The quantum state cannot be interpreted statistically?

[nazarbaz]

I made claims about how reasonable people use language and reason logically. Is that what you call "making claims about how the reality works"? Or are you utterly unable to appreciate the difference between pointing out poor use of language and illogical reasoning with proposing a particular flavor of ontology.Physics is simply the study of nature. Nature is what exists. The object is nature (reality). We can legitimately debate what nature is and if you want to argue that only experimental outcomes exist, do that and we will examine the merits. What I'm arguing against right now is your suggestion that Nature is knowledge.Attempting to go deeper without grasping the basics is folly.
OK let's examine one of your previous phrases from post #157:As anyone with even one eye can see, the above statement makes the following assumptions:
- There is such a thing as an actual truth of nature.
- Something is being characterized.

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

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

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

The belief that nature is limited by what our small brains can know and understand is the mind projection fallacy and you are clearly demonstrating it here.That was a typo, But you knew that already didn't you?


I have. Have you? You are way off base on what he means. You are claiming that since physics theories is all we have to describe nature, there is therefore nothing more to nature than what physics theories describe. This IS the mind projection fallacy.When you say "better" you must have assumed that the current knowledge as represented by the current theory is not the complete truth. Which implies you secretly believe there is truth independent of what we currently know. If there is more truth that we know, how can it all be epistemology. Unless you really do not understand the difference between the meanings of the terms.More evidence that you are not ready to go any deeper. You are still confused about the basics.

Their vision is a mere nonsense... Nietzsche killed god and manhood to free and to celebrate our lives in nature, Heidegger killed humanism to venerate the epiphany of a much profound being and criticize the suprematism of technology and scientism... But the postmodernists, who are the degenerate heirs of this beautiful tradition, are killing the universe to celebrate their ideas... Their arguments are neither scientific nor philosophical but aesthetic... They think that somehow, if we get to truth, our experience of the world will be impoverished... The logical consequence for them is to sterilize science and its "realist" ambition : the world does not exist or it is unknowable by nature...
This is a ridiculous radicalism, a stupid nihilism and a naive subjectivism... How could we think if we deny the most basic assumption of the human history : that we really exist and that there is something out there to think about and to deal with... We're not even at thinking on the status of knowledge, but the conditions of its possibility... That's not a way back to the naive realism of the old epistemology... The scientific experience needs a point of view, a justified "bias", to study the structure and the substructures of the universe... The whole thing is to combine different standpoints and criteria to give a rigorous view of the objects... The question that the epistemists need to ask is whether what they call the "next theories" are going to modify radically our knowledge of the atom or to complete it and by the way see if there is some progress or only radical nicks in science...
This whole debate is probably the worst controversy in the history of science... Paradoxically, their position is totally dependent on the ontological difference between the mathematical models and the real objects... What they urge us to do is to identify one by the other, but what we need is to rethink the relation between them... Which could not be a simple mirror image but a rigorous, rational, consistent, coherent and creative outlook on it...
Why some mathematical constructs are good in describing reality... ?

 

[my_wan]

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

Ok, I think I see, and might help explain some of your objections. So when you said the "definition" isn't used in the proof it wasn't a claim that the authors didn't use the "definition". This has a number of consequences in trying to make sense of your interpretation. One, that you are at odds with PBR's interpretation of their theorem. This you verify farther down this post. So now a quick outline of some implications of your interpretation.

1) That you are at odds with the "interpreted statistically" used in the title.​

Note: This is not the only interpretation of statistics, merely one interpretation of statistical that is ostensibly common among certain types of realist. Hence taking issue with it has another implication about your interpretation.

2) That "interpreted statistically" has a singular interpretation.​

This is wrong. Nor did the PBR paper imply that "interpreted statistically" as used in the title was the only way to interpret "statistically". This implies:

3) That your rejection of "interpreted statistically", as used in the title, is consonant with the articles rejection of "interpreted statistically" on the basis of the theorem.​

Why then are you taking issue with "interpreted statistically" as used in the title? This implies:

4) You must hold a differing interpretation as to what "interpreted statistically" entails.​

Fine, so do I in the QM context. But to reject the incongruent take on "interpreted statistically" as used in the title implies it is not valid a priori. Leaving no point in defining a theorem to rule it out. This implies we are back to:

2) That "interpreted statistically" has a singular interpretation.​

And around in circles we go.

Yet the fact remains that not only that interpretation, ostensibly common among certain types of realist, requires that it get a fair shake at falsification, but it says nothing a priori about your alternative characterization of "interpreted statistically". In effect your interpretation is ostensibly consonant with the results of the theorem, yet are are taking issue with the authors rejection of an interpretation of "interpreted statistically" that you yourself do not ascribe to.

This seems to be a symmetrical characterization of why/how you could assign ontological/epistemic labels in a manner that is exactly opposite of how someone else could apply those same labels in a potentially valid way, using the same definitions of ontological/epistemic. That's why I tried to get you to look at ontological/epistemic characterization outside of the QM proper to begin with. To illustrate how the labeling can legitimately be reversed without affecting the legitimacy of the labels under the same definitions.

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

If you are not making any assumptions about "properties", how do you go about specifying the argument in terms of a qubit? In order for a qubit to be a qubit it must in some sense contain the "properties" of a qubit. Furthermore, to be a qubit with qubit properties entails that the "outcomes" of experiments on a qubit have certain characteristics. I recognize, as you reiterate below, that you did not deem the definition as I restated it as unreasonable, but it appears to me that you are hinging your absolute characterizations on descriptive elements of the model that fall bellow the level of empirically accessible "outcomes". Not a problem in general except for the absolute character of those characterizations. The same absolutes I am taking issue with when you specify X with either an ontological or epistemic characterization. It's not the characterization it that is at issue, it is the unique law of the excluded middle characterization that is at issue.

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

Ontological specifications have a character very similar coordinate choices in math. A coordinate choice is not a physical choice. Yet how a system is ontological characterized is often contingent upon that coordinate choice. Several (non)paradoxes hinge on this, like whose clock is really the slow clock of the two? What is the true momentum of that mass? Is that variable really an ontic or an epistemic variable? Given the HS definitions, a system described from one perspective can specify a variable as ontic, whereas the same variable described from another equally perspective will specify it as epistemic, using the exact same HS definition. Neither one is any more right or wrong than whose clock is really going slower in SR. See my problem when you designate an ontological characterization and presume that that ontological characterization is in itself sufficient to invalidate the legitimacy of a characterization?

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

So apparently you restricted the meaning of "determines outcomes" to entail a narrower meaning than what was provided. In fact, if λ determines "probabilities of outcomes" that is in part the outcome which λ determines. To say that A determine B does not entail that B ≠ probabilities of outcomes.

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

But it is not strictly "other definitions" than those provided by HS, rather other equally valid context in which the same variables are defined, that those same HS definitions entail assigning the same variables different ontological characterizations. That is why I previously pointed out that if you partition a set of epistemic variables you can then create a new set of derivative variables in which the partition epistemic variables are, by HS definition, ontic relative to the derivative variables.

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

Fine. Then address these issues I have pointed out wrt ontological specifications of variables. Simply assigning epistemic/ontic characterizations and presuming legitimacy from that alone will get you nowhere until these issues are addressed.

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

As a matter of fact that is exactly the way I intended it, but I have to admit that by qualifying "determines" with "uniquely" I left it poorly defined.

Here's the difficulty. In classical probability a probabilistic state does not correspond to any actual state. It's merely a model state due to limited knowledge. In QM, in some sense, this probabilistic state is apparently in fact the actual state of the system itself, not just the model, at least to some extent. The PBR article constructed a pair of states to demonstrate this. Empirically predicated on non-probabilistic outcomes, i.e., a zero probability of differing outcomes. Hence, unlike classical probabilities, the resulting state is apparently an actual outcome, rather than state of the model alone.

So classically saying that "λ uniquely determines an outcome" means the same thing as "λ uniquely determines the probability of every outcome" makes no sense, in QM probabilities it apparently does mean the same thing in some sense. So if I characterized "outcomes" in a manner that did not allow for the possible inclusion of "probability of outcome" it would be tantamount to rejecting the results of the PBR theorem a priori.

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

Of course not. The pair pure quantum state was explicit chosen to avoid mixed states, not deny their existence. Though I am still lost as to how your labeling of epistemic verses ontological are relevant in the domain of all possible models, nor can get you to even attempt to clarify, I do agree that interesting part of PBR succeeded ruling out models that attempt to separate the probabilistic state from the ontic state, or treat the probabilistic state as purely a modeling artifact like it is in classical physics.

So we are not so far apart wrt our interpretations when limited to the context of QM as it presently formulated, but in the space of all possible models, exactly equivalent or not, I see the narrow epistemic/ontological labels breaking down as any sort of meaningful label.

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

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

Yes, and I agree to a large extent. But here is the problem, is it possible to formulate a theory in which a pool ball either has a non-zero kinetic energy or not? No. Its kinetic energy, and whether it's zero or not, depends solely on the non-physical choice of what coordinate system it is considered under. Hence the fact that QM does not provide for assigning 0 or 1 to each possible measurement result is not at all strange, nor fall outside the possibility of characterizing with a purely ontic substructure. It only requires properties to be derivative, rather than innate, like the "magic" Ken G spoke of, to whatever ontic constructs are posited.

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

There it is in the last sentence. The core of the issues I have been attempting to articulate and get clarification from you on. Yet the last sentence of that paragraph appears to directly contradict the first. If the epistemic states of one theory correspond to the ontic states of another then we are still talking about ψ-epistemic and ψ-ontic. Hence it still depends on the context in which you define ψ, as your first sentence notes. So how does this not justify everything I have been trying to get you to articulate?

 

[Ken G]

However, now that I think about it, "system" is just an undefined idea that we associate with the theory, just like "complete list of properties" is an undefined idea that we associate with ontic states. We use such terms only because they give us a convenient way to organize our thoughts.

Exactly, the terms themselves come with a fundamentally epistemic character, yet we choose to afford them with ontic character to achieve a kind of parsimony of thought and language. This serves us well, but involves entering into a kind of pretense that normally doesn't bite us-- but we have to watch out when we start trying to prove things whose foundation ignores this little cheat we started with.

In this case, there's no need to involve either of the terms "system" or "qubit" (or "property"). Our goal is simply to prove that there's no local ψ-epistemic ontological model for a quantum theory with a 2-dimensional Hilbert space.

Yes, I think that is a good separation to make. If we stick to proving that, then we are simply learning something about our own theory, but that something will only limit valid interpretations within fairly narrowly defined additional assumptions. It seems to me that proof is valid, at least I don't know any flaws in it, but I don't think we should ever expect models that are either "local" or "ontological" to survive rigorous logic. That's because the standard of truth is much broader in physics than in mathematics-- physical truths are effective and useful, mathematical truths are formal and tautological. Mixing the two, and hoping to learn something from it, is very tricky.

I don't understand the "if we are even to assume..." comment, or why you keep coming back to this. The goal is to prove that there is no local ψ-epistemic ontological model for a quantum theory with a 2-dimensional Hilbert space.

But that's just the issue-- I am willing to grant that this has been proven within certain tight definitions of the terms, although I realize that you want to understand the formal elements of the proof better. But any attempt to understand the ramifications of the words like "psi-epistemic" and "ontological" requires this wider context.

So why are you all "oh no, ontic states are bad"?

I'm not saying ontic states are bad, I'm saying that if one is trying to prove ontic character of the states, one had better watch carefully any ontic character that is being assumed rather than proven.

The logic goes like this: Either there is an ontological model for this quantum theory or there isn't.

No, the logic is trying to rule out the possibility of epistemic character within the context of certain ontological assumptions. So it is very much a crucial question, how much ontology do you have to assume before you can eliminate an epistemological interpretation? Had the authors framed their result as "here is how much ontology you need to build into your interpretation in order to rule out an epistemic interpretation of a state", I would have no objection. Instead, the result is framed as "given mild assumptions, quantum mechanics is inconsistent with an epistemic interpretation of its states."

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

The "choice" I refer to is not the basis, that does not alter the state. The "choice" is in creating the concept of the state in the first place. I'm saying the qubit is the state, the building block of the theory, but it represents various choices (one of them being what we will regard as a "system", another being what we will regard as describing the "preparation" of the system. In reality, of course, there is no such thing as "a system", there is a universe, and there is no two preparations are ever the same. But we just can't do physics that way, so we make alternative choices.)

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

I'm not disputing that, I'm asking how much of the structure is just being assumed by saying that. If too much is being assumed, then the "proof" is not really saying anything about quantum mechanics, it is only saying something about how we are choosing to think about quantum mechanics-- getting out only what is being put in. We need to understand how much of that is going on, before we can claim to have learned anything about quantum mechanics.

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

If contextuality enters into measurements, it enters into preparations as well. That's because all the language of physics is conditioned by the measurement concept, including how we can talk about preparations. Anything we say about a preparation is going to have to be in the context of a measurement of some kind, or else what we are saying has no physical meaning.

Note that the $|\xi_i\rangle$ aren't tensor product states. They are linear combinations of two tensor product states. That means that the two qubits are entangled. How did they end up that way? There is nothing in the quantum theory of the spin of a silver atom that can entangle two spins that start out isolated.

Actually, that is not going outside quantum mechanics, it is fundamental to quantum mechanics, because the particles in the atoms are indistinguishable. No particles in quantum mechanics have "their own" wavefunction, so all particles are automatically entangled all the time. But the entanglements often don't matter too much, or even at all, to the physicist-- so we often choose to treat particles as if they did have their own state, their own "preparation", because we have objectives that will not be compromised by not doing quantum mechanics perfectly correctly. This is standard fare-- physics in action is very much about the choices made by the physicist, as much as it is about some formal theory.

 

[Fredrik]

Sorry guys, I think I'm done with this discussion. It's taking too much time, and too much of it isn't going anywhere. So I will just write down a summary of my views, and that's probably it for my involvement in this thread, unless someone wants to talk about the technical details. I'm thinking about starting a new thread just for that.

• I would never use the word "theorem" for something that's not even a mathematical statement.
• What the article describes as its "main assumption" (after preparation, the quantum system has some set of physical properties) is not a mathematical statement (because the term "properties" is undefined), so it can't be used as the starting point of a proof of a theorem.
• Immediately after declaring that they are going to explain what they mean by the two views, they reference HS, and then they proceed to state conditions that are clearly intended to match the HS definitions of ψ-ontic, ψ-complete, ψ-supplemented and ψ-epistemic ontological models for QM. The only possible interpretation of what they're saying is that they're defining the statistical view as "there's a ψ-epistemic ontological model for every quantum theory".
• The article proves a theorem on page 2, but the content of the theorem isn't explicitly stated. To figure out how to state the theorem correctly, you have to separate the mathematical from the non-mathematical, and compare what they're saying with the HS definitions.
• The theorem that's proved on page 2 is "There's no local ψ-epistemic ontological model for a quantum theory with a 2-dimensional Hilbert space".
• This is a purely mathematical statement, so all philosophical concerns about issues like whether ontic states really represent "properties" are completely irrelevant to its proof.
• They don't mention locality at all, but I can't make sense of the probability ">q²" unless I assume locality.
• If I'm right about the locality, then they haven't disproved what they defined to be the statistical view. But they can of course just add the word "local" to that definition.
• I'm still not 100% sure that the proof is valid, but I think it probably is.

A thorough discussion about the significance of this result is going to take too much time, so I'm going to skip that. I'll just say that it certainly doesn't justify a title like "The quantum state cannot be interpreted statistically".

For those who haven't followed the discussion: HS = This article by Harrigan & Spekkens. It's reference [11] in the PBR article.

 

[Fredrik]

Actually, that is not going outside quantum mechanics, it is fundamental to quantum mechanics, because the particles in the atoms are indistinguishable. No particles in quantum mechanics have "their own" wavefunction, so all particles are automatically entangled all the time.

I didn't say "outside quantum mechanics". (I would define QM as the framework in which quantum theories are defined). I said outside of the quantum theory of a qubit that doesn't interact with anything. However, the $|\xi_k\rangle$ vectors are a basis for the Hilbert space of the theory of two non-interacting qubits, so they are possible states of a non-interacting two-qubit system. But the theory of two non-interacting qubits also says that if they start out without entaglement (and we are assuming that, by assuming that the preparation procedures give us states like $|0\rangle\otimes|0\rangle$ and $|0\rangle\otimes|+\rangle$), they will remain unentangled. So we have to at least add interactions to the theory. This makes me wonder if we're really proving anything about the theory of a single non-interacting qubit.

 

[ThomasT]

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

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

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

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

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

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

/Fredrik

In case anybody might be puzzled wrt your reference to 'Tomas' and 'Thomas', I think you're referring to a post that I deleted. I decided that the paper wasn't worth discussing -- despite what the popularized Nature article, and at least one notable physicist, said about it. Which is not to say that what several of the commenters in this thread had to say isn't interesting or correct, because a lot of it is, imho. There's a few statements that I currently disagree with (or would at least phrase differently), but I've decided not to nitpick those. Maybe, after learning more, I'll agree with them ... who knows.

Anyway, all things considered, nice thread imho, as is usual for the quantum physics forum at PF where I've learned much beyond my basic/sketchy knowledge of qm.

 

[Ken G]

I didn't say "outside quantum mechanics". (I would define QM as the framework in which quantum theories are defined). I said outside of the quantum theory of a qubit that doesn't interact with anything.

OK, but I would say that such a quantum theory is a kind of idealization of formal quantum mechanics, in which what constitutes an "interaction" is only vaguely characterized. The physicist is not saying "there are no interactions here, so I can use two unentangled qubits", the physicist is saying "I am going to treat the systems as independent, in cases where I find it doesn't change the outcome if I do that." However, when the systems come together, the physicist cannot say that any more. There is no need for any new "interactions" to appear, all that is happening is an idealization is not working any more. The idealization was always just an approximation, but it went from being a good approximation to being a bad approximation when the systems comes together-- even without any interactions. This is already built into quantum mechanics-- it is always the entire system that has a wave function, not its parts, but the latter can be a good approximation in many situations, and can go from being a good approximation to being a bad approximation if a situation evolves.

But the theory of two non-interacting qubits also says that if they start out without entaglement (and we are assuming that, by assuming that the preparation procedures give us states like $|0\rangle\otimes|0\rangle$ and $|0\rangle\otimes|+\rangle$), they will remain unentangled.

That is what I am claiming is untrue, even without any additional interactions.

 

[Fredrik]

That is what I am claiming is untrue, even without any additional interactions.

The Hamiltonian for the non-interacting two-qubit theory is defined as $H=H_1\otimes 1+1\otimes H_2$, where $H_1$ and $H_2$ are the Hamiltonians of the two single-qubit theories. Since the two terms commute, we have
$$e^{-iHt}|\sigma\rangle\otimes|\tau\rangle=e^{-i(H_1\otimes 1)t}e^{-i(1\otimes H_2)t}|\sigma\rangle\otimes|\tau\rangle= e^{-iH_1t}|\sigma\rangle\otimes e^{-iH_2t}|\tau\rangle$$ for arbitrary $|\sigma\rangle,|\tau\rangle$. So a tensor product state remains a tensor product state.

OK, but I would say that such a quantum theory is a kind of idealization of formal quantum mechanics, in which what constitutes an "interaction" is only vaguely characterized.

In this case, it's easy to give it an exact definition. Two qubits are not interacting if the time evolution of each component of an arbitrary tensor product state is exactly the same as in the single-qubit theory. (The calculation above shows what that looks like). I think that's actually equivalent to saying that all unentangled states remain unentangled.

I would say that each choice of Hamiltonian on $\mathcal H\otimes\mathcal H$ where $\mathcal H$ is the Hilbert space of the single-qubit theory, defines a unique two-qubit theory. A term in the Hamiltonian of the form $A\otimes B$ where neither A nor B is an identity operator would be an interaction term.

The physicist is not saying "there are no interactions here, so I can use two unentangled qubits", the physicist is saying "I am going to treat the systems as independent, in cases where I find it doesn't change the outcome if I do that."

In this case, it should be "I'm going to consider the non-interacting two-qubit theory to see if I can use it to prove the theorem. If I fail, I'll try something else, maybe an interacting theory".

However, when the systems come together, the physicist cannot say that any more. There is no need for any new "interactions" to appear, all that is happening is an idealization is not working any more. The idealization was always just an approximation, but it went from being a good approximation to being a bad approximation when the systems comes together-- even without any interactions.

There are no approximations here, just a choice of what theory to consider.

 

[Fra]

In case anybody might be puzzled wrt your reference to 'Tomas' and 'Thomas', I think you're referring to a post that I deleted.

Thanks for that note. I didn't find your post in retrospect and I was confused myself.

Since some some months I become a father, so I've got even less time than I used to for these things. I was going to write some more comments on a comment someone made in response to one of KenG's posts, where one referred to the mind projection fallacy as defined by et jaynes ,but havend't had time yet.

There is one particular way where dismissing things due to the "mind projection fallacy"(MPF) risks turning into a DIFFERENT fallacy: and this has to do with hat things to COUNT when you construct an expectation value - just because something can not be deductively EXCLUDED as a ontological possibility (as then we would blame the MPF) just becuase we don't KnOW about it, does not mean everything we do not KNOW about must be included in the space over possibilities - this risks overcounting and thus divergences and known infinity problems. My point refers to two view of probability: descriptive view and decision theoretic view. Jaynes is nice, but I think in certain respects I think he also fails to get the decision picture. I think Jaynes is more of an objective bayesian, while I am a more on the subjective side thinking that the "ontic" objectivity has no scientific justification (which does NOT mean i KNOW it does not exist - ie. I do not fall into MPF) but it DOES clearly mean that MY actions are independent of it. Ie. when you consider the ACTION of the OBSERVER... things get far more complicated than I think Jaynes desciprtions admits.

In fact Jaynes is too fast in this reconstruction of probability theory, he introduces the real number as representing "degrees of beliefes" too carelessly. And that exact thing is a prime example of the subtle fallact I talk about that is the symptom of over-interpreting the MPF.

/Fredrik

 

[my_wan]

Sorry guys, I think I'm done with this discussion. It's taking too much time, and too much of it isn't going anywhere. So I will just write down a summary of my views, and that's probably it for my involvement in this thread, unless someone wants to talk about the technical details. I'm thinking about starting a new thread just for that.

I understand not wanting to continue this discussion in its present form. The technical details do seem to have accomplished what was stated. The problem (not a problem with the proof itself) is that once you start trying to wrap those details into any particular interpretation it becomes a moving target. This includes epistemic/ontic characterizations even when those definitions remain constant.

The article proves a theorem on page 2, but the content of the theorem isn't explicitly stated. To figure out how to state the theorem correctly, you have to separate the mathematical from the non-mathematical, and compare what they're saying with the HS definitions.

I don't think this content can be explicitly stated in a model independent format that is satisfactory to everybody, even when the models have equivalent empirical content or validity. Hence the objections of some concerning the title, which I don't have an issue with. The proof merely used the formal specification of ψ, which is a sort of model in itself. Hence the target within that singular context did not suffer the moving target issue, like the "interpreted statistically" in the title does. However, trying to characterize ψ in any manner not explicitly provided by its formal specification gets arguments with or without the PBR theorem. Yet those characterizations not presently provided by the formal specification is the target of such theorems, to place limits on what kind of alternative modeling constructs can be considered valid.

Here's my best attempt at stating the consequences of the theorem:
Any model which attempts to characterize quantum observables strictly in terms of A xor B, 0 xor 1, is invalid. Yet it does explicitly allow these properties to be defined in terms of partitioned (separable) entities.

My take on this:
In terms of the space of possible valid models the partitioning may or may not be an idealization of the state, and the included middle, 0 or (inclusive) 1, may or may not be applicable to a system in which the 0's and 1's are derivatives rather than identities of the substructure. Yet any potential model must, to be valid, be capable characterizing these particular variables in a manner consistent with the specifications given. Simply appending 0 xor 1 onto these partitioned variables and explaining away the inclusive character of the 0's and 1's as a modeling artifact of randomization of those same variables is NOT valid, per the PBR theorem.

 

[ThomasT]

Thanks for that note. I didn't find your post in retrospect and I was confused myself.

Since some some months I become a father, so I've got even less time than I used to for these things. I was going to write some more comments on a comment someone made in response to one of KenG's posts, where one referred to the mind projection fallacy as defined by et jaynes ,but havend't had time yet.

There is one particular way where dismissing things due to the "mind projection fallacy"(MPF) risks turning into a DIFFERENT fallacy: and this has to do with hat things to COUNT when you construct an expectation value - just because something can not be deductively EXCLUDED as a ontological possibility (as then we would blame the MPF) just becuase we don't KnOW about it, does not mean everything we do not KNOW about must be included in the space over possibilities - this risks overcounting and thus divergences and known infinity problems. My point refers to two view of probability: descriptive view and decision theoretic view. Jaynes is nice, but I think in certain respects I think he also fails to get the decision picture. I think Jaynes is more of an objective bayesian, while I am a more on the subjective side thinking that the "ontic" objectivity has no scientific justification (which does NOT mean i KNOW it does not exist - ie. I do not fall into MPF) but it DOES clearly mean that MY actions are independent of it. Ie. when you consider the ACTION of the OBSERVER... things get far more complicated than I think Jaynes desciprtions admits.

In fact Jaynes is too fast in this reconstruction of probability theory, he introduces the real number as representing "degrees of beliefes" too carelessly. And that exact thing is a prime example of the subtle fallact I talk about that is the symptom of over-interpreting the MPF.

/Fredrik

Thanks for the, unexpected, reply. I'll think about what you've written and maybe incorporate it into my future opinions.

More importantly, congratulations on becoming a father.

 

[mysearch]

As somebody who has only recently started to take an interest in QM, and therefore not qualified to comment on the in-depth debate, I was struck, while trying to learn from this thread, by what appears to be a worrying aspect of QM. The scope of this entire thread, consists of some 200+ posts, some from people who clearly have an in-depth understanding of the subject plus makes references, see below, to many other equally informed debates. However, it would seem that all this knowledgeable debate has been triggered by the PBR article, which is less than 4 pages, if the appendices is excluded. As such, I wondered if anybody feels that following quotes have, or are becoming, too relevant to some aspects of QM? While I am conscious that this question might appear rude to some members of this forum, it is not intended to be so, as some further insight would be genuinely helpful.

John Barrow: “Unwilling to confess their ignorance of the formula or unable to question its relevance to the question at hand, his opponents accepted his argument with a nod of profound approval.”

Maurice Allais: “Any author who uses mathematics should always express in ordinary language the meaning of the assumptions he admits, as well as the significance of the results obtained. The more abstract his theory, the more imperative this obligation. In fact, mathematics are and can only be a tool to explore reality. In this exploration, mathematics do not constitute an end in itself, they are and can only be a means.”

Summary of references made throughout this thread:

PBR Article: The Quantum State Cannot be Interpreted Statistically
http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.3328v1.pdf

Matt Leifer
http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/

Nature Article
http://www.nature.com/news/quantum-theorem-shakes-foundations-1.9392

Guest Post: David Wallace on the Physicality of the Quantum State
http://blogs.discovermagazine.com/c...lace-on-the-physicality-of-the-quantum-state/

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

Lubos Motl
http://motls.blogspot.com/2011/11/nature-hypes-anti-qm-crackpot-paper-by.html

Einstein, incompleteness, and the epistemic view of quantum states
http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.2661v1.pdf

More on the Statistical Interpretation
http://www.tjradcliffe.com/?p=621

The interpretation of quantum mechanics: where do we stand?
http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.0958v1.pdf

Primitive Ontology and the Structure of Fundamental Physical Theories
http://www.niu.edu/~vallori/AlloriWfoPaper-Jul19.pdf[/URL]

 

[DarMM]

However, it would seem that all this knowledgeable debate has been triggered by the PBR article, which is less than 4 pages, if the appendices is excluded. As such, I wondered if anybody feels that following quotes have, or are becoming, too relevant to some aspects of QM? While I am conscious that this question might appear rude to some members of this forum, it is not intended to be so, as some further insight would be genuinely helpful.

John Barrow: “Unwilling to confess their ignorance of the formula or unable to question its relevance to the question at hand, his opponents accepted his argument with a nod of profound approval.”

Maurice Allais: “Any author who uses mathematics should always express in ordinary language the meaning of the assumptions he admits, as well as the significance of the results obtained. The more abstract his theory, the more imperative this obligation. In fact, mathematics are and can only be a tool to explore reality. In this exploration, mathematics do not constitute an end in itself, they are and can only be a means.”

I don't think those quotes are relevant, because I don't think any of the discussion here or in the references is discussing mathematics as an end in and of itself. Rather we have a short paper which discusses a unintuitive consequence of QM and a lot of discussion on the relevance of the assumptions and conclusions.

 

[billschnieder]

There is one particular way where dismissing things due to the "mind projection fallacy"(MPF) risks turning into a DIFFERENT fallacy: and this has to do with hat things to COUNT when you construct an expectation value - just because something can not be deductively EXCLUDED as a ontological possibility (as then we would blame the MPF) just becuase we don't KnOW about it, does not mean everything we do not KNOW about must be included in the space over possibilities - this risks overcounting and thus divergences and known infinity problems. My point refers to two view of probability: descriptive view and decision theoretic view. Jaynes is nice, but I think in certain respects I think he also fails to get the decision picture. I think Jaynes is more of an objective bayesian, while I am a more on the subjective side thinking that the "ontic" objectivity has no scientific justification (which does NOT mean i KNOW it does not exist - ie. I do not fall into MPF) but it DOES clearly mean that MY actions are independent of it. Ie. when you consider the ACTION of the OBSERVER... things get far more complicated than I think Jaynes desciprtions admits.

In fact Jaynes is too fast in this reconstruction of probability theory, he introduces the real number as representing "degrees of beliefes" too carelessly. And that exact thing is a prime example of the subtle fallact I talk about that is the symptom of over-interpreting the MPF.

/Fredrik

I don't think you are correctly representing Jaynes views. The distinction you are imposing on his views (ie descriptive vs decision theoretic, is artificial). This is what he says:

In our system, a probability is a theoretical construct, on the epistemological level, which we assign in order to re present a state of knowledge, or that we calculate from other probabilities according to the rules of probability theory. A frequency is a property of the real world, on the ontological level, that we measure or estimate. So for us, probability theory is not an Oracle telling how the world must be; it is a mathematical tool for organizing, and ensuring the consistency of our own reasoning. But it is from this organized reasoning that we learn whether our state of knowledge is adequate to describe the real world.
This point comes across much more strongly in our next example, where belief that probabilities are real physical properties produces a major quandary for quantum theory, in the EPR paradox. It is so bad that some have concluded, with the usual consistency of quantum theory, that (1) there is no real world, after all, and (2) physical influences travel faster than light.

As concerns the mind projection fallacy, here is how he characterized it:

The experiments designed to test this, of which the one of Alain Aspect (1985, 1986) is perhaps the most cogent to date, have with only one exception ended with the verdict "quantum theory confirmed", and accordingly there has been quite a parade of physicists jumping on the bandwagon, declaring publicly that they now believe in psychokinesis. Of course, they do not use that word; but at the 1984 Santa Fe Workshop (Moore & Scully, 1986) more than one was heard to say: "The experimental evidence now forces us to believe that atoms are not real." and nobody rose to question this, although it made me wonder what they thought Alain's apparatus was made of.

The failure of quantum theorists to distinguish in calculations between several quite different
meanings of `probability', between expectation values and actual values, makes us do things that don't need to be done; and to fail to do things that do need to be done. We fail to distinguish in our verbiage between prediction and measurement. For example, the famous vague phrases: `It is impossible to specify ... '; or `It is impossible to define ... ' can be interpreted equally well as statements about prediction or statements about measurement. Thus the demonstrably correct statement that the present formalism cannot predict something becomes perverted into the logically unjustified -- and almost certainly false -- claim that the experimentalist cannot measure it!
We routinely commit the Mind Projection Fallacy: supposing that creations of our own imagination are real properties of Nature, or that our own ignorance signifies some indecision on the part of Nature. It is then impossible to agree on the proper place of information in physics. This muddying up of the distinction between reality and our knowledge of reality is carried to the point where we find some otherwise rational physicists, on the basis of the Bell inequality experiments, asserting the objective reality of probabilities, while denying the objective reality of atoms! These sloppy habits of language have tricked us into mystical, pre-scientific standards of logic, and leave the meaning of any QM result ambiguous. Yet from decades of trial-and-error we have managed to learn how to calculate with enough art and tact so that we come out with the right numbers!

So when someone says "There is no quantum world. There is only an abstract physical description.", he is committing the mind projection fallacy. Or when someone says "what we know is all there is" or "epistemology is ontology", he is committing the mind projection fallacy according to Jaynes.

References:
http://bayes.wustl.edu/etj/articles/prob.in.qm.pdf
http://bayes.wustl.edu/etj/articles/cmystery.pdf

 

[Ken G]

The Hamiltonian for the non-interacting two-qubit theory is defined as $H=H_1\otimes 1+1\otimes H_2$, where $H_1$ and $H_2$ are the Hamiltonians of the two single-qubit theories.

That is a definition of an idealization that has already occured. It comes down to what is meant by "noninteracting." That means quite a bit more than just "no interaction term in the Hamiltonian", because these are indistinguishable particles. As such, in formal quantum mechanics, they must not have their own wavefunctions-- they must respond to the same joint wavefunction, and that can already be thought of as a kind of "interaction," along the lines of the Pauli exclusion principle. It is merely awkward to include this formal requirement in calculations when the systems are separated-- it is doing extra work with no benefit. So the expression you cite is used instead, but it is not formally correct, it is an idealization-- a choice made by the physicist, like the choice to treat the Earth as a sphere when calculating its gravity, or the choice to use Newtonian gravity, etc.

When you think about it, physics is always rife with choices like that, which is why I'm always skeptical of "proofs" used in physics-- they tend to rely a lot on the assumptions going in, those choices by the physicists. You're right this doesn't mean your expression is "outside physics", but it is outside formal quantum mechanics, yet inside effective or useful quantum mechanics. But the distinction becomes important when the systems are later rejoined, and the idealization breaks down-- for one thing, the idealization suggests that systems that are originally unentangled must remain so, but they were not originally unentangled, they were merely being originally treated as unentangled. It was a choice made by the physicist, that worked initially but breaks down if the systems are combined. It is the same if a white dwarf star accretes additional "unentangled" electrons-- it can lead to a supernova because they really weren't unentangled at all.

In this case, it should be "I'm going to consider the non-interacting two-qubit theory to see if I can use it to prove the theorem. If I fail, I'll try something else, maybe an interacting theory".

But the problem is, what does "failure" mean? Does it mean the theory failed, or just the way it was applied, the idealizations made to it? I count statements like "properties cause the outcomes" to be those kinds of idealizations, choices about how to apply a theory that are nowhere in the actual formal theory. When proofs rely on them, then we are not proving things about the formal theory, we are proving things about how we think about our own theory, how we make idealizations to get the theory to be simpler or make sense to us.

There are no approximations here, just a choice of what theory to consider.

That's a tricky issue-- what constitutes "a theory"? If I, like countless astronomers might, choose to treat some star as a sphere to calculate its gravity, am I considering a different theory, one called "the theory of gravity of spheres", or am I just taking Newtonian gravity and applying an approximate idealization to it? All theories must have these approximations applied to become useful, so I don't think we can call such approximations separate theories-- and proofs involving these idealizations don't really prove anything about the theory absent the idealizaitons That's why I would characterize the PBR proof as basically proving that if QM is idealized and approximated as having an ontological core, then the wavefunction must take on an ontological character. That is the crux of the circularity I have objected to.

 

[Ken G]

So when someone says "There is no quantum world. There is only an abstract physical description.", he is committing the mind projection fallacy. Or when someone says "what we know is all there is" or "epistemology is ontology", he is committing the mind projection fallacy according to Jaynes.

Jaynes' view on the "mind projection fallacy", which is his own term, is indeed strangely internally inconsistent. First of all, we must distinguish the claims "there is no quantum world" or "atoms are not real" from the claims "nothing is real" or "there is no such thing as reality." It all must begin with the recognition that there is such a thing as an "effective" or "useful" truth, and these are the truths that physics manipulates. This also includes the truth in the attributes that we conceptualize reality as having. Reality itself is clearly an undefined primitive element of the philosophy of realism, yet its attributes come under the sway of phyics.

Once we recognize this very basic fact, we see that Jaynes' odd attachment to the idea that atoms are absolutely and undeniably real is certainly an example of the mind projection fallacy, as his own distinctions between prediction and measurement show. Atoms are never measured, it's just that simple. All we can say is that imagining the existence of atoms helps us explain our measurements. Now, unless Jaynes is going to claim that any time imagining something helps us understand measurements, then the thing we imagine must be real, he has fallen victim to his own complaint of confusing the abstract concepts we manipulate in our minds for the measurements we confirm in the laboratory. If he doesn't recognize that difference, I have one question for him: is the force of gravity real? What would Jaynes have said in 1800 had he been asked that? In 1900? In 2000? The most basic facts of the history of physics show clearly that elements of physical theories, like atoms, are never real, and imagining that they are is a clear example of the mind projection fallacy! Jaynes has an odd way of categorizing the things he doesn't like as mind projection fallacies, and the things he does like as basic common-sense non-mystical examples of reality. Very convenient.

So, the mind projection fallacy is valid enough, Jaynes selective application of it is not.

 

[billschnieder]

There is no quantum world. There is only an abstract physical description.

Description of what? What is it you purport to be describing. Humans did not just wake up one day and decide to have a description without any object. You are the naive one here.

That's easy, know knowledge. You think the answer is "know truth", but that's because your views are quite simplistic.

Same thing here. Just like you think we are describing the description, you also think you are knowing Knowledge. This is such gobbledigook it's outrageous that you would say such a thing in the same sentence in which you accuse someone else of being simplistic. You can't even use language consistently or think logically yet you want to go deeper?

Consider for example a dog's knowledge of the truth of its master. Is a dog's conception of its master true?

The above statement does not make sense unless the following assumptions are made
- There exists a master.
- There exists a dog.
- There exists information in the mind of the dog about it's master. The dog's belief.

By asking if the dog's conception it's master is true. You are making all those assumptions. The question is asking if the information in the dog's mind matches the true independent existence of the master (independent of the dog's brain). Without accepting those assumptions, the question is nonsensical.

Is it the dog's truth, or a real truth?

Truth is truth. You can not characterize truth as "the dogs truth". You really need to study some basic epistemology. What you are really asking is: "Is the dog's belief true?"

Can a dog know it's master

Knowledge is simply "a true belief". False beliefs are not knowledge. For the dog to know his master:
1 - The dog must belief some information about it's master
2 - The information must be true, or correspond to reality

Does it make a difference if we define "master" as the "relationship of the dog to its human overseer" versus if we define it as "the relationship of the human overseer to his/her dog"?

Yes it makes a difference because what the master "knows" about the dog is different from what the dog "knows" about the master. The master may know a different set of true facts than the dogs with some overlap. Knowledge does not mean you must know ALL true facts; any true fact believed is knowledge. But there is only one truth, which includes the reality of the master, the dog, and the physical interaction between the two and all true facts which correspond to reality. It is this reality (truth) which determines whether the master's or dog's "beliefs" about the relationship are true (and is therefore is knowledge) or not.

There are many layers of complexity when dealing with "knowledge of the truth" in something as uncomplicated as a dog and its owner

It is not complicated at all if you have a basic understanding of the meanings of "Truth", "Belief" and "Knowledge". But if you are confused about these words, the results are chaotic.

As I said, you have badly misinterpreted the mind projection fallacy. In actual fact, the mind projection fantasy that Jaynes is talking about is much closer to the opposite of what you think--

See my previous post.

I would certainly not claim that what we currently know has no connection with what is true, if indeed there is something that is true.

You appear to be agnostic that there is any truth, in line with your earlier statement "know knowledge". Yet you are certain that there is knowledge. This is utter confusion. Knowledge implies the existence of truth, by definition. If you disagree please define "knowledge".

How it can all be epistemology is simply that epistemology is all we get, we want truth and we get epistemology.

You mean we want to know the truth and we get epistemology. Which is tautology because epistemology is knowledge. It is exactly what we want. Nothing else can exist in our brain. But what you still fail to understand that is that knowledge by definition assumes that truth which is independent from our brains exists, otherwise we would not be trying to know it. And we have coined the term "ontology" to refer to that truth. It is carelessness to make and defend proclamations such as "ontology is epistemology" or "there is no quantum world just an abstract description".

Again, any other view of the situation seems downright bizarre.

I suppose by this you mean any suggestion that atoms actually exist is bizarre.

Note also that nothing I said requires there exist such a thing as absolute truth-- all I actually said is that physics isn't it, nor is any epistemology, but what epistemology is is a set of choices about what will be regarded as useful or effective truths, provisional truths that are predicated on what we are able to know and what we decide to regard as knowledge. Like physics, for example.

Again you are mixing terms. Truth is truth. There is no such thing as "effective truth" or "provisional truth". You have beliefs which are either true or false. Knowledge only refers to true beliefs. Probability as Jaynes explains, represents our degree of confidence that what we belief is true. It doesn't mean if we assign a probability of 1, then what we belief is certainly true. It simply means we believe it is. Reality is what determines which beliefs are true and which ones are false. Probability theory provides a method for rationally assigning degrees of belief.

 

[billschnieder]

Jaynes' view on the "mind projection fallacy", which is his own term, is indeed strangely internally inconsistent. First of all, we must distinguish the claims "there is no quantum world" or "atoms are not real" from the claims "nothing is real" or "there is no such thing as reality." It all must begin with the recognition that there is such a thing as an "effective" or "useful" truth, and these are the truths that physics manipulates. This also includes the truth in the attributes that we conceptualize reality as having. Reality itself is clearly an undefined primitive element of the philosophy of realism, yet its attributes come under the sway of phyics.

You still do not understand Jaynes. The point is that you can not deny the premise of your argument without denying your argument. This is the point you do not seem to get. Let me use the following argument which you have come very close to making, to illustrate the point:

Argument: "There is no such thing as absolute truth"

What makes the above statement true then. It is self defeating. If we accept the argument as true, then the statement can not be absolute which means the argument is false.

Similarly, you can not build a theory by assuming that there exists ontological entities such as atoms and then use the theory to claim that "there is no atom" just the abstract theory. Whether the atom really exists or not is not the point. The point is that you have already assumed that it exists in order to build the description. You can not turn around and claim that all you have is the description.

You really need to read Jaynes paper to understand his view because you do not.

All we can say is that imagining the existence of atoms helps us explain our measurements. Now, unless Jaynes is going to claim that any time imagining something helps us understand measurements, then the thing we imagine must be real, he has fallen victim to his own complaint of confusing the abstract concepts we manipulate in our minds for the measurements we confirm in the laboratory.

You can not reject your premise an keep the conclusion at the same time if you are reasoning logically. This is the crucial point.

The most basic facts of the history of physics show clearly that elements of physical theories, like atoms, are never real, and imagining that they are is a clear example of the mind projection fallacy!

And what are those facts which show clearly that atoms are not real? Provide them and we will see if you are not the one committing the mind projection fallacy.

 

[bohm2]

Reality is what determines which beliefs are true and which ones are false. Probability theory provides a method for rationally assigning degrees of belief.

This is a big aside, but I'm guessing here you mean "mind-independent reality" or the Kantian notion of "things-in-themselves", etc. There are many cognitive scientists/linguists/psychologists who question whether, in fact, we are born with the capacity to have "access" to the class of "true" theories/reality (whether via math or our scientific/conceptual models). Here's the basic argument:

Since the structure of our experience and state of our knowledge is largely a reflection of our particular, biologically-given cognitive structures, there is no guarantee that “mind-independent reality” will ever conform to the structure of our intelligence. Thus, like all other organisms, we are trapped within our epistemic boundaries. As a result, all our claims to knowledge ultimately break down to belief statements (reflecting the nature of our minds). As such, some seriously doubt our ability to literally know the world’s “true” character. As such, they reject all our claims to knowledge, at least, in the strict philosophical sense (i.e. true justified beliefs). And there exists strong support for these type of arguments, in the cognitive sciences. To begin with, there is the “poverty of stimulus” argument (i.e. “torrential output” from “meagre” input), which claims, on empirical grounds, that:

Proximal stimulation typically contains ‘less information’ than the perceptual beliefs that it engenders (sensation underdetermines perception).

The implication here (a sound one, in my opinion), is that our biologically-determined properties of the mind/brain play a crucial role in determining what and how we perceive the “external” world, since the perceptual knowledge we attain vastly transcends any environmental input. Even evolutionary arguments that try to show that our innate cognitive structures would have to have a considerable degree of correspondence to external reality, (either because they are a product of natural law or for reasons of ‘natural selection’), are not very compelling because as others have pointed out, there is no difficulty “in designing a device (say, programming a computer) that is a product of natural law, but that, given data, will arrive at any arbitrary absurd theory to ‘explain’ these data." As Pinker writes:

We are organisms, not angels, and our minds are organs, not pipelines to the truth. Our minds evolved by natural selection to solve problems that were life-and-death matters to our ancestors, not to commune with correctness. Thus, it's argued that our minds like most other biological systems/organs are likely poor solutions to the design-problems posed by nature. They are, "the best solution that evolution could achieve under existing circumstances, but perhaps a clumsy and messy solution." Thus, it seems we cannot have direct knowledge of how the world is like as the knowledge has to be routed in terms of the resources available to our theory-building abilities/mental organs and these are not likely to be "pipelines to the truth".

Having said that, even though such claims cannot be refuted, one can still believe that we can have a type of knowledge (or at least, a system beliefs-not knowledge about the real nature of things) that is useful for the organization of our experience and for the conduct of our lives: This kind of knowledge is not that which previous dogmatic philosophers had sought, knowledge of the real nature of things. Rather it consists of information about appearances, and hypotheses and predictions about the connections of events and the future course of experience (RH Popkin in The History of Skepticism from Erasmus to Descartes, p. 133).

Basically, this approach is the one taken by the natural sciences. But I think this position has always and should continue to embrace "scientific realism" (treat some of our mathematical models as if they capture some "true" aspects of unknowable reality) versus "instrumentalism". So one can still embrace Kant's philosophy (if they like) without throwing out scientific realism. Just my opinion.

 

[Ken G]

Description of what? What is it you purport to be describing.

That's easy, I purport to be describing whatever it is that I am describing. There just isn't any other way to say it that is at all logically internally consistent. You and Jaynes both make the fundamental error of imagining that you can tell the difference between an attribute of reality that is actually real, versus one that is "mind projected". That is just so obviously logically fallacious I don't understand why I have to point it out. Jaynes is the worst victim of mind projection fallacy that I've seen, even though it is his own term. He imagines that his mind can tell when it is projecting, versus when it has a handle on something real (like, he thinks, atoms). Basically, his philosophy is that if his mind thinks it, it qualifies as real, and if someone else's mind thinks it, they are projecting. Talk about a fallacy!

Humans did not just wake up one day and decide to have a description without any object. You are the naive one here.

I asked you once before to define "object", you chose not to. I wonder why? Actually, I have no idea what you think that word means, but I'm sure that if you do try to define it, you will commit the mind projection fallacy in the process.

You appear to be agnostic that there is any truth, in line with your earlier statement "know knowledge". Yet you are certain that there is knowledge. This is utter confusion.

Actually, no. It is consistent use of language. Of course we can know knowledge, that is part of the definition of both knowing and knowledge. Or course we cannot say what is true in some absolute sense, that has nothing to do with knowledge. Knowledge is all about deciding the provisional senses to which we will claim truth, there is absolutely no difference between knowledge and a type of claim on truth, and neither is the same as absolute truth. Consistent use of language, terms with meaningful definitions. You prefer not to define anything, substituting naive beliefs instead. There is no definition of truth beyond "that which is true" (and the obvious tautology it evinces), unless you adopt the effective or useful truths that I have been talking about all along. Still, you prefer to hold to inconsistent language, a house of cards where actual definitions could be applied instead.

Knowledge implies the existence of truth, by definition. If you disagree please define "knowledge".

I certainly do disagree with that obvious logical fallacy. You just claimed a definition could dictate existence! No, definitions just don't work that way, nothing can imply the existence of something else "by definition." Instead, what actually happens is that when we make a definition, we are making choices about what we will regard as true, or what we will regard as existing. Hence, your definition is an obvious example of the mind projection fallacy, as is much of what Jaynes claims to be true.

I can define "knowledge" quite easily. Knowledge is what we choose to regard as true, based on some self-contained criterion that can differ widely in different subdisciplines or different modes of inquiry. We make this choice because it serves certain goals for us, what we are "knowing" is some effective or useful truth, something that we do not naively imagine is actually true, but rather what we find advantages in imagining is true. Those are the provisions under which we can have knowledge, and what we have knowledge of are these provisional truths. That is the only way to use the language correctly and logically consistently, everything else is pure pretense.

You mean we want to know the truth and we get epistemology. Which is tautology because epistemology is knowledge.

That's right, it is tautology. That's the point-- knowledge is epistemology, including knowledge of ontology. So yes, it's the "mind projection fallacy", but guess what, that's all we have. A "fallacy" is a bad thing in mathematics, but in physics, it's downright inescapable. Physics is the artful manipulation of idealizations, approximations, and rigorous fallacies, to achieve effective and useful knowledge. That's just exactly what physics has always been, and I see no reason to beguile ourselves that it will one day be something different.

That is the fundamental crux here, and we can go around and around all day but if this is not understood, there's just no point. Jaynes is just as much a perpetrator of the mind projection fallacy as those he accuses, and the reason is simple: epistemology is ontology in physics, and the mind projection fallacy is the constant companion of the physicist, our "right hand" in the endeavor. All we can do is recognize this-- and that's exactly what Jaynes and you do not.

Truth is truth. There is no such thing as "effective truth" or "provisional truth". You have beliefs which are either true or false. Knowledge only refers to true beliefs.

I'm afraid those are the most definitively naive remarks that I can imagine in this subject. As I said at the start-- would that it were all really this simple.

Reality is what determines which beliefs are true and which ones are false.

Reality has nothing to do with our beliefs, I doubt "reality" could even understand them.

 

[Ken G]

Basically, this approach is the one taken by the natural sciences. But I think this position should embrace "scientific realism" (treat some of our mathematical models as if they capture some "true" aspects of unknowable reality) versus "instrumentalism". So one can still embrace Kant's philosophy (if they like) without throwing out scientific realism. Just my opinion.

And I think it's a perfectly valid opinion, and I agree with much of it. I just think that scientific realism is already more or less a given-- so the issue to watch out for is avoiding its pitfalls, rather than the need to defend it.

 

[billschnieder]

That's easy, I purport to be describing whatever it is that I am describing.

Hehe, even you can not say that with a straight face. That statement itself says everything about how ridiculous your view is. Together with others such as "we know knowledge".

Where are you going Ken G? I'm going wherever it is I'm going.
What are you eating Ken G? I'm eating whatever it is I'm eating.
What is it your are trying to know Ken G? I'm trying to know whatever it is I'm trying to know.

Just evasion.

You and Jaynes both make the fundamental error of imagining that you can tell the difference between an attribute of reality that is actually real, versus one that is "mind projected". That is just so obviously logically fallacious I don't understand why I have to point it out.

One minute you are claiming you know what Jaynes wrote better than I did, when I prove you wrong by quoting Jaynes, you are now claiming "I and Jaynes" ... etc. This demonstrates a type of arrogance in which you claim to know and speak of things you know nothing about. Why should anyone take you seriously when you criticize Jaynes if you do not bother to even read what the man wrote.

I asked you once before to define "object", you chose not to. I wonder why?

Because the meaning is so basic I assumed you knew it already.

Of course we can know knowledge

More goobledigook. Repeating it a hundred times does not make it true.

Or course we cannot say what is true in some absolute sense

Just because you cannot say it does not mean nothing is true in some absolute sense.

Knowledge is all about deciding the provisional senses to which we will claim truth, there is absolutely no difference between knowledge and a type of claim on truth, and neither is the same as absolute truth.

That is called "belief". Just because you think what you believe is true does not mean it is. By defining truth as what we believe to be true, you are in fact committing the mind projection fallacy.

There is no definition of truth beyond "that which is true" (and the obvious tautology it evinces), unless you adopt the effective or useful truths that I have been talking about all along.

Truth is what exists. Logic and probability theory permit us to assign degrees to our beliefs and organize our thoughts. To some we can assign a high degree of confidence and to others we can assign a low degree. Just because you choose to confuse matters by calling things "effective truth" or "useful truths" does not mean there is no consistent understanding of the words "truth", "belief", "knowledge".

You just claimed a definition could dictate existence! No, definitions just don't work that way, nothing can imply the existence of something else "by definition." Instead, what actually happens is that when we make a definition, we are making choices about what we will regard as true, or what we will regard as existing. Hence, your definition is an obvious example of the mind projection fallacy, as is much of what Jaynes claims to be true.

Are you unable to understand that by choosing to make an argument in which your premise includes regarding something as existing, it is not different from the argument "implying that it exists"? The whole point is that by throwing out the assumptions implicit in the definition, the definition becomes meaningless. The argument can not be true if you turn around and immediately reject the premises you made to support it!?

Jaynes is just as much a perpetrator of the mind projection fallacy as those he accuses, and the reason is simple: epistemology is ontology in physics, and the mind projection fallacy is the constant companion of the physicist, our "right hand" in the endeavor. All we can do is recognize this-- and that's exactly what Jaynes and you do not

the MPF is your right hand companion not "every physicists". Again you really have to read what Jaynes wrote before you have any standing to criticize him.

Reality has nothing to do with our beliefs, I doubt "reality" could even understand them.

You are right about the first part. Reality has nothing to do with our beliefs. Nobody but you ever suggested that. However, knowledge has a lot to do with reality, and we belief things because we consider them as true/reality. In other words, reality is the object of our attempts to know, and our beliefs. It is reality which WE THINK we are describing, and it is reality which WE THINK we are knowing. This doesn't mean what we belief is reality as you are quick to errorneously conclude. It simply means by believing and trying to know, we inherently have already ASSUMED that there is a reality whether we admit it or not. Therefore statements such as "there is no quantum world, only an abstract description" demonstrate the level of naivity I'm criticizing here. In fact to bring out the stupidity of that statement let me add two words to the end of it.

"There is no quantum world, only an abstract description of it"

Did I hear somebody say "reality" could or could not understand something? If that means anything at all.

 

[Fra]

I don't think you are correctly representing Jaynes views. The distinction you are imposing on his views (ie descriptive vs decision theoretic, is artificial).

That was admittedly my distinction.

I'll try to get time to elaborate later, I don't think my point came across.

I'll just say meanwhile: I think Jaynes has written alout of REALLY good stuff (I'm not REALLY picking on Jaynes). His book on prob theory as logic of science is a recommended reading indeed! Where I disagree is wether his system for inference is adequate for current problems in physics (and here I have in mind unification, and cosmological theories).

Objective inference ideas means the rules for inference have an almost ontological status. In my view, even the rules of inference are evolving and subjectively so. It's not just the prior that is evolving in my view.

/Fredrik

 

[Ken G]

Hehe, even you can not say that with a straight face. That statement itself says everything about how ridiculous your view is.

No, I can say that with a completely straight face-- what science is describing is whatever it is that science is describing. There, I said it again, no break in my face at all. Indeed, there is no other correct answer to what science is describing that is not itself a description, which is of course what science is trying to do. We certainly cannot say what science is describing by using science to describe it-- I would have thought that was obvious. I guess you just don't get this.

The real point is, science has no need whatsoever to say what it is describing, it only needs to describe it, to the best of its ability. The concepts of "absolute reality" or "absolute truth" not only have no place in science, they weigh science down, hurting its progress. Science has never been about any of those things, just look at its history-- science has always been about effective truths, useful descriptions, achieving goals and a sense of understanding (of, yes, whatever it is that it is understanding). Not only is there no need to say anything more, there is no way to, without simply lying to yourself. But it seems to be working for you, so go with it.

Anyway, we've gotten far off the track of the PBR proof. I really don't think there's much chance you will ever understand the point I'm making, so we'll have to leave it at that. Jaynes may be a great probability theorist, and I suspect he understands well the role of probability in physics, but his views on "what is real" are completely unimportant, naive, and downright logically inconsistent. He is saying that whatever he thinks is real must be, and whatever he doesn't think is real is a fallacious projection of (someone else's) mind. This opinion of his has nothing to do with any of his contributions to probability theory, which is just as well.

 

[DrChinese]

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

...

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

Against 'Realism'

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

Norsen believes in the Bohmian class of theories, i.e. ones featuring non-locality. As is characteristic of interpretations of QM, you tend to see according to what you tend to believe. In Norsen's mind, realism is not really at play in Bell and therefore to a certain extend, Bell implies non-locality. That is the essence of that paper.

Which is strange because there are plenty of us that tend to see it the other way around, that Bell implies non-realism (and locality is not at play). But I also believe that strictly speaking, Bell has both realism and locality in play and therefore local realism should be excluded (the normal conclusion, which leaves multiple interpretations on the table).

Despite the PBR reference to Norsen, his perspective is closely aligned with those that already accept Bohmian (non-local) interpretations. So it would not be considered anything like consensus, and PBR won't change that (although it is a very nice boost for Travis). Like most, I do not belong to Group I being excluded by PBR. I believe the wave state/function is "real" (and can be manipulated as such) and there is no underlying reality to unmeasured particle observables. So to me, it makes perfect sense that two particles in the same pure state are in fact NOT in different states (until placed into different states by future observation).

There have been a number of developments in the past few years that tend to pit the non-realist position against the non-local position. If there were any trend, and I am not sure there is, I would say the non-local position has not made much progress whereas the non-realistic has made some. For example, the latest experiments on entanglement swapping tend to cast doubt on the usual time ordering limits (causality) which is in essence an attack on the Bohmian side. However, I would say there is nothing out there that will convince either side at this point. But as papers like PBR place tighter and tighter limits on what is left, something may have to give eventually.

 

[DrChinese]

No, I can say that with a completely straight face-- what science is describing is whatever it is that science is describing. There, I said it again, no break in my face at all. Indeed, there is no other correct answer to what science is describing that is not itself a description, which is of course what science is trying to do. We certainly cannot say what science is describing by using science to describe it-- I would have thought that was obvious. I guess you just don't get this.

The real point is, science has no need whatsoever to say what it is describing, it only needs to describe it, to the best of its ability. The concepts of "absolute reality" or "absolute truth" not only have no place in science, they weigh science down, hurting its progress. Science has never been about any of those things, just look at its history-- science has always been about effective truths, useful descriptions, achieving goals and a sense of understanding (of, yes, whatever it is that it is understanding). Not only is there no need to say anything more, there is no way to, without simply lying to yourself. But it seems to be working for you, so go with it.

Anyway, we've gotten far off the track of the PBR proof. I really don't think there's much chance you will ever understand the point I'm making, so we'll have to leave it at that. Jaynes may be a great probability theorist, and I suspect he understands well the role of probability in physics, but his views on "what is real" are completely unimportant, naive, and downright logically inconsistent. He is saying that whatever he thinks is real must be, and whatever he doesn't think is real is a fallacious projection of (someone else's) mind. This opinion of his has nothing to do with any of his contributions to probability theory, which is just as well.

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).

 

[Fra]

Again you are mixing terms. Truth is truth. There is no such thing as "effective truth" or "provisional truth". You have beliefs which are either true or false. Knowledge only refers to true beliefs. Probability as Jaynes explains, represents our degree of confidence that what we belief is true. It doesn't mean if we assign a probability of 1, then what we belief is certainly true. It simply means we believe it is. Reality is what determines which beliefs are true and which ones are false. Probability theory provides a method for rationally assigning degrees of belief.

This section contains a lot of things that I think represents where Jaynes analysis is insufficient.

One problem is the situation that we have two observers, each encoding certain degrees of beliefs about each other as per their own inference system. And they are interacting in accordance to this.

One problem is that no observers can hold an objective description of this interaction.(except as an equilibrium case; where the observers sort of hold more information that they actaully encode, but then they just THINK they have an objective view, and as long as that's not challanged then well fine - but this is a special case) All you can do is introduce a third observer trying to describe the previous complex of observers, but which then obviously is also interacting with the two first observers. Nothing is accomplished except a kind of renormalized view (seen from distance).

Another problems is how to communicate degrees of beliefs between observers of difference complexity.

These are subquestions that appear at least in my analysis of the open problems in physics, relating to how an interacting "looks like" from the point view of another observer, where it's clear that the interaction itself is between other observers, and how that VIEW influences the BACKreaction of the third observer to the two first. (In general of course this represents the ENVIRONMENTs backreaction).

Either one asks there questions or one does not. To each his own. However, if one does (like I do), Jaynes analysis makes some leaps, that does however not mean it's not good for many things. I mentioned it before but the first thing is the introduction of real numbers and representing degrees of beliefs.

My understanding is that Jaynes really did NOT have alll this weird stuff such as defining observables in quantum gravity etc in mind when he discussed probability. I personally think the original debate with Einsteins objections is sort of outdate these days. there are worse issues with "probability" and observables to face.

/Fredrik

 

[DevilsAvocado]

... I believe the wave state/function is "real" (and can be manipulated as such) and there is no underlying reality to unmeasured particle observables. So to me, it makes perfect sense that two particles in the same pure state are in fact NOT in different states (until placed into different states by future observation).

There have been a number of developments in the past few years that tend to pit the non-realist position against the non-local position. If there were any trend, and I am not sure there is, I would say the non-local position has not made much progress whereas the non-realistic has made some. For example, the latest experiments on entanglement swapping tend to cast doubt on the usual time ordering limits (causality) which is in essence an attack on the Bohmian side. However, I would say there is nothing out there that will convince either side at this point. But as papers like PBR place tighter and tighter limits on what is left, something may have to give eventually.

[my bolding]

Thanks DrC, very nice, finally something "real" to discuss... phew. (And thanks bohm2!)

I know you’re man who think first, and talks thereafter (unlike "some others"), but I must ask you about the bold part. Is this really compatible to Matt Leifer’s conclusion?

[Pulled from Matt Leifer's blog]

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

ψ-epistemic: Wavefunctions are epistemic and there is some underlying ontic state.

ψ-epistemic: Wavefunctions are epistemic, but there is no deeper underlying reality.

ψ-ontic: Wavefunctions are ontic.

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

Is it possible to combine ψ-ontology with non-realism (for the 'particles')?

(Or did I get it wrong)


P.S. Congrats, it’s your 4,000-post-birthday! Keep up the good work!

P.S.2. I recommend reading the comments, "Nick Herbert: Well, it’s clear I’m really confused about PBR. But so are smarter folks like Stapp and Motl." = (for me) there’s no need to get 'stressed' over not getting everything immediately. :)

P.S.3. I’m starting to like Nick Herbert more and more ..."HAREM OF HIDDEN VARIABLES"... sounds like an interesting place...

 

[billschnieder]

This section contains a lot of things that I think represents where Jaynes analysis is insufficient.

One problem is the situation that we have two observers, each encoding certain degrees of beliefs about each other as per their own inference system. And they are interacting in accordance to this.

One problem is that no observers can hold an objective description of this interaction.(except as an equilibrium case; where the observers sort of hold more information that they actaully encode, but then they just THINK they have an objective view, and as long as that's not challanged then well fine - but this is a special case) All you can do is introduce a third observer trying to describe the previous complex of observers, but which then obviously is also interacting with the two first observers. Nothing is accomplished except a kind of renormalized view (seen from distance).

Another problems is how to communicate degrees of beliefs between observers of difference complexity.

These are subquestions that appear at least in my analysis of the open problems in physics, relating to how an interacting "looks like" from the point view of another observer, where it's clear that the interaction itself is between other observers, and how that VIEW influences the BACKreaction of the third observer to the two first. (In general of course this represents the ENVIRONMENTs backreaction).

Either one asks there questions or one does not. To each his own. However, if one does (like I do), Jaynes analysis makes some leaps, that does however not mean it's not good for many things. I mentioned it before but the first thing is the introduction of real numbers and representing degrees of beliefs.

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:

- Degrees of Plausibility are represented by real numbers.
- Qualitative correspondence with common sense
- If a conclusion can be reasoned out in more than one way, then
every possible way must lead to the same result
- 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.
- always represents equivalent states of knowledge by equivalent plausibility assignments. That is, if in two problems the state of knowledge is the same (except perhaps for
the labeling of the propositions), then the same plausibility must be assigned in both.

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

Probability theory as he described it, is a self consistent theory. 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.

 

[Fredrik]

So the expression you cite is used instead, but it is not formally correct, it is an idealization-- a choice made by the physicist, like the choice to treat the Earth as a sphere when calculating its gravity, or the choice to use Newtonian gravity, etc.

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).

Your entire post looks like a fallacy to me, similar to starting to worry about gravity in the middle of a SR calculation. (There is no such thing as gravity in the fictional universe described by SR).

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.

You're right this doesn't mean your expression is "outside physics", but it is outside formal quantum mechanics,

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".

But the problem is, what does "failure" mean? Does it mean the theory failed, or just the way it was applied, the idealizations made to it?

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 if I take this way out, I seem to be making a crucial part of the argument non-mathematical, which is the exact opposite of what I'm trying to do. I need to think about this some more.

I count statements like "properties cause the outcomes" to be those kinds of idealizations, choices about how to apply a theory that are nowhere in the actual formal theory.

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.

That's a tricky issue-- what constitutes "a theory"?

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.

 

[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