characterize the preparation of that system in a certain way. So we don't actually know the probability of being in an ontic state that associates with that epistemic state, and indeed there might not be any such unique probability function Q, since probability has to be subject to certain contextual constraints that we must decide. To me, this all speaks to the issue of how the subtle ways that we can bring ontological interpretations into fundamentally epistemic situations might "queer the result" of our analysis, leading us to conclude the presence of ontic influences that are in fact only there because we put them there from the start.

So I say that whenever we mention probability, we should regard them as conditional-- conditional on some assumptions about the context, which here refers to the preparation. So if we connect the quantum state with the way we have chosen to describe the preparation, then there is no guarantee, or even reason to expect, that what we have preserved from the preparation (encoded in the quantum state) also preserves the probabilities of being in the various possible ontic states. If it does not, then not only can we not say that the state suffices to specify those probabilities, we cannot say that those probabilities even exist.

In other words, probabilities exist after one has afforded onesself with some kind of prescription for establishing a context that can give the probabilities testablity, and the only way a quantum state by itself has established that context is in regard to talking about probabilities of various outcomes, not ontic states. That's what the quantum state is for. This keeps getting back to the potential for circularity-- if there can be no demonstrable difference between the quantum state and the process for using that state to determine probable outcomes, and if the process for determining probabilities is characterized as ontic, then the state ends up having to be ontic too.

Suppose that the qubit is a silver atom, and that the 0 and 1 kets are eigenstates of S_z, while the + and - states are eigenstates of S_x. What sort of measurement on two silver atoms has four possible results corresponding to the $|\xi_k\rangle$?

This connects to the fact that every measurable corresponds to a Hermitian operator on the state space, but not every Hermitian operatore corresponds to a measurement that we know how to do. The significance of this fact has never been clear to me-- a strict empiricist would say that if we don't know how to do the measurement, then it is not part of the reality that we can talk about, it is some kind of hypothetical reality like Alice in Wonderland. But in the structure of quantum mechanics, it fills in the gaps between the measurements we can do, and the status of such operators might have some analogous meaning to the concept of an "ontic state."

 

[Fra]

I sympthatise with some of what Tomas said. I didn't follow the long thread, but skimmed the early part of the paper as well as some other papers referred to in this thread (such as the one trying to define psi-ontic and psi-epistemic etc) and I don't quite like choice of describing the problems.

My impression is that a lot of the questions and distinctions one tries to make doesn't really fit into my stance on this anyway. I read if more as beloning to some realist-seeking branch of physicists.

If we talk about QM as we know it, and in the domain it's TESTED (ie leaving out cosmo stuff and QG) then I agree with Thomas that it should be reasonably clear what a quantum state is. It first of all RELIES on a classical observer context (or classical INSTRUMENT). And it also refers to statistics of repetitive experiments (ensembles).

The BIG problems I see are obvious when one tries to understand unification and other things and in that context I think the referred papers is not interesting.

It seems the "problems" that the authors try to address here... is the lack of realism in quantum theory, and thus interpretational and existential issues. AFAIK this is not even a problem in the scientific sense.

Maybe I missed something, but maybe someone can recap WHICH important question all this aim to answer? I am right it's a "pure interpretational" thing as often?

/Fredrik

 

[Fredrik]

You are talking about the probability that the qubit is in some given ontic state, but it is only the system itself, not its qubit, that can have such a probability (if we are even to assume that ontic states exist in the first place).

What I meant by a "qubit" is any physical system for which there's a quantum theory with a 2-dimensional Hilbert space. The qubit is the system. However, now that I think about it, "system" is just an undefined idea that we associate with the theory, just like "complete list of properties" is an undefined idea that we associate with ontic states. We use such terms only because they give us a convenient way to organize our thoughts. In this case, there's no need to involve either of the terms "system" or "qubit" (or "property"). Our goal is simply to prove that there's no local ψ-epistemic ontological model for a quantum theory with a 2-dimensional Hilbert space.

I don't understand the "if we are even to assume..." comment, or why you keep coming back to this. The goal is to prove that there is no local ψ-epistemic ontological model for a quantum theory with a 2-dimensional Hilbert space. So why are you all "oh no, ontic states are bad"? The logic goes like this: Either there is an ontological model for this quantum theory or there isn't. So we consider those two cases separately. If there isn't, then the statement we're trying to prove is trivially true. If there is, then we use the PBR argument, and the "existence" of ontic states is unquestionable because that's part of what defines what we're talking about right now. (Note that nothing is assumed about what ontic states "really" are).

The qubit is a choice, by a physicist, to characterize the preparation of that system in a certain way.

I don't understand this comment either. Are you defining the "qubit" to be the $\{|0\rangle,|1\rangle\}$ basis?

So we don't actually know the probability of being in an ontic state that associates with that epistemic state, and indeed there might not be any such unique probability function Q, since probability has to be subject to certain contextual constraints that we must decide.

The definition of "ontological model for QM" includes the requirement that such a probability function exists and is uniquely determined by a state vector.

If I understand contextuality, that may enter the picture when we start talking about measurements, but right now we're talking about preparations.

This keeps getting back to the potential for circularity-- if there can be no demonstrable difference between the quantum state and the process for using that state to determine probable outcomes, and if the process for determining probabilities is characterized as ontic, then the state ends up having to be ontic too.

I don't know what this means, or why you think that there's a potential for circularity.

This connects to the fact that every measurable corresponds to a Hermitian operator on the state space, but not every Hermitian operatore corresponds to a measurement that we know how to do. The significance of this fact has never been clear to me

It's not clear to me either.

Note that the $|\xi_i\rangle$ aren't tensor product states. They are linear combinations of two tensor product states. That means that the two qubits are entangled. How did they end up that way? There is nothing in the quantum theory of the spin of a silver atom that can entangle two spins that start out isolated. So we have go go outside of the theory we're supposed to prove a statement about. I'm not sure what that means yet.