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

[PeterDonis]

an observer at the end of the branches cannot interact or see other branches.

Yes.

This observer is no longer the same themselves that ended in the other branches.

In one sense this is true, since the observer in each branch observes a different outcome. But they all have an equal claim to be "the same observer" as before the branching; there is nothing that picks out any particular one as "the" observer. In particular, there is no "random choice" that marks one as "real" or "preferred" as compared to the others.

 

[pines-demon]

In one sense this is true, since the observer in each branch observes a different outcome. But they all have an equal claim to be "the same observer" as before the branching; there is nothing that picks out any particular one as "the" observer. In particular, there is no "random choice" that marks one as "real" or "preferred" as compared to the others.

So? Most of these observers get results that map correctly to the predictions of quantum mechanics. That is what matters. If they are "the same" themselves (whatever that means) as before the branching is not very relevant here.

 

[pines-demon]

@PeterDonis Maybe this example would help:
Bob ask his students, who have a state $\sqrt{3}|0\rangle+|1\rangle$ (up to normalization), "what do you think it is the result that you would get after measurement?". Then we get that:

• Copenhagen Alice, would say: 0 with 75% probability and 1 with 25% probability
• MWI-advocate Alice would have to say: both!

I would argue that MWI Alice is right with respect to the terminology, but that is semantics, I do not think it is of much relevance. If MWI Alice wants to be pragmatic and become predictive she could say something like 75% of the outcomes are going to be 0. The distribution of results maps to the predictions of QM, you can call it probability or something else if you prefer.

 

[PeterDonis]

Most of these observers get results that map correctly to the predictions of quantum mechanics.

"Most" is subjective. So is "map correctly", since we are talking about statistical comparisons.

But leaving that aside, if you are going to say that "probability" in the MWI means "relative frequencies of observed outcomes in a particular world (i.e., decoherent branch of the wave function)", then you are defining "probability" so that you can adopt the Born Rule as an additional postulate and using a version of the "MWI" that includes that additional postulate. But MWI proponents don't do that. They claim they can derive the Born Rule in the MWI without having to assume it as an additional postulate. And they can't do that by defining "probability" to mean "relative frequencies of observed outcomes in a particular world", because then their claimed "derivation" of the Born Rule would be circular. They have to come up with some independent formulation of the concept of "probability" in the MWI that doesn't depend on relative frequencies of observed outcomes in a particular world, and then use that to derive the Born Rule.

If they are "the same" themselves (whatever that means) as before the branching is not very relevant here.

If it's not very relevant, why did you go to the trouble of making a claim about it?

That said, I agree the question of whether observers are "the same" before and after branching is indeed irrelevant to formulating a concept of probability in the MWI. But in the posts I was responding to (by others, not by you), claims were made about "random selection" of which outcome an observer observes. Getting clear about exactly what "an observer" means (and doesn't mean) in this context is relevant to rebutting those claims, which is what I was doing. You, as far as I can tell, have not made those claims, so you might not be making the same conceptual mistakes the other posters I was responding to were making.

 

[PeterDonis]

I would argue that MWI Alice is right with respect to the terminology

Yes! She is. And if the MWI is true, Copenhagen-Alice is wrong. That is what the MWI says.

but that is semantics, I do not think it is of much relevance.

No, it's not just "semantics", and it is extremely relevant. The MWI says Copenhagen-Alice is wrong. But then MWI proponents try to construct a notion of "probability" that lets Copenhagen-Alice be right. But they can't have it both ways.

If MWI Alice wants to be pragmatic and become predictive she could say something like 75% of the outcomes are going to be 0.

No, she can't. There are only two outcomes, 0 and 1. The only "percentage of outcomes" that makes sense here is 50% for each--but that is true regardless of the relative weights of the outcomes in the wave function. This is why @PeroK and others have repeatedly pointed out that any notion of "probability" in the MWI that depends on relative weights of outcomes breaks down as soon as the weights are unequal.

 

[kered rettop]

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. That doesn't mean I wish to make or defend any claim. I started this thread to ask a question, not to engage in polemics. 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?

For me, one reason to be suspicious of that counting of equally likely scenarios is that this runs into robustness issues again with very small probabilities like 10^-1000. You would have to construct a correspondingly huge amount of equally likely scenarios. But the very existence of such scenarios would imply an entropy much larger than physically reasonable. In fact, that entropy could be forced to be arbitrarily large.

Only in a system with infinite degrees of freedom, otherwise the entropy has an upper limit. The "number of possible states" required for the entropy calculation is exactly the same as the limit on the number of possible scenarios in world-counting done correctly.

But you sound like you know a more obvious way to see why those counting arguments are a bad idea.

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

 

[pines-demon]

But leaving that aside, if you are going to say that "probability" in the MWI means "relative frequencies of observed outcomes in a particular world (i.e., decoherent branch of the wave function)", then you are defining "probability" so that you can adopt the Born Rule as an additional postulate and using a version of the "MWI" that includes that additional postulate. But MWI proponents don't do that. They claim they can derive the Born Rule in the MWI without having to assume it as an additional postulate. And they can't do that by defining "probability" to mean "relative frequencies of observed outcomes in a particular world", because then their claimed "derivation" of the Born Rule would be circular. They have to come up with some independent formulation of the concept of "probability" in the MWI that doesn't depend on relative frequencies of observed outcomes in a particular world, and then use that to derive the Born Rule.

I agree, some MWI proponents (not Vaidman) claim that they can rederive the Born rule. However it is circular to postulate Born rule and use it as the weight rule. But again I was trying to ground this to the problem of probability and not on the Born rule as OP suggested.

If it's not very relevant, why did you go to the trouble of making a claim about it?

You have said similar things before but I do not know what was the point there.

That said, I agree the question of whether observers are "the same" before and after branching is indeed irrelevant to formulating a concept of probability in the MWI. But in the posts I was responding to (by others, not by you), claims were made about "random selection" of which outcome an observer observes. Getting clear about exactly what "an observer" means (and doesn't mean) in this context is relevant to rebutting those claims, which is what I was doing. You, as far as I can tell, have not made those claims, so you might not be making the same conceptual mistakes the other posters I was responding to were making.

Great that we agree.

No, it's not just "semantics", and it is extremely relevant. The MWI says Bob is wrong. But then MWI proponents try to construct a notion of "probability" that lets Bob be right. But they can't have it both ways.

In that example Bob is just asking "what do you get". But yeah Copenhagen Alice is wrong according to MWI Alice.

No, she can't. There are only two outcomes, 0 and 1. The only "percentage of outcomes" that makes sense here is 50% for each--but that is true regardless of the relative weights of the outcomes in the wave function. This is why @PeroK and others have repeatedly pointed out that any notion of "probability" in the MWI that depends on relative weights of outcomes breaks down as soon as the weights are unequal.

We almost agreed in what we meant but this. Earlier somebody posted a pdf with Sean Carroll's derivation of the probabilities (he claims it derives Born rule but I remain unconvinced as anyone else). In that Carroll just postulates several additional pseudo-worlds in such a way that there are 3 times more worlds with 0 than with 1. So 75% are 0 and the rest 1, as my MWI Alice says.

 

[PeterDonis]

In that Carroll just postulates several additional pseudo-worlds

Yes, which I find unconvincing, to say the least. There are no "pseudo-worlds" in the math, and the math is supposed to be the ultimate basis for any interpretation.

 

[pines-demon]

Yes, which I find unconvincing, to say the least. There are no "pseudo-worlds" in the math, and the math is supposed to be the ultimate basis for any interpretation.

Sure it is unconvicing if you wanted to derive the Born rule from MWI. Yet it works as a valid way to get a distribution of outcomes. That's all the point I was trying to make. If you want to avoid calling that "probability" I may agree but I hope it answers the question of OP.

 

[PeterDonis]

it works as a valid way to get a distribution of outcomes

"Valid" in what sense?

 

[pines-demon]

"Valid" in what sense?

It provides you a distribution of outcomes that can be compared with the predictions of usual QM. It may match or not match the predictions depending on what you assume are the weights (again in Carroll's sense of weights).

 

[kered rettop]

Sure it is unconvicing if you wanted to derive the Born rule from MWI. Yet it works as a valid way to get a distribution of outcomes. That's all the point I was trying to make. If you want to avoid calling that "probability" I may agree but I hope it answers the question of OP.

It does not!

 

[pines-demon]

It does not!

In QM interpretations, one can only hope

 

[PeterDonis]

It provides you a distribution of outcomes that can be compared with the predictions of usual QM.

No, it doesn't. The "distribution of outcomes" that we measure (in the context of the MWI) is relative frequencies in one world. It is not the relative weightings of different worlds in the wave function. So any claim about "distribution" that involves relative weightings is irrelevant to comparing our measurements with predictions. I pointed this out a while ago in the thread.

 

[pines-demon]

No, it doesn't. The "distribution of outcomes" that we measure (in the context of the MWI) is relative frequencies in one world. It is not the relative weightings of different worlds in the wave function. So any claim about "distribution" that involves relative weightings is irrelevant to comparing our measurements with predictions. I pointed this out a while ago in the thread.

I know that you are unconvinced but see it this way, if they repeat the experiment many times, for most observers at the end of the branch in a given world, both their past branch frequencies and the weights for the different branches for a given future measurement will agree.

 

[kered rettop]

It provides you a distribution of outcomes that can be compared with the predictions of usual QM.

Exactly. If it looks like probability and quacks like probabiity then it...
... isn't probability, duh!

It may match or not match the predictions depending on what you assume are the weights (again in Carroll's sense of weights).

Well, there shouldn't be any assumption, other than that the probabilities are equal. The thing is - and I think I may have to set up a hotkey to write this, it comes up so often - to derive a probability rule using counting, you have to add the microstates i.e. their amplitude vectors, and add the unknown but equal probabilities. It's not hard. If the microstates arise because of decoherence, they are orthogonal and the Born Rule jumps right out. Carroll's psuedo-branches are not orthogonal, in fact they are parallel. But the outcomes are not independent, they are 100% correllated. You have to use the rule for combining correlated probabilities. And that's assuming you can find a meaning for probability that includes psuedo-branches.

 

[PeterDonis]

see it this way

The argument you are making here has been made in the literature by multiple people, going back, IIRC, some decades. I am not the only one who is not convinced by it. In any case, it is not something we are going to resolve here. Putting the various viewpoints on record here is fine, but we should not expect to actually reach a resolution when the community as a whole has not done so despite discussing this for far longer than we have here.

 

[pines-demon]

The argument you are making here has been made in the literature by multiple people, going back, IIRC, some decades. I am not the only one who is not convinced by it. In any case, it is not something we are going to resolve here. Putting the various viewpoints on record here is fine, but we should not expect to actually reach a resolution when the community as a whole has not done so despite discussing this for far longer than we have here.

I was trying to contest the general idea that probabilities cannot be defined. Putting that term probability aside, there are proposals to do get different distributions that can be compared with usual QM. This last part that does not seem to be a huge point of disagreement between the advocates of MWI. What seems to be a problem is if those proposals derive the Born rule (I am far from being the only one that has arrived to this conclusion here). Anyway, outside advocates of MWI, I do agree that sources disagree in many things.

 

[pines-demon]

Well, there shouldn't be any assumption, other than that the probabilities are equal. The thing is - and I think I may have to set up a hotkey to write this, it comes up so often - to derive a probability rule using counting, you have to add the microstates i.e. their amplitude vectors, and add the unknown but equal probabilities. It's not hard. If the microstates arise because of decoherence, they are orthogonal and the Born Rule jumps right out. Carroll's psuedo-branches are not orthogonal, in fact they are parallel. But the outcomes are not independent, they are 100% correllated. You have to use the rule for combining correlated probabilities. And that's assuming you can find a meaning for probability that includes psuedo-branches.

Not sure I am following. I will answer to a few things. As I read it from the pdf, I think the pseudo-branches are indeed orthogonal (do not ask me to justify that!). I am also avoiding to discuss "probabilities" as it seems to convey a specific nuance that I have not been able to narrow down in this conversation.

 

[PeterDonis]

I was trying to contest the general idea that probabilities cannot be defined.

Yes, and as I said, that debate has been ongoing in the literature for decades now. Your point of view certainly has proponents in the literature, but it also has opponents. The issue is still open.

 

[PeterDonis]

s I read it from the pdf, I think the pseudo-branches are indeed orthogonal

No, they're not, because they are all associated with the same outcome (and in fact "they" are just one actual branch, which can't possibly be orthogonal to itself--that's mathematically impossible).

 

[PeterDonis]

I am also avoiding to discuss "probabilities"

Then I am very confused about why you are even posting in this thread, which, as its title explicitly says, is about the meaning of probability in the MWI.

 

[pines-demon]

Yes, and as I said, that debate has been ongoing in the literature for decades now. Your point of view certainly has proponents in the literature, but it also has opponents. The issue is still open.

Sure but that does not say much, that's why we are exploring those issues.

No, they're not, because they are all associated with the same outcome (and in fact "they" are just one actual branch, which can't possibly be orthogonal to itself--that's mathematically impossible).

Read the pdf, see the probabilities that they get and make you own mind about the orthogonality. These seem to be different branches with similar results. Postulate a hidden quantum number if you will, again it is worked out to reobtain the Born rule.

Then I am very confused about why you are even posting in this thread, which, as its title explicitly says, is about the meaning of probability in the MWI.

I have explained what I meant by it, that is to provide some measure that can be compared with QM. I just trying to formulate something pragmatic, I do not want to enter into these ontic-epistemic debates just by saying the term, I leave that to you.

 

[PeterDonis]

Read the pdf

I have. Its argument has, again, been made in the literature multiple times over decades, and has not resolved the issue (and, as I've said, I don't find it convincing). The reference is given and readers can make up their own minds.

 

[pines-demon]

I have. Its argument has, again, been made in the literature multiple times over decades, and has not resolved the issue (and, as I've said, I don't find it convincing). The reference is given and readers can make up their own minds.

To be clear I am not necessarily inviting you to adhere to it. In this specific exchange I was just trying to clarify a remark by another user related to the paper. Let us not dig too much into the intricacies of the paper.

 

[jbergman]

Yes. But that doesn't mean "we" only observe one world, because "we" are in every world, and the "we" in every world believe that "our" observations are of only one world.

You smuggled a lot of hidden assumptions in this comment, i.e., that we are a single entity after branching.

I know Carroll doesn't espouse this view and instead argues that after branching we are effectively different agents. If you take the point of view you are espousing then there is only the wave function. But as emergent concepts in the classical realm, me and another version of me on a different branch are completely different entities, IMO. This can be made more precise by appealing to decoherence.

 

[PeterDonis]

that we are a single entity after branching

I made no such assumption. In at least one other post (not in response to you) I acknowledged that after the branching, each "we" is different to the extent that "we" have observed a different measurement outcome. I also said that no "we" is privileged over any other; they are all on the same footing and they all have the same "we" before branching in their past. When I talked about the "we" in every world, in what you quoted, that was all I meant.

If you take the point of view you are espousing

I'm not. See above.

there is only the wave function.

There is only the wave function in the MWI. That and the dynamics of the wave function always being unitary (no collapse) are the MWI's primary features. There isn't some other version of the MWI where there is something else in addition to the wave function. The wave function is all there is in the MWI.

me and another version of me on a different branch are completely different entities, IMO. This can be made more precise by appealing to decoherence.

Sure, decoherence is what defines "branching" in the MWI (more precisely, it cleared up what used to be a serious missing piece of the MWI, namely what did define "branching"). That doesn't contradict anything I said above or in my previous posts.

 

[kered rettop]

Done.

It's still there!

 

[kered rettop]

Yes, which I find unconvincing, to say the least. There are no "pseudo-worlds" in the math, and the math is supposed to be the ultimate basis for any interpretation.

I kind of agree except I would say that they cannot be treated the same way as worlds in a world-counting derivation of the Born Rule. Therefore either Carroll isn't doing that, or he has made a giant mistake, or my assertion is wrong.

 

[pines-demon]

I kind of agree except I would say that they cannot be treated the same way as worlds in a world-counting derivation of the Born Rule. Therefore either Carroll isn't doing that, or he has made a giant mistake, or my assertion is wrong.

Nobody is denying that it is an unconvincing way to get the Born rule, is cooked that way. Also to be fair, that pdf is not exactly Carroll's. He does not call them pseudo-branches, here is Carroll's take (see section 3.2):

https://arxiv.org/pdf/1405.7577.pdf

 

[kered rettop]

The argument you are making here has been made in the literature by multiple people, going back, IIRC, some decades. I am not the only one who is not convinced by it. In any case, it is not something we are going to resolve here. Putting the various viewpoints on record here is fine, but we should not expect to actually reach a resolution when the community as a whole has not done so despite discussing this for far longer than we have here.

It would be nice to know why they cannot reach consensus though. Perhaps someone should start a thread on it.

 

[PeterDonis]

It's still there!

Not the post where you used the words "SEP definition" and then cut it off. That's been deleted.

If there is some other post you meant, please give me its number.

 

[PeterDonis]

It would be nice to know why they cannot reach consensus though.

I don't think there is even consensus on that. That can be expected to happen when you are dealing with questions that cannot be resolved by experiment, in a domain where what can be resolved by experiment is highly counterintuitive and is known not to have any simple resolution that meets our natural classical expectation.

 

[jbergman]

For me it's relatively straightforward. In the MWI there is a branching into "worlds" where a world is isolated from the other worlds that make up the wavefunction.

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

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

The harder part is to pin down what exactly are the worlds.

 

[kered rettop]

I don't think there is even consensus on that.

So it would seem, assuming PF users are representative. Still, putative explanations and meta-explanations do shed some light on the physics issues even if the reason for there being no consensus remains a mystery.