Under what circumstances does the wave function collapse?

[atyy]

Hardy does seem to reach the same conclusion I was pondering, though I had a question about this: " Axiom 5 (which requires that there exists continuous reversible transformations between pure states) rules out classical probability theory. If Axiom 5 (or even just the word "continuous" from Axiom 5) is dropped then we obtain classical probability theory instead." How can Hardy say that dropping "continuous" from Axiom 5 yields classical probability theory instead of QM? Surely dropping an axiom that QM obeys cannot require you to obtain a probability theory that QM does not obey. Perhaps he means that if you don't require continuity, then you open the door for classical probability theory, but you have to replace it with some other axiom that QM does not obey to actually get classical probability theory, that replaces QM.

I think you are right, and it should be that without continuity, one has either classical or quantum probability.

Edit: Here's support for Ken G's correction from Hardy's later version (but with slightly different axioms) http://arxiv.org/abs/1303.1538 : "Classical probability theory and quantum theory are only two theories consistent with the following postulates. ... To single out quantum theory it suffices to add anything that is inconsistent with classical probability and consistent with quantum theory."

 

[Ken G]

Yes, that certainly makes more sense. But I really like this way of characterizing quantum and classical probability theories as just two different classes of probability theories, with remarkably minor differences in the axioms that have such major implications on what seems normal vs. bizarre.

 

[StevieTNZ]

The real reason is decoherence:
http://www.ipod.org.uk/reality/reality_decoherence.asp

In so far as we have an explanation that is - it doesn't explain the so called problem of outcomes without going into exactly what that is.

The modern view would be an observation occurs once decoherence happens, which causes apparent collapse. The classical common-sense world we see around us is explained by the fact everything is observed by the environment.

From Fred Kuttner, co-author of Quantum Enigma:

You make an excellent argument. The resolution is to note that decoherence does not give us a classical world. Rather, it gives us a world which is still in a superposition, but in which the off-diagonal elements in the density matrix, which would allow us to measure the superposition, vary so rapidly in space so that measured with any macroscopic instrument they average to zero.

The quantum Zeno effect, on the other hand, requires an actual collapse, and no resulting superposition. Thus there is really no contradiction as long as you realize the bogus argument made by some decoherence proponents.

The email is in response to this I sent him:

It is often claimed on www.physicsforums.com that we experience a classical world due to decoherence. However, decoherence is simply ignorance of the whole state of the environment entangled with the system. If it were true that the environment is constantly observing the macroscopic world, and because of the Quantum Zeno Effect, wouldn’t the macroscopic world stay static because its being observed all the time?

Wouldn’t the above be a good argument against decoherence producing the classical world around us – because the classical world doesn’t remain static?

 

[atyy]

Regarding Kuttner's response:

1) It is true that decoherence is insufficient to explain the classical real world with its continuous sequence of particular outcomes even when one is not looking - one needs needs to add an interpretation such as Bohmian Mechanics to do that

2) However, the quantum Zeno effect is not a good argument against decoherence constantly observing the world - there is the formalism of continuous measurements in which the the system continues to evolve.
http://arxiv.org/abs/quant-ph/0611067
http://arxiv.org/abs/math-ph/0512069
http://arxiv.org/abs/quant-ph/0201115v2

The Belavkin paper is interesting because it obtains equations like those in Continuous Spontaneous Localization theories (which go beyond quantum mechanics) by using the quantum formalism and the idea of continuous measurement.

 

[bhobba]

It is true that decoherence is insufficient to explain the classical real world with its continuous sequence of particular outcomes even when one is not looking - one needs needs to add an interpretation such as Bohmian Mechanics to do that

There seems to be a bit of confusion about what I wrote, so I will repeat it with the key point highlighted:

The real reason is decoherence:
http://www.ipod.org.uk/reality/reality_decoherence.asp

In so far as we have an explanation that is - it doesn't explain the so called problem of outcomes without going into exactly what that is.

I didn't want to get into the issue, but the tangent this has gone off at means it looks like I have to.

The problem of outcomes is basically what makes an improper mixture a proper one. That is the extra assumption that allows decoherence to resolve the measurement problem. That is the key unexplained issue of decoherence - and different interpretations tackle differently. I tackle it head on and simply declare it the same - how - blank-out. BM assumes an objective trajectory and position so trivially an improper mixed state is a proper one. MW assumes each outcome of the improper mixture is a separate world. Consistent Histories doesn't even have observation - QM for that interpretation is the stochastic theory of histories.

Stevie TNZ quoated:
'It is often claimed on www.physicsforums.com that we experience a classical world due to decoherence. However, decoherence is simply ignorance of the whole state of the environment entangled with the system. If it were true that the environment is constantly observing the macroscopic world, and because of the Quantum Zeno Effect, wouldn’t the macroscopic world stay static because its being observed all the time?'

I haven't seen that claimed that often, and when done me and others correct it.

My claim, and the claim of those that use interpretations incorporating decoherence is that dechoerence, and SOME OTHER ASSUMPTION explains the classical world.

I know sometimes me and others forget to mention the second bit - so even though its annoying having to go over the same territory for the umpteenth time - fair cop - you have to explain it again. But this time I think I was pretty careful about what was said.

Thanks
Bill

 

[atyy]

The problem of outcomes is basically what makes an improper mixture a proper one. That is the extra assumption that allows decoherence to resolve the measurement problem. That is the key unexplained issue of decoherence - and different interpretations tackle differently. I tackle it head on and simply declare it the same - how - blank-out. BM assumes an objective trajectory and position so trivially an improper mixed state is a proper one. MW assumes each outcome of the improper mixture is a separate world. Consistent Histories doesn't even have observation - QM for that interpretation is the stochastic theory of histories.

There are two aspects to the appearance of a classical world. The first is the appearance of a classical world, given an observer. The second is the existence of a classical reality independent of an observer (usually the second one is the measurement problem).

By postulating that an improper mixture is a proper mixture, that is essentially collapse, and yes decoherence and the formalism of continuous measurement can probably solve the first question about the appearance of a classical world. However, this takes place within the Ensemble Interpretation with a Heisenberg cut, so it cannot solve the problem of the existence of an observer-independent classical reality. That second problem requires something like Bohmian Mechanics or Many-Worlds, if it works.

 

[Ken G]

To me, I'll repeat that the problem just goes away if you simply put the physicist into the physics. Why wouldn't we do that anyway, it's the one thing about physics that's actually obvious! We just need to look at what the physicist is doing, and get away from this strange need to pretend that the "laws of physics" function in some sense independently of what we ourselves use them for. We never test the former, only the latter, so why force onto it the former interpretation when it only causes problems?

What I mean about making the problem go away by simply putting the physicist in the picture is what you mean by the other assumption, beyond decoherence. All we have to do is say that "collapse" is simply the choice made by the physicist to study the system in terms of discrete outcomes, which are the eigenvalues. We choose the environments that decohere around these different discrete outcomes, like the frequencies of light in a spectrometer, and we ignore everything else that is going on because none of that other stuff helps us understand what is going on. Nature didn't hand us spectrometers, we built them, or evolved crummy ones in our eyes. But we do that to gain knowledge of the state, it's all about how we choose to interact with things, to prepare things in states that we understand, ignoring all the complexities of what we don't understand and choose not to care about. Bohr famously said there is no quantum world, but he should have added that there is no classical world either!

We have no real reason to be surprised by any of this, of course we are never going to know exactly what to add to the assumptions of quantum mechanics until we understand how our own minds work, what knowledge is, and what information is, but the one thing you can be sure of is that when we finally do understand those things, it will mean that the physicist will forever be part of the physics. In this case, that means understanding collapse means understanding ourselves, but if we can't do that now, we just assert whatever machinery we need to to make quantum mechanics work for us. That's the bottom line-- we need physics theories that do what they are supposed to do, and that's not remove us from the picture, for why would we ever want a theory to lie to us?

 

[bhobba]

There are two aspects to the appearance of a classical world. The first is the appearance of a classical world, given an observer. The second is the existence of a classical reality independent of an observer (usually the second one is the measurement problem).

By postulating that an improper mixture is a proper mixture, that is essentially collapse, and yes decoherence and the formalism of continuous measurement can probably solve the first question about the appearance of a classical world. However, this takes place within the Ensemble Interpretation with a Heisenberg cut, so it cannot solve the problem of the existence of an observer-independent classical reality. That second problem requires something like Bohmian Mechanics or Many-Worlds, if it works.

I agree with that.

The advance oner previous treatments is decoherence is a purely quantum phenomena so you can unambiguously put 'collapse' right there - of course collapse is a bit different than the usual version since it applies regardless of if the system is destroyed or not.

Thanks
Bill

 

[TrickyDicky]

There are two aspects to the appearance of a classical world. The first is the appearance of a classical world, given an observer. The second is the existence of a classical reality independent of an observer (usually the second one is the measurement problem).

By postulating that an improper mixture is a proper mixture, that is essentially collapse, and yes decoherence and the formalism of continuous measurement can probably solve the first question about the appearance of a classical world. However, this takes place within the Ensemble Interpretation with a Heisenberg cut, so it cannot solve the problem of the existence of an observer-independent classical reality.

I don't think this problem can be solved within the QM theory(formalism), it is deeply built in it. You would have to invent a different theory to make it work.

That second problem requires something like Bohmian Mechanics or Many-Worlds, if it works.

It doesn't work. As I was saying the Heisenberg cut is inherent to QM, IOW the measurement problem cannot be solved within the theory formalism. QM interpretations can never solve it no matter how they may have the appearance of doing it.
One is left with the choice of believing the classical/quantum divide really exists in nature and therefore QM reflects it as the measurement problem or it doesn't, and QM is an effective approximation to a theory without a Heisenberg cut.

 

[bhobba]

QM interpretations can never solve it no matter how they may have the appearance of doing it.

I have been thinking a bit about this and your point isn't gelling.

So, picking an interpretation at random, say Consistent Histories, how doesn't it solve the measurement problem because it doesn't even have measurements - for it QM is the stochastic theory of histories.

Thanks
Bill

 

[TrickyDicky]

So, picking an interpretation at random, say Consistent Histories, how doesn't it solve the measurement problem because it doesn't even have measurements - for it QM is the stochastic theory of histories.

Hmm, the measurement problem is clearly an open problem for QM after almost 90 years, so I don't know what you mean by claiming CH solves it, and after looking it up in wikipedia where it says that it has an interpretational observer role that regards QM as a theory of measurement I don't know what you mean by " it doesn't even have measurements" either.

 

[TrickyDicky]

My point was that within the QM formalism the Heisenberg cut is unavoidable, interpretations may have more or less clever ways to hide the cut or put it outside what they define as QM so as to give the appearance of solving the problem.

 

[bhobba]

My point was that within the QM formalism the Heisenberg cut is unavoidable, interpretations may have more or less clever ways to hide the cut or put it outside what they define as QM so as to give the appearance of solving the problem.

That I agree with.

One must go outside it to fix the issue.

Thanks
Bill

 

[Ken G]

To which I would say actually one must go inside to fix the issue-- inside the mind of the person who is trying to use the theory to understand something, yet feeling a strange and historically unjustified need to imagine that the theory is talking about something that nature is doing rather than something that their mind is doing. What I would like to know is, when it is perfectly clear that a theory is something our mind is doing, just look at what it is, from where comes this need to pretend it isn't?

 

[TrickyDicky]

To which I would say actually one must go inside to fix the issue-- inside the mind of the person who is trying to use the theory to understand something,

I take it you are choosing the second alternative in the choice of #39.

yet feeling a strange and historically unjustified need to imagine that the theory is talking about something that nature is doing rather than something that their mind is doing. What I would like to know is, when it is perfectly clear that a theory is something our mind is doing, just look at what it is, from where comes this need to pretend it isn't?

Agree, but that is psychology and this is a physics fourum.

 

[stevendaryl]

To which I would say actually one must go inside to fix the issue-- inside the mind of the person who is trying to use the theory to understand something, yet feeling a strange and historically unjustified need to imagine that the theory is talking about something that nature is doing rather than something that their mind is doing. What I would like to know is, when it is perfectly clear that a theory is something our mind is doing, just look at what it is, from where comes this need to pretend it isn't?

Well, the theory agrees with experiment very well, so it's not JUST about what the mind is doing.

 

[Ken G]

I take it you are choosing the second alternative in the choice of #39.

What I'm saying is that the only "problem" in the "measurement problem" appears if we ask "how does reality actually collapse"? But we have no evidence that reality does any such thing, our scientific evidence is that collapse is a step in our process of connecting theories to experiments, a process that quite demonstrably occurs in our head because where else is it occurring? Just look at the evidence: the experiment is something we built to try and understand something, the result is something that we are interpreting as a kind of result, the theory makes a prediction that relates to that result, and everything I just said is quite demonstrably a list of processes going on in our heads, including the final step of matching up the two any saying "yes, it worked." And the "problem" in all that is...? It's only even there when you ask "but how does reality actually do this?" We ask a question like that, and we get to be surprised there's a problem?

That type of problem isn't even unique to quantum mechanics, it was there in Newtonian mechanics (the "problem" of determinism), it was there in thermodynamics (the "problem" of the arrow of time), it's just the problem that appears every single time we take some physics theory and ask "but how does nature actually do what the theory says it is doing?" The "solution" is recognizing that we are simply mistaking the way our minds make sense of things with what nature is "actually doing," and when we recognize this, the problem is just gone. So what I'm saying is, the real problem is that the simple solution to the problem is not the one we crave. We are the problem.

Agree, but that is psychology and this is a physics fourum.

True, but that's shooting the messenger-- the "measurement problem" is demonstrably a psychological problem, as there certainly is no problem when it comes to actually doing the science, correct?

 

[atyy]

Interpretations of QM are all essentially psychology, are they not? The "measurement problem" is demonstrably a psychological problem-- certainly there is no problem there when it comes to actually doing the science, correct?

Let me try to understand what you are saying. One way to show that Bell Tests cannot demonstrate nonlocal reality is to say that there are never any results obtained at widely separated distances. Every result I see is seen by me only near me. Thus I, Bob, deny that Alice had a result a great distance from me. The only result I acknowledge is that Alice reported to me, here and now, that she had a result at a great distance. So there are no distant results, and no nonlocality. Nonlocality is a psychological problem with me making up a reality about Alice and her distant results, which I never saw. In other words, if psychology is a valid way to solve the measurement problem, then it is also a valid way to deny nonlocal reality.

 

[Ken G]

Let me try to understand what you are saying. One way to show that Bell Tests cannot demonstrate nonlocal reality is to say that there are never any results obtained at widely separated distances. Every result I see is seen by me only near me.

That would be a radical solution, but would just represent more examples of taking our understanding of things and imposing it on reality. The solution I have in mind is just not doing that-- recognizing what physics has always been, and the history of it is quite clear on this, is our effort to make sense of reality, so the "Heisenberg cut" is just another way to say "the gulf that always exists between how we understand nature and what nature actually is." Why not study that gap, instead of always trying to make it go away? We are selling physics short by always trying to not be in the picture of how we understand nature.

Thus I, Bob, deny that Alice had a result a great distance from me. The only result I acknowledge is that Alice reported to me, here and now, that she had a result at a great distance.

There is no need to deny that Alice got the result she reports, just as there is no need to deny that Alice invoked her conscious mind to communicate that result to our conscious mind. It is demonstrably true that is what she just did, so why do we need to pretend that she did not?

So there are no distant results, and no nonlocality.

There are those things, but what they "are" has to do with what we make them, in our minds and in Alice's very similar mind. We are all doing physics, this means we are engaging our minds. Are we not?

In other words, if psychology is a valid way to solve the measurement problem, then it is also a valid way to deny nonlocal reality.

The way psychology solves the problem is not by denying something, indeed it is by not denying. We simply stop denying what we deny if we hold that nature is doing all these things with no input from how we make sense of it, when we are demonstrably trying to make sense of it. The Heisenberg cut is not a cut between quantum and classical worlds, as neither of those worlds actually exist-- what exists is nature, and our attempts to understand nature, and the cut is what is between those, in quantum mechanics and in every other physical theory ever created.

 

[Ken G]

Well, the theory agrees with experiment very well, so it's not JUST about what the mind is doing.

Yes, I agree-- I would not say "just", like those who say evolution is "just" a theory. These theories are what they are, and they are not "just" something, they are doing what they are supposed to be doing. There is no problem with them, we create the problem by asking them to be something they never were. They do agree with experiment very well-- that's exactly why there is no problem with them. We are the problem because we cannot accept a theory for what it is.

Now, this does not mean we cannot ask what is happening that theories do not predict, that's fine-- that's how we find the next theory. But note the difference between asking the two proper questions to put to a theory: "what are we observing that this theory is not predicting" and "what is this theory predicting that we have not yet observed", and the improper question "why isn't the theory telling us exactly what nature is doing such that we observe what we do." We should always expect a problem when we pass from that first class of questions to that last one, and we should never think the problem there is with our theory, it is with what we are asking out theory to be that it is not.

In short, I'm saying the measurement problem, and the problem with all the interpretations of quantum mechanics, is that we are trying to interpret the theory as something a theory just isn't, nor have any of the other theories ever been. It is not an interpretation problem, it is a problem in interpretation itself.

 

[atyy]

The way psychology solves the problem is not by denying something, indeed it is by not denying. We simply stop denying what we deny if we hold that nature is doing all these things with no input from how we make sense of it, when we are demonstrably trying to make sense of it. The Heisenberg cut is not a cut between quantum and classical worlds, as neither of those worlds actually exist-- what exists is nature, and our attempts to understand nature, and the cut is what is between those, in quantum mechanics and in every other physical theory ever created.

Are you saying that we can simply accept that quantum mechanics is an incomplete description of reality ("nature"), or are you saying that every theory necessarily has a Heisenberg cut?

Also, are you saying that we can in principle extend the wave function to the whole universe, and the problem is that we don't know that Hamiltonian and state of our mind and its interaction with the external world?

 

[Ken G]

Are you saying that we can simply accept that quantum mechanics is an incomplete description of reality ("nature"), or are you saying that every theory necessarily has a Heisenberg cut?

I'm saying both those things, because I'm saying making the Heisenberg cut is just how we do physics. We might want to reframe how we do physics to not do that, but it would require a better understanding of how our minds work, and we're probably not there yet. We take the physicist out of the physics because we don't know what else to do, not because it is the correct thing to do, so we get Heisenberg cuts all over the show.

Also, are you saying that we can in principle extend the wave function to the whole universe, and the problem is that we don't know that Hamiltonian and state of our mind and its interaction with the external world?

The idea that the universe has a wavefunction is just that-- an idea. As any idea, it may have value, and limitations. There's never a particularly good reason to imagine the universe "really has" any of these ideas, but we can certainly look at how the ideas advance our understanding of the universe. Ideas are thus our servants, but we never want to be the slave of our own servants, especially when doing so just creates problems for us without any other benefit.

 

[stevendaryl]

Yes, I agree-- I would not say "just", like those who say evolution is "just" a theory. These theories are what they are, and they are not "just" something, they are doing what they are supposed to be doing. There is no problem with them, we create the problem by asking them to be something they never were. They do agree with experiment very well-- that's exactly why there is no problem with them. We are the problem because we cannot accept a theory for what it is.

I don't see how it is possible for a theory to both agree with experiment, and to be not about the world, but about our minds. It's certainly true that there is something going on our minds when we decide to use this wave function (or density matrix) rather than that one, but if afterwards the choice has great predictive value, then that would seem to be evidence that the mathematical construct has some relation to what's true in the world.

 

[TrickyDicky]

The Heisenberg cut is not a cut between quantum and classical worlds, as neither of those worlds actually exist-- what exists is nature, and our attempts to understand nature, and the cut is what is between those, in quantum mechanics and in every other physical theory ever created.

You are simply substituting the Heisenberg cut with the older Cartesian cut(matter/nature vs. mind). Probably the former is just the specific form of the latter in QM. How does this improve things for QM issues with collapse and measurement?

 

[kith]

Regarding the Copenhagen interpretation, I've been thinking along similar lines as Ken G. Maybe the lesson of the measurement problem is not that something is wrong with QM (there are arguably no experimental hints of this) but that something is wrong with the naive realist interpretation of previous theories.

 

[atyy]

I'm saying both those things, because I'm saying making the Heisenberg cut is just how we do physics. We might want to reframe how we do physics to not do that, but it would require a better understanding of how our minds work, and we're probably not there yet. We take the physicist out of the physics because we don't know what else to do, not because it is the correct thing to do, so we get Heisenberg cuts all over the show.

The point of the measurement problem is to show that both statements are compatible - the existence of an observer independent reality "nature" of which quantum mechanics is an incomplete description, and the existence of a Heisenberg cut. In classical physics, we have no problem with saying there are hidden variables, and that reality really exists, and the cut reflects our ignorance. In quantum mechanics, historically there was the idea that there is a conflict, and one cannot have naive reality. Since Bohm, we know that these two statements are compatible, and that this is a viable philosophy. Thus the measurement problem is solved.

The idea that the universe has a wavefunction is just that-- an idea. As any idea, it may have value, and limitations. There's never a particularly good reason to imagine the universe "really has" any of these ideas, but we can certainly look at how the ideas advance our understanding of the universe. Ideas are thus our servants, but we never want to be the slave of our own servants, especially when doing so just creates problems for us without any other benefit.

Another point of the measurement problem is that the idea that the universe has a wave function is not an idea - not a tenable idea even in principle (unless Many-Worlds works). So if the wave function of the universe does not exist even in principle, but if we believe that there is a theory that can describe the whole universe, then this represents a theoretical opportunity - it's just like quantum gravity where the theory itself says there is a cut, even though experiments have never demonstrated the theory to fail. It is not any different from having Maxwell's equations and Newtonian gravity and realizing that something has to give - maybe the principle of relativity - even before the Michelson-Morley experiment.

 

[atyy]

Regarding the Copenhagen interpretation, I've been thinking along similar lines as Ken G. Maybe the lesson of the measurement problem is not that something is wrong with QM (there are arguably no experimental hints of this) but that something is wrong with the naive realist interpretation of previous theories.

Yes, one can do that. I respect the view. I just don't think that's what Ken G was saying.

 

[bhobba]

Hmm, the measurement problem is clearly an open problem for QM after almost 90 years, so I don't know what you mean by claiming CH solves it, and after looking it up in wikipedia where it says that it has an interpretational observer role that regards QM as a theory of measurement I don't know what you mean by " it doesn't even have measurements" either.

In Consistent Histories observations are replaced by the concept of a history, which is simply a sequence of projection operators. It is also required they satisfy a certain consistency condition, but decoherence usually enforces it.

In that interpretation QM is the stochastic theory about histories:
http://www.siue.edu/~evailat/pdf/qm12.pdf
'Hence, CH adopts non-contextual property realism (albeit of the weak sort) and dethrones measurement from the pivotal position it occupies in the orthodox interpretation.'

What I said wasnt quite correct - the proponents of Consistent Histories believe because observations are removed (dethroned from central importance as the above quote says would be better - there is no way to remove the concept of course) they have solved the measurement problem - others however are not so sure.

Thanks
Bill

 

[Ken G]

I don't see how it is possible for a theory to both agree with experiment, and to be not about the world, but about our minds.

Does it have to be one or the other of those possibilities? Why can't a theory be what a theory is: the attempt of our mind to predict and understand and gain power over nature? If we treat theories the way they demonstrate to us they really are, these problems just go away. But instead, we try to "interpret the theory", but we have the wrong idea of what the interpretation of a theory is.

We should take the lead from the mathematics of modeling theory. Mathematics always has the problem that it is fundamentally about syntax and not semantics, but we need it for its semantics. We teach it to children for semantic purposes, because "it gives true answers." How do we handle this schizophrenic mishmash of syntax and semantics? In modeling theory, an interpretation of a theory is simply a way to embed the theory into a metatheory, such that the syntax of the rules of the metatheory replace the semantic meaning of the theory, and a good model is one where the syntax of the metatheory functions just like the semantic truths of the theory. So you prove the completeness of arithmetic by embedding it in a larger theory that spawns both arithmetic and the things that seem to be true about arithmetic. (Of course, you can't prove the metatheory is itself complete or consistent, but you just hope it is consistent and you don't care if it is complete because you only need it to know things about arithmetic.)

That's what the interpretations of quantum mechanics do for us too-- they replace the semantic truths, which are the outcomes of experiments, with a syntactical structure that allows these things to be proven true without doing any experiments. But that also means the interpretation is not attempting to create a list of semantic truths (here meaning "things that nature is actually doing), it's whole purpose is to be purely syntactic! Yet missing this point, we discuss the semantics of our interpretations when we ask "which interpretation is what nature actually doing".

That's also why I feel that all the interpretations of quantum mechanics are scientifically the same and only psychologically different, because they supply different syntactical structures to yield the same semantics (the experimental outcomes). The point is, none of this creates any problems if we interpret correctly what an interpretation is supposed to be, and recognize that nature isn't supposed to have a correct interpretation any more than arithmetic does, interpretations are part of how we understand nature, or arithmetic, and need not be unique, merely equivalent in regard to the testable results.

It's certainly true that there is something going on our minds when we decide to use this wave function (or density matrix) rather than that one, but if afterwards the choice has great predictive value, then that would seem to be evidence that the mathematical construct has some relation to what's true in the world.

It certainly is evidence that the mathematical construct has value to us, that it connects in some useful way to nature. Is there something else that a scientist means by "what's true in the world"? Do not scientists like to stay within what can be demonstrated, and shy away from what others could regard purely as an unevidenced belief system?

 

[Ken G]

In classical physics, we have no problem with saying there are hidden variables, and that reality really exists, and the cut reflects our ignorance.

But we do have a problem there, we have a completely deterministic theory built from fundamentally time reversible equations that is trying to describe a set of experiences where we seem to have choices and a special arrow to time. We just kind of stopped bothering with these problems when we discovered it was no longer the most fundamental theory available. We should expect the same eventual fate for the quantum measurement problem, if history will be our guide.

In quantum mechanics, historically there was the idea that there is a conflict, and one cannot have naive reality. Since Bohm, we know that these two statements are compatible, and that this is a viable philosophy. Thus the measurement problem is solved.

That is one way to frame the measurement problem, but that's not how I look at it. What I think you are saying is that you have found a particular interpretation of quantum mechanics, a metatheory that adds axioms that allow the semantic truths of experimental outcomes in quantum type experiments to be derived from the syntactic structure of that particular metatheory. Yet that's what all the interpretations of quantum mechanics do, so why would that imply there would be a measurement problem without the Bohmian metatheory? In my mind, the measurement problem takes your solution to the next step and asks "is reality really doing what your interpretation says it is doing?" That's the "problem" that cannot be scientifically resolved (unless we get some new predictions to test), and which I am arguing is only a problem if we think that's a valid question to ask in the first place.

Another point of the measurement problem is that the idea that the universe has a wave function is not an idea - not a tenable idea even in principle (unless Many-Worlds works). So if the wave function of the universe does not exist even in principle, but if we believe that there is a theory that can describe the whole universe, then this represents a theoretical opportunity - it's just like quantum gravity where the theory itself says there is a cut, even though experiments have never demonstrated the theory to fail. It is not any different from having Maxwell's equations and Newtonian gravity and realizing that something has to give - maybe the principle of relativity - even before the Michelson-Morley experiment.

The Michelson-Morley experiment is an example of an experiment that comes out A if we resolve the cut one way and B if we resolve it a different way. That means the cut is scientifically explorable. The "cut" between what nature is actually doing, and our approaches to understanding nature, is not explorable as long as we frame physics to be something that does not have us in it.