Undergrad Some (unrelated) questions about the measurement problem

[Derek P]

What are the possible spacetime reference frames that could describe the quantum configuration space? One Bohmian mechanic researcher proposed reciprocal space to house the pilot waves. There are dozens and dozens of such models in the arxiv...

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What I want to know is simply this. If the configuration space is located an actual Reciprocal space as some arxiv researchers seemed to suggest. Does it mean the pilot wave could have substance as part of their dynamics or is it purely wave? Note in momentum space with energy and momentum as axis.. it doesn't mean object with distance can't exist. Hence does reciprocal space means only wave can exist or particle can only exist?

Why talk about Bohmian mechanics? The traditional wavefunction lives in phase space, not physical space. So it cannot be a physical wave. And I am reliably informed, the pilot wave in BM does all the work of the WF while the particles just go along for the ride. I have even heard BM described as "Many Worlds in denial".

 

[Derek P]

I think Tegmark works within MWI. I'm not sure MWI works, but stated within MWI it seems more difficult to say exactly why it is wrong.

Also, it is true within BM, since BM has unitary evolution with the addition of hidden variables.

Basically decoherence does nothing for the measurement problem. It is a basic fact of quantum mechanics, and necessary for the interpretations that work such as Copenhagen (FAPP) and BM (in non-relativistic QM).

MW works too. But its agenda is far wider-reaching than Copenhagen and BM so

I think Tegmark works within MWI. I'm not sure MWI works, but stated within MWI it seems more difficult to say exactly why it is wrong.

Also, it is true within BM, since BM has unitary evolution with the addition of hidden variables.

Basically decoherence does nothing for the measurement problem. It is a basic fact of quantum mechanics, and necessary for the interpretations that work such as Copenhagen (FAPP) and BM (in non-relativistic QM).

I'm trying to figure out what you mean by a model working. Copenhagen requires that observed values are definite doesn't it? In which case Bell's theorem implies that the CI violates causality in some frames. Can it still be said to work? Effects preceding their causes? MWI, on the other hand, avoids definiteness and therefore does not violate causality so I'm not sure why you think it may not work.

 

[atyy]

I'm trying to figure out what you mean by a model working. Copenhagen requires that observed values are definite doesn't it? In which case Bell's theorem implies that the CI violates causality in some frames. Can it still be said to work? Effects preceding their causes? MWI, on the other hand, avoids definiteness and therefore does not violate causality so I'm not sure why you think it may not work.

I'm being deliberately sloppy. CI works in the sense that it makes sense, but it does not solve the measurement problem. In fact, CI is the poster child for the measurement problem. Operational causality is not violated by CI.

 

[stevendaryl]

[Bell's] theorem does not rule out a theory that does not have definite values. Which is precisely the picture you get if you say the wavefunction is fundamental.

I agree with you (I think). It seems to me that any interpretation besides MWI implicitly involves denying that QM is a fundamental theory that applies to every system, no matter how large or small. Copenhagen or the Ensemble Interpretation or the "Minimal Interpretation" all seem to require a distinction between measurement results and microscopic properties. Measurement results have definite values (the observer measured "spin up" or "spin down") while microscopic properties can be superpositions with a certain amplitude for having this value or that value. If you think of the measurement results as configurations of macroscopic quantum systems, then there is no good reason to believe that they have definite values any more than microscopic properties do. So basically, QM taken seriously as a fundamental, universal theory to me leads to MWI.

Which doesn't mean that I like MWI very much, either. There's been articles about the question of whether probabilities make sense for a deterministic theory, but I have a more basic doubt about MWI.

If the only fundamental object is the wave function evolving unitarily, then I would think that any observed properties of the universe would be properties of the wave function (or maybe the Hilbert space that it lives in, or maybe the Hamiltonian). Let's assume that the whole universe is described by a universal wave function that evolves according to Schrodinger's equation (for now, I'm going to ignore relativity, because QFT makes things a lot more complicated---hopefully this simplification isn't throwing the baby out with the bath water). So let's diagonalize the Hamiltonian, and so an arbitrary state of the universe can be described along the lines of:

|\psi(t)\rangle = \sum_n |\phi_n\rangle e^{-i E_n t}

where |\phi_n\rangle satisfies the equation H |\phi_n\rangle = E_n |\phi_n\rangle

(I guess I'll assume a discrete spectrum, for the sake of discussion. I don't think anything I have to say will be changed a lot by allowing a continuous spectrum.)

If the wave function is all there is, then it seems like all the phenomena that we see in the world--planets and particles and humans, etc--have to be somehow implicit in that expression. And I think they clearly are not.

Now, I think you can get something like a description of real physical objects out of such a universal wave function. Pick some observable, say the location of some macroscopic object. Then you can certainly rewrite the universal wave function |\psi(t)\rangle as a superposition of "possible worlds" where in each of them, that object has a more-or-less definite macroscopic properties. But the choice of how to split the universal wave function into possible worlds doesn't seem motivated by the quantum mechanics. It seems arbitrary.

I suppose you could say that our universe consists of two things: (1) a universal wave function, and (2) a recipe for dividing the wave function into possible worlds. But (2) seems to me to be an additional fact about the universe, beyond just the universal wave function.

 

[Derek P]

I'm being deliberately sloppy. CI works in the sense that it makes sense, but it does not solve the measurement problem. In fact, CI is the poster child for the measurement problem. Operational causality is not violated by CI.

Ah deliberate sloppiness... well I thought it was uncharacteristic of you. BMW

 

[Derek P]

... But the choice of how to split the universal wave function into possible worlds doesn't seem motivated by the quantum mechanics. It seems arbitrary.

I suppose you could say that our universe consists of two things: (1) a universal wave function, and (2) a recipe for dividing the wave function into possible worlds. But (2) seems to me to be an additional fact about the universe, beyond just the universal wave function.

Well there is a preferred basis - observable states that are robust under decoherence - and, according to those who know about these things (I mean Bill of course), it depends on the interaction Hamiltonian (usually?) having a radial dependence. So decoherence gives us our classical world as opposed to some zany classical world that would accrue if interactions were not distance-dependent. As yet I don't see this radial dependency as part of QM. What do you think?

 

[Mentz114]

[]

I suppose you could say that our universe consists of two things: (1) a universal wave function, and (2) a recipe for dividing the wave function into possible worlds. But (2) seems to me to be an additional fact about the universe, beyond just the universal wave function.

The universe is made of matter, energy and maybe other stuff and cannot 'consist of' a formula that helps us predict probabilities. Probability is not stuff and nothing can 'consist of' probability.

Do you mean that the ultimate description of the universe is probabilistic ? Because that is possible if some information is not available in principle.

 

[Derek P]

The universe is made of matter, energy and maybe other stuff and cannot 'consist of' a formula that helps us predict probabilities. Probability is not stuff and nothing can 'consist of' probability.

Do you mean that the ultimate description of the universe is probabilistic ? Because that is possible if information is not available.

The description Steve is talking about is deterministic and ontic. Probabilities are frequencies in a history. So the ultimate description doesn't need to mention probabilities except as an emergent phenomenon, like cats or beer.

 

[stevendaryl]

The universe is made of matter, energy and maybe other stuff.

Well, from the point of view of a universal wave function, those things are particular projections, if you want to call it that, of the universal wave function.

 

[Mentz114]

Well, from the point of view of a universal wave function, those things are particular projections, if you want to call it that, of the universal wave function.

That does not actually help me. We have some common groond because you seem to say that a probabilistic description cannot be sufficient and other information is required to complete the description.

I would just say that the WF is useful ( and necessary) if we do not have all the information we think we need but it cannot ever be a complete picture.

 

[stevendaryl]

That does not actually help me. We have some common groond because you seem to say that a probabilistic description cannot be sufficient and other information is required to complete the description.

I would just say that the WF is useful ( and necessary) if we do not have all the information we think we need but it cannot ever be a complete picture.

Yes, I agree with that, but it's not at all clear to me how to complete it without putting in things that are actually contrary to QM.

For example, the Copenhagen Interpretation (or ensemble interpretation, or "minimal" interpretation) can roughly speaking be thought of as declaring that what's real is the macroscopic: Results of measurements, observations. The microscopic is only used as a calculational aid for computing probabilities for macroscopic properties. I think that's a good enough heuristic for using quantum mechanics, and we need not delve any further into it. But it seems a little incoherent to me---macroscopic properties are, as far as we can tell, just made up of lots of microscopic properties.So it's hard to understand how the macroscopic could be more real than the microscopic.

 

[Mentz114]

Yes, I agree with that, but it's not at all clear to me how to complete it without putting in things that are actually contrary to QM.

For example, the Copenhagen Interpretation (or ensemble interpretation, or "minimal" interpretation) can roughly speaking be thought of as declaring that what's real is the macroscopic: Results of measurements, observations. The microscopic is only used as a calculational aid for computing probabilities for macroscopic properties. I think that's a good enough heuristic for using quantum mechanics, and we need not delve any further into it. But it seems a little incoherent to me---macroscopic properties are, as far as we can tell, just made up of lots of microscopic properties.So it's hard to understand how the macroscopic could be more real than the microscopic.

Ok - but one thing jumps out, which I've highlighted.
Things are not 'microscopic' or 'macroscopic' - they just are themselves. We decide which label to apply and therein is our problem.
This assumption

macroscopic properties are, as far as we can tell, just made up of lots of microscopic properties

is probably oversimplification. One suportable view is that QM is a linearized approximation to the underlying dynamics in which case the above is not always true.

It is an intesting issue and worth looking at.

 

[stevendaryl]

Ok - but one thing jumps out, which I've highlighted.
Things are not 'microscopic' or 'macroscopic' - they just are themselves. We decide which label to apply and therein is our problem.
This assumption

Well, whatever you want to call it, when you test QM, you are gathering statistics about some things (the number of click on a geiger counter, the number of spots on a photographic plate, etc.), while others (positions and momenta of individual particles) are unobservable. The heuristic for applying quantum mechanics treats some of these things as having definite values and some of these things as only having amplitudes associated with them.

 

[kith]

If the only fundamental object is the wave function evolving unitarily, then I would think that any observed properties of the universe would be properties of the wave function (or maybe the Hilbert space that it lives in, or maybe the Hamiltonian).

Doesn't thinking along these lines also make classical mechanics a bit unsatisfactory? If you have a phase space of dimension d, and you know the state and the Hamiltonian, you cannot tell whether there's one particle in d dimensions or d/6 particles in 3 dimensions.

But the whole idea that the only fundamental objects of a certain physical theory may be certain mathematical objects doesn't make sense to me. Physics is not a branch of mathematics. So I don't think that we should expect the MWI to work this way. If the MWI is the interpretation of a physical theory, we need to specify what the physical objects are supposed to be.

 

[Derek P]

Doesn't thinking along these lines also make classical mechanics a bit unsatisfactory? If you have a phase space of dimension d, and you know the state and the Hamiltonian, you cannot tell whether there's one particle in d dimensions or d/6 particles in 3 dimensions.

But the whole idea that the only fundamental objects of a certain physical theory may be certain mathematical objects doesn't make sense to me. Physics is not a branch of mathematics. So I don't think that we should expect the MWI to work this way. If the MWI is the interpretation of a physical theory, we need to specify what the physical objects are supposed to be.

It doesn't make sense to me either. Fortunately MWI is perfectly clear as to what exists. That would be the wavefunction.

 

[stevendaryl]

It doesn't make sense to me either. Fortunately MWI is perfectly clear as to what exists. That would be the wavefunction.

But as I said, the wave function by itself is compatible with a universe in which nothing at all happens. Write the universal wavefunction as a superposition of energy eigenstates: |\psi\rangle = \sum_n C_n |\phi_n\rangle e^{-i E_n t}. So you can interpret that as a superposition of "possible worlds", each of which is time-independent (or changes with time by at most a phase). Of course, you can also split the same wave function into a superposition of possible worlds, each of which does change with time. But if all that exists is the wave function, then there is no sense in which the second interpretation is implied by the physics of the wave function.

At best, such a universal wave function is a rorschach that you can see birds and trees in, but it's unclear that they're really there.

 

[kith]

Where does the idea come from that the MWI doesn't refer to physical objects like particles but only to the state vector of the universe? Max Tegmark's Mathematical Universe Hypothesis states this but this is not the MWI.

Everett conceived of his interpretation as being about relative states, and I just skimmed David Wallace's 2007 paper "The Quantum Measurement Problem: State of Play" where he reviews the different current viewpoints in the Many-Worlds literature. Nowhere is the state vector of the universe the starting point; the state vectors used are that of certain physical objects and observers.

And about the viewpoint which he calls "the bare theory" (which may or may not be along these lines), Wallace remarks on p.26: "The consensus seems to be that [...] 4) Any attempt to solve the measurement problem along Everettian lines cannot be ‘bare’ but must add additional assumptions."

 

[stevendaryl]

Where does the idea come from that the MWI doesn't refer to physical objects like particles but only to the state vector of the universe? Max Tegmark's Mathematical Universe Hypothesis states this but this is not the MWI.

Where does the idea come from that the MWI doesn't refer to physical objects like particles but only to the state vector of the universe? Max Tegmark's Mathematical Universe Hypothesis states this but this is not the MWI.

Everett conceived of his interpretation as being about relative states, and I just skimmed David Wallace's 2007 paper "The Quantum Measurement Problem: State of Play" where he reviews the different current viewpoints in the Many-Worlds literature. Nowhere is the state vector of the universe the starting point; the state vectors used are that of certain physical objects and observers.

And about the viewpoint which he calls "the bare theory" (which may or may not be along these lines), Wallace remarks on p.26: "The consensus seems to be that [...] 4) Any attempt to solve the measurement problem along Everettian lines cannot be ‘bare’ but must add additional assumptions."

That's a very nice survey of the various approaches, and the problems with each of them. I appreciate his observation (or his quoting of other people's observation) that the difficulties with making sense of probability in Many-Worlds are really no worse than the difficulties of making sense of classical probability.

 

[Derek P]

At best, such a universal wave function is a rorschach that you can see birds and trees in, but it's unclear that they're really there.

I don't understand that. A bird-world is a world which is fully consistent with having a bird in it. A tree-world has a tree. MWI explains phenomenal reality. I can't see the need for any other kind, even if the worlds do turn out to be superposed.

 

[Derek P]

That's a very nice survey of the various approaches, and the problems with each of them. I appreciate his observation (or his quoting of other people's observation) that the difficulties with making sense of probability in Many-Worlds are really no worse than the difficulties of making sense of classical probability.

Try telling Ruth Kastner that!

 

[Derek P]

Where does the idea come from that the MWI doesn't refer to physical objects like particles but only to the state vector of the universe? Max Tegmark's Mathematical Universe Hypothesis states this but this is not the MWI.

Well the WF's evolution is all that appears in the theory. You can sprinkle particles onto the wavefunction if it makes you feel good, but they can't take part in any interactions and they can't affect the WF. They must be puppets of the WF. You then have Bohmian Mechanics, which, for this very reason, has been described as "Many Worlds in denial".

 

[Derek P]

But if all that exists is the wave function, then there is no sense in which the second interpretation is implied by the physics of the wave function.

Sure there is. Decoherence imposes a preferred basis. Stationary state superpositions, intriguing though they may be, are not phenomenal. The Rorchasch cards have plain backs.

 

[stevendaryl]

Sure there is. Decoherence imposes a preferred basis.

A basis preferred by US, since it is more like the classical physics we're used to. Why should it be preferred by the physics?

 

[stevendaryl]

A basis preferred by US, since it is more like the classical physics we're used to. Why should it be preferred by the physics?

I understand that the basis that gets selected by decoherence has certain desirable properties, such as stability. But why does it make that basis more real than other bases?

 

[akvadrako]

I understand that the basis that gets selected by decoherence has certain desirable properties, such as stability. But why does it make that basis more real than other bases?

It doesn't have to be more real from an objective viewpoint; it just happens to be our perspective. The other perspectives might be real too. If they are unstable, they won't contain configurations like us and won't be observed. The state can even be static as long as our perspective keeps evolving.

 

[Derek P]

I understand that the basis that gets selected by decoherence has certain desirable properties, such as stability. But why does it make that basis more real than other bases?

I don't think it does. In fact I don't think physics talks about degrees of reality - Bell realism and Einstein realism are misnomers. Being real just means that something exists without qualification. MWI asserts the onticity of the wavefunction - although, of course, it may be derivative on path integrals etc. I don't think it is the job of physics to declare that such-and-such a subset of possible worlds is more real than others. More likely, that's all.

 

[Derek P]

But as I said, the wave function by itself is compatible with a universe in which nothing at all happens.

At best, such a universal wave function is a rorschach that you can see birds and trees in, but it's unclear that they're really there.

Having thought about it, I don't think I agree. Yes you can decompose the state into stationary states but they don't exist in isolation. They are in superposition, which means that the universe as a whole is not static. Specifically, if the superposition of stationary states is projected on a "world" base, we see interference between the "stationary" components, which, of course, have huge phase frequencies. This "interference pattern" is identical to the phenomenal world. Which means that the dynamic phenomena of our familiar world emerge through interference between the static states.

 

[Derek P]

They assume that, in the setup they consider, the interference can be seen at a single detector. But it cannot. It is only seen in coincidences (correlations) between two detectors. When this is taken into account, their argument does not longer work.

I don't think it's only their setup. Intuitively: if the correlator has a non-zero output corresponding to a single-slit pattern then the real pattern at the detector cannot have any dark regions.
I'm thinking that to see an interference pattern, the state must be of the form (|L>+|R>)*|xyz>, which is not an entanglement. And whatever you do with xyz you can't tag an |L> (or an |R>) state. Which is very nice because I'd been wondering for a while now why the Kim et al DCQE uses a state where no interference pattern is seen. Looks like the requirement to be able to tag signal photons as belonging to different patterns actually rules any visible-interference setup out. Am I correct?

 

[Derek P]

I don't think it does. In fact I don't think physics talks about degrees of reality.

Well perhaps Heisenberg did but I can't help feeling it shouldn't

 

[stevendaryl]

Having thought about it, I don't think I agree. Yes you can decompose the state into stationary states but they don't exist in isolation. They are in superposition, which means that the universe as a whole is not static. Specifically, if the superposition of stationary states is projected on a "world" base, we see interference between the "stationary" components, which, of course, have huge phase frequencies. This "interference pattern" is identical to the phenomenal world. Which means that the dynamic phenomena of our familiar world emerge through interference between the static states.

It seems to me that you can't really talk about interference in QM without specifying initial and final states. If you prepare a system as a superposition of two states, |\psi\rangle = \alpha |A\rangle + \beta |B\rangle, then the probability of finding it in state C will involve interference:

P = |\alpha \langle C|A\rangle + \beta \langle C|B\rangle|^2 = |\alpha|^2 |\langle C|A\rangle|^2 + |\beta|^2 |\langle C|B\rangle|^2 + 2 Re(\alpha^* \beta \langle A|C\rangle \langle C|B\rangle)

The last term is the interference term.

So yes, if you choose to project the state of the universe onto a basis other than the energy eigenstates, then you will find interference terms. But doing that projection is not forced on you by the universal wave function.

To me, it seems that you need something external to, or in addition to, the universal wave function in order to meaningfully say that the universal wavefunction should be interpreted as alternative possible worlds.