The quantum state cannot be interpreted statistically?

[Fredrik]

Might it mean Einstein's original 2 views about the nature of the wave function? See p. 194-195 with direct Einstein quotes, in particular. All of Chapter 7 is pretty interesting. Maybe that is why this theory if accurate rules out Einstein's arguments ? I'm not sure.

http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/valentini.pdf

The question was rhetorical. I meant that PBR couldn't have meant anything else.

If the quote at the start of page 195 is what defines the two views mentioned on page 194, then I would say that this can't be the two views that PBR are comparing, not only because I have already made up my mind about what they are comparing, but also because Einstein's "view I" clearly contradicts QM (and experiments). So there's no need to compare those two views now.

 

[DevilsAvocado]

I haven’t read more than to #141, sorry if something is already dealt with.

Now ask yourself if temperature is a classical epistemic or ontic variable. Though it is the product of presumably ontic entities it is a variable that is not dependent on the state of any particular ontic entity nor singular state of those entities as a whole. It is an epistemic state variable, in spite of having a very real existence. In this sense I would say it qualifies as "epistemic ontic", since it is an epistemic variable in which it's existence is contingent upon on underlying ontic group state. Momentum is another epistemic variable, since the self referential momentum of any ontic entity (lacking internal dynamics) is precisely zero. That's the whole motivation behind relativity.

Thanks my_wan, interesting posts.

I enjoy the discussion, but sometimes I wonder if we are getting 'stuck in words'... I think Ken G’s comment is a quite striking (and entertaining):

The issue isn't local vs. nonlocal, it is in the whole idea of what a hidden variables theory is. It's an oxymoron-- if the variables are hidden, it's not a theory, and if they aren't hidden, well, then they aren't hidden! The whole language is basically a kind of pretense that the theory is trying to be something different from what it actually is.

If the variables are hidden, it's not a theory... Well, that’s it guys – problems solved!

From my perspective, the discussion what "hidden variables" are, and what properties they might posses, and how they commute these properties, is interesting but maybe 'premature', because I could claim that "hidden variables" are "Little Green Men with Flashlights" representing on/off, |0⟩ or |1⟩, and it would be quite hard to prove me wrong...

Therefore, this is clearly a question on realism. Is there "something" there when no one is watching?

Now, the PBR theorem has clearly a strong connection to the standard Bell framework, and therefore we cannot talk about realism without the other strongly related concept locality (despite Ken G’s 'aversion').

If we take your picture of the "temperature model" and implement it in an EPR-Bell context:

[PLAIN]http://upload.wikimedia.org/wikipedia/commons/6/6d/Translational_motion.gif[B]<---->[/B][PLAIN]http://upload.wikimedia.org/wikipedia/commons/6/6d/Translational_motion.gif

Now is this going to make our day?

I don’t think so... Even if we one day do find those "temperature particles" that 'triggers' the measured value – they can never be 'classical ontic particles', because if they are *real* they must also be *non-local*.

And this is something we can prove already today, it doesn’t matter which 'camp' you belong to. Very soon it will be an empirical fact that will never change, no matter what fancy theories comes along in the future; realism is 'doomed' to be non-local.

I think it interesting to examine the outcome of the PBR theorem:

[Pulled from Matt Leifer's blog]

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

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

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

And see what it means if we adopt it to the Bell framework:

1. ψ-epistemic: Obsolete, does not work anymore.
   
   
2. ψ-epistemic: local non-realism* / non-local non-realism.
   
   
3. ψ-ontic: non-local realism.

This is what we have to play with, and as said, it doesn’t matter if we are talking "Little Green Men" or something else.

Now, does it matter? Is it a breakthrough?

Well, I’m not the man to judge this... The 'feeling' I have is that non-realism feels very 'strange', and if I could choose, I go for non-locality instead...

*non-realism aka non-separable


P.S. I have to leave now, get back tomorrow.

 

[bohm2]

And see what it means if we adopt it to the Bell framework:

1. ψ-epistemic: Obsolete, does not work anymore.
   
   
2. ψ-epistemic: local non-realism* / non-local non-realism.
   
   
3. ψ-ontic: non-local realism.

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".

but also because Einstein's "view I" clearly contradicts QM (and experiments). So there's no need to compare those two views now.

I didn’t think that Bell-inspired derivation attacked that part of Einstein’s arguments. Isn’t that what PBR is supposed to do? Bell’s establishes no local hidden variable theory can agree with QM's predictions 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:

Perhaps the best known contemporary advocate of option 1 is Rob Spekkens, but I also include myself and Terry Rudolph (one of the authors of the paper) in this camp. Rob gives a fairly convincing argument that option 1 characterizes Einstein’s views in this paper, which also gives a lot of technical background on the distinction between options 1 and 2.

Hence since PBR shows that we can distinguish with certainty (complete), QM must be non-local? Well, unless, you're a anti-realist. Then it doesn't matter, I guess.

 

[Fredrik]

I didn’t think that Bell-inspired derivation attacked that part of Einstein’s arguments. Isn’t that what PBR is supposed to do?

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?

Bell’s establishes no local hidden variable theory but doesn’t address the arguments put forth by Einstein in 1927 that QM itself cannot be both complete and local.

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

Isn't that the whole meaning of this quote by Matt Leifer:
...
Hence since PBR shows that we can distinguish with certainty (complete), QM must be non-local?

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.

 

[Fredrik]

My previous attempt to explain the argument wasn't quite successful, so let's try again.

Suppose that there's a ψ-epistemic ontological model for the quantum theory of a single qubit. (The terminology is defined in HS. See also ML). Denote the set of ontic states of that model by \Lambda. Then \Lambda\times\Lambda is the set of ontic states in an ontological model for the two-qubit quantum theory.

I'm going to simplify the presentation of the argument by pretending that \Lambda has a finite number of members. (I want to avoid technical details about probability measures). Denote that number by n, and denote the members of \Lambda by \lambda_1,\dots,\lambda_n.

Let \mathcal H be the Hilbert space of the quantum theory of a single qubit. Then \mathcal H\otimes\mathcal H is the Hilbert space of the quantum theory of two qubits. Let \{|0\rangle,|1\rangle\} be an orthonormal basis for \mathcal H. Define
<br /> \begin{align}<br /> |+\rangle &amp;=\frac{1}{\sqrt{2}} \left(|0\rangle+|1\rangle\right)\\<br /> |-\rangle &amp;=\frac{1}{\sqrt{2}} \left(|0\rangle-|1\rangle\right).<br /> \end{align}<br /> \{|+\rangle,|-\rangle\} is another orthonormal basis for \mathcal H.

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&#039;\rangle\in\mathcal H\otimes\mathcal H and each (\lambda,\lambda&#039;)\in\Lambda\times\Lambda, let Q_{\psi\psi&#039;}(\lambda,\lambda&#039;) denote the probability that the two-qubit system is in ontic state (\lambda,\lambda&#039;). We assume that
Q_{\psi\psi&#039;}(\lambda,\lambda&#039;) =Q_\psi(\lambda)Q_{\psi&#039;}(\lambda&#039;) for all values of the relevant variables.

Let X be a self-adjoint operator on \mathcal H\otimes\mathcal H with the eigenvectors
<br /> \begin{align}<br /> |\xi_1\rangle &amp;=\frac{1}{\sqrt{2}} \left(|0\rangle\otimes|1\rangle +|1\rangle\otimes|0\rangle\right)\\<br /> |\xi_2\rangle &amp;=\frac{1}{\sqrt{2}} \left(|0\rangle\otimes|-\rangle +|1\rangle\otimes|+\rangle\right)\\<br /> |\xi_3\rangle &amp;=\frac{1}{\sqrt{2}} \left(|+\rangle\otimes|1\rangle +|-\rangle\otimes|0\rangle\right)\\<br /> |\xi_4\rangle &amp;=\frac{1}{\sqrt{2}} \left(|+\rangle\otimes|-\rangle +|-\rangle\otimes|+\rangle\right)<br /> \end{align}<br /> Note that each of the state vectors
<br /> \begin{align}<br /> &amp;|0\rangle\otimes|0\rangle\\<br /> &amp;|0\rangle\otimes|+\rangle\\<br /> &amp;|+\rangle\otimes|0\rangle\\<br /> &amp;|+\rangle\otimes|+\rangle<br /> \end{align}<br /> is orthogonal to exactly one of the |\xi_k\rangle.

The result of an X measurement that corresponds to eigenvector |\xi_k\rangle will be denoted by k. For all k and all \psi,\psi&#039;\in\mathcal H, let P_{\psi\psi&#039;}(k|X) denote the probability assigned by the ontological model for the two-qubit quantum theory to measurement result k, given that we're measuring X, and that the epistemic state of the two-qubit system is Q_{\psi\psi&#039;}. For each k and each \lambda,\lambda&#039;\in\Lambda, let P(k|\lambda,\lambda&#039;,X) denote the probability assigned by the ontological model for the two-qubit quantum theory to the result k, given that we're measuring X and that the ontic state of the two-qubit system is (\lambda,\lambda&#039;).

Now let \lambda be an ontic state of a single qubit that's assigned a non-zero probability by both Q_0 and Q_+. Define q=\min\{Q_0(\lambda),Q_+(\lambda)\}. Since |0\rangle\otimes|0\rangle is orthogonal to |\xi_1\rangle, we have
0=\left|\langle\xi_1| \left(|0\rangle\otimes| 0\rangle\right)\right|^2 =P_{00}(1|X)=\sum_{i=1}^n \sum_{j=1}^n Q_{00}(\lambda_i,\lambda_j) P(k|\lambda_i,\lambda_j,X) Since every term is non-negative, this implies that all terms are 0. In particular, the term with \lambda_i=\lambda_j=\lambda is 0.
0=Q_{00}(\lambda,\lambda)P(1|\lambda,\lambda,X)
Since Q_{00}(\lambda,\lambda) =Q_{0}(\lambda)Q_{0}(\lambda)\geq q^2&gt;0, this implies that P(1|\lambda,\lambda,X)=0.

A very similar argument based on the fact that |0\rangle\otimes|+\rangle is orthogonal to |\xi_2\rangle implies that P(2|\lambda,\lambda,X)=0. A similar argument works for all four values of k, so we can prove that P(k|\lambda,\lambda,X)=0 for all k\in\{1,2,3,4\}. This implies that \sum_{k=1}^4 P(k|\lambda,\lambda,X)=0\neq 1. This implies that at least one of the assumptions that told us that we were dealing with a ψ-epistemic ontological model for the two-qubit quantum theory must be false.

 

[my_wan]

Definitions of ψ-ontic and ψ-epistemic from the HS article.

• ψ-ontic - Every complete physical or ontic state in the theory is consistent with only one pure quantum state.
• ψ-epistemic - There exist ontic states that are consistent with more than one pure quantum state.

Now since what we are dealing with experimentally is a supposed complete description, known or not, we call the complete description λ. So the two definitions correspond to:
Ontic if theory λ uniquely determines an outcome.
Epistemic if theory λ allows for multiple outcomes.

Now let's forget QM and ψ and simply see what kind of trouble we can get in. We have a theory λ of dice roll. It states that the probability of rolling any given number is 1 in 6. But any of those 6 outcomes is consistent with λ. This entails that our theory λ is epistemic in nature. Now we take a large number of n dice and dump them. Our epistemic theory λ now tells us that the number rolled is 3.5(n). Given some margin of error we see that the number rolled is indeed consistently 3.5(n). Since our theory λ now uniquely specifies the resulting state has our epistemic theory λ now been proven to be an ontic theory?

This exact same situation entails the same thing about classical thermodynamics, statistical mechanics and the associated state variables such as pressure, temperature, etc. The certainty with with we can uniquely determine a state variable tells us nothing about the nature of the variables used to arrive at that unique value. It can be said that Brownian motion has proved that classical thermodynamics is an ontic construct. Yet if QM is held to be a purely epistemic construct, no deeper underlying reality, and the classical ontic entities are a product of QM then isn't our classical ontic entities actually purely epistemic entities?

The fact is that if we partition a set of epistemic variables they can be treated for all intent and purposes as if ontic entities. Thus proving that some variable associated with some observable posses characteristics associated with ontic variables says nothing about the character of their constituents. The classical world is in effect a partitioned set of QM properties. We generally only see leaks in this partitioning at a very fine scale.

 

[Ken G]

My previous attempt to explain the argument wasn't quite successful, so let's try again.

OK, thanks for that distillation of their argument. It seems to me that the crux of it is that if there really is an ontological theory that underlies QM (in the sense that the ontological theory explains every prediction QM makes), and the ontological theory is the complete description of the situation (it involves the true properties of the system), then the state vectors of quantum mechanics must have a certain relationship with that complete ontological theory: they must be a subset of the same ontics. By that I mean, overlapping state vectors always imply overlapping properties, and complete overlap of the properties requires the same state vector (modulo the usual isometries that go into the state vector concept). That means that complete knowledge of the ontics of the ontological theory suffices to uniquely determine the state vector, I don't need to know anyone's knowledge of the system before I can say what they think the QM state vector will be. Another way to say this is "individual systems really have unique state vectors if a complete ontological theory underlies QM."

We might then say that "QM is a subset of the ontics of the ontological theory", and "QM must itself be an ontological theory." Here by "an ontological theory" I mean a theory that bears this relationship with the "true theory of the actual properties", that the properties determine the state (though not necessarily the other way around because that would require that QM itself be the true and complete ontological description).

Which brings be back to my initial objection-- the assumption that there exists such a true and exact ontological theory underlying quantum mechanics, the assumption that there are "properties." I'm really not surprised that if ontological properties exist, and if QM makes true predictions, then QM connects directly to those properties. What bothers me is the PBR attitude that "realism" is a "complete commitment to a belief in properties." To me, properties are clearly mental constructs of our theories, that get relaxed or become more sophisticated in some other theory, like how exact position is a construct of classical mechanics that is relaxed in quantum mechanics. Since when did being a "realist" depend on denying the demonstrably true character of every physics theory we've ever had? I think having the "existence of properties" as an assumption behind a proof casts the applicability of any such proof into serious doubt.

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. Hence, a "property" is an "element of a theory", and does nothing to separate "ontic" theories from "epistemic" theories. Indeed, theories aren't either ontic or epistemic, they are just theories. What is ontic or epistemic is our philosophical choices about how we talk about a theory, and these choices are not testable, because the same theory can be either. I think the various interpretations of QM make that clear. Now, PBR says that we can't interpret QM as both realist and epistemic, but that's only because they already adopt too narrow of an interpretation of what a "realist" theory is that it leaves no room for epistemology. It was their philosophical choice to do that, it doesn't really tell us much of importance about quantum mechanics if we simply reject that choice.

 

[Ken G]

The fact is that if we partition a set of epistemic variables they can be treated for all intent and purposes as if ontic entities.

Yes, this is what I have been saying also-- the key is in what is meant by "all intents and purposes." To PBR, the only intents and purposes they have in mind must be consistent with the idea that properties provide a complete physical description, such that everything that happens can be traced directly back to the properties. But QM has no step where you convert a preparation into a set of properties, you only connect the preparation to the outcomes, and along the way you might typically embrace the concept of properties (like quantum numbers) but you never need to attach any mechanistic connection between the properties and the outcomes. Any such connection amounts to belief in magic, in effect-- like those who believed that gravity was a force that appears (magically) due to the presence of a mass, or a curvature of spacetime that appears (magically) because of stress energy properties. PBR says that to be a realist, one must introduce this intermediate and unnecessary step of, in effect, believing in magic, but I say, being a realist means treating a physical theory like a physical theory. It is a realist attitude to treat ontological descriptions as a kind of intentional fantasy that we enter into because it is parsimonious to do so. 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.

 

[my_wan]

Even if you move away characterizations of variables in terms of ontic, epistemic, and contextual, and move to actual physical constructs, the problem of such definitions do not go away. This can be illustrated by asking if a hurricane should be characterized as an ontic, epistemic, and contextual object. Its presumably ontic constituents are defined by the molecules and their behavior or phase space. But consider those properties.

1) No individual molecules have any property that is at all distinct from properties present in any other circumstance with no hurricane or even wind present.

2) If you attempt to define a distinct point like position moment of the hurricane there may in fact be no molecules, or anything else, at that position.

3) If you attempt to define the boundaries, within which the hurricane resides at a given moment, no such distinct boundaries exist.

In terms of constituent properties the hurricane, for all intent and purposes, does not "exist". Its existence is solely dependent on the contextual relations between the constituent properties of its parts, and not the constituent properties themselves. We can of course call these contextual properties a distinct higher order property. We can call this a purely contextual construct or entity, in which the ontic elements defining it may or may not be ontic. The constituent elements, presumed ontic, may or may not be contextual entities in themselves.

So can we delineate between ontic and epistemic or contextual variables simply on the properties they posses? Well our hurricane has a location, trajectory, and leaves a very distinct path of destruction in its wake. All the hallmarks of an ontic entity. Yet we cannot say when, where, or if ever, a reduction of parts will ever lead us to variables that represent actual ontic entities. Our knowledge is restricted to an epistemic regime. We can say that under circumstances in which epistemic variables can be partitioned, to some degree or the other, that we can treat those partitioned properties as if they were ontic.

The problem many realist have is not with contextual or epistemic variables in general, but the end game question: Is it really turtles all the way down? Of course the non-realist will say we have already hit bottom, and their is no deeper reality.

Now, wrt the PBR article, I think it makes some interesting points. Yet trying to delineate between ontic or epistemic characterizations based on possessing characteristics of partitioned properties shouldn't get very far. Our hurricane is, more or less, partitioned in space also.

Right now I'm going to eat some epistemic turkey.

 

[qsa]

all these epistemic-ontic arguments are well and good. but do they shed any light on the real problematic issue of wave-particle duality.

 

[Ken G]

The problem many realist have is not with contextual or epistemic variables in general, but the end game question: Is it really turtles all the way down? Of course the non-realist will say we have already hit bottom, and their is no deeper reality.

Exactly, and I'd like to offer the third choice: a realist is exactly the person who recognizes that the concept of "reality" as a whole is an effective notion, just like the way you described the reality of a hurricane. After all, is it not "realistic" to expect all of reality to have the same character as the elements we talk about as making up that reality?

Now, wrt the PBR article, I think it makes some interesting points. Yet trying to delineate between ontic or epistemic characterizations based on possessing characteristics of partitioned properties shouldn't get very far.

I completely agree.

Right now I'm going to eat some epistemic turkey.

Yes, and indeed, that jest alludes to a serious point often made by those who hold to a more naive version of realism-- that only the realist can account for why a rock hurts when it falls on your toe, and only a fool would deny the ontology of that rock. But that's just naivete talking-- logically, it is perfectly possible for me to form an ontological construct in my head that is consistent with my experiences, like rocks and pain and hurricanes, without that construct in my head having "true properties." There's just no connection there. I say the realist is the person who does not believe in magic, who does not believe that the rock has some innate propeties that "caused" it to hurt my toe. How does a rock have innate properties, and become such an action hero, anyway?

 

[Fredrik]

I believe I have found a flaw in the paper.

In short, they try to show that there is no lambda satisfying certain properties. The problem is that the CRUCIAL property they assume is not even stated as being one of the properties, probably because they thought that property was "obvious". And that "obvious" property is today known as non-contextuality.
...
They first talk about ONE system and try to prove that there is no adequate lambda for such a system. But to prove that, they actually consider the case of TWO such systems. Initially this is not a problem because initially the two systems are independent (see Fig. 1). But at the measurement, the two systems are brought together (Fig. 1), so the assumption of independence is no longer justified.

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.

 

[Fredrik]

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. 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.

 

[DevilsAvocado]

... 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. Hence, a "property" is an "element of a theory", and does nothing to separate "ontic" theories from "epistemic" theories. Indeed, theories aren't either ontic or epistemic, they are just theories.

Bewildering gibberish...

This could be quite confusing for the 'casual reader', since you are making up your own rules for what is what. Realism is never associated to scientific theories, in the meaning of truth, this is just nonsense, and I have no idea why you are making theses associations. It should be well known that any physical theory is always provisional, in the sense that it is only a hypothesis; you can never prove it.

Another very important factor of scientific theories is that they must be refutable, i.e. you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory.

As anyone can see, it would be ridiculous to claim that realism, to be true, must be refutable and provisional. If (non-local) realism one day is found to be true, i.e. an empirical fact, then one of its "main features" is that it is not refutable and not provisional; i.e. it must be true forever, to qualify for an empirical fact!

What is ontic or epistemic is our philosophical choices about how we talk about a theory, and these choices are not testable,

More gibberish...

Could you please explain how we could ever test and validate our theories? If "these choices are not testable"??

It seems like you talk more about to philosophical realism in metaphysics, than realism in physics.

Local Realism as defined by physicists:

There is a world of pre-existing particles (objects) in the microscopic world, having pre-existing values for any possible measurement before the measurement is made (=realism), and these real particles is influenced directly only by its immediate surroundings, at speed ≤ c (=locality).​

As we can see, this definition of local realism will also make sense to "Joe the Plumber", if explained.

Now, is the "Joe the Plumber Realism” testable??

Of course it is!

Local Realism is tested and proven false by 99%, and all that remains is the Grand Funeral!

To say that we cannot test our theories, and via them, find out what is true or not true in nature, is just false.


Denial of facts and twisting of terms is something that never has appealed to me...

 

[Ken G]

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.

And that raises another important ontological issue: is a probability an ontic notion, or is it always fundamentally epistemic? In other words, is there "any such thing" as the probability of an outcome? If you deal me a card from a deck, is "the probability" 1/52 of the ace of hearts, or are all probabilities necessarily contingent on our information about that deck? This connects to my objection to the concept of a "property." I would argue that decks do not have properties that determine these probabilities-- what determines every probability that anyone ever used in connection with a deck of cards was their knowledge about that deck of cards, and no probability is ever worth anything more than that knowledge. I'm not just questioning the definition, because a definition is just a definition-- I'm questioning the ramifications of the definition, i.e., what can be assumed to come along with the definition. We can certainly define "ontic" to mean something that maps from a concept of a property to a concept of a probability, but both ends of that map are still concepts. So we cannot take that definition and say that an ontic model actually supports an underlying truth in which there are properties that determine probabilities. In other words, whether we have an ontic model or an epistemic model, however we define those terms, the only thing that ever determines a probability in any physics theory is always the knowledge of the physicist. This is so demonstrably true, that I marvel at what ends up getting called "realist."

 

[Ken G]

Bewildering gibberish...

I'm afraid you are falling into logical fallacy again. Here's the problem. You claim what I just said is gibberish. That means you didn't understand it (which is true, you didn't). Unfortunately, since you did not understand it, this means no one should pay any attention to your judgement of it (which they shouldn't).

Another very important factor of scientific theories is that they must be refutable, i.e. you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory.

Hmm, that's certainly true, now what on Earth does that have to do with anything I said? I just can't pass judgement on the argument you are presenting, because I don't understand it at all. All that is clear to me is that you took not a single word of my intention correctly.

 

[Fredrik]

is a probability an ontic notion, or is it always fundamentally epistemic?

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'm not sure there's a meaningful distinction between the terms "ontic" and "epistemic" outside of that framework, but maybe that was your point.

By the way, something that assigns a probability P(k|λ,M) to the result k, given an ontic state λ and a measurement procedure M, is almost what I would call a "theory of physics". We just need to add some rules that associate preparation procedures with probability measures on \Lambda, and we're good to go.

I would argue that decks do not have properties that determine these probabilities

You don't think the order of the cards will influence the probabilities? (That's what it sounds like, but I assume that you meant something else).

 

[nucl34rgg]

If QM as we learned it is wrong, why does it work so well? Also, how can anyone know anything is "really there" when all you can actually know about "reality" is what you measure and observe? We can only scientifically make statements about measurements we take.

The moon really basically isn't there unless something interacts with it to confirm that it is there. Otherwise there is no reason to believe it is actually there at all. The measurement doesn't just disturb the system in QM. It seems to define it.

 

[Ken G]

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. 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? 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. 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'm not sure there's a meaningful distinction between the terms "ontic" and "epistemic" outside of that framework, but maybe that was your point.

Yes, the distinction is artificial. They assume a distinction exists, then prove certain constraints on the distinction, but there is nothing in quantum mechanics that suggests or requires that distinction exists. That's clear enough, but I'm saying that adding "realism" to quantum mechanics actually does nothing to alter that situation-- unless one takes the narrow (and dubious) stance that realism should be identified with belief that hidden properties determine everything. I call that belief in magic-- all we have in physics are our theories, and the next theory will have different variables than the last one, but that doesn't make any of them any "less hidden" than the ones before.

By the way, something that assigns a probability P(k|λ,M) to the result k, given an ontic state λ and a measurement procedure M, is almost what I would call a "theory of physics". We just need to add some rules that associate preparation procedures with probability measures on \Lambda, and we're good to go.

Yes, I completely agree. So you can see why I object to a claim that the mere existence of theories of physics requires that we must regard them as fundamentally ontological! That's the circularity I object to, most of what this theorem "proves" is embedded in its assumptions, all that's left to prove is a minor issue that is not fundamental to what any physics theory actually is.

You don't think the order of the cards will influence the probabilities? (That's what it sounds like, but I assume that you meant something else).

The "order of the cards" is not a property that determines observables, it is an observable. If I deal the cards out one by one, and you say "see, the order of the cards determined the order of the cards", I accuse you of tautology.

 

[Ken G]

The measurement doesn't just disturb the system in QM. It seems to define it.

Yes I agree, and indeed, this is nothing new in quantum mechanics-- it was always true in physics. QM is simply the place where we are forced to confront the issue, we always got away with lazy (yet highly parsimonious) ways of describing the situation in classical physics. Realism should not be regarded in the naive belief that the distinction does not exist, instead it should be associated with not making the distinction when it is not necessary to do so.

 

[qsa]

So what is the relation between the nature of psi, its interpretation and the wave-particle daulity. would a choice for one affect the others. or is that too much to ask.

 

[billschnieder]

There is a lot of confusion going around on this thread making it difficult to actually discuss what the authors of this article are talking about. Let me attempt to through some light to this:

Ontological - means "what is real", "what exists", independent of whether we know it or not.
Epistemological - means "what we know"

Words like "ontic" and "epistemic" are simply variants of those words, so phrases such as "ontic epistemic" or "ontic ontological" are just unnecessary confusion.

Let's use the example of a die to make these concepts more clear.

Reality (Ontology): Our die is a cube with six sides, with dimensions x,y,z, and physical properties i, j, k, ... etc. In other words, the ontology of the die is the complete specification of all existing physical properties of the system. Note that no two dice can have the same physical properties if these properties have been completely specified.

Epistemology (What we know): We could simply know the physical properties of a given die. But note a few very important points:
* Just because the die has a given physical property does not mean we can know it -- reality by definition exists whether we know it or not. Therefore we can never be sure we know all the possible physical properties of any system.
* Without absolute knowledge, we can never be certain that we know the exact value of any given knowable physical property. We could however have a value together with a confidence interval or a margin of error within which the real value lies.
* Our knowledge of the system may not even be represented in terms of the physical properties exactly but some other properties which are derived from some combinations of the hidden physical properties of the system.
* In the case in which a die is thrown and we have to predict the outcome, even if you know the complete physical properties of the with certainty, you will not know the outcome with certainty unless you also know the complete physical properties/conditions of the experiment. Probabilities arise ONLY due to uncertainty. The presence of probabilities in ANY theory implies lack of information or INCOMPLETE knowledge.
* You can only know something that is true or exists. It makes no sense to know nothing. In other words, our knowledge itself can not be the thing we are knowing. Therefore the idea that you can have a epistemic theory floating in the aether with nothing as it's object is not even wrong. Once you seriously look at what it is the theory is trying to know, the veil begins to lift just a bit.

The real question here is: does |ψ|^2 apply to an individual system or to a class of systems. Note that the quantum particle may be completely specified but if the preparation of of the experiment is not completely specified, the outcome will not be uniquely determined by ψ.

 

[my_wan]

Yes, this is what I have been saying also-- the key is in what is meant by "all intents and purposes." To PBR, the only intents and purposes they have in mind must be consistent with the idea that properties provide a complete physical description, such that everything that happens can be traced directly back to the properties. But QM has no step where you convert a preparation into a set of properties, you only connect the preparation to the outcomes, and along the way you might typically embrace the concept of properties (like quantum numbers) but you never need to attach any mechanistic connection between the properties and the outcomes.

Yes, and I'm still interested in this article because it does appear to establish some theoretical constraints. Even though I'm a lot less convinced that the characterization of those constraints as outlined really hold in general.

Any such connection amounts to belief in magic, in effect-- like those who believed that gravity was a force that appears (magically) due to the presence of a mass, or a curvature of spacetime that appears (magically) because of stress energy properties.

When I read this I got a bad impression. However, I looked back at your previous post #101, where the last paragraph clears it up for me and I would concur. For me this "magic" you speak of has a lot to do with how Bell's theorem gets interpreted, where properties are used as proxies for physical states while effectively denying a distinction, i.e., assuming the proxies are the real thing. Classical physics itself is replete with this particular kind of "magic" thinking and, from my perspective, almost certainly in need systematic revisions.

This reminds me of reading about the electron a a pre-teen. I was thinking: Yeah right, so you have a point entity lacking internal dynamics. Yet because of a "property" it possesses it has these dynamics. Meanwhile other point entities have different "properties". My take was BS, if this is how things are then what's to stop my toy car from being endowed with the "properties" of my parents car.. Without getting into detail this lead me to EPR type paradoxes, if such logic held, before I had ever heard of EPR.

PBR says that to be a realist, one must introduce this intermediate and unnecessary step of, in effect, believing in magic, but I say, being a realist means treating a physical theory like a physical theory. It is a realist attitude to treat ontological descriptions as a kind of intentional fantasy that we enter into because it is parsimonious to do so. And because that's exactly what we do, that is the realist stance-- ontology is epistemology.

I find it interesting simply on the grounds that it seems to indicate that a property set should, at least in principle, be able to accomplish this. Something QM really makes no provisions for and previous "property" modeling attempts have left a lot to be desired. I think that if the theorem holds, and a property set can in principle accomplish what this paper seems to indicate, it is an important result. However, I am with you in that this property set is still just an epistemological rendering representing only a valid symmetry between the model and the actual state. Valid and true are not synonymous. So I can appreciate the fact of the symmetries the article seems to indicate should hold without applying an undue reality to how things really are.

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.

I have my own take on this. I am a realist, and concur that everything we can know about the Universe is epistemology. At a young age I came to this conclusion for reason quiet similar to some of the things our Dr Chinese said in "Hume’s Determinism Refuted". My thinking was that rinsing the "magic" off of the notion of ontic elements left you with entities that did not posses any properties in the usual "magic" sense you spoke of. Since properties is what defines measurements this made any ontic elements that might underpin the universe unobservables in any direct way, like the independent variables Dr Chinese spoke of. This, however, does not mean that you can't theorize about them and build a hierarchy of epistemological sets of observables from them. It does mean that any emergent observables have to be built out of relational data, where all empirically accessible variables are more akin to verbs than nouns, including the constants.

So unlike Dr Chinese I don't hold the position that the inability to empirical access ontic state properties, or independent variables, as a death blow to their existence or potential theoretical usefulness. However, it is true that claiming existence of X in any absolute real sense remains a non-starter. Fundamentally no different from a theoretical field specification except the properties are emergent rather than innate. Modeling attempts of this type are not even conceivable when either realism is interpreted as a property set sprinkled on a set of ontic entities or realism is rejected outright claiming no deeper ontic underpinning exist, only properties. Anyway, that's my take on it, not that it's likely to get me anywhere, and in terms of what we know it still doesn't remove the fundamental fact that our knowledge is limited to the epistemological regardless of what a successful theoretical construct is predicated on.

 

[Ken G]

* In the case in which a die is thrown and we have to predict the outcome, even if you know the complete physical properties of the with certainty, you will not know the outcome with certainty unless you also know the complete physical properties/conditions of the experiment. Probabilities arise ONLY due to uncertainty. The presence of probabilities in ANY theory implies lack of information or INCOMPLETE knowledge.

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. 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." 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.

Therefore the idea that you can have a epistemic theory floating in the aether with nothing as it's object is not even wrong.

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 the quantum particle may be completely specified but if the preparation of of the experiment is not completely specified, the outcome will not be uniquely determined by ψ.

Note that one 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. Even the very concept of "a quantum particle", when interpreted in the narrow way you interpret ontology, is quite a dubious notion. Your position is really just a bunch of sweeping generalizations, and even though they are very common, there really is a lot deeper that we can dig into these kinds of fairly superficial assumptions.

 

[my_wan]

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. Hence, a "property" is an "element of a theory", and does nothing to separate "ontic" theories from "epistemic" theories. Indeed, theories aren't either ontic or epistemic, they are just theories.

Bewildering gibberish...

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.

 

[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&#039;\rangle\in\mathcal H\otimes\mathcal H and each (\lambda,\lambda&#039;)\in\Lambda\times\Lambda, let Q_{\psi\psi&#039;}(\lambda,\lambda&#039;) denote the probability that the two-qubit system is in ontic state (\lambda,\lambda&#039;). We assume that
Q_{\psi\psi&#039;}(\lambda,\lambda&#039;) =Q_\psi(\lambda)Q_{\psi&#039;}(\lambda&#039;) 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
<br /> \begin{align}<br /> |\xi_1\rangle &amp;=\frac{1}{\sqrt{2}} \left(|0\rangle\otimes|1\rangle +|1\rangle\otimes|0\rangle\right)\\<br /> |\xi_2\rangle &amp;=\frac{1}{\sqrt{2}} \left(|0\rangle\otimes|-\rangle +|1\rangle\otimes|+\rangle\right)\\<br /> |\xi_3\rangle &amp;=\frac{1}{\sqrt{2}} \left(|+\rangle\otimes|1\rangle +|-\rangle\otimes|0\rangle\right)\\<br /> |\xi_4\rangle &amp;=\frac{1}{\sqrt{2}} \left(|+\rangle\otimes|-\rangle +|-\rangle\otimes|+\rangle\right)<br /> \end{align}<br />

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?