I Danger for the Many-Worlds Interpretation?

[DarMM]

Yes, I see it must be something more fundamental. If mixed states aren't "mixtures" of something else, what can they be? For example if your finite volume system is a single qubit that would in NRQM be described as the pure state of spin up?

I know this sounds like an empty answer initially, but they are just a state then. Not classical uncertainty about some smaller set of "real" states, i.e. pure states. Really you might characterize a pure state as one for which there is a single measurement (of some observable $\mathcal{O}$) for which one of its outcomes is certain, i.e. a pure state has a single determined experiment.

This result would then say for actual real finite volume systems there is no such experiment, i.e. there is no operation that has utterly determined results.

 

[Minnesota Joe]

Her comment "This [MWI] is clearly not what we observe." suggests that perhaps she doesn't get how decoherence mimics wavefunction collapse.

Maybe, but in that same video she is explicit that decoherence by itself doesn't solve the measurement problem. And that is true as I understand it. Decoherence leaves all the approximate eigenstates in the sum.

 

[PeterDonis]

@Michael Price, you have earned yourself a warning and a thread ban. Your conduct in this thread has become indistinguishable from trolling.

 

[PeterDonis]

As I said that statement needs some important assumptions and it is not valid "in QFT" in general without them.

Every theorem requires assumptions. If you want to claim that a theorem is not relevant physically, you need to describe some actual physical situation in which key assumptions of the theorem are not met. Just pointing out that the theorem requires assumptions is not enough and contributes nothing useful to the discussion. Please take note.

 

[vanhees71]

Really? That finite volume states in QFT are mixed.

I think now I understand, where our mutual misunderstanding comes from: You discuss the impossibility of pure states with finite support in QFT in the infinite-volume limit, while I understood the whole time you mean the finite-volume regularized model... That of course resolves the issue.

 

[Elias1960]

Maybe, but in that same video she is explicit that decoherence by itself doesn't solve the measurement problem. And that is true as I understand it.

Moreover, decoherence requires additional structure, thus, to apply decoherence, MWI would have, first, to introduce this additional structure.

In all the practical applications of decoherence, this additional structure exists in a quite obvious way. Namely, we need the subdivision of the universe into the quantum system under consideration and the environment. Of course, this subdivision is obvious in all practical applications. But if you don't have it, you cannot even start to apply decoherence techniques.

Every theorem requires assumptions. If you want to claim that a theorem is not relevant physically, you need to describe some actual physical situation in which key assumptions of the theorem are not met. Just pointing out that the theorem requires assumptions is not enough and contributes nothing useful to the discussion. Please take note.

A quite strange requirement. Haag-Kastler are axioms about a particular set of theories, not of actual physical situations. So, it is even in principle meaningless to claim that key assumptions of the theorem are applicable or not to such a particular situation. Any actually imaginable physical situation can be certainly described by a theory which does not fulfill the Haag-Kastler axioms. If there exists a theory fulfilling the Haag-Kastler axioms compatible with, say, the SM, remains unclear. But even if that would be possible, the requirement you have made makes no sense.

QFT in the modern understanding is not required to fulfill these axioms, it may be as well simply an effective field theory, which is not even consistently defined for arbitrary small distances, but meaningful only as a large distance approximation of a trans-Planckian theory which has nothing to do with the Haag-Kastler axioms - it may not even have such an animal as a spacetime.

 

[Tendex]

According to Darmm it is not applicable in the context of renormalizable 4-dimensional perturbative quantum field theory, that I think is relevant physically, so I'm just pointing out this. His insistence on stating it for QFTs in general seems misleading IMO. On the other hand I'm also reminding that neither Haag-Kastler nor Wightman axioms have been rigurously used to date to prove a theory for the physically relevant 4-dimensional interacting QFT.

 

[Minnesota Joe]

Moreover, decoherence requires additional structure, thus, to apply decoherence, MWI would have, first, to introduce this additional structure.

In all the practical applications of decoherence, this additional structure exists in a quite obvious way. Namely, we need the subdivision of the universe into the quantum system under consideration and the environment. Of course, this subdivision is obvious in all practical applications. But if you don't have it, you cannot even start to apply decoherence techniques.

Assuming I understand what you mean by "additional structure" (macroscopic and microscopic subsystems) I would think that MWI could help themselves to it, just like everyone else. Do you disagree? Is this more profound a problem for MWI specifically?

 

[DarMM]

According to Darmm it is not applicable in the context of renormalizable 4-dimensional perturbative quantum field theory

I never said that, at all. I said it applies to field theories which obey the appropriate subset of the Haag-Kastler axioms. There's nothing forbidding renormalized theories from obeying the Haag-Kastler axioms. And for most field theories constructed their perturbation theory matches that of conventional "physicist" field theory.

 

[PeterDonis]

Haag-Kastler are axioms about a particular set of theories, not of actual physical situations.

We only care in physics about particular mathematical theories because we expect to use them to describe particular physical situations. Discussion of mathematical theories independent of any physical application belongs in the math forum, not this one.

Any actually imaginable physical situation can be certainly described by a theory which does not fulfill the Haag-Kastler axioms.

This is a very strong claim. Can you back it up?

 

[Tendex]

I never said that, at all. I said it applies to field theories which obey the appropriate subset of the Haag-Kastler axioms. There's nothing forbidding renormalized theories from obeying the Haag-Kastler axioms. And for most field theories constructed their perturbation theory matches that of conventional "physicist" field theory.

You said "this concerns infinite volume QFTs with no cutoffs". There maybe nothing forbidding renormalized theories from obeying it but its proof doesn't include those. Or as you said it has nothing to do with the regularized theory.

 

[DarMM]

You said "this concerns infinite volume QFTs with no cutoffs". There maybe nothing forbidding renormalized theories from obeying it but its proof doesn't include those. Or as you said it has nothing to do with the regularized theory.

When you renormalize you impose the regularization, perform the subtractions and then remove the regularization. Thus it can apply to QFT after renormalization. There's nothing in its proof that excludes renormalized theories. In fact we know of renormalized theories that obey it.

 

[Tendex]

When you renormalize you impose the regularization, perform the subtractions and then remove the regularization. Thus it can apply to QFT after renormalization. There's nothing in its proof that excludes renormalized theories. In fact we know of renormalized theories that obey it.

Sure, it may but there is no proof for the relevant dimensions, and this is a physics forum where we should be talking about proofs with physical relevance, not just about proofs in nice theoretical constructions that seem to be most dear to you but that just might or might not have anything to do with something physical, and even less presenting them as if they definitely did.

 

[DarMM]

Sure, it may but there is no proof for the relevant dimensions

I already told you above there was, that Balaban has established Yang-Mills has the properties required for the proof to go through.
Perhaps you could say which Haag-Kastler axioms you think will fail for 4D QFTs and prevent the establishment of the theorem. Given that we already know Yang-Mills has Type III factors, what exact form are you expecting this failure to take? That on coupling with fermions a Type I structure is restored or something? (that would be provably impossible)

Since the fact that renormalized Yang-Mills has the structures required isn't enough for you, what is? What has to be true for the theorem to be relevant.

 

[Elias1960]

Assuming I understand what you mean by "additional structure" (macroscopic and microscopic subsystems) I would think that MWI could help themselves to it, just like everyone else. Do you disagree? Is this more profound a problem for MWI specifically?

Of course, there may be possibilities to solve these issues. But this would require to define what is necessary to start decoherence.

And these additional structures, subdivisions of the universe into different systems, have to be defined on the fundamental level. They cannot simply use laboratories, measurement devices, and so on, because these are not defined at the fundamental level. It could be something like, say, fermions are one system, bosons the other system. Given that the real observable particles are "dressed", thus, complex combinations of the fundamental, undressed, fermions and bosons, I doubt that one can start a reasonable theory of decoherence with this toy idea.

Whatever, they have to define the additional structures they need to use decoherence.

And this puts them into a different position. They can no longer argue against dBB theory that it needs a split of the phase space into configuration space and momentum space, while MWI can do everything with the wave function alone. They cannot.

 

[Quanundrum]

And this puts them into a different position. They can no longer argue against dBB theory that it needs a split of the phase space into configuration space and momentum space, while MWI can do everything with the wave function alone. They cannot.

This is what baffles me about MWI proponents. They tend to be a clever bunch, but somehow they have allowed the elegance of a naïve toy model MWI to persuade them to insist that the Born Rule, additional structure etc. are just "details". It reminds me a whole lot about the infatuation people had with the early versions of supersummetry pre-LHC. They were elegant, the rest were details, then reality said: "No, I'm not that simple"

 

[Minnesota Joe]

Of course, there may be possibilities to solve these issues. But this would require to define what is necessary to start decoherence.

And these additional structures, subdivisions of the universe into different systems, have to be defined on the fundamental level. They cannot simply use laboratories, measurement devices, and so on, because these are not defined at the fundamental level. It could be something like, say, fermions are one system, bosons the other system. Given that the real observable particles are "dressed", thus, complex combinations of the fundamental, undressed, fermions and bosons, I doubt that one can start a reasonable theory of decoherence with this toy idea.

Whatever, they have to define the additional structures they need to use decoherence.

I don't know enough about MWI or foundations to speak to whether or not they need to do this. I'm not sure I understand what you are saying they need to do, specifically.

And this puts them into a different position. They can no longer argue against dBB theory that it needs a split of the phase space into configuration space and momentum space, while MWI can do everything with the wave function alone. They cannot.

That isn't their main objection surely? From what I've read the main objection is the extra guidance equation and all the trouble it entails. (Whereas others would see that guidance equation as fixing a lot of problems, mind.)

Still, I'm also pretty skeptical that the MWI party line leans so heavily on the simplicity claim. Because it sure seems like they are making the interpretation a good deal more complex if nothing else. That's just moving propositions from one side of the balance sheet to the other and in a pretty angels-dancing-on-pinheads sort of way.

 

[bhobba]

It's not that there are no proposed solutions, but neither of the proposed solutions is generally accepted in the MWI community, let alone outside of the community.

Yes that is one of its big issues. I personally think it's just a simple matter of applying Gleason, and Wallace, in his book the Emergent Multiverse, although he gives the betting strategy argument, also proves a no contextuality theorem that makes Gleason harder to refute.

I actually do not like MW as its usually interpreted - that the different worlds are actually in some sense real - rather I like Gell-Mann's view - which is exactly what does real mean - he would prefer, as do I, treated on equal footing rather than real:


When you do that then MW is basically the same as decoherent histories. I actually learned a lot about Decoherent Histories from reading Wallace's book.

Thanks
Bill

 

[Quanundrum]

Yes that is one of its big issues. I personally think it's just a simple matter of applying Gleason, and Wallace, in his book the Emergent Multiverse, although he gives the betting strategy argument, also proves a no contextuality theorem that makes Gleason harder to refute.

I actually do not like MW as its usually interpreted - that the different worlds are actually in some sense real - rather I like Gell-Mann's view - which is exactly what does real mean - he would prefer, as do I, treated on equal footing rather than real:


When you do that then MW is basically the same as decoherent histories. I actually learned a lot about Decoherent Histories from reading Wallace's book.

Thanks
Bill

How is this not "MWI in permanent denial" though? You add an extra postulate of one world somehow magically being real, without any explanation of why that history is real while the others magically vanish?

 

[DarMM]

How is this not "MWI in permanent denial" though? You add an extra postulate of one world somehow magically being real, without any explanation of why that history is real while the others magically vanish?

It's just taking the probability assignments as simply that, the probability for that history to occur. Rather than some measure of the number of such worlds. The worlds no more vanish than the other dice outcomes "vanish" in a given roll.

 

[DarMM]

I personally think it's just a simple matter of applying Gleason, and Wallace, in his book the Emergent Multiverse, although he gives the betting strategy argument, also proves a no contextuality theorem that makes Gleason harder to refute

Having read Wallace his theorem is a very different beast to Gleason's theorem as far as I can tell. Can you expand on this a bit?

 

[bhobba]

Having read Wallace his theorem is a very different beast to Gleason's theorem as far as I can tell. Can you expand on this a bit?

See page 474 on the Everettian Inference Theorem. It uses as well as proves the POVM version of Gleason. But on reacquaintance with it, it may still rely on some of his decision theory arguments in previews chapters - it makes use of the Born Rule Theorem that I seem to remember uses it for example.

Thanks
Bill

 

[DarMM]

See page 474 on the Everettian Inference Theorem. It uses as well as proves the POVM version of Gleason. But on reacquaintance with it, it may still rely on some of his decision theory arguments in previews chapters - it makes use of the Born Rule Theorem that I seem to remember uses it for example.

Thanks
Bill

I've read it before and worked through it, but the assumptions are quite different as far as I can see. He uses a combination of assumptions about a Savage style decision theory, as well as complex dynamical and partitioning assumptions about macroscopic sectors of the Hilbert space to develop something close enough to contextuality to use a Gleason style proof.

However the whole orientation of the proof is quite different from Gleason. In Gleason we take the observable algebra as fundamental and derive the state as a probability assignment on it. In Wallace the state is fundamental and we develop a Savage decision theory for occupation in a macroscopic coarse graining of it. Mathematically the later part of Wallace's theorem simply looks somewhat like Gleason's theorem, but the motivation, background and the majority of the legwork of the proof are quite different.

At least as far as I can see.

 

[akvadrako]

It's just taking the probability assignments as simply that, the probability for that history to occur. Rather than some measure of the number of such worlds. The worlds no more vanish than the other dice outcomes "vanish" in a given roll.

That doesn't explain anything. In many worlds all the dice outcomes are real too; they don't vanish. At least that's a common assumption to work under when talking about a large multiverse.

 

[DarMM]

That doesn't explain anything. In many worlds all the dice outcomes are real too; they don't vanish. At least that's a common assumption to work under when talking about a large multiverse.

I'm not sure exactly what you mean, but @Quanundrum was asking about non-MWI views. What part doesn't explain anything, or what is it failing to explain?

In those views the other outcomes weren't present and then suddenly vanish, the quantum state is simply a type of probability assignment, so you don't have to explain how the unobserved outcomes vanished since you aren't saying that the state giving them a non-vanishing assignment implies they are present in some sense.

Unless I have you wrong. Are you saying when you roll a dice there are worlds out there where you rolled the other outcomes, i.e. there are worlds even for classical probability.

 

[Quanundrum]

It's just taking the probability assignments as simply that, the probability for that history to occur. Rather than some measure of the number of such worlds. The worlds no more vanish than the other dice outcomes "vanish" in a given roll.

The problem with that is that you don't explain how this world manifests or emerges from something ontological, not to mention that it is wildly indeterminist. If you are ok with antirealism and randomness being at the heart of reality that is of course fair, but... yeah, it's the two things most people into MWI disagree with the most.

 

[Demystifier]

I actually do not like MW as its usually interpreted - that the different worlds are actually in some sense real - rather I like Gell-Mann's view - which is exactly what does real mean - he would prefer, as do I, treated on equal footing rather than real:

Yes, I like that view. In that sense, Bohmian mechanics is MW theory too. A version of MW with a natural solution of the Born-rule problem.

 

[DarMM]

The problem with that is that you don't explain how this world manifests or emerges from something ontological, not to mention that it is wildly indeterminist. If you are ok with antirealism and randomness being at the heart of reality that is of course fair, but... yeah, it's the two things most people into MWI disagree with the most.

Yes of course, but we must strictly separate issues in order to properly discuss interpretations. Copenhagen like views don't have explain how the worlds vanish since they aren't saying there are all these worlds in the first place. They don't claim the wave-function is a real wave or something so they don't have to explain where parts of it went. They claim it's just a collection of expectations.

Now of course there is non-representationalism and indeterminism in Copenhagen and one might have a problem with them, but they are separate issues.

I should also say that most Copenhagen people acknowledge that a non-representational theory isn't what you would like fundamentally. However they just don't agree that QM is giving you a representational account, i.e. they'd also prefer a representational view but they simply think the mathematical structure of QM implies it isn't such an account.

 

[akvadrako]

I'm not sure exactly what you mean, but @Quanundrum was asking about non-MWI views. What part doesn't explain anything, or what is it failing to explain?

In those views the other outcomes weren't present and then suddenly vanish, the quantum state is simply a type of probability assignment, so you don't have to explain how the unobserved outcomes vanished since you aren't saying that the state giving them a non-vanishing assignment implies they are present in some sense.

Unless I have you wrong. Are you saying when you roll a dice there are worlds out there where you rolled the other outcomes, i.e. there are worlds even for classical probability.

I know it's not about MWI; it's the single-outcome case that contains an element of arbitrariness. Saying it's just like dice roles doesn't explain it because it doesn't tell you why one outcome is seen and not the others. You might say it depends on initial conditions, but then you have to explain why one initial condition is chosen over the others. The vanishing might be happening earlier, but it still needs to happen. The mystery is only removed if all initial conditions lead to the same outcome.

I guess it seems like you are suggesting that it should be taken for granted that classical probability makes sense, so when the results can be explained without resorting to a non-separable state, single outcomes start to make sense. But I would say it's not a big difference; before quantum probability people didn't think about the measurement problem as much because it wasn't as obvious.

 

[DarMM]

Saying it's just like dice roles doesn't explain it because it doesn't tell you why one outcome is seen and not the others

Of course, it's a probabilistic view. Thus there isn't an explanation given to the appearance of a given outcome. Nobody would deny the mystery you're pointing out here. What most people would argue is that you can't pass from wanting such an explanation to the claim that QM actually provides it, which in a sense would be the main difference between non-representational and representational views of QM.

You might say it depends on initial conditions

Nobody with a Copenhagen view would say this as the events are viewed as intrinsically indeterminate. It wouldn't even be compatible with how they view QM, as to them the initial conditions in QM are simply initial values for probabilities for measurement events not representational initial conditions for the system's intrinsic properties.

I guess it seems like you are suggesting that it should be taken for granted that classical probability makes sense

Classical probability is mathematically well-founded and well defined as a subset of measure theory. I think that is without question. So you must mean something else here by "makes sense".

Do you think classical probability must also be taken in a Many Worlds sense?