Some (unrelated) questions about the measurement problem

[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.

 

[Derek P]

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.

I don't see the need to justify interpreting it one way or the other! The fact that it can be decomposed into phenomenal worlds is sufficient to explain... phenomena. What more could you want?

 

[stevendaryl]

I don't see the need to justify interpreting it one way or the other! The fact that it can be decomposed into phenomenal worlds is sufficient to explain... phenomena. What more could you want?

I think that's back to the Rorschach images. If it can be interpreted as a picture of a butterfly, it is a picture of a butterfly.

 

[Demystifier]

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?

No. Kim et al consider a setup in which interference is only "seen" in the correlations.

 

[Derek P]

I think that's back to the Rorschach images. If it can be interpreted as a picture of a butterfly, it is a picture of a butterfly.

With the additional factor that the only entity that can see the picture of a butterfly is the butterfly in the picture.

 

[Derek P]

No. Kim et al consider a setup in which interference is only "seen" in the correlations.

I thought I was being perfectly clear - I was talking about visible interference at the signal detector. There isn't any.

 

[haushofer]

I got the book by Travis Norsen and started reading, so hopefully it will address some of my questions. I would like to return to my "consciousness questions". To me, ontologically, the idea that concsiousness collapses the wavefunction is ontologically as reasonable as the idea that Chuck Norris collapses the wavefunction by his telepathic abilities, but it is a persistent idea by many. So that's why I'd like to hear more comments on my questions 2 and 3, if any. Are there any clear arguments directly against the (Von Neumann-) Wigner interpretation involving consciousness from e.g. certain experimental results?

 

[kith]

why not simply use the simple double slit experiment, put a detector near one of the slits, and only look at the screen? I assume we'll still see the interference pattern (right?), so doesn't this conclusively exclude the possibility that "a conscious observation near one of the slits is needed to make the interference pattern disappear"?

I don't think that proponents of the von Neumann-Wigner interpretation would say that a conscious observation is needed near the slit. They would would say that collapse happens neither at the detector near the slit, nor at the screen, but only as soon as the conscious observer looks at the screen.

About the Von Neumann-Wigner interpretation: is there any way to "break out of the Von-Neumann chain of regression" without hidden variables or imposing extra dynamics on top of the Schrodinger equation?

The Many Worlds interpretation goes one step further by saying that even consiousness as the last link in the von Neumann chain doesn't collapse the state vector but is itself in superposition. Copenhagen at least removes the problem of the interation between consiousness and the state vector as physical entities by stating that the state vector is an epistemic entity and not a physical one. Time-symmetric interpretations may also get around it although one can consider them hidden variable theories where the hidden variables are in the future, so they wouldn't meet your criterion.

I see that people often use this Von-Neumann chain to motivate the Von Neumann-Wigner interpretation. And how do adherents of this interpretation explain cosmic events like e.g. the CMB we're receiving from events billions of years ago?

Do you really see this often? I have never met someone who actually follows the von Neumann-Wigner interpretation. My impression is that it is mostly a historical interpretation and that people who were in it for the realism part now prefer some sort of Many Worlds, and people who were in it for the consiousness part now prefer Copenhagen, for the reason that it doesn't give good answers to questions like yours. See e.g. Penrose's quote in the Wikipedia article.

 

[haushofer]

I don't think that proponents of the von Neumann-Wigner interpretation would say that a conscious observation is needed near the slit. They would would say that collapse happens neither at the detector near the slit, nor at the screen, but only as soon as the conscious observer looks at the screen.

Ok, fair enough. What I meant was: put a detector at one of the slits and don't look at its outcome. Then the interference pattern disappears without being conscious about the precise outcome the slit detector.

Do you really see this often? I have never met someone who actually follows the von Neumann-Wigner interpretation. My impression is that it is mostly a historical interpretation and that people who were in it for the realism part now prefer some sort of Many Worlds, and people who were in it for the consiousness part now prefer Copenhagen, for the reason that it doesn't give good answers to questions like yours. See e.g. Penrose's quote in the Wikipedia article.

Actually, "often" is not the right word. I see it with people who don't know their quantum mechanics and mix Von Neumann-Wigner with esoteric or religieus beliefs. That Penrose quote is interesting, thanks!

 

[haushofer]

What I still don't get is the following: it is sometimes claimed, see e.g. here by Bhobba (maybe he's reading along),

https://www.physicsforums.com/threa...e-observer-the-double-slit-experiment.765350/

that the cut in the Von-Neumann chain/regression is most naturally put at the moment decoherence kicks in. I don't get that. I understand the Von Neumann chain as the claim that everything between process and measurement is described by the Schrodinger equation and hence you need something "nonmaterial" to make the wavefunction collapse (i.e. to give non-unitary evolution). But decoherence doesn't make the wavefunction collapse, it gives "merely" a classical probability distribution. So why is it claimed that decoherence is the natural place to put the cut? How can it be if decoherence doesn't solve the measurement problem? Or is this again a "FAPP"-thing?

 

[Lord Jestocost]

So why is it claimed that decoherence is the natural place to put the cut?

Who claims this? Decoherence cannot explain the process of factualization of potentiality; that's outside quantum theory and has to be put in "by hand".