Danger for the Many-Worlds Interpretation?

[Minnesota Joe]

You could create "non-interacting" branches in a classical probability tree.

There's a purely classical model called Spekkens toy model where you have interfering probabilities, but where a form of tracing causes the interference terms to die off. As @PeroK said above in classical probability theory you have non-interacting branches, but Spekkens model is even closer to QM in that you have interacting branches but coarse grained branches become non-interacting (i.e. have a form of decoherence).

Yes, something about PeroK's statement caught my eye-- it sounded like it was hinting at another approach. How does that work with Schrodinger equation though?

 

[DarMM]

Yes, something about PeroK's statement caught my eye-- it sounded like it was hinting at another approach. How does that work with Schrodinger equation though?

Well the analogue of Schrodinger's equation in a classical model would be the Stochastic evolution equations. They will naturally "branch" as time goes in. For example set up the statistical mechanics of some gas + detector. There you will get branching under Liouville evolution.

 

[Minnesota Joe]

Well the analogue of Schrodinger's equation in a classical model would be the Stochastic evolution equations. They will naturally "branch" as time goes in. For example set up the statistical mechanics of some gas + detector. There you will get branching under Liouville evolution.

Very interesting. This is another independent interpretation?

 

[DarMM]

Very interesting. This is another independent interpretation?

What part? That classical stochastic equations have branching isn't an interpretation of QM. Or did you mean Spekkens model?

 

[Minnesota Joe]

What part? That classical stochastic equations have branching isn't an interpretation of QM. Or did you mean Spekkens model?

Earlier I was talking about the many world people's commitment to use only the Schrodinger equation. This is one of the superficial things in its favor (because it is easily generalized to modern physics, is simple, etc.). But that means that decoherence has to come from the SE as well. I wasn't sure where you were going with the classical analog of the Schrodinger equation or the Spekkens model.

 

[DarMM]

Earlier I was talking about the many world people's commitment to use only the Schrodinger equation. This is one of the superficial things in its favor (because it is easily generalized to modern physics, is simple, etc.). But that means that decoherence has to come from the SE as well. I wasn't sure where you were going with the classical analog of the Schrodinger equation or the Spekkens model.

Just that Spekkens model is classical model that contains virtually all the features used to motivate Many Worlds and that branching isn't something unique to QM, but occurs in probability theories in general.

 

[Minnesota Joe]

Just that Spekkens model is classical model that contains virtually all the features used to motivate Many Worlds and that branching isn't something unique to QM, but occurs in probability theories in general.

I take it that here you are using "branching" more generally than MWI does? I ask because I've in talking about many worlds I've strictly used branching to refer to the result of decoherence, so I guess there is an ambiguity here I have to watch out for.

 

[DarMM]

I take it that here you are using "branching" more generally than MWI does? I ask because I've in talking about many worlds I've strictly used branching to refer to the result of decoherence, so I guess there is an ambiguity here I have to watch out for.

Actually in a way no it is not more general. Branching is a feature of classical stochastic models and in QM we get branching from decoherence because decoherence is precisely the process that converts classical probabilities into quantum probabilities.

 

[timmdeeg]

... in QM we get branching from decoherence because decoherence is precisely the process that converts classical probabilities into quantum probabilities.

As an aside question does Everett's relative-state interpretation require decoherence?

 

[akvadrako]

So you similarly can't make sense of classical statistical mechanics and Wiener processes or other Stochastic processes as they similarly have no rule* for when to apply Bayesian updating?

*Although I would say the do, i.e. when you make an observation and obtain a result.

I haven't given classical theories much thought; I just don't find it compelling. But if there is no rule about when to apply which form of evolution, then I don't see how one can make predictions. There must be some other information that's implicitly used to make that choice.

This introduces "worlds" directly into the basic postulates of the theory even though "worlds" only really emerge after decoherence. How does decoherence work in such a picture exactly?

I think it's confused by there really being two Born rules. One is the measure on Hilbert space, which is needed for decoherence, to be able to say two parts of $\psi$ evolve independently. I think Vaidman is also assuming this. Two is connecting $\psi$ to subjective experience, which is what this quote is about.

Another way to think is that worlds are like points similar to Bohmian mechaincs and never split, but diverge. So what in a splitting view one might call one world is a collection of an infinite number of worlds, which will diverge sometime in the future. In this sense I don't think you need decoherence to define a world density.

 

[Minnesota Joe]

As an aside question does Everett's relative-state interpretation require decoherence?

According to Sean Carroll's book and Adam Becker's book, Everett original idea didn't involve decoherence and he wasn't familiar with it. It seems to him the central idea is just superpositions of macroscopic objects that entangle with microscopic objects. So this is a step before decoherence if I understand this correctly. Sean Carroll does claim he thought of them as "worlds", but I put that in quotes intentionally, because I don't know for sure.

People cite H. Dieter Zeh in 1970 https://link.springer.com/article/10.1007/BF00708656 for introducing decoherence, but I don't understand how long the idea was kicking around before that, if it was. So I don't myself know if it was even possible for Everett to be familiar with the concept when he wrote his dissertation.

 

[DarMM]

I haven't given classical theories much thought; I just don't find it compelling. But if there is no rule about when to apply which form of evolution, then I don't see how one can make predictions. There must be some other information that's implicitly used to make that choice

The problem is it's not "evolution" in a mechanical sense. Collapse is just Bayesian updating. Bayesian updating has a clear rule for when it is applied, i.e. when you make an observation. I don't really understand what the issue is or how this is "not predictive". Clearly these theories are predictive.

Surely you find regular statistics or statistical mechanics "compelling"?

In a normal statistical model what is the "implicit information" used to apply Bayesian updating?

 

[Minnesota Joe]

I think it's confused by there really being two Born rules. One is the measure on Hilbert space, which is needed for decoherence, to be able to say two parts of $\psi$ evolve independently. I think Vaidman is also assuming this. Two is connecting $\psi$ to subjective experience, which is what this quote is about.

Oh, hey, this might solve a mystery for me. I was really puzzled why Carroll thought it permissible to derive the Born rule from epistemic probability after decoherence if decoherence requires the Born rule. Maybe this is motivation?

 

[akvadrako]

The problem is it's not "evolution" in a mechanical sense. Collapse is just Bayesian updating. Bayesian updating has a clear rule for when it is applied, i.e. when you make an observation. I don't really understand what the issue is or how this is "not predictive". Clearly these theories are predictive.

Surely you find regular statistics or statistical mechanics "compelling"?

Why? And why do you think Bayesian updating isn't evolution? It changes the state — that seems like evolution.

 

[DarMM]

Why? And why do you think Bayesian updating isn't evolution? It changes the state — that seems like evolution.

Do you mean "Why is statistical mechanics compelling"?

I don't really care too much about whether evolution is the correct word. Obviously the state changes but it's not meant to be a physical process. My point is more why is Bayesian updating a problem in QM and not in classical statistics or theories that use it?

 

[timmdeeg]

According to Sean Carroll's book and Adam Becker's book, Everett original idea didn't involve decoherence and he wasn't familiar with it. It seems to him the central idea is just superpositions of macroscopic objects that entangle with microscopic objects. So this is a step before decoherence if I understand this correctly.

Yes, that's what I thought. So this seems to make the difference if one compares Everett's relative states with MWI's branches. In contrast to the former the latter requires decoherence. But how is that justified?

 

[akvadrako]

Oh, hey, this might solve a mystery for me. I was really puzzled why Carroll thought it permissible to derive the Born rule from epistemic probability after decoherence if decoherence requires the Born rule. Maybe this is motivation?

I think so. He's really trying to derive probability and you don't need probability to get decoherence. Look at his conversation with Eric in the comments from the link below. Maybe he's improved his argument since then.

http://www.preposterousuniverse.com...hanics-is-given-by-the-wave-function-squared/

 

[akvadrako]

Do you mean "Why is statistical mechanics compelling"?

I don't really care too much about whether evolution is the correct word. Obviously the state changes but it's not meant to be a physical process. My point is more why is Bayesian updating a problem in QM and not in classical statistics or theories that use it?

That's what I mean; I really have never given it much thought and I don't see how it'll shed much light on this issue. I'm not saying QM is different; it seems to me that Bayesian updating is always an approximation and you'll get different results depending on when you apply it. It's QM that makes this most clear, not thinking on terms of other theories.

 

[Minnesota Joe]

Yes, that's what I thought. So this seems to make the difference if one compares Everett's relative states with MWI's branches. In contrast to the former the latter requires decoherence. But how is that justified?

I think you are correct that it makes a difference. But we could also flip it around and ask how Everett was justified in thinking that the terms in his branches are worlds. Decoherence provides the mechanism for considering them to be approximately "separate" in some sense, like two perpendicular vectors. And it isn't just many world's that finds this idea useful, it is used in other contexts and interpretations too.

 

[Minnesota Joe]

I think so. He's really trying to derive probability and you don't need probability to get decoherence. Look at his conversation with Eric in the comments from the link below. Maybe he's improved his argument since then.

http://www.preposterousuniverse.com...hanics-is-given-by-the-wave-function-squared/

That alone is very enlightening, thanks! It's why I was asking @DarMM about details around the decoherence calculation. I was wondering if it involved amplitudes (perhaps squared), but not probabilities, necessarily. According to Carroll in that thread it doesn't involve probabilities and off diagonal elements are "small". Whether or not that is true, he believes it, so it makes his project make more sense.

 

[DarMM]

That's what I mean; I really have never given it much thought and I don't see how it'll shed much light on this issue.

What issue do you mean? If it's about the "problem" of collapse most consider this to be the resolution. I'm the opposite, I don't see how it doesn't instantly resolve this whole "two evolutions" problem. Collapse is mathematically just a generalization of Bayesian conditioning. I don't really see the "issue" as such.

 

[DarMM]

That alone is very enlightening, thanks! It's why I was asking @DarMM about details around the decoherence calculation. I was wondering if it involved amplitudes (perhaps squared), but not probabilities, necessarily. According to Carroll in that thread it doesn't involve probabilities and off diagonal elements are "small". Whether or not that is true, he believes it, so it makes his project make more sense.

Decoherence requires probabilities and thus the Born rule. Carroll's argument in that link makes little sense to me. "Magically" decoherence happens, then we get branches, then we get probabilties.

 

[akvadrako]

What issue do you mean? If it's about the "problem" of collapse most consider this to be the resolution. I'm the opposite, I don't see how it doesn't instantly resolve this whole "two evolutions" problem. Collapse is mathematically just a generalization of Bayesian conditioning. I don't really see the "issue" as such.

This doesn't resolve anything; it just suggest Bayesian updating also has the same issue.

 

[DarMM]

This doesn't resolve anything; it just suggest Bayesian updating also has the same issue.

What issue?

 

[timmdeeg]

No. It's part of the minimal "shut up and calculate" machinery of QM. It's independent of any interpretation. You have to do it in order to make the predictions from the mathematical machinery match actual experimental data.

But the "shut up and calculate" perspective contradicts the MWI anyway. So I wonder what Hossenfelder's statement

"The wave-function collapse, I have to emphasize, is not optional. It is an observational requirement."

clarifies in addition. Isn't that just expected?

 

[akvadrako]

What issue?

Of two different forms of evolution.

 

[DarMM]

Of two different forms of evolution.

But how is that really an issue? Several physical theories have it, classical statistics has it, QM has it. All are predictive and confirmed in every observation we have. What exactly is the issue?

Let me reiterate this. This two evolution issue occurs in any probabilistic theory, so this is really just a problem with probabilistic theories is it not?

 

[PeterDonis]

the "shut up and calculate" perspective contradicts the MWI anyway

No, it doesn't. The minimal "shut up and calculate" perspective doesn't contradict any QM interpretation. It provides the minimal common basis for all the interpretations: the mathematical machinery for making predictions and the minimal requirements for those mathematical predictions to match experiment. Any QM interpretation that contradicted that would be obviously wrong since it wouldn't match experiment.

 

[PeterDonis]

I wonder what Hossenfelder's statement

"The wave-function collapse, I have to emphasize, is not optional. It is an observational requirement."

clarifies in addition.

It clarifies that the mathematical operation of "wave function collapse" is part of the minimum requirements for the mathematical predictions to match experiment. But that minimal interpretation takes no position about whether that mathematical operation corresponds to a physical operation or not. MWI says it doesn't.

However, MWI proponents often talk as though even the mathematical operation of "wave function collapse" is not needed--they say things like there is no collapse in MWI because all outcomes happen. Hossenfelder's point is that if you stop there, the MWI obviously contradicts experiment because nobody observes all outcomes happening; everybody only observes one outcome. So you have to do the mathematical operation of collapse to match experiment; the MWI does not remove the need to do that. And she thinks a lot of MWI proponents are not acknowledging that fact about the MWI, because if it is acknowledged the MWI loses a lot of its appeal; the appeal of the MWI was supposed to be that you could just do unitary evolution and that's it, that you never had to worry at all about "wave function collapse" and all the issues that go along with it.

 

[Minnesota Joe]

Decoherence requires probabilities and thus the Born rule. Carroll's argument in that link makes little sense to me. "Magically" decoherence happens, then we get branches, then we get probabilties.

Yeah, I have to remain agnostic about whether or not it is circular, given what we discussed earlier, until I know more. I should probably read his paper, because he certainly didn't go into any detail in his book. I think he ought to have mentioned it, frankly. All I was arguing is that, given that he believes it at least I understand his project better.

He claims to do it without density matrices too:
http://www.preposterousuniverse.com/blog/2014/07/24/why-probability-in-quantum-mechanics-is-given-by-the-wave-function-squared/comment-page-4/#comments

...Constructing the reduced density matrix” is a purely mathematical process, completely well-posed whether or not you have the Born Rule. The question is what meaning we should attach to it, which is what our argument addresses. In Appendix B we address this in gruesome detail, and in the shorter paper we do the whole thing without ever using density matrices, just to assuage skepticism.

Of course, you do need to use the inner product on Hilbert space to construct the reduced density matrix. But the inner product is part of the theory, and nobody is going to make sense of quantum mechanics without assuming it."

 

[akvadrako]

But how is that really an issue? Several physical theories have it, classical statistics has it, QM has it. All are predictive and confirmed in every observation we have. What exactly is the issue?

Let me reiterate this. This two evolution issue occurs in any probabilistic theory, so this is really just a problem with probabilistic theories is it not?

That's what I think I've said about 5 times now. It's not specific to QM - any theory with two forms of evolution which can't be reconciled into one seems obviously self-contradictory because you get different results depending on which form of evolution you apply. So I don't see how such theories even make predictions.

 

[DarMM]

That's what I think I've said about 5 times now. It's not specific to QM - any theory with two forms of evolution which can't be reconciled into one seems obviously self-contradictory because you get different results depending on which form of evolution you apply. So I don't see how such theories even make predictions.

You might have said it a lot but you haven't really shown the contradiction or how these theories are not predictive. Quantum Mechanics and Statistical Mechanics clearly are predictive. Could you give an example of such a contradiction in a specific scenario?

If it's easier just show the contradiction in a classical statistical model like any kind of Stochastic process. You're claiming a contradiction in abstract. Please provide a concrete example.

 

[DarMM]

Yeah, I have to remain agnostic about whether or not it is circular, given what we discussed earlier, until I know more. I should probably read his paper, because he certainly didn't go into any detail in his book. I think he ought to have mentioned it, frankly. All I was arguing is that, given that he believes it at least I understand his project better.

He claims to do it without density matrices too:

I'd have a read of the papers of Kent and Vaidman (one a critic of MWI, the other a proponent) which for similar reasons find Carroll's derivation flawed.

https://arxiv.org/abs/1408.1944http://philsci-archive.pitt.edu/14389/

 

[A. Neumaier]

It's not specific to QM - any theory with two forms of evolution which can't be reconciled into one seems obviously self-contradictory because you get different results depending on which form of evolution you apply.

But there is no contradiction in QM: Unitary evolution applies only to isolated systems, and Born's rule (with some form of collapse) only to measured systems. The latter are clearly not isolated. Thus the two forms of evolution apply to disjoint contexts. How could they ever be contradictory?

 

[akvadrako]

But there is no contradiction in QM: Unitary evolution applies only to isolated systems, and Born's rule (with some form of collapse) only to measured systems. The latter are clearly not isolated. Thus the two forms of evolution apply to disjoint contexts. How could they ever be contradictory?

If there is a rule about when one can apply either form of evolution than it's fine. I'm saying there needs to be such a rule - it can't be a subjective thing.