Danger for the Many-Worlds Interpretation?

[Minnesota Joe]

Because your copy in one of the branch worlds has no way of knowing that the other branches even exist, let alone the relative weight of their branch as compared with all of the other branches.

Sure. But my statement wasn't made in that context.

 

[PeterDonis]

my statement wasn't made in that context

I don't understand what you mean. You asked a question, I answered it. What "context" are you talking about?

 

[Minnesota Joe]

Not just very, very unlikely: impossible given the expected time for such an event to happen.

Yikes! So I don't feel so bad for saying never. Very interesting.

 

[Minnesota Joe]

I don't understand what you mean. You asked a question, I answered it. What "context" are you talking about?

The context of the scenario I had in mind is one where you know many worlds is true and I was arguing that it explains that the collapse is only apparent. Both outcomes still occur and if you are a person in a branch world, knowing MWI is true, you aren't going to think "collapse" is incompatible with the Schrodinger equation.

ETA: Typo

 

[PeterDonis]

The context of the scenario I had in mind is one where you know many worlds is true and I was arguing that it explains that the collapse is only apparent.

But that's just an assumption; you have no way of testing it by experiment. As I said in response to @WWGD, if there were a way of testing it by experiment, MWI would not be an interpretation of QM; it would be a different theory from standard QM and we could test experimentally which one was right.

Both outcomes still occur and if you are person in a branch world, knowing MWI is true, you aren't going to think "collapse" is incompatible with the Schrodinger equation.

But you are still going to have to "collapse" the wave function you use to predict your own probabilities for future measurement results. You might say the other branches of the wave function exist, but you won't actually calculate as if they exist; you will calculate as if your own branch is the only one that exists, because that's the only one you will use in your calculations. And doing that is not compatible with the Schrodinger Equation, because there is no "collapse" in the SE. The SE does not tell you to calculate using only one branch. It tells you to calculate using all the branches.

In other words, when the MWI says "collapse is only apparent and there is no contradiction with the Schrodinger Equation", it doesn't really mean that literally; it can't, since taking it literally leads you to calculate things that are contrary to what you actually observe.

 

[zonde]

I think Sabine is really talking about the problem of the Born rule in the many-worlds interpretation (MWI). If that interpretation is true, then where do probabilities come from and why are they given by the Born rule? This is indeed one of the main unsolved problems in MWI.

I think that very similar argument can be said about probabilities. Instead of wondering why particular outcome happens with predicted probability, in MWI we can wonder why my consciousness ended up in particular branch (say there are two branches with unequal weight) with predicted probability.
Only questions about consciousness are not really in domain of physics so we shift the question outside physics domain and we can pretend that physics part is just fine. Sounds a bit like cheating.

 

[PeterDonis]

in MWI we can wonder why my consciousness ended up in particular branch

If consciousness is a matter of the physical state of the brain, then this is not an issue: your consciousness is different in each branch in the MWI because the physical state of your brain is different in each branch.

If consciousness is not a matter of the physical state of your brain, then that is a separate issue that has nothing to do with which interpretation of QM you adopt.

 

[PeroK]

I think that very similar argument can be said about probabilities. Instead of wondering why particular outcome happens with predicted probability, in MWI we can wonder why my consciousness ended up in particular branch (say there are two branches with unequal weight) with predicted probability.
Only questions about consciousness are not really in domain of physics so we shift the question outside physics domain and we can pretend that physics part is just fine. Sounds a bit like cheating.

In classical physics, with the roll of a die for example, there is no mystery about why you can one outcome. Nor is there any real sense of the die being in a superposition before it is thrown.

 

[timmdeeg]

The wave-function collapse, I have to emphasize, is not optional. It is an observational requirement. We never observe a particle that is 50% here and 50% there. That’s just not a thing. If we observe it at all, it’s either here or it isn’t. Speaking of 50% probabilities really makes sense only as long as you are talking about a prediction.

If Hossenfelder's statement is true then I think the MWI fans have a problem, because they can't deny that outcomes are observed which then requires the wave-function collapse.

But is this statement true?

Any comments appreciated.

 

[zonde]

If consciousness is not a matter of the physical state of your brain, then that is a separate issue that has nothing to do with which interpretation of QM you adopt.

If in this context consciousness is not a matter of the physical state of your brain, then MWI is not an interpretation of QM but rather philosophical theory that just as well could be incompatible with philosophical basis of science, don't you agree?

 

[zonde]

I think the problem is this:

The wave-function collapse, I have to emphasize, is not optional. It is an observational requirement. We never observe a particle that is 50% here and 50% there. That’s just not a thing. If we observe it at all, it’s either here or it isn’t. Speaking of 50% probabilities really makes sense only as long as you are talking about a prediction.

If Hossenfelder's statement is true then I think the MWI fans have a problem, because they can't deny that outcomes are observed which then requires the wave-function collapse.

But is this statement true?

Yes, it's true. In science we have to have physical facts against which we compare our models and decide which models are discarded. If some observations are questioned then they have to be replaced with other observations that we could consider more reliable.

 

[entropy1]

What does it even mean to have fractions of different real outcomes?

Then again, what does 'real' mean anyway.

The way I see it is that a measurement outcome doesn't represent the wave function that was measured (unless the corresponding amplitude of the wavefunction is 1), and I guess I consider the wave function the whole story/whole reality. The amplitudes span the wavefunction as vectors. Outcomes don't because they get amplitude 1. So measurement outcomes don't represent the entire reality (the wavefunction ). One should be able to reconstruct the wavefunction from outcomes, but that is not so, except in ensembles where the examined wavefunction is reproduced many times.

 

[timmdeeg]

Yes, it's true.

Thanks.

So how would you comment this reasoning:

"If Hossenfelder's statement is true then I think the MWI fans have a problem, because they can't deny that outcomes are observed which then requires the wave-function collapse."

 

[zonde]

So how would you comment this reasoning:

"If Hossenfelder's statement is true then I think the MWI fans have a problem, because they can't deny that outcomes are observed which then requires the wave-function collapse."

MWI fans deny that objective outcomes are observed. Outcomes are subjective experience of "collapsed consciousness".
You can argue against MWI only using philosophical arguments that, while it might be true, it's a dead end in the aspect of gaining new knowledge about reality, like solipsism and superdeterminism. If MWI fan denies relevance of philosophical arguments you have no other grounds on which you can argue against MWI.

 

[DarMM]

Nicely put, okay, that makes sense to me. I guess that person $B$, before she looks at the detector, reasons that it is rational to assign $p\left(\omega\right) = 1/n$ for number of outcomes $n$ if the amplitudes in the original setup are equal. Otherwise, she adjusts her credence accordingly to the amplitudes $p\left(\omega\right) = |a(\omega)|^2$. Person $A$ I guess has to put himself in his copies' shoes but argues the same way.

ETA: This is Sean Carroll's version anyway, typo.

The difficulty is in justifying why she would adjust her credences to be $|a(\omega)|^2$ in the non-uniform case. That's essentially what all proofs of the Born Rule in MWI attempt to do, but none manage it in a way that is considered generally convincing in the Foundations community.

If you want to look into the attempted proofs fall into three rough classes. Frequency type proofs offered by de Witt and others that build on the work of Everett. Proofs based on a certain type of invariance under swapping of environmental states due to Zurek and the proofs based on decision theoretic arguments by Wallace and Deutsch.

 

[PeterDonis]

If in this context consciousness is not a matter of the physical state of your brain, then MWI is not an interpretation of QM but rather philosophical theory that just as well could be incompatible with philosophical basis of science, don't you agree?

If consciousness is not a matter of the physical state of your brain, then no theory of physics can account for your conscious experience. But this has nothing to do with whether the MWI is an interpretation of QM or a different theory; that depends only on whether the MWI makes different experimental predictions from standard QM. As MWI is currently formulated, it doesn't.

 

[Minnesota Joe]

The difficulty is in justifying why she would adjust her credences to be $|a(\omega)|^2$ in the non-uniform case. That's essentially what all proofs of the Born Rule in MWI attempt to do, but none manage it in a way that is considered generally convincing in the Foundations community.

If you want to look into the attempted proofs fall into three rough classes. Frequency type proofs offered by de Witt and others that build on the work of Everett. Proofs based on a certain type of invariance under swapping of environmental states due to Zurek and the proofs based on decision theoretic arguments by Wallace and Deutsch.

Yeah, I think the frequentist approach has all the problems that frequentism has in probability theory. I don't know anything about the invariance approach, thanks! The last approach is what Hossenfelder complains about at the end of her video and what David Albert addresses in his interview with Sean Carroll.

Meanwhile it seems like Carroll argues that, in the non-uniform case, you are forced to make the $|a(\omega)|^2$ choice to prevent future branching from changing the probabilities on parallel branches.

 

[Minnesota Joe]

But you are still going to have to "collapse" the wave function you use to predict your own probabilities for future measurement results. You might say the other branches of the wave function exist, but you won't actually calculate as if they exist; you will calculate as if your own branch is the only one that exists, because that's the only one you will use in your calculations. And doing that is not compatible with the Schrodinger Equation, because there is no "collapse" in the SE. The SE does not tell you to calculate using only one branch. It tells you to calculate using all the branches.

In other words, when the MWI says "collapse is only apparent and there is no contradiction with the Schrodinger Equation", it doesn't really mean that literally; it can't, since taking it literally leads you to calculate things that are contrary to what you actually observe.

Hmm. It doesn't mean literally? You mean they would agree that really there is Schrodinger equation violating collapse? Because they don't seem to, but I could be misunderstanding them.

It seems to me there is a distinction between the universal wave function collapsing and a branch-bound observer ignoring other current, non-interacting branches in order to describe future branches. But I don't know. And it's making my head hurt. An example would be appreciated.

 

[DarMM]

Yeah, I think the frequentist approach has all the problems that frequentism has in probability theory.

It's problems are separate technical ones related to certain limiting operators not converging.

I don't know anything about the invariance approach, thanks! The last approach is what Hossenfelder complains about at the end of her video and what David Albert addresses in his interview with Sean Carroll.

Carroll's proof is in the same class as the invariance proofs. The decision theoretic proofs are a bit different.

Meanwhile it seems like Carroll argues that, in the non-uniform case, you are forced to make the $|a(\omega)|^2$ choice to prevent future branching from changing the probabilities on parallel branches.

It doesn't work out as even other Many Worlds advocates have noted. See here:
http://philsci-archive.pitt.edu/14389/

 

[PeterDonis]

It seems to me there is a distinction between the universal wave function collapsing and a branch-bound observer ignoring other current, non-interacting branches in order to describe future branches.

There is according to the MWI, yes: the MWI says the universal wave function never collapses, and it also says that an observer who observes a particular measurement result can ignore all other branches except his own. The MWI has to say that because it's the only way to make it consistent with experiment.

The problem Hossenfelder is pointing out, as I understand it, is that admitting the latter claim, that an observer can ignore all branches other than his own, means the former claim, that the universal wave function never collapses, is untestable by definition, which makes it unscientific.

 

[Minnesota Joe]

Carroll's proof is in the same class as the invariance proofs. The decision theoretic proofs are a bit different.

That helps!

It doesn't work out as even other Many Worlds advocates have noted. See here:
http://philsci-archive.pitt.edu/14389/

Ugh, what a mess. I'm not sure what to think about that or what should be granted or challenged in Sean's description.

I'm just trying to understand the outline of the MWI argument and the motivation right now.

The claim seems to be that the Schrodinger equation describes a branching structure that introduces an uncertainty in your epistemic situation so that it makes sense to apply elementary probability theory to the branch structure at some stage so that you can derive the Born Rule which would justify your claim to having derived the Born Rule from only the Schrodinger equation and simpler stuff that everyone agrees with.

Sound right?

 

[timmdeeg]

The problem Hossenfelder is pointing out, as I understand it, is that admitting the latter claim, that an observer can ignore all branches other than his own, means the former claim, that the universal wave function never collapses, is untestable by definition, which makes it unscientific.

Sabine Hossenfelder claims [s. the OP]:

To "evaluate the probability relative to the detector in one specific branch at a time" is "logically entirely equivalent to the measurement postulate."

But isn't this claim not just Kopenhagen view? And if yes, so what? On the other side this reasoning seems too simple, so how would you comment on that?

 

[DarMM]

I'm just trying to understand the outline of the MWI argument and the motivation right now.

The claim seems to be that the Schrodinger equation describes a branching structure that introduces an uncertainty in your epistemic situation so that it makes sense to apply elementary probability theory to the branch structure at some stage so that you can derive the Born Rule which would justify your claim to having derived the Born Rule from only the Schrodinger equation and simpler stuff that everyone agrees with.

That is roughly claim as it was in the late 1990s. Problems include the fact that to derive the branching structure you need the Born rule, so to take a branching structure as given and then use it to derive a Born rule is already quite circular.

Thus most MWI people now try to get the branch structure out without using the Born rule. This has not succeeded yet. Thus it's not yet an interpretation of QM strictly speaking as it is unknown if it can real replicate the predictions.

 

[Minnesota Joe]

That is roughly claim as it was in the late 1990s. Problems include the fact that to derive the branching structure you need the Born rule, so to take a branching structure as given and then use it to derive a Born rule is already quite circular.

Thus most MWI people now try to get the branch structure out without using the Born rule. This has not succeeded yet. Thus it's not yet an interpretation of QM strictly speaking as it is unknown if it can real replicate the predictions.

Perhaps my phrasing was poor, because I don't understand this. The only thing MWI has is the Schrodinger equation. It's just a real wave equation to them. The branching comes through entanglement and decoherence which are features of the Schrodinger equation and matter. It isn't necessary to assume probability at this stage, just interaction. So the branching structure doesn't assume the Born Rule.

 

[DarMM]

Perhaps my phrasing was poor, because I don't understand this. The only thing MWI has is the Schrodinger equation. It's just a real wave equation to them. The branching comes through entanglement and decoherence which are features of the Schrodinger equation and matter. It isn't necessary to assume probability at this stage, just interaction. So the branching structure doesn't assume the Born Rule.

Decoherence requires the Born rule, it's not purely a feature of the Schrodinger equation .

 

[Minnesota Joe]

Sabine Hossenfelder claims [s. the OP]:

To "evaluate the probability relative to the detector in one specific branch at a time" is "logically entirely equivalent to the measurement postulate."

But isn't this claim not just Kopenhagen view? And if yes, so what? On the other side this reasoning seems too simple, so how would you comment on that?

This is why I muddied up your nice thread to show that there is different content to the claims of the MWI people. They are not evaluating the probability relative to the detector in a single branch and saying: the wave function collapses. So how is it "logically equivalent"?

I mean, maybe she is correct. But she doesn't elaborate enough for me in her video, post, or comment thread. She doesn't show how, necessarily, "evaluate the probability relative to the detector in one specific branch at a time" entails "the measurement problem".

And how can she? The measurement problem is that the Copenhagen Interpretation doesn't explain why we update our probability to 100%. It just says: do it. MWI tells you why this occurs.

I'm not defending MWI by the way, despite what it might seem like. I'm trying to understand the bloody thing. I just don't want to dismiss it as the same thing as the Copenhagen interpretation too hastily and not give MWI its due.

 

[DarMM]

And how can she? The measurement problem is that the Copenhagen Interpretation doesn't explain why we update our probability to 100%

I would say it doesn't say "how" the outcome of a measurement comes about. Why you update your probabilities is obvious, i.e. because that's the outcome you witnessed.

 

[Minnesota Joe]

Decoherence requires the Born rule, it's not purely a feature of the Schrodinger equation .

I don't think so. It is when macroscopic things (your detector) become entangled with everything else in its environment. So the wave evolves into a superposition of terms involving your detector. That evolution is described by the Schrodinger equation. No Born Rule is required, but we are talking about many particles and interaction potentials,etc.

 

[DarMM]

I don't think so. It is when macroscopic things (your detector) become entangled with everything else in its environment. So the wave evolves into a superposition of terms involving your detector. That evolution is described by the Schrodinger equation. No Born Rule is required, but we are talking about many particles and interaction potentials,etc.

It does. To derive decoherence you need to use tracing over subsystems. Tracing as an operation assumes the Born rule. Nielsen and Chuang's famous text probably has the best introductory exposition on this.

 

[Minnesota Joe]

I would say it doesn't say "how" the outcome of a measurement comes about. Why you update your probabilities is obvious, i.e. because that's the outcome you witnessed.

MWI explains why we would develop an interpretation of quantum mechanics that just gives up and asserts the collapse postulate. You might need Bohr, Pauli, and Heisenberg and a bad attitude too.

 

[Minnesota Joe]

It does. To derive decoherence you need to use tracing over subsystems. Tracing as an operation assumes the Born rule. Nielsen and Chuang's famous text probably has the best introductory exposition on this.

Decoherence doesn't require that we interpret the square magnitude of amplitudes as giving the probability of a result of measurement. There are amplitudes of course, but that just comes from solutions to the Schrodinger equation.

 

[DarMM]

MWI explains why we would develop an interpretation of quantum mechanics that just gives up and asserts the collapse postulate. You might need Bohr, Pauli, and Heisenberg and a bad attitude too.

The collapse postulate is just a form of Bayesian conditioning. Once you view QM as involving probability theory as Copenhagen does you're going to have the collapse postulate as you always update after witnessing an event.

For example the probability that a given dice roll occurred "collapses" upon learning the outcome was even, i.e. the probabilities update.

It's more the issue of how the outcome occurs rather than "Why collapse?"

 

[DarMM]

Decoherence doesn't require that we interpret the square magnitude of amplitudes as giving the probability of a result of measurement. There are amplitudes of course, but that just comes from solutions to the Schrodinger equation.

That's not related to what I'm saying. I'm saying that decoherence requires the Born rule due to the use of the tracing operation which itself assumes the Born rule.

 

[Minnesota Joe]

That's not related to what I'm saying. I'm saying the decoherence requires the Born rule due to the use of the tracing operation which itself assumes the Born rule.

Okay, maybe we are victims of physics jargon. What Born Rule are you talking about?

ETA: I'm specifically referring to Max Born's 1926 probabilistic interpretation of the wave function.

 

[DarMM]

Okay, maybe we are victims of physics jargon. What Born Rule are you talking about?

ETA: I'm specifically referring to Max Born's 1926 probabilistic interpretation of the wave function amplitudes.

That's what I'm referring to ultimately as well. Though for decoherence you can't just use wave functions you need density matrices. In it's most general form that the probability for some event represented by a POVM element $E$ is $Tr(\rho E)$ with $\rho$ the state.