Are quantum interpretations physically meaningful?

Question

(this is a self-answered question)

In the context of e.g. these discussions, I was wondering if quantum interpretations have any physical significance.

Distinct quantum interpretations appear to be incompatible with logical positivism, because distinct interpretations still make the same predictions about the universe, e.g. the choice of interpretation does not affect the value of the wave function, scattering amplitudes, and so on.

Thus, my question is: Are "interpretations" of quantum mechanics compatible with logical positivism? Are they of physical value?

Comments

It is not clear to me what you are asking for. First you assert that ''quantum interpretations are incompatible'' and then you ask whether interpretations of quantum mechanics are compatible.

Please clarify.

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@ArnoldNeumaier It must stay here. Until all things are clarified including the question. Atleast I would vote against moving it.  

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@dimension10: If it were graduate+ level, yes, but I don't see that it is - you can see it for example at the lacking upvotes. I don't mind soft questions in Q&A if they are likely to generate nontrivial substance through their discussion, and I don't mind discussions in chat by PO participants about interpretations in general. This makes Chat the right place for the present discussion.

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We arrive at nothing while discussing this matter, so the Chat room is the right place for it.

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the basis of all what these interpretations have weird, is related to the Bell theorem and to the experiments which claim having using it. Bell assumes an imaginary Malus law, taken in its simplest form. With a law fitting  better the experimental measures, the Bell theorem loses its ability to distinguish between interpretations. I showed it with detailed examples (pdf to take as an inspiration for a physicist work ) and since it is a matter of counter examples, one is sufficient. Better existentialist questions follow.

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@Prathyush: By the nature of the topic, all things will never be clarified; this is an additional reason for moving the thread to chat. I also don't see why VK's answer that has been moved to chat is of less quality than the others.

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In addition to what @ArnoldNeumaier says, the whole topic of quantum interpretation (apart from consistent histories that strongly remind me of path integrals) looked rather philosophical to me personally, as it does not impact the outcome of computations in QM.

So I personally tend to answer the second question rather with no, and agree with Arnold that judging the merits of the different interpretations is probably not possible in a unique objective way.  Even though the question and discussion has merit, chat therefore might be a better home.

Answer 1

Insofar as interpretations are not empirically equivalent, they are different theories. GRW, for example. This is a matter of definition, indeed a definition that makes interpretations empirically equivalent is empty relative to a definition of logical positivism that makes it empty.

There is another aspect, however, that within QM we have a lot of freedom to decide what Hilbert space and what algebra of observables to use when modeling a given experiment. String theory is a quantum theory, so is a qubit model with a particular choice of Hamiltonian. We have to look at all the information we have and decide which is relatively important, which only experts can do well, then apply engineering rules for deciding whether some aspect of a condensed matter system, say, might be adequately modeled using Majorana fermions, say. Such engineering rules (or, for Lakatos, bridge principles) are generally quite ad-hoc, and they are not part of the central core of quantum theory that is by now given axiomatically, but they tell us how to use the mathematics.

I suggest that a worthwhile interpretation structures the engineering rules --- that which is outside the central core of QM, particularly to include as much expert knowledge as possible --- to give good ideas easily for which model to use for a given experiment, and that this definition makes "interpretation" a more worthwhile topic of inquiry. I suggest that this parallels your answer: that with the same core of QM different interpretations give us different ideas for what QM model to use first. The "core of QM" can of course be made larger if we find one particular way of formulating the non-core rules to be justified to be elevated to the status of an empirical principle.

Comments

Postscript: I just received, since posting the above, a notification from Springer of a new book, "The Message of Quantum Science", edited by Philippe Blanchard and Jürg Fröhlich, that at first sight looks interesting, http://link.springer.com/book/10.1007/978-3-662-46422-9.

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@PeteMorgan, very interesting collection, thanks for the information!

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You're right, GRW is distinct from standard quantum mechanics, as is Bohmian mechanics, etc. I wouldn't really classify them as "interpretations", though, for exactly this reason. I was mostly talking about things like consistent histories, the Copenhagen interpretation, many worlds, etc.

The rest of the answer is a very interesting read, and +1.

Answer 2

Years ago, I spent a lot of time to understand the various interpretations of quantum mechanics, before I came up with my own thermal interpretation. The reason was that I was thoroughly puzzled about the meaning of the formalism.

Quantum mechanics is special among all physical theories in that the meaning is so far removed from the formalism that even after almost a century since the Schroedinger equation appeared, there is no consensus among physicists what it means - the only consensus (to current experimental accuracy) is how to use it to get verifiable answers, i.e., the positivistic aspect of the problem. For me it is very important that a theory is understandable, not only applicable. Of course, in order to qualify as a valid interpretation, the interpretation must be compatible with the positivistic stance (''shut up and calculate"), in this sense, the answer to your question is yes, by definition of an interpretation.

But an interpretation must satisfy beyond that certain non-mathematical criteria - simplicity, naturalness, closeness of the interpretation to the formalism, etc., and here the different interpretations differ widely and give possible approaches to the ''true'' meaning. 

The value of a good interpretation is that it makes teaching the subject far easier. Lack of interpretation is impossible as one must somehow relate the formalism to reality. That's why interpretations are necessary. In my opinion, a satisfying interpretation must be such that it can be essentially reconstructed inside the formalism, in the same way as the foundations of mathematics (by ZFC, say) can be reconstructed internally inside mathematics (except that, due to Goedel's theorems, one can prove inside a tiny little less only).

I believe that the dynamics of the universe (the only experimentally accessible one) is ultimately realistic and deterministic, though we currently do not yet understand how. I don't find Bohmian mechanics a satisfying answer (see, e.g., here) - it is counterintuitive in many respects (though it doesn't contradict the experiments related to bell's inequalities). I find the many worlds interpretation even less satisfying, as it postulates the existence of all possible worlds, and thus explains nothing. But without thinking through the most relevant alternatives available it is unlikely that one can find something better.

Comments

I don't understand what the question you are answering.

Define your question precisely?

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The question posed at the top of the thread was

Are "interpretations" of quantum mechanics compatible with logical positivism? Are they of physical value?

Answer 3

Quantum interpretations do have physical value, although they are not capable of making predictions (because they should, by definition, be completely compatible with what quantum mechanics says). I mean "they have physical value" in an absolutely non-rigorous and hand-waving sense, what I mean is e.g. the relation between the Many-Worlds-Interpretation and the information theoretic uncertainty principle.

Logical positivism doesn't say that quantum interpretations are meaningless, rather only that it doesn't make sense to claim one way or the other, in that one can't say that "consistent histories is wrong, the copahagen interpreation is right" - "which interpretation is right" is a meaningless question of only philosophical (=zero) value, unless the interpretation is not an interpretation at all, but rather a different model that makes different predictions, like Bohmian mechanics, whose merit can be argued.

The best analogy I can think of is dualities in string theory and quantum field theory - it's not meaningful to say that "Horava-Witten theory is wrong, \(E_8\times E_8\) heterotic is accurate", but this doesn't make specific formulations useless.

Comments

I always thought that decoherence is rather a physical process related to what happens to the off-diagonal elements of the density matrix (forgot the exact details) , than a quantum interpretation?

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@Dilaton You're right, I meant to write "consistent histories", a very silly mistype.

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@VladimirKalitvianski Let's continue this discussion in chat before it gets too long.

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only philosophical (=zero) value

Don't underrate the value of philosophy, the mother of all sciences - it is essential always when the concepts are not clear enough to dispense with philosophical arguments. Unfortunately, the foundations of quantum mechanics have the latter characteristics, proved by 90 years of unending discussions....

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The value of a good foundation lies in making the teaching of quantum physics much easier. 

Answer 4

Positivism emphasizes practical utility over abstract Truth. I tend to agree with many positivist positions - science isn't about discovering undefined (and unnecessary) global Truths with capital T, but about developing useful models of reality - local truths with lowercase t - that work in practice, make correct predictions in specific application scopes, and permit building better machines.

So some positivists think one shouldn't waste too much time over quantum interpretations that produce exactly the same practical results in all application scopes.

But here I disagree, because interpretations of quantum physics (or everything else) can be (at least subjectively) very different when it comes to their ability to power intuitive speculations. For example, I find Everett's interpretation useful in this sense - regardless of whether it's "True" or not. Now, utility over Truth IS a positivist position, so I would conclude that positivists should be interested in quantum interpretations...

Answer 5

The word interpretation is abused so much in the context of quantum mechanics that no one seems to know exactly what they are talking about.

The question that is significant to me is how does one correctly use and think about quantum mechanics correctly. And I think there is a unique answer to that question.

The question is vague, and so I will share my broad views as Arnold asked.

Quantum mechanics is characterized by the restriction of having to predict the out comes of experiments in probabilistic terms. 

The probability amplitude of a given experimental outcome is given by the sum of amplitudes of each possible way to realize a given outcome. Probability is the modulus square of the probability amplitude. 

\(P = |\Psi|^2 = |\Psi_1+\Psi_2|^2 \)

There is no way to ascribe a meaning to the quantum state (or wavefunction) without its relationship to an experimental apparatus.

For instance the attempt to precisely determine how a particular outcome was realized will destroy interference between possible realizations of the final outcome.

The experimental apparatus is treated to be heavy in comparison to the system under observation. Under these conditions one can use classical quantites in the description of experiment.

The attempt to observe the quantum mechanical nature of the apparatus will require a delicate arrangement (often not practicable).

Quantum mechanics (in my current understanding) establishes that it is only meaningful to talk about experiences. Beyond that that the word reality could be ambiguous. It is meaningless to ask about what the electron did in between if an experiment was not performed to observe this.

The notion of classicality is in spirit equivalent to the notion of overwhelming odds.

Comments

@Prathyush Shouldn't this be a comment, rather than an answer? You're right that some "interpretations" are not interpretations at all, rather different theories altogether (I'm talking about hidden variables here), but mostly the term is used correctly.

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I think it answers the question.atleast the way you expressed it.

Hidden variables is pointless(and meaningless) in my opinion.

@Dimension10 I have not found any good reason to take hidden variables seriously.

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@Prathyush I didn't say hidden variables are useful : ) But it's not that they're meaningless, or "not even wrong", Bohmian mechanics is meaningful, it's just wrong, because of Bell's experiments. It's scientific, falsifiable, compatible with logical positivism, and all. It's just that it got falsified.

@Prathyush I didn't say hidden variables are to be taken seriously any longer, rather that they aren't ill-defined, they're falsified, and only falsifiable things can be falsified.

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@dimension10 A Bohmian theory makes exactly the same predictions as the corresponding quantum theory. There might be technical reasons why a Bohmian counterpart simply can't be constructed for some quantum theories, or you might object because it has a preferred frame or for some other conceptual reason; but when a Bohmian theory does exist, it has no empirical problems, because it makes the same predictions as QM.

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I think there is a unique answer to that question

You forgot to say in your ''answer'' what this unique answer is, in your opinion.  (In my opinion, there are different useful ways to think about QM correctly, depending on which problem one is thinking about.)

[Downvote undone after the answer was expanded.]

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The correct formula is the following:

$|\Psi^2|=|\Psi_1^2+2\Psi_1\Psi_2+\Psi_2^2|$  

    ;-)

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@VladimirKalitvianski I put the square outside Either that or you have to multiply with the complex complex conjugate.

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Quantum mechanics (In my current understanding) establishes that it is only meaningful to talk about experiences. Beyond that that the word reality could be ambiguous. It is meaningless to ask about what the electon did in between if an experiment was not performed to observe this.

Again, this is a philosophical question. It's not QM that tells us that it's only meaningful to talk about actual observations, it's logical positivism.

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@dimension10: Hmm... I wonder now... what is the norm of the square of a complex number? If you don't get the joke, just don't laugh, don't say a correct (but purposefully obtuse) formula is wrong.

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Oh, I get it - he's ridiculing the pointless debate between quantum interpretations

Exactly!

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@dimension10: You made an incorrect statement regarding Bohmian mechanics earlier--- Bohmian mechanics is nonlocal and violates Bell's theorem just the same as normal QM. It's useful as a counterexample to the wrong claim that hidden variables theories are impossible, but it is not persuasive as actual physics because it is extremely arbitrary and much "larger" computationally than what a reasonable hidden variable theory "should" look like given computational prejudices about the size of the putative classical universe underneath QM (if such exists).

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@dimension10 I usually don't use terminology used in philosophy, Logical Positivism or not doesn't matter. If you want to discussion foundational issues with me you have express it in layman's terms.

But it is true that nature does not allow us to meaningfuly talk about questions like which slit did the electron without a modification to the experimental apparatus.

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The interpretation problem consists precisely in answering the question how an essentially classical apparatus (though describable by quantum mechanics as a multiparticle system) reaches a definite measurement result. Your opinion is a version of the Copenhagen interpretation that says it must be considered classically. But this leaves the question open how the classical and the quantum are related. 

You say that

It is meaningless to ask about what the electron did in between if an experiment was not performed to observe this.

But then it would also be meaningless to ask about the quantum physics of the universe before there was anyone who could observe this. But no cosmologist would follow your logic. 

It would also be meaningless to talk objectively about nuclear processes inside the sun, as we cannot observe them but only some of there effects, and minutes later. But no astrophysicist could live with your restricted view of what is meaningful.

This defect of the Copenhagen interpretation made it important for many to come up with improved interpretations where objectively talking about unobserved (or only much later observed) events is meaningful. 

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@ArnoldNeumaier I think the question about cosmology would involve a clarification form QG, but this is not what the questioner is asking about.

I think we must restrict ourselves to discussions involving terrestrial experiments for a start.

Then we can talk about more general situations once the meaning in the context of terrestrial experiments is clear.

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But this leaves the question open how the classical and the quantum are related. 

As I've said it already many times, the classical is an inclusive (or average, if you like) picture when many different events are "summed up" and ascribed to something "objective", but hopelessly simplified in our mind. I can safely say in this respect that the classical does not exist (at least, without certain context).

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@VladimirKalitvianski: Summing up things to something measurable is the domain of statistical mechanics. Thus statistical mechanics should be the place where the relationship of quantum mechanics to measurements is discussed.

Assuming a measurement process in the foundations of quantum mechanics is as inappropriate for good quantum foundations as it is for good classical foundations: In classical foundations, measurement is either taken as trivial and not needing consideration, or is a matter of analyzing the dynamics of a classical system coupled to a measurement device. In quantum mechanics, foundations are adequate  (and discussion about the ''correct'' or ''best'' interpretation will die out) only when the same status is reached.

Answer 6

I am very late to the game, but I would like to leave a comment for posterity. Arnold Neumaier's highlighting of the distasteful aspect of Copenhagen interpretation as failing to explain how a classical system and a quantum system should differ, is an important and insightful one. In fact, it is one that was realised by the masters: At the Solvay conference, they considered that too. In particular, de Broglie used two atoms as the detector for a system emitting a photon in which of two directions. And historically, that was also how time dependent perturbation methods were found in standard QM. 

The insight that de Broglie introduced, was that the observer, and the observing process, should all be considered quantum mechanical, since quantum theory is supposed to be the fundamental theory of everything. In that, the de Broglie Pilot Wave Theory actually succeeded, although Pauli gave a wrong mathematical example that made everyone confused. The problem Pauli gave happened to have a mathematical mistake, not a physical one, but people did not understand that it was the example that was wrong, and instead wrongly rejected de Broglie's PWT. If you read the actual Solvay conference proceedings (Now prettified as "Quantum Theory at the Crossroads", which is available on arXiv), you will see that de Broglie's PWT is actually better than Bohm's and the whole structure actually is a satisfactory interpretation of QM, albeit with serious relativistic issues. 

On top of these, Feynman in Character of Physical Law also had something to say about philosophies in physics. Before the quantum revolution, there were three ways to approach physics, and since they had been proven equivalent, the differences were entirely down to philosophy. The 1st was Newtonian Forces, the 2nd was Maxwellian local fields, and the 3rd was Principle of Least Action. If a person had decided beforehand that interpretations and philosophical aspects of physics should be entirely removed from physics, then when the quantum revolution came and the 1st system was irrevocably killed, then that person should also get out of physics. The fact of the matter is simply that any good theorist would have a few different systems of thought kept in mind, just so that any new problem would be analysed in many different ways, just so see if something interesting happens. The philosophies guide future research in important ways, so they actually do matter. 

Disclaimer: I hate MWI as not able to explain anything, but am able to work in it, I consider Copenhagen rules not as full-blown interpretations that ought to explain those rules (though back then, it was huge), and before QT@C, I did not like PWT either, though now a lot better. I am more of a transactional person myself.