Why is there no consensus about the meaning of probability in MWI?

[PeterDonis]

In the MWI there is a branching into "worlds" where a world is isolated from the other worlds that make up the wavefunction.

Yes.

Then the probability of something happening or being observed after measurement is literally just,

# of worlds with outcome A / total # of worlds.

No, it isn't. Every possible outcome happens. So the probability of any outcome with a nonzero amplitude in the wave function happening is ##1##. It doesn't matter what the weight of that particular outcome is, since that weight makes no difference to whether the outcome happens or not. It always happens as long as there is any nonzero weight at all.

In any particular world, you can formulate a notion of "probability" of something happening based on its relative frequency in that world. But that's not the same thing as the ratio you give. This is one of the key issues with formulating a concept of probability in the MWI, and has been discussed in the literature for decades with no resolution.

 

[pines-demon]

No, it isn't. Every possible outcome happens. So the probability of any outcome with a nonzero amplitude in the wave function happening is ##1##. It doesn't matter what the weight of that particular outcome is, since that weight makes no difference to whether the outcome happens or not. It always happens as long as there is any nonzero weight at all.

In any particular world, you can formulate a notion of "probability" of something happening based on its relative frequency in that world. But that's not the same thing as the ratio you give. This is one of the key issues with formulating a concept of probability in the MWI, and has been discussed in the literature for decades with no resolution.

We have discussed it and I see how it could be a definitional issue, but is it a point of non-consensus though? Does criticism in literature centers about this? Clearly this is no point of conflict between MWI advocates so I guess it is brought by detractors?

 

[PeterDonis]

is it a point of non-consensus though? Does criticism in literature centers about this?

It is one of multiple points that are not resolved in the literature.

Clearly this is no point of conflict between MWI advocates

Yes, it is. That's part of the problem: even MWI advocates don't all agree on these questions.

 

[PeterDonis]

either Carroll isn't doing that

As far as I can tell from Carroll's "self-locating uncertainty" paper, he isn't. His approach there is different.

 

[pines-demon]

It is one of multiple points that are not resolved in the literature.


Yes, it is. That's part of the problem: even MWI advocates don't all agree on these questions.

Could you provide some sources about this criticism? From what I can read from Wikipedia or Carroll's differences between MWI proposals are not based at all on the problem of branch counting being an issue. What seems to matter is if their respective ways of counting really derive the Born rule or not.

 

[gentzen]

No, it isn't. Every possible outcome happens. So the probability of any outcome with a nonzero amplitude in the wave function happening is ##1##.

is it a point of non-consensus though?

It is one of multiple points that are not resolved in the literature.

Clearly this is no point of conflict between MWI advocates

Yes, it is. That's part of the problem: even MWI advocates don't all agree on these questions.

Can you provide a quote from any MWI advocate saying that "the probability of any outcome with a nonzero amplitude in the wave function happening is ##1##"? Why should a MWI advocate use the word "probability" in that way?

 

[PeterDonis]

Could you provide some sources about this criticism.

I think some have already been given in this thread, in the form of papers by different MWI proponents saying different, incompatible things.

 

[PeterDonis]

Can you provide a quote from any MWI advocate saying that "the probability of any outcome with a nonzero amplitude in the wave function happening is ##1##"?

Of course not, because MWI advocates, when they discuss this aspect at all, avoid pointing out the obvious fact that all outcomes happen in the MWI. They avoid pointing it out precisely because it would invite the reader to make the observation I made, and that would undermine MWI advocates' attempts to formulate a meaningful concept of probability. At least, that's my skeptical take on it. If you want an MWI advocate's take on it, you would need to ask them: but ask them how the probability of any outcome can be anything except ##1## when the MWI says all outcomes are guaranteed to happen.

 

[pines-demon]

I think some have already been given in this thread, in the form of papers by different MWI proponents saying different, incompatible things.

Sure but being incompatible does not mean that they are being incompatible due to your argument.

I sincerely think that we either need to dig into the sources or let this thread end. I am no longer even sure that the question of the thread is justified by the sources.

 

[pines-demon]

Of course not, because MWI advocates, when they discuss this aspect at all, avoid pointing out the obvious fact that all outcomes happen in the MWI. They avoid pointing it out precisely because it would invite the reader to make the observation I made, and that would undermine MWI advocates' attempts to formulate a meaningful concept of probability. At least, that's my skeptical take on it. If you want an MWI advocate's take on it, you would need to ask them: but ask them how the probability of any outcome can be anything except ##1## when the MWI says all outcomes are guaranteed to happen.

Usually good academic papers tend to point out the different arguments against them. Carroll's does that but not this point in specific. Maybe that argument is found elsewhere in critics of MWI.

 

[PeterDonis]

dig into the sources

As I have commented before, the sources go back decades. The ones dating from before decoherence theory was developed are less useful because they don't take that into account. But even the ones since still cover at least 3 decades. There is a lot of literature on this topic.

 

[jbergman]

No, it isn't. Every possible outcome happens. So the probability of any outcome with a nonzero amplitude in the wave function happening is ##1##. It doesn't matter what the weight of that particular outcome is, since that weight makes no difference to whether the outcome happens or not. It always happens as long as there is any nonzero weight at all.

Sure, everything happens. But I don't think that invalidates the probability definition I gave.

You can think of it likes this. Each observer after measurement, will only be able to see the outcome in their world. So the probability measures the fraction of observers who will experience outcome A. It's not that complicated.

The much harder part is to move from equal probability situations to unequal ones.

 

[PeterDonis]

everything happens. But I don't think that invalidates the probability definition I gave.

And there are MWI proponents who agree with you. But there are also ones who don't. And of course there are plenty of MWI skeptics (including me) who don't. So, as with anything to do with QM interpretations, this comes down to a difference of opinion. Neither side can convince the other because there is no way to settle the question by experiment: both sides make the same predictions for all experimental results.

 

[jbergman]

Sure but being incompatible does not mean that they are being incompatible due to your argument.

I sincerely think that we either need to dig into the sources or let this thread end. I am no longer even sure that the question of the thread is justified by the sources.

Agree. I think most accept the definition of probability in Many Worlds. David Albert is one I know who objects, though.

 

[PeterDonis]

Each observer after measurement, will only be able to see the outcome in their world.

Yes.

So the probability measures the fraction of observers who will experience outcome A.

But no observer can ever measure this. So on this view nobody ever measures the probability of outcome A. Which makes this definition useless.

 

[jbergman]

And you will find MWI proponents who agree with you. But there are also ones who don't. And of course there are plenty of MWI skeptics (including me) who don't. So, as with anything to do with QM interpretations, this comes down to a difference of opinion. Neither side can convince the other because there is no way to settle the question by experiment: both sides make the same predictions for all experimental results.

I consider myself and MWI skeptic but for different reasons. I don't understand a physical justification for the measure assigned to worlds for the exact reasons you brought up before, i.e. what is the justification of introducing additional state to give the needed number of worlds to get the right probabilities.

 

[jbergman]

But no observer can ever measure this. So on this view nobody ever measures the probability of outcome A. Which makes this definition useless.

You can measure by making multiple measurements under the assumption your world assignment is random.

 

[gentzen]

It makes it clear that you don't intent to give references which support your claim. What is still unclear is whether you intent to give reasons or arguments for your claim beyond "(and rather obviously so)".

Lighten up! You asked for an opinion about your own inference about my personal view. I opined that it was probably valid. That means nothing more than I think you have correctly understood me.

I am simply pointing out that saying "and rather obviously so" without any supporting arguments is a bit disappointing in a discussion like this.

To remind you: I claimed that a world-counting argument to derive probabilities is only valid if the worlds have equal probabilities a priori. I am not sure what sort of reference would back that up. Perhaps a link to a Wiki article about logical thinking?

Your logical thinking is fine, but your rhetorics (the art of persuasion) has room for improvement.
So your argument is that the principle of indifference cannot be applied in cases where there obviously is a difference. This seems to be a good argument against some of the misguided stuff that came up during this discussion. I think you (or someone else) made that argument before, and I liked that post. But apparently not, because I am unable to find that post again.

I was hoping for a simple convincing argument why trying to reduce all probabilities in MWI to the case of equal probabilities is misguided. My argument was an elaboration of my reaction to your disagreement with Peter Donis about "nonzero amplitude" for flying pigs

I've already told you: I don't think the wave function has a nonzero amplitude for what you're claiming. It's up to you to show that it does, since you are the one that made the claim about flying pigs. You have already agreed with me that a nonzero amplitude in the wave function for such a transition is necessary to support your claim. So it's up to you to show that in fact such a nonzero amplitude exists. You can't just assume that there is a nonzero amplitude for anything you like.

namely that focusing on "nonzero" vs "exactly zero" is not a robust way to look at things.

Which counting arguments? Some are obviously wrong, others appear to be perfectly valid.

The counting arguments which try to reduce all probabilities in MWI to the case of equal probabilities.

You see, I had hoped for a "MWI proponent" that could engage in discussions like

Of course not, because MWI advocates, when they discuss this aspect at all, avoid pointing out the obvious fact that all outcomes happen in the MWI. They avoid pointing it out precisely because it would invite the reader to make the observation I made, and that would undermine MWI advocates' attempts to formulate a meaningful concept of probability. At least, that's my skeptical take on it.

and come up with convincing arguments for the MWI side. My arguments go along the line of "do you have a reference for this?", but of course that is normally hardly convincing.

 

[kered rettop]

I sincerely think that we either need to dig into the sources or let this thread end. I am no longer even sure that the question of the thread is justified by the sources.

The fact that you have cluttered up the thread with inconclusive side-issues, doesn't mean it should be closed. If anyone has the right get it closed it would be the OP, viz me. Please recall that as soon as PeterDonis answered, I said I wanted to digest his answer properly before answering. I haven't done so yet but as far as know there is no forum requirement to do so within a time limit measured in days. Isn't the subject difficult enough without having people trying to veto it? If you want to terminate your off-topic subthread, feel free, but please don't try to scupper my attempt to understand the issue.

 

[pines-demon]

The fact that you have cluttered up the thread with inconclusive side-issues, doesn't mean it should be closed.

If you want to terminate your off-topic subthread, feel free, but please don't try to scupper my attempt to understand the issue.

Which side-issues? I have tried to stay on topic.

If anyone has the right get it closed it would be the OP, viz me. Please recall that as soon as PeterDonis answered, I said I wanted to digest his answer properly before answering. I haven't done so yet but as far as know there is no forum requirement to do so within a time limit measured in days. Isn't the subject difficult enough without having people trying to veto it?

I agree, please be free to continue the discussion or specify what you are not getting. I just feel that we are repeating the same arguments.

As the OP why do you think there is no consensus on the meaning of probability in MWI? What made you think that? What do you mean by "meaning"? Is it that people define different probabilities? or is it that nobody can agree that even probabilities can be made? By consensus, you mean consensus between MWI advocates or all physicists?

Sources on that problem/motivation are welcome.
Edit: to be clear I said dig into the sources or end it, but it was mostly to motivate the former not the latter

 

[PeterDonis]

You can measure by making multiple measurements under the assumption your world assignment is random.

But your world assignment isn't random. It is determined by the sequence of measurement results you observe, and each measurement deterministically produces all possible results. There is no randomness anywhere. Once you specify what measurements are to be made and in what order, you have completely specified what is in every resulting world. There is no room for any random selection.

 

[PeterDonis]

focusing on "nonzero" vs "exactly zero" is not a robust way to look at things

We don't have to consider any of the outlandish cases you mention, where this becomes an issue. Even if we just limit ourselves to measurements on qubits where there are finite but unequal weights (say 1/3 and 2/3), all of the issues we are discussing are already in play.

 

[PeterDonis]

there is no forum requirement to do so within a time limit measured in days

That is correct.

 

[pines-demon]

Agree. I think most accept the definition of probability in Many Worlds. David Albert is one I know who objects, though.

Can you provide a source or comment on his view? this might help the conversation.

 

[gentzen]

We don't have to consider any of the outlandish cases you mention, where this becomes an issue. Even if we just limit ourselves to measurements on qubits where there are finite but unequal weights (say 1/3 and 2/3), all of the issues we are discussing are already in play.

Do you have a "simple convincing argument why trying to reduce all probabilities in MWI to the case of equal probabilities is misguided"? My argument (for why this is misguided) doesn't work at all for simple fractions like 1/3 and 2/3, and would not be very convincing for "nearly" simple fractions like (1+ϵ)/3 and (2-ϵ)/3. That is why I focused on the outlandish cases.

 

[kered rettop]

I am simply pointing out that saying "and rather obviously so" without any supporting arguments is a bit disappointing in a discussion like this.

No, you asked for references to support a point of logic.

Your logical thinking is fine, but your rhetorics (the art of persuasion) has room for improvement.

Ha! When I want lessons on the art of persuasion, I'll be sure to let you know. To be honest this thread is about convincing me, my views are actually off-topic.

Enough of this banter! Let's get back to some physics and see whether it's relevant. Deal?

So your argument is that the principle of indifference cannot be applied in cases where there obviously is a difference. This seems to be a good argument against some of the misguided stuff that came up during this discussion. I think you (or someone else) made that argument before, and I liked that post. But apparently not, because I am unable to find that post again.

Could be #90

I was hoping for a simple convincing argument why trying to reduce all probabilities in MWI to the case of equal probabilities is misguided.

Let me clear this up. Decomposing a state into orthonormal equiprobable microstates is key to deriving the Born Rule. So my own view is that it is the very opposite of miguided. Messing around creating any other decomposition is misguided in this context.

you: You see, I had hoped for a "MWI proponent" that could engage in discussions like

" Of course not, because MWI advocates, when they discuss this aspect at all, avoid pointing out the obvious fact that all outcomes happen in the MWI. They avoid pointing it out precisely because it would invite the reader to make the observation I made, and that would undermine MWI advocates' attempts to formulate a meaningful concept of probability. At least, that's my skeptical take on it." - PeterDonis

you: and come up with convincing arguments for the MWI side. My arguments go along the line of "do you have a reference for this?", but of course that is normally hardly convincing.

Well, I am not really a proponent. I can play Devil's Advocate but you'll only get my take on it. And I adamantly refuse to use an argument from authority. That said, I don't see anyone else here doing it so maybe "needs must when the devil drives". But only so far as saying "this seems to make sense to me", not polemically defending it a claim.

The correct reponse is then "no, you're going wrong here" not "give us reference!"

So where's the physics? I could tell you whether I think that PeterDonis's argument makes sense, but do you really have to ask?

Sorry about the formatting. Bring back Usenet I say!

 

[kered rettop]

As the OP why do you think there is no consensus on the meaning of probability in MWI? What made you think that?

Umm, that would be PeterDonis's assertion in another thread.

 

[PeterDonis]

Do you have a "simple convincing argument why trying to reduce all probabilities in MWI to the case of equal probabilities is misguided"?

No, because that's not the argument I was referring to. The argument I was referring to is that we can "count worlds" by the relative weights of terms in the wave function. That argument, if it is valid at all, has to hold even for simple cases of unequal weightings.

The simple argument for why it is wrong to "count words" by relative branch weights is that the number of branches in the wave function, which is the number of worlds, is not the same as the relative weights of the branches.

 

[kered rettop]

I consider myself and MWI skeptic but for different reasons. I don't understand a physical justification for the measure assigned to worlds for the exact reasons you brought up before, i.e. what is the justification of introducing additional state to give the needed number of worlds to get the right probabilities.

You don't do that. It is a gross misrepresentation of how MWI works. For a start you don't strictly count "worlds" at all. You count orthogonal microstates. And you don't introduce "additional states to give the needed number of worlds to get the right probabilities". You introduce additional decoherence until the number of microstates is big enough for the next step in the argument to be valid. It's not even a mathematical sleight-of-hand. It is a physical process which continues indefinitely but is complete, for all practical purposes, in less than an attosecond for ordinary objects.

 

[PeterDonis]

For a start you don't strictly count "worlds" at all. You count orthogonal microstates.

The standard MWI terminology as I understand it is that "worlds" are decoherent branches of the wave function. Is that what you mean by "orthogonal microstates"?

 

[kered rettop]

As far as I can tell from Carroll's "self-locating uncertainty" paper, he isn't. His approach there is different.

I should hope not too. So we are actually discussing something that does not exist. This is getting surreal.

The standard MWI terminology as I understand it is that "worlds" are decoherent branches of the wave function. Is that what you mean by "orthogonal microstates"?

No. I mean the components in a sum-of-products decomposition of such a branch.

 

[PeterDonis]

I mean the components in a sum-of-products decomposition of such a branch.

I don't understand what this means. Can you give either a reference or an example?

 

[kered rettop]

I don't understand what this means. Can you give either a reference or an example?

Sure. But not tonight.

 

[romsofia]

Can you provide a source or comment on his view? this might help the conversation.

There is a book called, "Many Worlds?: Everett, Quantum Theory, & Reality" in which a whole section is for critical replies, and his essay is included titled 'Probability in the Everett Picture', which you can find some of their talks here if you'd rather listen: https://vimeo.com/user1742588 (David Albert's own talk on probability is here: )

Or, check out https://philsci-archive.pitt.edu/22650/ page 15 he gives citations for both defenders, and critics.

 

[jbergman]

But your world assignment isn't random. It is determined by the sequence of measurement results you observe, and each measurement deterministically produces all possible results. There is no randomness anywhere. Once you specify what measurements are to be made and in what order, you have completely specified what is in every resulting world. There is no room for any random selection.

It's a fair point and not easily rebutted. I would have to understand better Carroll's notion of self-locating uncertainty, I think, to counter what you wrote here.

Still, it instinctually feels right to me to consider this a random process where before the measurements I won't know which of the branches I will end up on. Yes, I will end up on all of them but each version of me will have only experienced one of them and doesn't know which beforehand. A bit of a paradox.