The quantum state cannot be interpreted statistically?

[Ken G]

It's a definition of a piece of mathematics that's part of a definition of a theory. Definitions are never "not formally correct" (unless they're logically inconsistent).

Calling it a definition does not change the fact that it is indeed an idealization. I can define the Newtonian gravity of a sphere to be whatever I get, or I can use a more general theory for deriving Newtonian gravity and apply it to a sphere. That is all you are doing, and either way it is still an idealization. The wave function of identical particles is a joint wave function, the whole concept of single-particle wavefunctions is an approximate idealization. We can use it, and do use it, when appropriate, say for isolated systems. But when the systems are brought together, the approximation is no longer appropriate. Had we written down the correct joint wavefunction right from the start, there would be no issue-- we'd still get the right answer for isolated systems, but we'd also get the right answer when the systems come together, with no claim for a need for some new way to handle the interactions, and no claim that unentangled systems have become entangled. This is exactly what happens when white dwarfs accrete additional electrons, does this not prove the point?

Yes, we're talking about a choice, but it's one that must be made. Without a choice of what theory to use, it all turns into word poop.

I don't understand what you are saying, it does not sound relevant to the issue. If you give me two widely separated H atoms, and ask me to write the electron wavefunctions, I certainly have a choice, and both choices would be considered quantum mechanics, but one would be more approximate than the other. One choice would be to write two independent pure-state electron wavefunctions, with no interactions in the Hamiltonian, as you have done, and equip them with an arbitrary phase relationship because we don't care about it. Another would be to write down a single joint wavefunction for the two electrons. If we still choose not to include any interactions in the Hamiltonian, then this second approach will give exactly the same answers as the first approach as long as the atoms remain separated, so they are both clearly quantum mechanics, and neither is using a different theory. However, the second choice is simply more general, as it can handle the situation when the atoms come together, whereas the first choice cannot handle that-- it is just plain wrong in that situation, because it was an idealization to begin with.

The joint wavefunction is of course also an idealization, but it is an idealization that will handle bringing the atoms together. There is no need to include any additional interactions if they are not desired, the joint wavefunction already handles the entanglement. Indeed, we will most likely adopt yet another idealization in the joint wavefunction, which is to build it from single-particle wavefunctions, but we will need to choose a phase relationship between them. We don't need that phase relationship when we don't use a joint wavefunction, and so we delude ourselves into thinking there is no entanglement, but in fact to have no entanglement we would need to use mixed states, not pure states, for those electrons.

The quantum theory of a single qubit is the simplest possible quantum theory, and "formal quantum mechanics" includes the standard way to combine two quantum theories into one, in this case two single-qubit theories into one two-qubit theory. So it is certainly not "outside formal quantum mechanics".

Yet you yourself admitted you did not know how to include the entanglement. That's because you don't realize they are already entangled, the entanglement just goes from not mattering to mattering when the atoms come together. Or, use mixed-state descriptions. Either would resolve your problem, that's my point.

It means exactly that the person who made the choice failed to find a mathematical proof of the mathematical statement he's trying to prove. I think that my choice to consider the non-interacting two-qubit theory was such a failure. A quantum theory doesn't have to be able to describe what a measuring device does, so the measurement process (or rather the theory that describes it) might be able to entangle the particles even if the two-qubit theory can't.

But the two-qubit theory can, you just have to apply it in the form of a joint wavefunction-- as is done with a Slater determinant for multi-electron atoms, for example. There is nothing in the interaction term in the Hamiltonian that dictates the Slater determinant, that is a completely general way to get multi-electron wavefunctions built from the idealization of single-particle wavefunctions and accounting for indistinguishability of Fermions.

They have nothing to do with this. They are just ways to organize our thoughts about a given theory. We are talking about choosing what theory to use.

True, but the theory is "quantum mechanics", not "quantum mechanics idealized to single-particle systems that later get moved together." The latter is not a theory at all, it doesn't work.

A piece of mathematics that assigns probabilities to members of some set, and a set of statements in plain English that describe how the members of that set correspond to actual measuring devices and results of measurements using those devices.

That's a reasonable definition of a theory, but it doesn't avoid the stickinesses. Quantum mechanics of single particle systems satisfies all of that, and one can argue that it is indeed a theory, but it is a theory that is known to be wrong in many contexts. "Quantum mechanics" is supposed to not be known to be wrong.

 

[Ken G]

Korzybski said "the map is not the territory" long before Jaynes came up with the somewhat similar Mind Projection Fallacy (OMG, bill and I agree on something ). The point being not to confuse your useful description (QM) with the underlying set of objects being described (the quantum world).

Yes, but I think Jaynes falls very much victim of his own fallacy. He claims that atoms are real, and it is the mind projection fallacy to claim they are a kind of abstraction! The map is not the territory, but when I look up the term "atom" in the index of a science book, I know quite well that what I will find there is a map, not a territory. Which do you think I will find there? And would Jaynes say that the electrons in my body are real, when quantum mechanics says (quite clearly) that there is no such "real" thing as "the electrons in my body" (being indistinguishable from electrons not in my body)? The fact is, science uses idealizations, and I worry greatly about the depth of scientific understanding of anyone who denies that. I think Jaynes understands probability in scientific epistemology, but probability says nothing about whether or not atoms are real. Indeed, what I would say is that "what is real" in science is whatever the scientist is choosing to regard as real, based on his/her objectives of the moment. Indeed, I would say that is pretty close to undeniable, just look at any scientist in the history of the field, and the ontological notions they embraced to make progress.

 

[Fredrik]

Calling it a definition does not change the fact that it is indeed an idealization.

You're missing the point. Sure it could be described as an idealized description of an aspect of reality, but we're trying to prove a mathematical statement. Reality doesn't enter into it.

Yet you yourself admitted you did not know how to include the entanglement. That's because you don't realize they are already entangled, the entanglement just goes from not mattering to mattering when the atoms come together. Or, use mixed-state descriptions. Either would resolve your problem, that's my point.

They're not already entangled, because the argument starts with the assumption that they're not. You have only realized that the theory we're talking about doesn't exactly agree with the real world. But there's no fact about reality or the theories that would allow us to ignore the assumption that's the starting point of a mathematical argument.

True, but the theory is "quantum mechanics", not "quantum mechanics idealized to single-particle systems that later get moved together." The latter is not a theory at all, it doesn't work.

Of course it's a theory. Every set of statements that makes unique probability assignments defines a theory, no matter how bad those assignments are.

 

[Ken G]

You're missing the point. Sure it could be described as an idealized description of an aspect of reality, but we're trying to prove a mathematical statement. Reality doesn't enter into it.

I understand that you are applying a theory, not reality. I'm saying the theory you are applying is an incorrect theory to handle the situation you are treating. To use a correct theory, you must write a joint wave function before you bring the systems together. The joint wave function must accommodate the indistinguishability.

They're not already entangled, because the argument starts with the assumption that they're not.

But the argument is wrong in quantum mechanics. In quantum mechanics, all identical particles that are treated as being in a pure state are always entangled by their indistinguishability. We just don't bother to include the entanglement in many idealizations. When we need the entanglement, as in your scenario, it is incorrect to state that they start out unentangled, unless you use a mixed-state description instead of a pure-state description.

Of course it's a theory. Every set of statements that makes unique probability assignments defines a theory, no matter how bad those assignments are.

Well, if we agree it is a bad theory, then what relevance is there in an incorrect application of a correct theory (or a correct application of an incorrect theory, whichever way you choose to think about it)? Either way, it isn't the theory of quantum mechanics.

 

[Fra]

Bill, you're right that he touches upon parts of the topics I mentioned in his book (decision theory in chapter 13 for example), and while I don't atm have the time to go back and and re-read his book I spent some time on this before and concluded that while he to a larger extent that what's common do pose some important questions he misses (IMHO) an important point.

His concept of "consistency" is in fact too strong.

Like I said, even if Jaynes does not have ALL answers, his book is indeed excellent. I originally considered my own view quite close to Jaynes (someone who has tried to follow his tradition is for example Ariel Caticha who things that the laws of physics are pretty much following from the rules of inference, and tries to reconstruct GR - he has not succeseeded yet but it's an extremely interesting idea... I like that too and have referred to them myself in previous discussions, but given that we have gotten that far, I have some subtle points where I disagree!)

The problems you describe do not arise in Jaynes framework. Early in his book in the chapter titled "Plausible reasoning" (http://bayes.wustl.edu/etj/prob/book.pdf) he derives the basic desiderata of the framework of probability theory which are:

Yes I am well aware of his construction. It's excellent and recommended reading to any scientist, as it provides a MUCH deeper insight into what probability theory comes from that is much more intuitive than say just the koglomorov axioms (even if the result is the same).

But...

- Degrees of Plausibility are represented by real numbers.

This I take issue with. I don't think it's wise to use an uncountable number system for this. It means the space of possible prior is not only infinite, it's moreover uncountable. This may seem like a "so what" objection but in the way I work on this, it IS a major problem. Countability is ESSENTIAL to calculating the measures of plausability. Sure one can sort of get around this, but then other problems arises that is close relative to divergencs and failure of renormalisation. At least that's my firm opinoin.

- Qualitative correspondence with common sense

Yes agreed, which is why it proves an outstanding prespective.

- If a conclusion can be reasoned out in more than one way, then
every possible way must lead to the same result

Well it's not that easy. This is where things become interesting and JAynes constraints are too strong.

If we slow down and ask: WHY must a conclusions as worked out by say difference observers lead to the same result? Well because otherwise they disagree of course, but so what?

In my view this is not an "inconsistency", it is exactly what is _responsible_ for an interaction.

When we get into this domain, I disagree with JAynes construction. Instead for me the "consistenecy" requirement is more to be understood as an emermgent equilibrium condition, NOT a forcing constraint on the reasoning.

Disagreements is not an inconsistency if the comparasion process is a physical interaction. This is also where the laws of the interaction are EMERGENT from the emergence or negotiating inference systems.

Note that these are MINE views, and so far no published so I just mentionn the ideas here. It's not meant to be complete in anywy. The complete exposition will be length and is not finished by far I afraid.

- must take into account all of the available evidence relevant to a question, without arbitrarily ignoring some of the information, and basing conclusions only on what remains.

He addressed the issues you raised in that chapter (Pages 13 to 17 of the linked PDF which is part of his Book).

Yes you'r right, some of the topics I mention like the problem of choosing a rational action GIVEN some state of degree of beliefs is there (which is indeed nice) I do not think he arrives at a satisfactory conclusion.

I think I should state again, that relative to say Einsteins objections are similar old isses, I consider myself very close to JAynes thinking. My issue with it are not in his general goals to apply inference to physics (this is exactly mine as well) but in HOW it's done.

If you are suggesting that a person with a different theory of reasoning might disagree about a result, all we would have to do is look at the desiderata of this alternative theory of reasoning and examine the self consistency.

My point is the "we" in your scentence is just another observer, with and equally typically incomplete view of the universe. All that can happen is that this obserber TAKES AN ACTION based on the "inconsistency". This is exactly my way ot handle it. But then this is the key to understanding the origina of interactions! It's not really a "consistency PROBLEM".

/Fredrik

 

[Fredrik]

I'm saying the theory you are applying is an incorrect theory to handle the situation you are treating.

That's possible.

To use a correct theory, you must write a joint wave function before you bring the systems together.

I assume that by "joint", you mean "entangled", because what I (and PBR) wrote down are two-qubit states. If we start with different states, then the entire argument goes down the toilet. Even if it can be saved, it would be a very different argument.

But the argument is wrong in quantum mechanics. In quantum mechanics, all identical particles that are treated as being in a pure state are always entangled by their indistinguishability.

The part you have a problem with is certainly not wrong in what I would call "quantum mechanics". You seem to define it as the quantum theory of all particles that actually exist in the real world. This doesn't make sense to me. I define it as the framework in which quantum theories are defined. The usual stuff about the Schrödinger equation is the quantum theory of a single spin-0 particle under the influence of a classical potential. The simplest possible quantum theory is the theory of a single qubit. These theories describe universes where nothing else exists (if they can be said to describe anything at all). The method we use to construct new theories from given ones is part of that framework too.

Well, if we agree it is a bad theory, then what relevance is there in an incorrect application of a correct theory (or a correct application of an incorrect theory, whichever way you choose to think about it)? Either way, it isn't the theory of quantum mechanics.

The relevance is of course that the PBR argument starts with unentangled states like |0\rangle\otimes|0\rangle. Isn't that what we're talking about? And it is quantum mechanics.

 

[my_wan]

Yes, but I think Jaynes falls very much victim of his own fallacy. He claims that atoms are real, and it is the mind projection fallacy to claim they are a kind of abstraction! The map is not the territory, but when I look up the term "atom" in the index of a science book, I know quite well that what I will find there is a map, not a territory. Which do you think I will find there? And would Jaynes say that the electrons in my body are real, when quantum mechanics says (quite clearly) that there is no such "real" thing as "the electrons in my body" (being indistinguishable from electrons not in my body)? The fact is, science uses idealizations, and I worry greatly about the depth of scientific understanding of anyone who denies that. I think Jaynes understands probability in scientific epistemology, but probability says nothing about whether or not atoms are real. Indeed, what I would say is that "what is real" in science is whatever the scientist is choosing to regard as real, based on his/her objectives of the moment. Indeed, I would say that is pretty close to undeniable, just look at any scientist in the history of the field, and the ontological notions they embraced to make progress.

Ken, I have justified you position plenty here but noted some personal differences in response to a promise to take us to task on it. It will state those differences as it is directly relevant to the debate this last day. This will also explain what has been falsely attributed to Jaynes falling victim to his own mind projection fallacy. I'll reuse the hurricane analogy to do so.

Suppose, for the moment (I'll loosen this claim later but accept it as factual for the moment), we know that the molecular soup of our atmosphere are indeed ontic (real) entities. We also know that the presents of this hurricane does not represent any new property associated with any of the distinct singular molecules defining it. Now given this state of affairs would you then define the hurricane as an ontologically real entity? Why or why not? In fact you have a philosophical choice here rather than a physical one. Let's look at the consequences of the two choices.

1) If the hurricane is an epistemic construct within these molecules then the claim that the molecules themselves are ontologically real entities may itself be false, and so on and so forth down the reductionist chain to include quantum entities. Such as the wavefunction itself. This, as I have stated previously, begs the question: Is it turtles all the way down. If it is turtles all the way down then it begs the question of whether there exist a bottom, even after a transfinite progression down the reductionist chain. To say that there is no reality beyond an epistemic wavefunction is tantamount to the claim that we hit bottom with no ontic entities anywhere.

2) If this hurricane is an ontologically real entity then even if the molecules in which the hurricane exist in are themselves epistemic constructs it makes the hurricane and the molecules no less ontologically real, so long it is not turtles all the way down. This entails that the wavefunction is an ontologically real entity, however limited our description or characterizations of it may or may not be. Once you allow this hurricane to be ontologically real there is no longer much room for labeling any observables or there characterization as purely epistemic constructs without also claiming it is turtles all the way down.

Of course people labeling themselves realist can fall into a number of categories, with a very broad distinction corresponding to ontic realist verses epistemic realist. An self described epistemic realist can also be an ontic realist by accepting that it is not turtles all the way down but take it as a pragmatic limit of what we can know. Alternatively a self described epistemic realist can reject an ontological foundation, and/or differing epistemic/ontologically positions wrt the hurricane and take the hurricane as real without accepting an ontically real underpinning at the bottom of the turtles. The variations thereof can be bewildering.

Personally, I operate on the presumption that it is not turtles all the way down, that there exist an ontic building blocks of some sort (likely transfinite) lacking any properties other than existing, where all properties are emergent constructs analogous to the way the hurricane is an emergent property. And I remain ambivalent toward the choice of definition as to whether a hurricane in itself is ontic or epistemic. It is merely a partitioned set of properties of a property set which are not more generally partitioned or partitionable in such a manner.

--------
Given these symmetries Jaynes view is not necessarily self contradictory. It doesn't even require the claim that it is not turtles all the way down, only that a hurricane is a physical entity in itself. Yet there is some contradictory elements to the definitions as they have evolved with physics. If you hold that by definition the classical world in which we interact consist of physical variables, knowing that they are derivative variables in some sense analogous to the hurricane, then it requires defining the hurricane as a physical entity in its own rite. To then deny a physical status in some sense to the wavefunction is then incongruent with the previous claim that you live in a physically defined world.

Note: I have blurred the distinction between map and territory here. This I justify not by the legitimacy or completeness of the map, but by the fact that there presumable is a territory (ontic and/or epistemic) in which the map refers. Otherwise the claim that legitimacy (not truth of) of the map is predicated on the limited empirical responses (experiments) of the territory is moot.

 

[Ken G]

The part you have a problem with is certainly not wrong in what I would call "quantum mechanics". You seem to define it as the quantum theory of all particles that actually exist in the real world.

No, that would be a completely impossible theory to use. I define it as a theory of all particles that matter in a given problem, and that is where it is misapplied in the problem you are considering. You are treating two independent qubits, then asking what happens when they come together. There is an illusion there that when they come together, they become entangled, whereas they weren't before, and that seems strange. But that is not the case-- if the particles are to come together, then quantum mechanics must treat the whole system from the start, or at least must choose a treatment that is consistent with that more complete description of the system. It's not like they are separate systems that become one, there is no such "real" thing as a "separate system", and whether or not one can use quantum mechanics to treat them as separate systems is very much dependent on whether or not they ever come together.

This doesn't make sense to me. I define it as the framework in which quantum theories are defined. The usual stuff about the Schrödinger equation is the quantum theory of a single spin-0 particle under the influence of a classical potential.

Subject to additional assumptions, like the spin-0 particle doesn't have any indistinguishable other particles in the vicinity. Quantum mechanics is fully capable of handling the case where there are such particles, but it's not the quantum mechanics treatment you are writing. QM isn't a single treatment, it is a single theory that constitutes many possible treatments, based on the idealizations chosen (so is classical physics, but QM throws in the wrinkle of indistinguishability). The physicist, having chosen to use quantum mechanics, must still tailor the treatment to the situation. Single-particle qubits are a very narrow form of treatment, useful in many situations, but not in the situation you are considering, unless the entanglement is recognized as being there from the start.

The simplest possible quantum theory is the theory of a single qubit.

Yes, and we should always choose the simplest possible treatment that works, but this one doesn't work. Choosing a joint wavefunction would work, though if we want to use pure states, additional information about the initial coherences is required. (Whether or not a joint wavefunction constitutes an entanglement is a tricky issue-- when we write a multiple-electron wavefunction as a Slater determinant, are those electrons entangled? We speak of valence electrons and so on, behaving rather independently of the rest of the electrons, yet we still have the Pauli exclusion principle that keeps the valence electron from falling down to the ground state. It certainly isn't entanglement in the sense that I can measure the spin of the valence electron and constrain the spin of the rest of the electrons.)

These theories describe universes where nothing else exists (if they can be said to describe anything at all). The method we use to construct new theories from given ones is part of that framework too.

Sure, but you were talking about two qubits, not one, and bringing them together. That's not a universe where nothing else exists, it's a universe where something else exists and that something can be brought together.

The relevance is of course that the PBR argument starts with unentangled states like |0\rangle\otimes|0\rangle. Isn't that what we're talking about? And it is quantum mechanics.

I presume the entanglement they achieve is the same as they'd have had they simply used a joint wavefunction from the start. I haven't looked closely at those technical details, I'm still trying to figure out if their proof iself is saying anything important, or if it is only their intepretation (or over-interpretation) of it that is of potential significance.

 

[Ken G]

To say that there is no reality beyond an epistemic wavefunction is tantamount to the claim that we hit bottom with no ontic entities anywhere.

Yes, and do you see a problem with that? I see none, that seems like a perfectly natural conclusion to me. I would also argue that there is absolutely nothing that happens in science that requires anything different, nothing that is any different if there are ontic entities anywhere, or if there is not. Science is precisely the same either way, so I argue that science has nothing to add to the issue, nor any interest in adding anything. That doesn't mean science doesn't use ontic entities-- it uses them as pictures, with no concern whatsoever for whether or not they are true or real or absolute in any way. This is quite fortunate, or science would never have even gotten off the ground in millennia past where the ontic elements were terribly ill-conceived in comparison to the ones we use today. This is also the reason that we still use ontic elements, like position and momenta, or forces of gravity, or action at a distance-- even after we have discovered that these ontic elements are not actually ontic at all in our universe.

An self described epistemic realist can also be an ontic realist by accepting that it is not turtles all the way down but take it as a pragmatic limit of what we can know.

The way I would put that is, an epistemic realist views ontic realism as a kind of useful fantasy. This should not surprise us, we start building useful fantasies from childhood. Scientists build more sophisticated useful fantasies, like the concept of a "fluid" even when we know many applications will require the atom concept, or the concept of "atom" even when we know that many applications will benefit more from the field concept, or the concept of "field" when we know that many applications will benefit from a virtual particle concept, or the concept of "virtual particle" when we know that many applications will require nonperturbative treatments. It's concepts, not turtles, all the way down, because that's all we get-- useful concepts. What else is there? What the heck is an "ontic entity" anyway, that isn't the same thing as a useful concept? And please tell me what "ontic entity," chosen from any in the history of science (other than new ones whose limitations we still don't yet know) is not shown up to be an idealization at some deeper level of investigation. As a random example to demonstrate this, consider the seemingly ontological question: does the Earth have a surface?

Personally, I operate on the presumption that it is not turtles all the way down, that there exist an ontic building blocks of some sort (likely transfinite) lacking any properties other than existing, where all properties are emergent constructs analogous to the way the hurricane is an emergent property.

And that is a perfectly valid stance to take, expressly because you recognize it is just a stance. Can Jaynes say the same? Not from the way his position is being characterized on this thread, and that does seem to be an accurate portrayal. He seems to believe that he is not choosing a philosophy, he is holding to truth. This is rather inconsistent behavior from someone who recognizes the pitfalls of mind projection!

If you hold that by definition the classical world in which we interact consist of physical variables, knowing that they are derivative variables in some sense analogous to the hurricane, then it requires defining the hurricane as a physical entity in its own rite. To then deny a physical status in some sense to the wavefunction is then incongruent with the previous claim that you live in a physically defined world.

I'm not sure what you mean by a "physically defined world". It isn't the world that is defined physically, because the world (for the realist) is not defined at all, except in the vaguest possible terms (like "point" in geometry). What is defined is the physicist's effort to understand the world, so we should not say a "physically defined world", we should say a "world that we benefit from attempting to define physically, recognizing that we can do this in very many ways, have done it in very many ways in history, and will likely continue to do in very many ways going forward." What's more, I would point out that in the history of physics, we see a very clear trend toward convergence in accuracy and generality of our predictions. But ask yourself this: do we see a similar convergence in the ontological constructs? Forces, spacetime manifolds, virtual particles, strings... where's the ontic convergence? Nowhere, it is a complete myth. And we are supposed to be the myth-breakers!

Note: I have blurred the distinction between map and territory here. This I justify not by the legitimacy or completeness of the map, but by the fact that there presumable is a territory (ontic and/or epistemic) in which the map refers.

I have no problem with asserting that there is a territory to which the map refers, that's basic realism. My issue is with confusing attributes of the map with attributes of the territory. There is just no such thing as an attribute of a territory-- all attributes are attributes of a map. That's Jaynes' mistake in a nutshell-- he seems to think he can tell the difference between the attributes of a map and the attributes of a territory, and his only criterion for doing so appears to be, if he believes it, it is an attribute of the territory. Logically, there is no justification for drawing that distinction, I'd love to hear someone try to navigate that logical morass. You can't have it both ways-- if there are mind projection fallacies, then the map is not the territory, and if the map is not the territory, then the attributes are found on the map. The territory is just the territory, it cannot have attributes without creating inconsistency of language.

 

[my_wan]

Yes, and do you see a problem with that? I see none, that seems like a perfectly natural conclusion to me.

Wait a minute. There is a contextual reason I required an assumption in the first sentence of my second paragraph and labeled it factual, in spite of explicitly stating I had no intention of maintaining that assumption as factual.

You pulled that quote out of the explicit context or assumptions under which it applied. It applied if and only if viewed under the context 1) provided. Hence to pull it out of that context and say you see a problem while ignoring that context is meaningless. It likes saying if A then B, and you arguing that it's invalid because you disagree with B, irrespective of whether B would result from A or not. I did not claim B, I said IIF A then B.

That post was explicitly constructed as a comparative description of the various perspectives, and not a judgement call on which of those perspectives were valid, true, or any other judgement, scientific or otherwise, on these various perspectives. With the one exception you mentioned below that I'll get to when I come to it.

I have my own perspective I'll discuss separately, which is at odds with the opinion you give here, but only if you recognize the context under which the above statement applied and recognize that by my having an opinion does not constitute a validity judgement on differing perspectives. In pulling that naked quote out of context I have no confidence those conditions are met, and your argument replacing the contextual perspective with your own is moot under the assumptions of the perspective it was intended to apply to.

The way I would put that is, an epistemic realist views ontic realism as a kind of useful fantasy.

Again, I am explicitly comparing the general class of all ontological perspectives for the explicit purpose comparative analysis, whether I personally share that perspective or not. Hence for you to object solely within the narrow range of your own perspective is just as moot as my personal perspective was in the comparison. Pulling a naked quote out and objecting is trivial when many of the perspectives provided are quiet at odds with even my own perspective. Reread it and get the context.

And that is a perfectly valid stance to take, expressly because you recognize it is just a stance. Can Jaynes say the same?

So the only place I state my own perspective you don't have a problem with. Yet you should recognize that the previous quotes where pulled from a contextual set of assumptions in which the quotes only applied in that context. Wrt Jaynes I will articulate more when I get to the one point where I offered an opinion, you objected to, on how these context apply.

I'm not sure what you mean by a "physically defined world".

And here it is. When I used the term "physically defined world" it was not to specify a singular ontological perspective under which that term applied, as it could mean any of the perspectives previously described. It was merely to indicate that if by definition the world in which we interact with directly is a "physically defined world" then that definition imposes itself on how we can go about defining the physicality of the hurricane analogy, without changing any of the ontological perspectives concerning it. Hence to understand Jaynes position you merely have to accept this tradition definition simply because it defined so. Yet does not change any of the various ontological flavors under which differing people interpret it. Hence I meant it in the sense in which anybody might interpret it, and not just my own interpretation. In fact I stated a personal ambivalence toward which definition was best a priori, even under the context of the modeling symmetries you ignored and pulled quotes from out of context.

I have no problem with asserting that there is a territory to which the map refers, that's basic realism. My issue is with confusing attributes of the map with attributes of the territory. There is just no such thing as an attribute of a territory-- all attributes are attributes of a map.

Certainly confusing map attributes with the territory is a sticky problem. In a singular very limited context that is exactly what the PBR theorem attempted to address. Getting into personal opinion again here, but to say that the territory has no attributes (however primitive) to me entails that there are no derivative attributes or empirical data whatsoever. To me the notion of derivative properties without something from which they derive is just as magical as dynamical properties sprinkled on fundamental point particles. Of course that is my opinion just like the old magical dynamical properties in particle physics. Such a primitive foundational property may not even be empirically accessible in and of itself, though given as a postulate potentially entails empirically accessible properties. Denying such is at least possible is a form of the mind projection fallacy.

One of the complaints previously given about properties is the lack of a definition. Try this one on for size: A property is a constraint in the degrees of freedom of a set of variables or points in space. This would apply whether it was a purely mathematical constraint, or a simple purely mechanical constraint in which one part restrict the freedom of another. Makes no difference whatsoever, and such mechanical constraint is subject to mathematical laws. Yet how could you possibly have a Universe without constrained degrees of freedom, i.e., properties. Without such constraints every point would be causally disconnected and independent from every other point making observations impossible. Just like the unobservable independent variables Dr Chinese spoke of in Hume's[/PLAIN] Determinism Refuted.

 

[Fredrik]

Sure, but you were talking about two qubits, not one, and bringing them together.

PBR said something about bringing them together. I don't think I did. I hope I didn't, because I don't think such statements belong in a proof.

I have thought some more about my version of the "simplified" argument from page 2, and I'm now fairly certain that it's (essentially) correct. I'm too tired to explain all aspects of it now (especially the one detail that I'm still unsure of), so I'll just adress one that we've been discussing. The entanglement issue isn't an issue. It doesn't matter that unentangled states will remain unentangled, because the entangled states in the argument are post-measurement states, and a quantum theory isn't required to say anything about the measuring device (other than what operator it corresponds to). So the correct mental picture here is that there are no interactions in the quantum theory, but the measuring device can still entangle them.

Of course, the argument doesn't depend on mental pictures. There's no need to imagine "bringing them together", or to imagine anything at all. We don't need to know how to perform a measurement that has the results |\xi_k\rangle. It's sufficient to know that such an operator can be defined on \mathcal H\otimes\mathcal H.

 

[my_wan]

I have thought some more about my version of the "simplified" argument from page 2, and I'm now fairly certain that it's (essentially) correct. I'm too tired to explain all aspects of it now (especially the one detail that I'm still unsure of), so I'll just adress one that we've been discussing. The entanglement issue isn't an issue. It doesn't matter that unentangled states will remain unentangled, because the entangled states in the argument are post-measurement states, and a quantum theory isn't required to say anything about the measuring device (other than what operator it corresponds to). So the correct mental picture here is that there are no interactions in the quantum theory, but the measuring device can still entangle them.

(My bold)
This particular issue has worried me a bit. In fact the primary concern wrt the legitimacy of the theorem. However, to the best of my thinking this appears correct to me.

 

[Fredrik]

The part that's bothering me is the assumption or theorem (not 100% sure which) that the ontological model for the quantum theory of a single qubit can be used to define an ontological model for the two-qubit theory. I think this is a non-trivial point. I don't see how it can make sense to take it as an assumption, because we later find that it's not an ontological model of the two-qubit theory. That's the contradiction that's supposed to disprove our initial assumption, but now it looks like it may have been the result of another assumption.

So I think it must be proved as a theorem. It's not sufficient to show that there's some kind of model with state space \Lambda\times\Lambda. We also need to show that it makes the same predictions as the two-qubit theory. In other words, we need a theorem that shows that if there's an ontological model with state space \Lambda for a quantum theory with Hilbert space \mathcal H, then there's an ontological model with state space \Lambda\times\Lambda for the quantum theory with Hilbert space \mathcal H\otimes\mathcal H. I think that this requires a pretty sophisticated argument, that comes with its own set of assumptions:

Physical justification for using the tensor product to describe two quantum systems as one joint system, by Diederik Aerts and Ingrid Daubechies.

 

[Ken G]

You pulled that quote out of the explicit context or assumptions under which it applied.

I wasn't saying you either did or did not agree with that conclusion, I was asking you if you did, and saying that I did agree with it-- I am fine with the idea that we hit bottom with no ontic entities anywhere, because I think that ontic entities are merely effective notions, not to be taken literally. Science has no need of a literal ontic entity, it works on effective and provisional ontic entities. It's just a fundamentally epistemological endeavor.

Hence for you to object solely within the narrow range of your own perspective is just as moot as my personal perspective was in the comparison.

Actually, I never objected at all, I merely said that among the alternatives you were considering, that is the one that I take as the correct position, in regard to how science works (rather than in regard to each person's individual assessment of the ramifications of science).

It was merely to indicate that if by definition the world in which we interact with directly is a "physically defined world" then that definition imposes itself on how we can go about defining the physicality of the hurricane analogy, without changing any of the ontological perspectives concerning it.

I still don't understand how you are using the term "physically defined world." We don't define the physicality of the hurricane analogy, we just define the hurricane, and its physicality is not something we get to define, it is something whose usefulness we test. And when we test it, we should expect it to be useful for some things, and break down for other things. So it is with ontic elements, we should never expect otherwise, and we certainly don't have the ability to define otherwise. The reason we can't define the physicality of a hurricane is because that is something we must test, we get to choose the definition of hurricane but not how well the concept will serve our physics.

The case of the atom is more immediate to the Jaynes issue. Jaynes claims that atoms are real, and that saying so is not an example of the mind projection fallacy. I claim it certainly is an example of just that. Neither of us can resort to definitions to support our cases, all we can do is define atom (and our definitions are the same), and see how the concept serves. We find it serves quite well, when it serves, and we find it is not very helpful when it does not serve.

For example, an ionized plasma may include atoms and particles in our description, but it also includes waves in fields and the combined effects of fields and atoms, sometimes called "dressed atoms." So is a dressed atom an atom, or isn't it? It's certainly not the same thing as an atom, that would simply be incorrect. Or we can go to more extreme environments, like a white dwarf star. The electrons in a white dwarf do not act like individual particles at all, they are so entangled with each other it would be closer to correct to imagine that the whole white dwarf is more like a single atom, than imagining it is comprised of independent particles. So is a white dwarf an atom, or isn't it? Surely if Jaynes is right, and atoms (and independent particles) are real, then we should be able to say if a white dwarf is a kind of atom, or if it is comprised of atoms. But we can't, the simplistic language fails us, because that's all it ever was-- simplistic language. The "atom" and "independent particle" concepts are just that-- epistemological constructs that we can get away with imagining are ontic in some situations, but not in others. I find Jaynes' characterizations of atoms to be surprisingly naive, he is projecting a simplifying concept onto reality in an overly narrow way. He is committing the mind projecton fallacy.

Certainly confusing map attributes with the territory is a sticky problem. In a singular very limited context that is exactly what the PBR theorem attempted to address. Getting into personal opinion again here, but to say that the territory has no attributes (however primitive) to me entails that there are no derivative attributes or empirical data whatsoever.

Derivative attributes and empirical data are whatever we make them. It's not one-or-the-other, that they either exist or have no value. That they have value is clear, but it does not make them real. In fact, this is just what we should expect.

One of the complaints previously given about properties is the lack of a definition. Try this one on for size: A property is a constraint in the degrees of freedom of a set of variables or points in space.

I don't think that solves the problem, because my issue was not that property was undefined, it was that the properties could determine what happens to the system. I don't think we can assume that what happens to a system is determined at all, at least not "determined" in the standard sense of "determinism." Where does this idea come from that behavior is determined? That's one of the most blatant examples of belief in magic, in my view.

Yet how could you possibly have a Universe without constrained degrees of freedom, i.e., properties.

That is exactly the question, yes. My answer is, "easy!" Indeed, I feel this should be our default assumption until otherwise demonstrated-- in the interest of basic skepticism.

Without such constraints every point would be causally disconnected and independent from every other point making observations impossible.

I feel that causal connection is a construct of how we think, just like properties. So I don't think we should imagine that its absence in some true ontology is a problem. Similarly, we should not conclude that some true ontology will include randomness-- we should be suspect of the entire notion of a true ontology.

 

[Ken G]

In other words, we need a theorem that shows that if there's an ontological model with state space \Lambda for a quantum theory with Hilbert space \mathcal H, then there's an ontological model with state space \Lambda\times\Lambda for the quantum theory with Hilbert space \mathcal H\otimes\mathcal H. I think that this requires a pretty sophisticated argument, that comes with its own set of assumptions:

Physical justification for using the tensor product to describe two quantum systems as one joint system, by Diederik Aerts and Ingrid Daubechies.

Yes, I think that paper makes it quite clear the limitations of making that particular choice about how to treat two qubit systems. That's the formal version of what I was saying-- if the systems come together, the assumptions are not satisfied, and the tensor product approach simply isn't valid quantum mechanics. I'm not sure if PBR are assuming invalid quantum mechanics as a result, but this is certainly something we should be worried about.

 

[Fredrik]

if the systems come together, the assumptions are not satisfied, and the tensor product approach simply isn't valid quantum mechanics.

I still strongly disagree with this line of reasoning. You seem to be mixing bits of reality into a mathematical argument where they don't belong. I'm as confused by your persistence about this as I would have been if we had been discussing a proof of the theorem that says that there's no rational number x such that x²=2, and you go on for days and pages about how we have failed to account for gravity or something like that.

The fact that a theory of two non-interacting subsystems isn't going to make accurate predictions in certain real-world situations is irrelevant, because we're trying to prove a mathematical statement about the purely mathematical part of theory of just one of those subsystems, by using the rules that tell us how to combine several theories into one. These rules are also part of the framework of QM. These joint theories are just mathematical tools. We only use the purely mathematical parts of them. Real-world concerns don't enter into it.

 

[Demystifier]

A new paper on the PBR theorem:
http://xxx.lanl.gov/abs/1111.6304

 

[DevilsAvocado]

A new paper on the PBR theorem:
http://xxx.lanl.gov/abs/1111.6304

Thank you very much Demystifier.

I’m still reading this interesting paper, and already on the second page the essence of the PBR theorem is expressed very efficiently [my bolding]:

Very recently, Pusey, Barrett and Rudolph (PBR) have given a completely novel ‘no-go’ theorem [1], which demonstrates that, under certain assumptions, distinct pure quantum states must have disjoint sets of underlying properties. In particular, partially overlapping wave functions cannot be considered as partially overlapping ensembles of underlying properties, in any model that satisfies the PBR assumptions. Rather, the corresponding ensembles must be nonoverlapping, implying that the wave functions must be considered precisely just as ‘real’ or ‘physical’ as the underlying properties themselves.

The strength of the PBR theorem is determined by the strength of the assumptions it relies on.

Could someone explain what this means:

Further, it is shown that an assumption of measurement independence may be dropped to obtain a related result having the same experimental significance (at the expense of a weaker conceptual significance). The latter is a remarkable feature of the PBR approach, given that Bell inequalities, steering inequalities and Kochen-Specker theorems all require an assumption of this type.​

[Any philosophical mumbo-jumbo, if this discussion is for real or not, is preferably transferred to the proper forum]

 

[Ken G]

This is from the abstract of that new paper: "The `factorisability' assumption used by PBR is replaced by a far weaker `compatibility' assumption for uncorrelated quantum subsystems which, moreover, does not require the assignation of separate underlying properties to each subsystem (i.e, reductionism)." It sounds like Hall has addressed my main objection-- that PBR assumed that the systems had properties that determined the outcomes, and used that assumption to argue that "the wave functions must be considered precisely just as ‘real’ or ‘physical’ as the underlying properties themselves." That was the problem with PBR-- anyone who did not regard such properties as real or physical would have no reason to carry those attributes over to the states themselves, they could safely ignore the PBR proof. Perhaps this new proof avoids that problem, I haven't digested it yet.

 

[Ken G]

I still strongly disagree with this line of reasoning. You seem to be mixing bits of reality into a mathematical argument where they don't belong. I'm as confused by your persistence about this as I would have been if we had been discussing a proof of the theorem that says that there's no rational number x such that x²=2, and you go on for days and pages about how we have failed to account for gravity or something like that.

If one is claiming to prove something about states in quantum mechanics, one must apply the state concept from a version of quantum mechanics that is applicable and relevant, consistent with whatever situation one is using quantum mechanics to treat. If we were proving a theorem about classical mechanics, and did not include any gravity, someone could quite correctly point out that the theorem has not been proven for any situation involving both classical mechanics and gravity. That is what I am pointing out-- if the theorem assumes unentangled systems in the way the quantum mechanics is set up, then later proves something about how those systems are entangled, it is not proving anything about correct quantum mechanics, it is proving something about incorrect quantum mechanics. I'm not saying it really did that, for that would make the proof wrong, I'm saying that's why you have to worry about assuming unentangled systems but then later bringing the systems together, which seemed to be what you were doing.

The fact that a theory of two non-interacting subsystems isn't going to make accurate predictions in certain real-world situations is irrelevant, because we're trying to prove a mathematical statement about the purely mathematical part of theory of just one of those subsystems, by using the rules that tell us how to combine several theories into one. These rules are also part of the framework of QM.

The first rule about how to combine theories of non-interacting subsystems is that the non-interacting subsystems had better never be brought together, so no questions about their entanglement had better be of interest in the proof. It's not an issue of real-world concerns, it is purely an issue of internal consistency of the treatment chosen.

 

[JK423]

OK, new summary. Simplified.

They are comparing two different schools of thought:

1. A state vector represents the properties of the system.
2. A state vector represents the statistical properties of an ensemble of identically prepared systems, and does not also represent the properties of a single system.

Their argument against the second view goes roughly like this:

Suppose that there's a theory that's at least as good as QM, in which a mathematical object λ represents all the properties of the system. Suppose that view 2 above is the correct one. Then λ doesn't determine the probabilities of all possible results of measurements.[/color] Yada-yada-yada. Contradiction! Therefore view 2 is false.​

I say that

• The entire article rests on the validity on the statement in brown, which says that view 2 somehow implies that "all the properties" are insufficient to determine the probabilities. (If that's true, then why would anyone call them "all the properties"?)
• The brown statement is a non sequitur. (A conclusion that doesn't follow from the premise).
• The only argument the article offers in support of the brown claim, doesn't support the brown claim at all.

Am I wrong about something?

Fredrik,
I had the same questions during my first reading of the paper. I think that i have understood what the authors are trying to say, so let's see if my understanding is correct. Let me note that i haven't read all the replies that you've got from other people, so excuse me if i repeat arguments someone else has already said!

I think that the key ingredient is to understand what the authors mean by 'Statistical interpretation' and what by the 'physical properties {λ}'.

1] Statistical interpretation according to the authors
In the abstract of the paper we read:
"Another (view) is that even a pure state has only a statistical significance, akin to a probability distribution in statistical mechanics"
Which means that they regard as the statistical interpretation of the state vector the same thing as a probability distribution in statistical mechanics.
But what happens in the classical case?
Lets assume that we got two ensembles of (classical) ideal gases, ensembles 1 & 2, in the same volume of space but in different temperatures. These ensembles do not interact (ideal).
Each ensemble ( i ) will be described by the Mawell-Boltzmann probability distribution that goes like P_{i}\proptoexp(-E_{i}/kT_{i}).
The energy levels E_{i} are the same for both gases, only the probabilities change. Now, we measure a random particle in the volume -without knowing beforehand in which of the two ensembles it belongs- and we get it's position and its momentum (even its trajectory!) which constitute its set of physical properties {λ}. But knowing {λ} in the classical case allows us to also know in which ensemble the particle belongs? Or in other words, by which probability distribution P_{i}\proptoexp(-E_{i}/kT_{i}) it's described?
The answer is no.
According to the authors, this is the fact that makes a classical distribution not a physical property of a classical system, but its only of statistical nature.
So, repeating this essential -to my opinion- point, in the classical case even if knowing all the physical properties {λ} of the system we still cannot distinguish the ensemble that this system belongs IF this ensemble's probability distribution overlaps with other ensemble's probability distribution to the physical properties {λ} that they assign probabilities to.


2] Physical properties {λ}
In classical physics, this set {λ} consists of things like position, momentum, energy, etc
But what does {λ} mean to quantum mechanics?
To my mind, there are 2 possibilities:
- The first is that {λ} represent all the good quantum numbers of the state vector. So Knowing {λ} you can immediately know the state vector. Ofcourse we assume the Schrodinger equation (or a better undiscovered equation) to hold. Let's give an example. If our particle is a potential V(x), then it has a specific energy spectrum and by solving the 'S' equation we can find all the eigenkets of the Hamiltonian. If energy is a good quantum number, then knowing 'E' (energy) allows us also to know the state vector of the particle. So in this simple case, the set {λ} consists of the energy E.
- The above would be okay if the particle's state has good quantum numbers. If it hasnt (is there a physical state without no good quantum numbers??) then the only option that comes to my mind (instead of saying {λ}=0 ) is that there is another undiscovered theory that gives us a set {λ}. If you can think of something better please tell me.

Let's hit the problem now, and repeat the argument of the authors (quote from Fredrik):
<<Suppose that there's a theory that's at least as good as QM, in which a mathematical object λ represents all the properties of the system. Suppose that view 2 (statistical) above is the correct one. Then λ doesn't determine the probabilities of all possible results of measurements.[/color] Yada-yada-yada. Contradiction! Therefore view 2 is false>>

I think that now it's clear what the authors mean. If the state vector is of statistical nature as is a classical probability distribution, then -according to what we said above about the classical distributions- even if we know the whole set of physical properties {λ}, we will still not be able to determine the state vector (aka the probabilities of all possible results of measurements).


Tell me your thoughts.



John

 

[bohm2]

A new paper on the PBR theorem: http://xxx.lanl.gov/abs/1111.6304

I'm still trying to understand the last paper but here's a quoted comment from Matt Leifer posted regarding this newest Hall paper:

As far as I can see, this paper is a fairly straightforward extension of PBR, but I only think that one of the weakened constraints is conceptually interesting. The original proof required a factorizability condition, i.e. for product states you have a Cartesian product of ontic state spaces and the distribution is independent over the factors. This can be replaced by a “local compatibility” condition, which is just the condition that if lambda is a possible ontic state for a single copy of a bunch of different states, then n copies of lambda is possible for any tensor product of n states chosen from that set. This drops the independence part of the assumption. Why this is true is very easy to see, since this is the only property of factorizability used in the original PBR result.

Hall also claims to have weakened this further to a condition of “compatibility”. This is supposed to go beyond reductionist models, which say that each system has its own individual ontic properties and the properties of composite systems are simply the collection of properties of all the parts. Hall tries to go beyond this by allowing the ontic state space of two systems to be arbitrarily different from the cartesian product of the ontic state spaces of the individual systems. I don’t think this has been achieved, since one still needs to know how the properties of the global system are related to the properties of the subsystems. Hall says that if we know that lambda is compatible with some states of one system, then we need only know that lambda is compatible with n-fold products of those states. However, since the state spaces are completely distinct, I don’t think that it makes sense to consider lambda as a possible ontic state for both a subsystem and the full composite system. This is not the case in the original theorem, or in the version with local compatibility, in which case the state on the global system is n copies of lambda rather than just one. Therefore, I don’t think that this part of the paper makes much sense.

Hall also points out that the probability distribution over the ontic state need not be independent of the choice of measurement, since only one measurement is considered for each pair of states. Whilst this is true, and perhaps interesting because it places a constraint on certain types of retrocausal theory, it does not allow the original PBR conclusion to be drawn. If another choice of measurement were made then the distributions could overlap and the quantum state would be epistemic. It is this loophole that I hope to exploit in developing an epistemic retrocausal theory. Perhaps this is worth saying, but it is certainly not groundbreaking.

http://www.scottaaronson.com/blog/?p=822

 

[Ken G]

I found this insight in that Leifer quote to be telling: "This is supposed to go beyond reductionist models, which say that each system has its own individual ontic properties and the properties of composite systems are simply the collection of properties of all the parts. Hall tries to go beyond this by allowing the ontic state space of two systems to be arbitrarily different from the cartesian product of the ontic state spaces of the individual systems. I don’t think this has been achieved, since one still needs to know how the properties of the global system are related to the properties of the subsystems." I think this quote makes it clear that Leifer views the algebra of "properties" to be an essential aspect of the PBR theorem, and he feels that the Hall modification does little to relax that. By "algebra of properties", I mean simply the way the concept of properties proliferates throughout the logic of the proof such that they allow us to draw conclusions about how composite systems can be treated in quantum mechanics, but these choices limit the validity to a version of quantum mechanics that supports the concept of properties-- which is very close to circular reasoning in the proof. Thus I continue to feel that the most important conclusions based on the proof are upheld only in a circular interpretation of the proof, and this limitation is apparently not much improved in the Hall modification.

 

[Fredrik]

If one is claiming to prove something about states in quantum mechanics, one must apply the state concept from a version of quantum mechanics that is applicable and relevant, consistent with whatever situation one is using quantum mechanics to treat.

You're already mixing in bits of reality where they don't belong. We're not "treating" anything, so terms like "applicable" don't make sense. We're talking about a mathematical property of a quantum theory with a 2-dimensional Hilbert space, and the standard procedure to define new theories from old ones.

If we were proving a theorem about classical mechanics, and did not include any gravity, someone could quite correctly point out that the theorem has not been proven for any situation involving both classical mechanics and gravity. That is what I am pointing out--

But what we're talking about (the page 2 argument, and my version of it from post #155) is nothing like that. A better analogy would be a theorem that says that in the classical theory of a single point particle in Galilean spacetime moving under the influence of no force at all, the world line is always a straight line.

 

[Fredrik]

I think that the key ingredient is to understand what the authors mean by 'Statistical interpretation' and what by the 'physical properties {λ}'.

Knowing what they mean by statistical interpretation is crucial. They are using the definitions of Harrigan & Spekkens. To them "a state vector can be interpreted statistically" means "there's a ψ-epistemic ontological model for this quantum theory".

I don't think the exact meaning of "properties" really matters here. It certainly plays no role in the mathematical part of the argument, since the term doesn't have a mathematical definition. Mathematically, λ is just a member of a set in another theory, one that makes the same predictions as QM. (In this theory, the probability of a result k of a measurement M is determined by λ,k and M).

Let's hit the problem now, and repeat the argument of the authors (quote from Fredrik):
<<Suppose that there's a theory that's at least as good as QM, in which a mathematical object λ represents all the properties of the system. Suppose that view 2 (statistical) above is the correct one. Then λ doesn't determine the probabilities of all possible results of measurements.[/color] Yada-yada-yada. Contradiction! Therefore view 2 is false>>

When I wrote this, I thought they were saying that "if view 2 is correct, then λ doesn't determine the probability distribution". They are actually defining view 2 as "there's an ontological model such that λ doesn't determine the probability distribution". So that particular bit of criticism was unfair.

I think that now it's clear what the authors mean. If the state vector is of statistical nature as is a classical probability distribution, then -according to what we said above about the classical distributions- even if we know the whole set of physical properties {λ}, we will still not be able to determine the state vector (aka the probabilities of all possible results of measurements).

Yes, I'd say that this is what they mean by statistical view, but the statement can be made more precise using the definitions of Harrigan & Spekkens. The statistical view (as they define it) is that every quantum theory has a ψ-epistemic ontological model.

 

[DevilsAvocado]

... That was the problem with PBR-- anyone who did not regard such properties as real or physical would have no reason to carry those attributes over to the states themselves, they could safely ignore the PBR proof. Perhaps this new proof avoids that problem, I haven't digested it yet.

I don’t think this is a problem related to PBR, but a total lack of understanding somewhere else.

It should be pretty obvious that those advocating a ψ-epistemic ontological model obviously regard such underlying properties as real.

 

[apeiron]

Hall tries to go beyond this by allowing the ontic state space of two systems to be arbitrarily different from the cartesian product of the ontic state spaces of the individual systems. I don’t think this has been achieved, since one still needs to know how the properties of the global system are related to the properties of the subsystems.

I thought My Wan's earlier comment is insightful here:

A property is a constraint in the degrees of freedom of a set of variables or points in space.

This is the non-reductionist or contextual view in a nutshell. What you find locally is what's left still to be free after global constraints have limited the freedoms that might otherwise have existed.

So wavefunction entanglement becomes not about the mixing of properties but the merging of constraints. Merged constraints are a relaxation which in turn makes the "properties" less definite. Collapse of the wavefunction is the tightening of constraints again to produce more definite "properties" once more.

Reductionism tries to build its model of the world atomistically from the bottom-up. Which leads to the view that the wavefunction must be some kind of extended object - a definite thing with its own location, existence and properties.

But the other way of looking at it is that the wavefunction is just our description of the constraints as they stand in reference to some location. It stands for the information that impinges to limit what exists. Entanglement then reduces the amount of information, creating increased uncertainty/more freedom.

A wavefunction could thus be ontic, but not in the sense of an object. Just as actually a set of constraints.

 

[DevilsAvocado]

... Personally, I operate on the presumption that it is not turtles all the way down, that there exist an ontic building blocks of some sort (likely transfinite) lacking any properties other than existing, where all properties are emergent constructs analogous to the way the hurricane is an emergent property. And I remain ambivalent toward the choice of definition as to whether a hurricane in itself is ontic or epistemic. It is merely a partitioned set of properties of a property set which are not more generally partitioned or partitionable in such a manner.

my_wan, I promised a 'voluminous' reply... but I realized this thread is rapidly going down the derailed track without my 'professional help'... ;) therefore; I rest my case.

I respect your ideas, and your way of debating – it’s sincere. But I’m afraid that your buddy is as far from your position one could come, and the quote above shows this clearly.

Ken G is advocating Idealism (when not beating around the bush), i.e. reality is fundamentally mentally constructed and a skepticism about the possibility of knowing any mind-independent thing, i.e. diametrically your position.

"So that is the sense that I am saying there is a crucial role of consciousness in quantum mechanics-- there simply is no such thing as quantum mechanics without it."​

And sometimes "quantum mechanics" is everything there is, the whole world and the universe. And sometimes it’s "quantum mechanics" in the microscopic world. And sometimes it’s the theory of quantum mechanics. And sometimes he replaces "quantum mechanics" for "physics", and then he picks and chooses as it fits...

= Impossible to debate

jfyi

 

[my_wan]

I wasn't saying you either did or did not agree with that conclusion, I was asking you if you did, and saying that I did agree with it-- I am fine with the idea that we hit bottom with no ontic entities anywhere, because I think that ontic entities are merely effective notions, not to be taken literally. Science has no need of a literal ontic entity, it works on effective and provisional ontic entities. It's just a fundamentally epistemological endeavor.

I see now that I was overly narrow in my interpretation your response. Though I often add some indication of my personal views, as a side note in such post, the main point is more often the range or space of possibilities neglected under any given opinion or characterization. For instance, when you say "ontic realism as a kind of useful fantasy" my take on this is that we do not know and often cannot know even in principle, what constitutes a "useful fantasy" verses an actual state. Hence to a priori label any of these foundational positions as a "fantasy" itself goes beyond what we can know. Certainly in some cases we know we are working with a "useful fantasy", but to say that because we are fundamentally limited in our capacity to "know" entails that all such characterizations are factually "useful fantasies" tacitly oversteps what we can factually know, such a claim is a mind projection fallacy. So I don't a priori reject alternative characterizations unless I can show it runs afoul of valid consequences, whether that be internal self consistency or empirical validity or both.

Wrt your question about my opinion specifically, I do not see that as a a perfectly natural conclusion. To fully justify that would require subverting this thread to an unwarranted degree, as it would require centering the debate solely around a personal view. However, in my opinion such a conclusion appears just as magical to me as the claim that fundamental point particles are real with magical properties sprinkled on like raisins. To some realist your opinion as stated does not even constitute realism. The same issues involving what constitutes realism is at the heart of why I used "physically defined world" in such an inclusive manner.

Actually, I never objected at all, I merely said that among the alternatives you were considering, that is the one that I take as the correct position, in regard to how science works (rather than in regard to each person's individual assessment of the ramifications of science).

Yes, my apologies. I recognize that the narrowness in which I interpreted your response was unwarranted, but it was formulated from your own singular opinion. I was explicitly trying to consider the space of all such opinions without a priori judging anyone opinion solely on the basis of of any other singular opinion.

I still don't understand how you are using the term "physically defined world." We don't define the physicality of the hurricane analogy, we just define the hurricane, and its physicality is not something we get to define, it is something whose usefulness we test. And when we test it, we should expect it to be useful for some things, and break down for other things. So it is with ontic elements, we should never expect otherwise, and we certainly don't have the ability to define otherwise. The reason we can't define the physicality of a hurricane is because that is something we must test, we get to choose the definition of hurricane but not how well the concept will serve our physics.

Some people describe "physical" purely in terms of ontic entities in a sense that hurricanes are not fundamentally a separable "physical" entity. To either this group or the group of opinions which do not define or label the world we live in as a physical world the term I provided does not apply. However, any group of opinions which defines or labels the world we live in a physical world, whether that includes ontic foundations or not, then that entails the same label to be associated irrespective of the foundational opinions used to define it. In other words it makes no sense to define the world in which we directly interact "the physical world" while also denying that the actual constituents from which the world is derived are not physical. Like denying atoms are not real, but hurricanes are. In a sense that is trying to have your cake and eat it to. So I'm not objecting to either an ontic or epistemic foundational characterization. I'm simple saying that if you label it one way at the experiential level then denying those same labels at a different level is incongruent.

For instance, I do do not object to you calling yourself a realist even though you do not attach the "real" part of [real]ist to the real existence of any ontic entities. Yet to many realist this is like saying: I'm a realist because I don't believe the Universe consist of any real ontic entities. You can object that real is not exclusive of things other than ontic entities, but neither is "physical" in "physically defined world".

The case of the atom is more immediate to the Jaynes issue. Jaynes claims that atoms are real, and that saying so is not an example of the mind projection fallacy. I claim it certainly is an example of just that. Neither of us can resort to definitions to support our cases, all we can do is define atom (and our definitions are the same), and see how the concept serves. We find it serves quite well, when it serves, and we find it is not very helpful when it does not serve.

Jaynes wrote the mind projection fallacy in far more detail than what can be accurately summed up with that one statement. For instance, you state the opinion that it is natural that real ontic entities are not the foundational basis of the universe. If I applied you judgement of Jaynes to this statement couldn't I insist that you are not a realist, and that calling yourself so constitutes a mind projection fallacy ostensibly to justify the [real]ity of your own opinion?

For example, an ionized plasma may include atoms and particles in our description, but it also includes waves in fields and the combined effects of fields and atoms, sometimes called "dressed atoms." So is a dressed atom an atom, or isn't it? It's certainly not the same thing as an atom, that would simply be incorrect. Or we can go to more extreme environments, like a white dwarf star. The electrons in a white dwarf do not act like individual particles at all, they are so entangled with each other it would be closer to correct to imagine that the whole white dwarf is more like a single atom, than imagining it is comprised of independent particles. So is a white dwarf an atom, or isn't it?

How does this differ from the hurricane analogy? It certainly does not make sense to talk about the wind shear forces in some region of the hurricane as independent variables from other regions. Hence without dressing the atoms such that the hurricane is structurally dependent on the whole distribution of atoms it is simply, in your words incorrect. Thus you have added absolutely nothing to the hurricane analogy with "dressed atoms" or group behavior (as though a single entity). You merely chose a more complex yet equivalent analogy. The hurricane is in fact

Surely if Jaynes is right, and atoms (and independent particles) are real, then we should be able to say if a white dwarf is a kind of atom, or if it is comprised of atoms. But we can't, the simplistic language fails us, because that's all it ever was-- simplistic language. The "atom" and "independent particle" concepts are just that-- epistemological constructs that we can get away with imagining are ontic in some situations, but not in others. I find Jaynes' characterizations of atoms to be surprisingly naive, he is projecting a simplifying concept onto reality in an overly narrow way. He is committing the mind projecton fallacy.

First off to say atoms are real does not entail that they are strictly independent, any more than a real hurricane is independent from the atmosphere, a white dwarf star is not independent of the mass it contains, etc. The hurricane maintains its existence as the result of the entanglement between its parts, and to get this entanglement requires nothing more than the fact that the (independent) parts cannot occupy the same space. Hence saying we should be able to tell if a white dwarf is a kind of atom is like saying if pool balls are real independent entities we should be able to say if pool balls are a type of triangle because they form a triangle in the raked position. The hurricane analogy was intended to make this lack of independence obvious, like your "dressed atoms", even when the molecules themselves are considered as independent entities. Though I relaxed this assumption that atoms are independent entities after the fact, not because of the hurricane superstructure but because they could have interdependent substructures of their own like the hurricane.

Derivative attributes and empirical data are whatever we make them. It's not one-or-the-other, that they either exist or have no value. That they have value is clear, but it does not make them real. In fact, this is just what we should expect.

No, we cannot make derivative attributes or empirical data what we want. They have a certain symmetry and we can represent these symmetries in whatever way we want. But only so long as that symmetry is strictly maintained. Under no circumstances can we describe it as a different symmetry without being invalid, period. That is why symmetries take center stage in modern physics. It's the only thing we can both know and is not subject to choice, such as ontological opinions are. It is also what makes theorems, such as PBR, possible and meaningful in constraining possible models or interpretations of QM.

I don't think that solves the problem, because my issue was not that property was undefined, it was that the properties could determine what happens to the system. I don't think we can assume that what happens to a system is determined at all, at least not "determined" in the standard sense of "determinism." Where does this idea come from that behavior is determined? That's one of the most blatant examples of belief in magic, in my view.

Though you are right that we cannot assume a priori determinism determines what happens in the usual sense, neither can we assume it doesn't in spite of contrary opinions. Doing so is a fallacy: We cannot assume X therefore not X, is a version of if we cannot know X therefore not X, is a version of if we cannot observe X therefore X does not exist. In the most general sense "determines" the properties could entail the determination of properties that are not deterministic, such as common interpretations of QM statistics.

That is exactly the question, yes. My answer is, "easy!" Indeed, I feel this should be our default assumption until otherwise demonstrated-- in the interest of basic skepticism.

I certainly have my own set of default assumptions. However, by designating some assumptions as default in general becomes a limiting factor in how we progress. Many non-realist attempt to characterize their assumptions as the only valid default assumption on the grounds of EPR and less often other no-go theorems. Thus attempting to invalidate research into various forms of contextualized variables. This is no more or less valid than realist making claims about how reality must be. So I do not hold that science or its practitioners should be held to standards of default assumptions, in the interest of exploring the space of possibilities. Just don't grandstand claims of how uniquely valid a particular set of default assumptions is in "reality".

I feel that causal connection is a construct of how we think, just like properties. So I don't think we should imagine that its absence in some true ontology is a problem. Similarly, we should not conclude that some true ontology will include randomness-- we should be suspect of the entire notion of a true ontology.

How we codify causal connections in science almost certainly is a construct of how we think. Yet the symmetries these causal connections entail are not. that is how and why we can formulate perfectly valid no-go theorems like PBR and still argue over the context it applies. Even if you had a perfectly valid model that was so strongly classical it would have made many of Newtons critiques happy, the range of interpretations at the experiential level would not diminish. However, the symmetries would impose constraints such that any valid interpretation of emergent or derivative constructs could in principle be mapped liked a coordinate transform. If one model gives property set A and another equally valid model gives property set B, then set A can be mapped onto set B and visa versa, else the two models would not be equally valid.

I think that you appear to be undervaluing the immutability of symmetries on the grounds that these symmetries can be contextualized in a myriad of different ways. In it's simplest form the true reality that some people chase is equivalent to arguing over whether the car was doing 70 mph or the ground was doing 70 mph under it. In more complex circumstances this non-physical coordinate attribute vastly changes the character and even apparent identity of what reality is. Even your "dressed atoms" is simply a regrouping of coordinates such that variable sets are regrouped as fewer sets of different variables. It doesn't invalidate the independent variables, made dependent through their interactions, it simply makes the problem more tractable by throwing away the details (large numbers of variables) not needed to characterize the system.

 

[my_wan]

my_wan, I promised a 'voluminous' reply... but I realized this thread is rapidly going down the derailed track without my 'professional help'... ;) therefore; I rest my case.

I respect your ideas, and your way of debating – it’s sincere. But I’m afraid that your buddy is as far from your position one could come, and the quote above shows this clearly.

Ken G is advocating Idealism (when not beating around the bush), i.e. reality is fundamentally mentally constructed and a skepticism about the possibility of knowing any mind-independent thing, i.e. diametrically your position.

"So that is the sense that I am saying there is a crucial role of consciousness in quantum mechanics-- there simply is no such thing as quantum mechanics without it."​

And sometimes "quantum mechanics" is everything there is, the whole world and the universe. And sometimes it’s "quantum mechanics" in the microscopic world. And sometimes it’s the theory of quantum mechanics. And sometimes he replaces "quantum mechanics" for "physics", and then he picks and chooses as it fits...

= Impossible to debate

jfyi

Yes, I really should let this go since it appears that no matter how I try to keep it with the space of possibilities it still keeps being dragged back down to the personal perspective level.