I Danger for the Many-Worlds Interpretation?

[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.

 

[A. Neumaier]

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.

There are pragmatic rules that work in practice, though it is difficult to formalize them.

 

[timmdeeg]

Thanks for your detailed answers, very much appreciated.

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

Got it.

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.

Some around here have been talking about the "apparent collapse" of the MWI (understandable for me) which nevertheless is observable. Is this the crucial point? The MWI agrees that "everybody observes only one outcome" but according to "shut up and calculate" being as you say "the minimal common basis for all the interpretations" and having as such an objective status denies the possibility of an "apparent collapse". From this point of view Hossenfelder seems to say "apparent collapse" and "real collapse" is the "same thing".

 

[akvadrako]

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.

I started this sub-thread to say that I don't think many worlders say a problem with Copenhagen is the need to derive the Born rule, just that collapse is inconsistent with unitary evolution. I would say Wigner's friend scenarios are part of that motivation, but on a more basic level it's just when someone does any measurement, say on a system in $1/\sqrt 2 (\uparrow + \downarrow)$ state and gets up, the state changes to $\uparrow$, but by unitary evolution the measuring device becomes entangled with the $\uparrow / \downarrow$ dimension. They describe different outcome states so only one can describe objective reality.

 

[Minnesota Joe]

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.

You represent the state as pure because you were caused to by what you detector reported. How can there be any violation of the Schrodinger equation? You are evolving by the Schrodinger equation when you "do the mathematical operation of collapse". The state is changing but where did a non-linear "collapse" ever occur? It's utterly deterministic. Can you give an example of this non-linear collapse?

 

[PeterDonis]

according to "shut up and calculate" being as you say "the minimal common basis for all the interpretations" and having as such an objective status denies the possibility of an "apparent collapse".

Huh? No, it doesn't. I explicitly said that minimal "shut up and calculate" makes no claim about whether the mathematical operation of "collapse" (the thing you have to do in the math to match experiment) corresponds to an actual physical operation or not. If it does, then there is some sort of "real collapse". If it doesn't, then there is only an "apparent collapse". So minimal "shut up and calculate" explicitly allows for the possibility of an "apparent collapse".

 

[PeterDonis]

You are evolving by the Schrodinger equation when you "do the mathematical operation of collapse".

You most certainly are not. This is one of the most basic possible mathematical points about QM. The Schrodinger equation most certainly does not tell you to take a linear combination of terms and discard all but one of them, and then re-normalize the one term that's left.

 

[PeterDonis]

The state is changing but where did a non-linear "collapse" ever occur? It's utterly deterministic.

Huh? You have a wave function which is a linear combination of multiple terms. "Collapse" tells you to discard all but one of them and then re-normalize the one that's left. And it can't tell you in advance which ones to discard and which one to keep; you only know that by actually observing the measurementl result. This is most certainly not deterministic.

 

[DarMM]

I started this sub-thread to say that I don't think many worlders say a problem with Copenhagen is the need to derive the Born rule, just that collapse is inconsistent with unitary evolution. I would say Wigner's friend scenarios are part of that motivation, but on a more basic level it's just when someone does any measurement, say on a system in $1/\sqrt 2 (\uparrow + \downarrow)$ state and gets up, the state changes to $\uparrow$, but by unitary evolution the measuring device becomes entangled with the $\uparrow / \downarrow$ dimension. They describe different outcome states so only one can describe objective reality.

How is that contradictory or inconsistent though? It happens even in classical statistical mechanics for a system compared with system + detector.

If there is a device in a room and it rolls a dice then it has some $p(\omega)$ over the outcomes prior to observing them. When it observes them it sets some pointer on itself to a corresponding value $\alpha$.

Another device is outside the room and cannot see in. It has some distribution $p(\omega , \alpha)$ for the dice and pointer pair. It will model them as correlated but not "collapsed" just as in the case of QM.

So inner observer has collapse, outer observer has uncollapsed with device-system correlation. There isn't any real problem here that I can see. What's the contradiction?

 

[timmdeeg]

So minimal "shut up and calculate" explicitly allows for the possibility of an "apparent collapse".

Understand, thanks for clarifying.

 

[vanhees71]

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?

Well, you hear this argument often, but it's not justified. The collapse assumption contradicts, within relativsitic QFT, the very mathematical foundations of this theory, according to which no instantaneous interactions are possible by construction. All there is is "Bayesian updating" of an observer, knowing the entangled state before the local (sic!) measurement and takes notice of the outcome of his measurement. This solves the apparent contradiction between the mathematics and the "soft part" of the interpretation and, within the ensemble interpretation, never leads to any contradictions.

One should also note that there are at least to main flavors of Copenhagen, the "gospel according to Bohr" (no collapse and much more carefully stated) and the "gospel according to Heisenberg". Unfortunately both tend to be overly philosophical rather than scientific in their expression, leading to a lot of unnecessary confusion and debates.