The quantum state cannot be interpreted statistically?

[DevilsAvocado]

(My bold)

This is how I see it more or less. More or less the point I was making with first-order verses higher-order logic. The [0,1] or law of the excluded middle models only appear to make sense if you are looking for particles that "own" properties like raisins in pudding. Once you allow two bowls of pudding to mix all bets are off as to which pudding the raisins belong to, or even whether the raisins will stay intact.

my_wan, I respect your knowledge, but this is really so simple that a 10-year-old can understand, if explained. (That’s why I understand! )

No tornado, raisins, pudding or middle models in the world could save your a**, it just doesn’t work.

The only way, is to refute empirical data and blame on loopholes, and I know you’re too smart for that. This is the simplest form of Bell's inequality:

N(+30°, -30°) ≤ N(+30°, 0°) + N(0°, -30°)​

And we could simplify it even more and say that Local Realism result in this:

1 + 1 = 2​

And QM theory + all EPR-Bell experiments performed this far result in this:

1 + 1 = 3​

No raisins in the world could ever get you out of this, trust me buddy!

 

[DevilsAvocado]

OK, that makes sense.

Okay

 

[Ken G]

I do think the PBR theorem considers an "ontological model" to be one that can be conceived as producing only probabilities of 0 or 1, that must be what they mean by the outcome being determined by a complete set of properties. If they say the complete set of properties only sets the probabilities, how is that a complete ontological description? Where is the "random number generator" in that ontology?

 

[apeiron]

(My bold)

This is how I see it more or less. More or less the point I was making with first-order verses higher-order logic. The [0,1] or law of the excluded middle models only appear to make sense if you are looking for particles that "own" properties like raisins in pudding. Once you allow two bowls of pudding to mix all bets are off as to which pudding the raisins belong to, or even whether the raisins will stay intact.

A more accurate analogy could be two vortices mixing. The "raisins" are contextual, the product of boundary constraints..

A couple of simulations of vortex merging...





Also, real life storms...

http://en.wikipedia.org/wiki/Fujiwhara_effect

 

[DevilsAvocado]

I do think the PBR theorem considers an "ontological model" to be one that can be conceived as producing only probabilities of 0 or 1, that must be what they mean by the outcome being determined by a complete set of properties. If they say the complete set of properties only sets the probabilities, how is that a complete ontological description? Where is the "random number generator" in that ontology?

I don’t understand the PBR theorem completely, but I can tell you that if you are going to discuss any "underlying ontic state" you need to take Bell in consideration.

 

[DevilsAvocado]

A more accurate analogy could be two vortices mixing. The "raisins" are contextual, the product of boundary constraints..

A couple of simulations of vortex merging...





Also, real life storms...

http://en.wikipedia.org/wiki/Fujiwhara_effect

Looks nice apeiron but even with these 'particles' outside each other’s light cone, gravity or whatever, is always ≤ c therefore this won’t help.

 

[my_wan]

I think this places us back into the context where we agree. I have been saying all along that ontic substructures, like the concept of exact position and momentum (often claimed to be an ontic substructure of classical mechanics, but I maintain it was never that at all, just a kind of lazy fiction that makes it easier to talk about classical mechanical predictions but is in no way central to those predictions and certainly was never a tested aspect of the theory), are always provisional and contextual. No theory ever required them, there is no such thing as a theory that is "founded on" such substructures, for the simple reason that all theories have to work in concert with how scientists actually do science. So the irony that you see in calling quantum mechanics "unreal" if it doesn't preserve the single most unrealistic, unnecessary, and undemonstrated element of how classical mechanics is often described, is the irony I see in claiming that quantum mechanics "realists" must believe in "a complete set of properties" that determine outcomes. That is a highly unrealistic assumption in my view, so what I have been trying to say is, we should not make the mistake of equating ontological descriptions with realist descriptions, when being realist should mean recognizing the limitations of ontological language about reality.

In our debate I was explicitly singling out our differences. My level of agreement with you has not diminished in the course of the debate.

We absolutely know, even without QM or the classical thermodynamics verses statistical mechanics analogy, that position is purely contextual. We even new it in terms of Galilean relativity in Newton's time. It's the main motivation behind a very fundamental principle called coordinate or background independence. Hence a coordinate choice is by definition not a physical choice. Relativity merely articulated how these contextual variables are related. Even on the face a velocity can be both zero and nonzero at the same time, depending on the nonphysical coordinate choice chosen.

The main point is that these contextual variables do not rule out ontic constructs in which we are then free to contextualize in a bewildering number of coordinate choices or spaces. Yet all valid choices transform into one another in one way or the other, no matter how different they appear on the surface or involve apparently incongruent definitions in one coordinate choice as opposed to another. To many ontic realist this is precisely because a nonphysical coordinate choice is merely an invention for contextualizing a common underlying ontic state. Even the apparent degrees of freedom can vary as a result of coordinate choice. Yet any valid model involving any coordinate choice still must transform via symmetries into each other, because the ontic system is the same system and is doing nothing different as a result of our coordinate choice. Epistemicists have their own varying ways of conceptualizing this commonality, which is no less empirically valid.

We even have coordinate independent mathematical formulations to explicitly recognize this fact. I'll even go a step farther and say, in my opinion, that philosophical stances, so long as they are not at odds with the underlying facts of the system, are equivalent to a nonphysical coordinate choice. No matter how diametrically opposed two philosophical stances appear on the surface. The best psychological profiles even explicitly treat it as a coordinate space.

So a coordinate choice by definition defines the coordinate space as nonphysical, while whatever it is that defines the commonalities that allows one to be transformed into the other is the reality. If you think of a model strictly in terms of the coordinate choice used to define it, and the apparent definitions that particular choice entails, then of course the only sane perspective to take is a purely epistemic one.

 

[apeiron]

Looks nice apeiron but even with these 'particles' outside each other’s light cone, gravity or whatever, is always ≤ c therefore this won’t help.

I don't get what you mean about the particles being outside any light cones in this intuition-priming example. If the two vortices are in fact interacting - via a merger of their boundary constraints, or "wavefunction entanglement" - then what are you talking about here?

 

[my_wan]

A more accurate analogy could be two vortices mixing. The "raisins" are contextual, the product of boundary constraints..

A couple of simulations of vortex merging...





Also, real life storms...

http://en.wikipedia.org/wiki/Fujiwhara_effect

Looks nice apeiron but even with these 'particles' outside each other’s light cone, gravity or whatever, is always ≤ c therefore this won’t help.

@apeiron
Nice. The raisin pudding was a tongue in cheek analogy. I used hurricanes previously but shied away from including hurricane interactions, though it makes as good an analogy. Just be careful that you are clear on the limitations of these classical analogies. They are limited in more ways just EPR.

@DevilsAvocado
Yes, information is limited to c, but only if you assume a fundamental ontic particle is required to carry directly accessible empirical information is this a problem. If a particle lacks any dynamics to store information then it carries no information. If it is not presently interacting with the Universe, position doesn't even have meaning outside it's relation to the Universe, then it carries no information. If those hurricanes are the particles, how are the hurricanes to send and receive information faster than the speed of sound? They can't. Certainly the speed of sound changes under different conditions, but only because there is a preexisting spacetime metric, defined by relativity, to provide a reference to measure it against. That doesn't limit the air molecules to the speed of sound. Very important fact about GR and c, under GR the speed c is a relativistic constant, not an absolute constant. Big distinction.

 

[DevilsAvocado]

I don't get what you mean about the particles being outside any light cones in this intuition-priming example. If the two vortices are in fact interacting - via a merger of their boundary constraints, or "wavefunction entanglement" - then what are you talking about here?

Probably some misunderstanding, let me give you the 'complete chain':

... PBR only rules out (local?) ψ-epistemic ontological models.

Nope, any ontological model must be non-local within the standard Bell framework.

I'm not sure that's accurate. I think Bell's theorem only rules out those local ontological models for QM that assign probabilities 0 and 1 to measurement results. I don't think it applies to models that can assign any number in [0,1]. Do you have some other theorem in mind?

Even if your statement is correct, that doesn't automatically mean that the word "local" shouldn't be there (in my statement about what the PBR theorem says). It only means that if it should, then the theorem doesn't prove anything we didn't know already.

I don’t agree. Any pre-assignment, not matter which form, needs non-locality.

Why!?

Because if the EPRB experiment is done properly A and B should be outside each other’s light cone when the randomly rotating polarizer stops.

You could pre-assign all numbers in the world and still it won’t help, because it’s the relative angle between A and B that is crucial.

I'm not sure that's accurate. I think Bell's theorem only rules out those local ontological models for QM that assign probabilities 0 and 1 to measurement results. I don't think it applies to models that can assign any number in [0,1]. Do you have some other theorem in mind?

Even if your statement is correct, that doesn't automatically mean that the word "local" shouldn't be there (in my statement about what the PBR theorem says). It only means that if it should, then the theorem doesn't prove anything we didn't know already.

(My bold)

This is how I see it more or less. More or less the point I was making with first-order verses higher-order logic. The [0,1] or law of the excluded middle models only appear to make sense if you are looking for particles that "own" properties like raisins in pudding. Once you allow two bowls of pudding to mix all bets are off as to which pudding the raisins belong to, or even whether the raisins will stay intact.

my_wan, I respect your knowledge, but this is really so simple that a 10-year-old can understand, if explained. (That’s why I understand! )

No tornado, raisins, pudding or middle models in the world could save your a**, it just doesn’t work.

The only way, is to refute empirical data and blame on loopholes, and I know you’re too smart for that. This is the simplest form of Bell's inequality:

N(+30°, -30°) ≤ N(+30°, 0°) + N(0°, -30°)​

And we could simplify it even more and say that Local Realism result in this:

1 + 1 = 2​

And QM theory + all EPR-Bell experiments performed this far result in this:

1 + 1 = 3​

No raisins in the world could ever get you out of this, trust me buddy!

To me it looked like my_wan was trying to refute Bell's inequality and EPR-Bell experiments with "raisins in pudding" and that’s what I replied on.

If you and my_wan are talking about something else, I apologize.

 

[my_wan]

To me it looked like my_wan was trying to refute Bell's inequality and EPR-Bell experiments with "raisins in pudding" and that’s what I replied on.

If you and my_wan are talking about something else, I apologize.

No, it in no way refutes Bell's inequality. It merely states the limits of what Bell's theorem can demonstrably rule out. Bell's theorem has essentially the same limits as the PBR theorem in terms of it's use of first-order logic in assigning properties to particles.

 

[my_wan]

Think of it this way. EPR proves A which implies, but does not prove, B. Nobody has definitively proved B is not a valid consequence of A. Hence EPR proves B.

Do you see the logical error there in the last sentence alone? That is the error often used in overstating the claims of what Bell's theorem did in fact prove.

 

[DevilsAvocado]

@DevilsAvocado
Yes, information is limited to c, but only if you assume a fundamental ontic particle is required to carry directly accessible empirical information is this a problem. If a particle lacks any dynamics to store information then it carries no information. If it is not presently interacting with the Universe, position doesn't even have meaning outside it's relation to the Universe, then it carries no information. If those hurricanes are the particles, how are the hurricanes to send and receive information faster than the speed of sound? They can't. Certainly the speed of sound changes under different conditions, but only because there is a preexisting spacetime metric, defined by relativity, to provide a reference to measure it against. That doesn't limit the air molecules to the speed of sound. Very important fact about GR and c, under GR the speed c is a relativistic constant, not an absolute constant. Big distinction.

my_wan, I’ve become a "Fifth Columnist" when it comes to EPR-Bell nowadays – I’m a believer!

Seriously, if you run a "standard universe" it doesn’t matter what you do or not do before the measurement (I was unclear in last post, sorry), as long as you say "Nope! I’m not going to use non-locality to solve this mess!", then you’re in deep trouble, i.e. assuming a 'standard' universe.

Now, if you could cope with an 'exotic' universe, like non-reality (aka non-separable), or something "outside it's relation to the Universe", or just plain MWI (last unclear also here, sorry), then you can make it.

But personally, I don’t see how this is ever going to save good old "Joe Six-pack" Local Realism... you substitute non-locality for some other 'weird stuff', and this will make Joe mad anyway... no?

 

[DevilsAvocado]

No, it in no way refutes Bell's inequality. It merely states the limits of what Bell's theorem can demonstrably rule out. Bell's theorem has essentially the same limits as the PBR theorem in terms of it's use of first-order logic in assigning properties to particles.

Okay, personally I think it’s 99% clear that Local Realism is not compatible with QM predictions or EPR-Bell experiments.

 

[DevilsAvocado]

Think of it this way. EPR proves A which implies, but does not prove, B. Nobody has definitively proved B is not a valid consequence of A. Hence EPR proves B.

Do you see the logical error there in the last sentence alone? That is the error often used in overstating the claims of what Bell's theorem did in fact prove.

Again, it’s so simple that a 10-year-old can understand. This is what it’s all about:

N(+30°, -30°) ≤ N(+30°, 0°) + N(0°, -30°)​

Personally, I don’t see the use of logical validation in this case, it’s basically first grade math we are talking about, 1 + 1 = 2. And in worst case, you might not see the forest for the trees:

All cups are green.
Socrates is a cup.
Therefore, Socrates is green.​

 

[my_wan]

Fair enough DevilsAvocado
I haven't been idle on the issue either

 

[DevilsAvocado]

Peace In Mississippi!

()

 

[Ken G]

We absolutely know, even without QM or the classical thermodynamics verses statistical mechanics analogy, that position is purely contextual.

Hang on-- from what I've seen on here, you and I are absolutely the only two people who believe that statement with the "even without" part in there. PBR certainly don't-- they hold that anyone who is a "realist" must hold that the basic building blocks of any theory that works must work because they are real. So if classical mechanics says there is a concept of exact position and it helps us get the answers right, then only some whacko "anti-realist" in 1860 could have claimed that exact position is not real. Indeed, if some analog of the PBR theorem were applied to classical mechanics, you can see what a "complete set of properties" would be interpreted as: exact positions. Everyone else seems happy with defining a realist as someone who believes a theory is about reality until it is found to not agree with some experiment, and that is certainly how PBR interpret realism in regard to quantum mechanics.

We even new it in terms of Galilean relativity in Newton's time. It's the main motivation behind a very fundamental principle called coordinate or background independence. Hence a coordinate choice is by definition not a physical choice.

The coordinate choice determines the label for the position, not the idea that there is a position there. By the definition of "realist" that everyone here seems all too happy to use, any classical mechanics realist would have to hold that exact positions are real, even if a coordinate choice is required to give those exact positions a numerical label. I'm saying it's high time we didn't require realists to be that naive.

Relativity merely articulated how these contextual variables are related. Even on the face a velocity can be both zero and nonzero at the same time, depending on the nonphysical coordinate choice chosen.

Again, that is conflating the numerical label of a velocity with the ontological construct of an exact velocity that may yet be unlabeled. Classical mechanics is usually framed as advancing that ontological construct, even though everyone knows the numerical labels are coordinate dependent. (Personally, I don't think classical mechanics should require that ontological construct at all, or indeed any fundamental ontological constructs, and on that I believe we are the only two here who agree.)

The main point is that these contextual variables do not rule out ontic constructs in which we are then free to contextualize in a bewildering number of coordinate choices or spaces. Yet all valid choices transform into one another in one way or the other, no matter how different they appear on the surface or involve apparently incongruent definitions in one coordinate choice as opposed to another.

Sure, they transform into one another in ways that are described by the theory. That means even the transformations between these fundamentally non-ontological constructs are also fundamentally non-ontological, they are all borrowed from the only place they actually exist: mathematical structures. The same holds for symmetries and group properties, all borrowed from the places where they actually exist to be used in epistemological applications to the real world, said like a true realist should say it.

To many ontic realist this is precisely because a nonphysical coordinate choice is merely an invention for contextualizing a common underlying ontic state.

Yes, I agree that self-styled "ontic realists" would say that, but that doesn't change the fundamental oxymoron living behind the term "ontic realist." Those words are contradictory because belief in a true ontology means committing to a reality that exists in one's own mind, where those mathematical structures exist, and the belief the reality is fundamentally housed in our minds is idealism, not realism.

Even the apparent degrees of freedom can vary as a result of coordinate choice. Yet any valid model involving any coordinate choice still must transform via symmetries into each other, because the ontic system is the same system and is doing nothing different as a result of our coordinate choice.

There is only one reason these transformation have to work like that: science demands they get the same answer. That's it, we throw out what doesn't get the same answer, and we are left with those kinds of transformations. There's nothing ontic about it, it's still pure scientific epistemology.

Epistemicists have their own varying ways of conceptualizing this commonality, which is no less empirically valid.

True, and also has the added advantage of being internally consistent, avoiding the mind projection fallacy.

We even have coordinate independent mathematical formulations to explicitly recognize this fact.

Yes, we have all kinds of useful mathematical structures that we borrow from to fit into scientific epistemology. None of that changes the demonstrable fact that the ontology is always housed in the mathematical structure, so always in the minds that recognize that structure. To claim that is where the reality lives is thus idealism, or else it is the quintessential mind projection fallacy.

Symmetries provide a good example. The ability to conceptualize a symmetry, and recognize its usefulness in practice, is demonstrably housed in the intelligence. A symmetrical rock has no idea it is symmetrical. We find that symmetries are exceptionally simple and powerful, so the temptation to imagine a true ontology there is hard to resist. Yet the realist should resist it, because the realist should recognize the trappings of idealism-- if reality has to look like my thoughts, then I am equating reality with my thoughts about reality. That's the mind projection fallacy! It doesn't make any difference how useful the thought is, it's still idealism. The realist should expect that ultimately, every symmetry was made to be broken.

I'll even go a step farther and say, in my opinion, that philosophical stances, so long as they are not at odds with the underlying facts of the system, are equivalent to a nonphysical coordinate choice. No matter how diametrically opposed two philosophical stances appear on the surface.

I agree with that to some degree-- but I would point out that if an ontic view can be transformed seamlessly into an epistemic one, which one was fundamentally correct in the first place?

So a coordinate choice by definition defines the coordinate space as nonphysical, while whatever it is that defines the commonalities that allows one to be transformed into the other is the reality.

The commonalities are commonalities in the mathematical structures that are being borrowed from. So if they are the reality, then the mathematical structures are the reality, yet the mathematical structures are recognized and identified and characterized in our intelligence. When reality is housed in the mind, that is idealism, or it is the mind projection fallacy. One cannot have one's cake and eat it too.

If you think of a model strictly in terms of the coordinate choice used to define it, and the apparent definitions that particular choice entails, then of course the only sane perspective to take is a purely epistemic one.

But the epistemic view can also include the recognition that the coordinates don't matter. It's still epistemic to notice that-- indeed, it is even more epistemic to notice the commonalities of thoughts that all lead to the same place. When there was an "aether", there was something much more ontic there than where there is relativity. What aspect of having all observers able to use the same laws makes those laws ontic in character? It is a quintessentially epistemic law that works for any mind that would try to use it, an ontic law shouldn't care if it requires preferred minds because it is true outside of those minds.

 

[Ken G]

A more accurate analogy could be two vortices mixing. The "raisins" are contextual, the product of boundary constraints.

Yes, this brings up an important limitation to what gets called "realism" in regard to quantum mechanics, which should really be called "reductionism." If there is a "complete set of properties" that determines everything, that is the reductionist dream-- properties removed from any contextual meaning, they just are. The whole is the sum of its properties, and nothing else is "realism." You talk a lot about the importance of top-down contraints, so where is the space for them in this "complete set of properties?" Is the PBR theorem still proving something if top-down constraints are fundamental to how any complete physical theory must work? I don't think it is, it seems to be relevant to hidden variables theories, but top-down constraints are not what most people mean by hidden variables, such variables are generally reductionist in character.

The definition of a scientific realist is someone who takes the elements of scientific theories literally in regard to reality. To avoid foolish naivete, they must at least allow that the correspondence still counts if it has been shown to be only approximate. Notwithstanding the logical quandary around "how approximate still counts", we still have the problem that scientific theories that are not purely reductionist still don't fit the PBR program, so taking the attributes of any top-down constraint literally as part of the reality is an example of a "realist" stance that PBR do not even recognize as realist.

 

[Fredrik]

I do think the PBR theorem considers an "ontological model" to be one that can be conceived as producing only probabilities of 0 or 1,

It's clear that they don't, since they reference Harrigan & Spekkens, and they don't. They might however be thinking that "What we really want to rule out are the ψ-epistemic models that only assign probabilities 0 and 1, but it's no more difficult to rule out the ones that assign arbitrary probabilities in the interval [0,1], so we'll do that just because we can."

If they say the complete set of properties only sets the probabilities, how is that a complete ontological description?

Since the term "property" is left undefined, there can't be a strong argument for it. You can only assume it, or explain why the definition of an ontological model makes it convenient to think of an ontic state as representing all the system's properties.

An expectation value in QM can be expressed as \langle\psi|A|\psi\rangle=\sum_k P(k|A,\psi)k. Here k is a measurement result, and P(k|A,\psi) is the probability of getting the result k, given that we're measuring A, after subjecting the system to one of the preparation procedures represented by |\psi\rangle. The ontological model is required to satisfy something like
P(k|A,\psi)=\sum_{\lambda\in\Lambda} P(\lambda|\psi) P(k|A,\lambda) I say "something like", because this notation is only appropriate when \Lambda is finite. The two functions on the right are also required to exist as part of the definition of an ontological model for the quantum theory. This equality makes it very convenient to think of P(\lambda|\psi) as the probability that the system has properties λ, given that the preparation procedure was consistent with |\psi\rangle, and to think of P(k|A,\lambda) as the probability that the result will be k, given that we're measuing A, and that the system's properties are λ. So I'd say that the definition gives us a reason to think of λ as properties, but obviously not a reason to think we know that λ "really" represents properties.

 

[apeiron]

You talk a lot about the importance of top-down contraints, so where is the space for them in this "complete set of properties?" Is the PBR theorem still proving something if top-down constraints are fundamental to how any complete physical theory must work? I don't think it is, it seems to be relevant to hidden variables theories, but top-down constraints are not what most people mean by hidden variables, such variables are generally reductionist in character.

I think the difference is that reductionism/hidden variables attempts to locate the critical information inside the wavefunction, whereas a contraints approach is about what happens outside.

If you take the case of a pair of entangled particles, then an act of measurement is an act of constraint, imposed from without, that reduces the degrees of freedom of what lies within. If there was a choice of up/down, then "wavefunction collapse" is a constraint of that freedom.

The difference is that the reductionist view is that all things are secretly definite, and so carry this definiteness around from one place to another. But a constraints-based view (after Peirce, I might say, who seems a little misunderstood here) is that the particles are ontically indeterminate until some further constraint is imposed to give them more definite properties.

Of course, you then have to accept some kind of retrocausality and non-locality. But that's OK.

So I took the PBR theorem to be closing the loophole of a statistical interpretation and increasing the weight of evidence for ontic realism of the wavefunction. It then seems a separate matter how the wavefunction is actually viewed - either as some kind of material object, like a pilot wave, in its own right, or instead merely the framework of measurements/interactions which impinge on some local potential to give it a more definite identity.

The definition of a scientific realist is someone who takes the elements of scientific theories literally in regard to reality. To avoid foolish naivete, they must at least allow that the correspondence still counts if it has been shown to be only approximate. Notwithstanding the logical quandary around "how approximate still counts", we still have the problem that scientific theories that are not purely reductionist still don't fit the PBR program, so taking the attributes of any top-down constraint literally as part of the reality is an example of a "realist" stance that PBR do not even recognize as realist.

I agree with you that we only model reality, so there is always the problem we can never claim we know reality in an absolute way. Which makes the Copenhagen interpretation a worthy default position.

But then the Peircean approach (which pre-dates QM) does seem to offer something of interest. It is a way of arguing that reality is itself "epistemic". It says the way our minds work (with ideas shaping impressions) is also the way that reality works (with top-down constraints shaping local events).

So epistemology says we only know our own minds. But what if we then actually can appreciate how our minds work. Is this not a form of ontic certainty? Probably not, but it seems at least a stronger basis for speculation than epistemic agnosticism (that anything might be the case, we can't even say anything definite about how our minds get more organised).

Then applying this to QM interpretations, we can start with the fact of how reality seems to us - classical until we get down to the kinds of experiments where some further constraint, some act of measurement, is needed to "collapse the wavefunction". Or rather, place still further limits on the degrees of freedom that are present at some location.

We know that it is at least definitely our choices that are limiting these degrees of freedom (the CI position). But we also have now a grounds to say that reality itself is operating the same way. There is still no surety. There never can be. But it is a reasonableness argument.

By contrast, a hidden variables argument seems very unreasonable. The idea of things that are secret and unmeasureable goes against the spirit of modelling. Whereas the constraints that impinge on a locale are visible and measurable.

 

[my_wan]

Hang on-- from what I've seen on here, you and I are absolutely the only two people who believe that statement with the "even without" part in there. PBR certainly don't-- they hold that anyone who is a "realist" must hold that the basic building blocks of any theory that works must work because they are real. So if classical mechanics says there is a concept of exact position and it helps us get the answers right, then only some whacko "anti-realist" in 1860 could have claimed that exact position is not real. Indeed, if some analog of the PBR theorem were applied to classical mechanics, you can see what a "complete set of properties" would be interpreted as: exact positions. Everyone else seems happy with defining a realist as someone who believes a theory is about reality until it is found to not agree with some experiment, and that is certainly how PBR interpret realism in regard to quantum mechanics.

We are obviously not the only two given that the community didn't need our help to define background independence as fundamental to all physical sciences. Yet you approach is making no distinction between the background and what is happening in the background. The simple fact that we cannot empirically define a background in a space with no immediate causal interactions with the Universe doesn't mean we can define it and derive the transforms that recreate the empirical background. It still constitutes potential degree of freedom, such that position can still have indirect meaning.

The coordinate choice determines the label for the position, not the idea that there is a position there. By the definition of "realist" that everyone here seems all too happy to use, any classical mechanics realist would have to hold that exact positions are real, even if a coordinate choice is required to give those exact positions a numerical label. I'm saying it's high time we didn't require realists to be that naive.

Why doesn't it involve the notion of a position? Whether we label it or not, or no matter how we choose to label it, it still constitutes a potential degree of freedom. Do you even know what a position is? I already said it, it's not a thing but a degree of freedom of a thing, however you want to contextualize "thing". So in that sense even a point far removed from our Universe still constitutes a possible future degree of freedom. Hence the "position" is not lacking for that lack of any constructs to actually occupy that degree of freedom and possibly put labels on it like we do.

Again, that is conflating the numerical label of a velocity with the ontological construct of an exact velocity that may yet be unlabeled. Classical mechanics is usually framed as advancing that ontological construct, even though everyone knows the numerical labels are coordinate dependent. (Personally, I don't think classical mechanics should require that ontological construct at all, or indeed any fundamental ontological constructs, and on that I believe we are the only two here who agree.)

You seem to be conflating a numerical coordinate label as an ontic thing in the minds of realist. Then when we label an ontic thing to track what (nonphysical) degree of freedom it partakes in you are accusing ontic realist of assigning ontic realness to those labels. Unless or until you can get what those differing from you actually think you can never even formulate a valid (much less correct) rebuttal of their opinions. So far, in terms of your characterizations of what ontic realist think, you are dead wrong at every turn. Presumably honestly, but that just means you believe your own strawman.

Sure, they transform into one another in ways that are described by the theory. That means even the transformations between these fundamentally non-ontological constructs are also fundamentally non-ontological, they are all borrowed from the only place they actually exist: mathematical structures.

So what (perhaps who) is doing the calculating when scientist are not paying attention?

Those words are contradictory because belief in a true ontology means committing to a reality that exists in one's own mind, where those mathematical structures exist, and the belief the reality is fundamentally housed in our minds is idealism, not realism.

And does not an abject denial that a possibly ontic world outside your mind actually consist of something constitute a mind rejection fallacy? You and I are on opposite ends of the spectrum in our approach to understanding the world. The difference to me seems to be that I try really hard to recognize all the ways I can be wrong, and even if not how what I can know is fundamentally limited. Hence the absolute claim that the Universe is dependent on ontic constructs is a moot scientifically meaningless claim.

The question is why would you then turn it around and deny such a possibility when you have no more access to what is "real" than I do. You even make it worse by conflating degrees of freedom with ontic entities as if they are the same thing, then using the logical consequences of coordinate choices as the basis upon which you justify your criticism of ontologist. It makes you demonstrably wrong even if you are right. Only I see no recognition of the "if" in "if" you are right in your own claims about what constitutes a legitimate characterization of the world. Even if an ontological characterization is wrong, so long as it is empirically valid it lacks no less legitimacy.

Why is ontology important even if it is wrong? Consider classical thermodynamics, CT, verses statistical mechanics, SM, again for instance. It is fundamentally impossible to derive SM from CT, but quiet trivial to derive CT from SM. Without SM we could not have properly predicted Brownian motion. Not to mention making a lot of engineering a lot simpler with a lot less empirical data to be experimentally derived on a case by case basis. Now the fact that the atoms and molecules upon which is rested may not themselves be constructs of ontic entities does not detract from that in the least. It added empirical value that a strict epistemological approach to science could not have derived. We would not be where we are at if ontologist hadn't stuck in there when epistemologist had the game wrapped up with CT. So right or wrong you do NOT throw away ontology for the sake of philosophical expediency, period. And I see no other case besides philosophical expediency provided, unless your motives are less transparent than I have any right to speculate on.

 

[Fredrik]

Haven't we gone too far off topic now? All I see are lengthy discussions about philosophical terms. Is anyone at all interested in discussing the actual articles and arguments?

 

[my_wan]

Haven't we gone too far off topic now? All I see are lengthy discussions about philosophical terms. Is anyone at all interested in discussing the actual articles and arguments?

Yes, I agree. I'll refrain from any more of the philosophical issues not directly concerned with interpreting PBR. Yours and other post have made significant contributions, and a few of mine I hope, to the PBR issue. Some I am still chewing on and well worth continuing with.

 

[Ken G]

Haven't we gone too far off topic now? All I see are lengthy discussions about philosophical terms. Is anyone at all interested in discussing the actual articles and arguments?

The issue behind the philosophical arguments is directly related to the article. The article assumes that realism implies that a "complete set of properties" determine everything that happens. The proof appears to require this assumption. So the question is, is this actually a fair statement of realism? I am saying it is only a fair statement of reductionism, which is not a "mild assumption". I haven't seen anyone suggest the proof is wrong if it is really true that some complete set of hidden variables (properties) determines everything that happens, in terms of either 0 or 1 probability (which is not probability at all). So the real question is, what does a proof that requires that assumption really tell us about quantum mechanics? I'm saying it depends entirely on one's philosophical commitments, so there is no way to discuss the importance of the proof without first understanding the landscape of philosophical possibilities. That's more or less the tenor of those blogs as well.

 

[Ken G]

If you take the case of a pair of entangled particles, then an act of measurement is an act of constraint, imposed from without, that reduces the degrees of freedom of what lies within. If there was a choice of up/down, then "wavefunction collapse" is a constraint of that freedom.

A fully reasonable perspective, in my view.

The difference is that the reductionist view is that all things are secretly definite, and so carry this definiteness around from one place to another. But a constraints-based view (after Peirce, I might say, who seems a little misunderstood here) is that the particles are ontically indeterminate until some further constraint is imposed to give them more definite properties.

Yes, I generally respect Peirce so I was dubious with taking his views paraphrased through someone else, I meant only to critique the paraphrasing.

So I took the PBR theorem to be closing the loophole of a statistical interpretation and increasing the weight of evidence for ontic realism of the wavefunction.

But I don't think it really closes much of a loophole, because it assumes that there are some complete set of properties that are deterministic of the outcomes. The properties cannot just produce statistical trends, perhaps engaged by the constraints, they have to really determine what happens or the PBR proof does not scan. To me, they have assumed away most of what they are trying to argue cannot work-- they say that a single set of properties cannot be in the hidden space of two different wavefunctions, so two overlapping wavefunctions cannot be statistical groupings that overlap.

But this requires the relatively naive structure of the properties to make true-- a single set of properties that nevertheless requires interaction with constraints in order to be active on the statistics of the outcomes can therefore still appear in two different wavefunction groupings, if what is statistical in the wavefunction includes what is being treated statistically about the interactions with the constraints. In other words, if properties are themselves only statistically deterministic, then the PBR proof does not go through, yet they claim their proof goes through for all "realist" interpretations. The constraint-based approach is being downgraded to being "non-realist" and absent from any set of "mild assumptions."

You raised some interesting philosophical points that I'd like to respond to, but I don't want to derail the thread, so I'll PM my reactions.

 

[Fredrik]

The article assumes that realism implies that a "complete set of properties" determine everything that happens.

The word "realism" (or "realist") doesn't even appear in the article. In the introduction, they're suggesting that the idea that systems don't have properties implies that a state vector is just a tool to calculate probabilities. Then they assume that systems do have properties, and that those determine the probabilities of measurement results.

I don't see the assumption you're talking about. I think their choice of words suggest that they believe that the converse of the implication I mentioned above holds too, even though they aren't actually saying it. Is this what you have in mind?

The proof appears to require this assumption.

I don't see why you think so.

You don't seem to be taking into account just how bad this article is. These guys either haven't figured out how to tie their ideas together, or are unbelievably bad at explaining them. Let me try to translate a few of the things they're saying to non-gibberish.

Our main assumption is that after preparation, the quantum system has some set of physical properties.​

Translation: "We're going to talk about ontological models for quantum theories, as defined by Harrigan and Spekkens".

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

Translation: "We will show that if state vectors correspond to epistemic states of some other theory, that theory can't make the same predictions as QM".

A better way of saying that is: "We will show that no quantum theory has a ψ-epistemic ontological model." This is a mathematical statement, so there's no way the correctness of a proof can depend on someone's opinion about what "realism" should mean.

 

[bohm2]

I'm guessing here that KenG is referring to page 6 of the PBR paper(Appendix B)?

An assumption is that the quantum system after preparation has physical properties, and that a complete list of these properties corresponds to some mathematical object λ. Each preparation method is associated with a probability distribution μ_i(λ) (i = 0, 1). This is to be thought of as the probability density for the system to have properties  after preparation.

Isn't realism the position that measurement results reflect preexisting properties?

 

[Fredrik]

I'm guessing here that KenG is referring to page 6 of the PBR paper(Appendix B)?

I didn't read that far, but the quote is saying essentially the same thing as the introduction on page 1. It's clear that the authors think of λ as properties, but that doesn't imply that you somehow have to think of them that way for the argument to make sense. (An argument that requires you to think that way would be garbage). The article by Michael Hall agrees with me about this point. The ontological model is required to satisfy a few mathematical conditions, as part of the definition of ontological model. Those conditions may not be intuitive unless we think of λ as a complete list of properties, but the argument is based on the mathematical conditions, not on their intuitiveness.

Isn't realism the position that measurement results reflect preexisting properties?

I like to avoid such terms entirely. They're all like "the Copenhagen interpretation". You won't be able to find two people who agree about what it means.

 

[my_wan]

The word "realism" (or "realist") doesn't even appear in the article.

No they don't but, but unlike epistemic or ontic or any variant thereof which is not contained in the article, the term "real" does occur in the context of realism as a variant. Hence any use of the term epistemic or ontic in characterizations of the article leaves me without any reference point as to how the authors used it, since they never did. The HS reference does not specify how the authors chose to contextualize those terms. But wrt "realism" or "real" there is some significant content to determine the PBR authors intended characterization, which I will outline.

In the introduction, they're suggesting that the idea that systems don't have properties implies that a state vector is just a tool to calculate probabilities.

Naturally, this is a direct result of the state vector characterized as not being "real" in the sense used by the authors. Note: This is a far more limited specification for realness than is often implied, such as in the debate between Ken G and I. It merely associates what is empirically accessible in real experiments as real, as opposed to to abacus procedure which has nothing to do with what the result is applied to.

Then they assume that systems do have properties, and that those determine the probabilities of measurement results.

Naturally. This in itself does not imply circular reasoning due to a simple fact. In order to formulate a proof it must first be stated in a form that allows a method of falsification. By making the statement that the state vector had empirically accessible properties they are not presuming it to be so a priori, they are merely putting it into a falsifiable form.

I don't see the assumption you're talking about. I think their choice of words suggest that they believe that the converse of the implication I mentioned above holds too, even though they aren't actually saying it. Is this what you have in mind?

I don't see why you think so.

Here I agree with you. It seems to me that an extreme position has characterized a differing position as an inverse yet equally extreme position wrt a more moderate point that the authors were trying to convey with the term "real".

You don't seem to be taking into account just how bad this article is. These guys either haven't figured out how to tie their ideas together, or are unbelievably bad at explaining them.

If the article was so bad why or how can you assume the terms in a referenced article, such as ontic and epistemic, can be characterized in a manner in which the authors provided no prototype use of the terms or variants in their article to judge how those authors would characterize them in a manner consonant with your own? Meanwhile, rejecting the characterization of terms or variants thereof they did use as meaningful indicators of what they were conveying.

Let me try to translate a few of the things they're saying to non-gibberish.

So let's compare our translations. Your translation:

Our main assumption is that after preparation, the quantum system has some set of physical properties.​

Translation: "We're going to talk about ontological models for quantum theories, as defined by Harrigan and Spekkens".

My Translation:
We are making assumptions about the system independent of assumptions about the model in order to allow the possibility of falsifying claims about what the model represents, in terms of realness as previously outlined.

Note how this translation specifically refers back to the same author provided content you characterized as gibberish, rather than a different paper altogether containing none of the words or variants thereof the authors actually used or had any hand in writing?

Your translation:

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

Translation: "We will show that if state vectors correspond to epistemic states of some other theory, that theory can't make the same predictions as QM".

My translation:
We will show that the empirical significant of the statistics defined by the state vector exceeds what is empirically possible if it only has "statistical significance".

So what does the term "statistical significance", used by the actual authors mean? Exactly what the authors said it means when they said in their own words (not the words of a referenced proxy author): "[...]statistical significance, akin to a probability distribution in statistical mechanics." To understand you have to consider the model and the system as two different things. In the statistical mechanics model the statistics are only a property of the model, not a property of the system being modeled. Thus the above translation says they will show it is impossible to define the statistics of a state vector as a model only property, that it must in some way also be a property of the system itself, unlike the statistical interpretation used in statistical mechanics.

A better way of saying that is: "We will show that no quantum theory has a ψ-epistemic ontological model."

No, it say nothing explicit about any other model than the one provided by standard QM. Though it does put hard constraints on how an alternative model can characterize the statistics used in QM. That is that the statistics, whether an alternative model characterizes them in terms of statistics or not, must not treat the QM statistic as if it is solely as a modeling property rather than a system property. Throwing in the term ψ-epistemic in the context of all possible models it can entail is invalid. It is only valid when you restrict it to one particular model and the characterizations that one model entails, even if that model is a derivative construct of the alternative model.

This is a mathematical statement, so there's no way the correctness of a proof can depend on someone's opinion about what "realism" should mean.

No, it's not a mathematical statement. Here's why. You have a system and a mathematical model of that system. If the two were the same thing then empirically invalidating the mathematical model would be impossible since there is nothing other than the model to invalidate it with. This does not depend on any version of "realism", only that the empirical justification is external to the model itself. So if you include the set of all potentially valid models, not systems, the supposed "mathematical statement" of what ψ-epistemic means takes a different character in each case.

So, if you want to use terms such as ψ-epistemic, you must restrict its relevance to a particular model, such as QM, and leave alternative models to be judged individually rather than on labels such as ψ-epistemic. I really get the impression that when the words used by PBR are characterized as gibberish it is the direct result of failing to note when they switch back and forth between characterizations of the model and characterizations of the system providing the empirical justification for the model.

If the authors own words are labeled gibberish how is it possible to discuss what the paper said? Even the ψ-epistemic terminology wouldn't be such a hindrance if it wasn't so inappropriately generalized as if its validity in the context of one model was an indicator of the validity in all possible models of the system in question.