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

[kered rettop]

If I am partly responsible for the inadvertent switch in terminology, I apologize.

Me likewise. But I wasn't complaining about the wrong use of terminology per se. One may allow for that and address what the other person probably means. However, in this case, outcomes, worlds and states are very different things and used in very different arguments.

 

[gentzen]

No they don't. MWI does not calculate probabilities the way you suggest. It never counts the number of outcomes to calculate probabilies. There is nothing to extend.

So you are making a more general claim here, compared to my suspicion that Vaidman would not use such an argument?

Are you sure that we are talking about a Vaidman paper here?

But PeroK's analysis was based on

a link to a pdf by Taha Dawoodbhoy (that is itself a derivation of the concept from Zurek and Carroll) that explains it in more detail

Principle of Indifference Proof:

Would you also subscribe to the more specific claim that Zurek and Carroll never count the number of outcomes to calculate probabilities in MWI?

 

[pines-demon]

So you are making a more general claim here, compared to my suspicion that Vaidman would not use such an argument?

What is Vaidman based on?

Would you also subscribe to the more specific claim that Zurek and Carroll never count the number of outcomes to calculate probabilities in MWI?

I am under the impression they do, given the pdf. They divide a branch with the same result into pseudo-branches and then the principle of indifference applies. This does not give them the Born rule (that would be circular) but seems like a valid probability definition so far...

 

[Fra]

Do you agree that if you accept that there are strange agents, then the probability could be defined?

Possibly.

But the question is still to explain the matter content in the universe. Unusual agents would imply unusual matter. For me the explanatin would involve allowing the branches to interact, but then that's not what mwi does, which imo is why it I'm not into that. Conceptually the idea is that the strange agents, aren't stable, and therefore while allowed, aren't ever observed. Had it been observed once, it would possibly not be distinguishable from noise anyway.

/Fredrik

 

[gentzen]

What is Vaidman based on?

I gave my opinion on this before in this thread:

In my opinion, Vaidman does admit that deriving the Born rule doesn't work.

I still dont understand the requirement that the Born rule should follow. Why can it not be an independent postulat?

This is exactly what Vaidman proposes: Put in the Born rule as an independent postulat.

My opinion is partly based on Vaidman's paper "Why the Many-Worlds Interpretation?"
https://arxiv.org/abs/2208.04618

 

[pines-demon]

My summary so far is that:

1) MWI can be unpleasing and non conventional because:

• it has multiple outcomes
• branches cannot interact
• ignorance is not defined in the usual way
  [*]and it leads to quantum suicide scenarios (preferential observers).
  

2) There is no consensus in how to derive the Born rule, and arguments are usually catalogued as circular
3) Probability cannot be obtained from binary branching
4) By consensus probability still can be rightfully defined by weighted branching or by postulating the Born rule.

By (4) I would say that the answer to the title is: there is some consensus, the conflict lies in the role of the Born rule.

Arguments against (4) seem to be:
a) Frequency of branching does not need to map to the frequency in a given branch measured by a given observer in a specific world
b) The whole point of interpretations is to reveal how the machinery works, but if the probabilities cannot derive the Born rule the interpretation loses reliability
c) Probability theory itself stills suffers from definitional problem for physics in general
d) Very high entropies

Did I miss something?

 

[kered rettop]

So you are making a more general claim here, compared to my suspicion that Vaidman would not use such an argument?

In that I think the argument would be invalid (and rather obviously so), I don't think anyone should. Vaidman being a respected authority, I therefore agree with your suspicions.

Would you also subscribe to the more specific claim that Zurek and Carroll never count the number of outcomes to calculate probabilities in MWI?

I think it very doubtful that they would, But I haven't done an in-depth witch-hunt to see if they ever have.

Does that make anything clear?

 

[gentzen]

In that I think the argument would be invalid (and rather obviously so), I don't think anyone should.

Does that make anything clear?

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)".

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.

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

 

[pines-demon]

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.

I agree but why do we care about the entropy of these many worlds? Does it has any physical consequences?

Also is it that high? With respect to what? Fluid diffusion is kinda similar...

 

[PeterDonis]

Just remove the knowledge that there is other people doing the experiment....

Which then makes it useless, since in the real universe we do know of other people doing similar experiments to ours. The MWI has to account for the real universe, not for some imaginary universe in which we can totally isolate people from each other and pretend they never share any knowledge.

 

[PeterDonis]

I do not say they are synonymous since the SEP "definition"

Did this post get cut off halfway through unintentionally?

 

[PeroK]

Which then makes it useless, since in the real universe we do know of other people doing similar experiments to ours. The MWI has to account for the real universe, not for some imaginary universe in which we can totally isolate people from each other and pretend they never share any knowledge.

In orthodox QM, we only see one outcome of each experiment. To some extent on account of this we have the measurement problem.

In any case, the scenario wasn't about MWI per se, but whether you could deterministically produce effective probabilities.

 

[PeterDonis]

the scenario wasn't about MWI per se, but whether you could deterministically produce effective probabilities.

But the simulation part of the scenario did reproduce the key aspect of the MWI, which is that all possible outcomes occur--every possible sequence of 33 coin flips happens. And that is a key obstacle to any attempt to "deterministically produce effective probabilities": if all possible outcomes happen, it makes no sense to talk about the "probability" of any outcome, unless you want to say that the "probability" of any possible outcome is $1$.

 

[PeterDonis]

whether you could deterministically produce effective probabilities

To go back to a point I made in a post a while ago in this thread, we already have a standard concept of probability in a deterministic scenario: the ignorance interpretation. The "effective probabilities" in such a case are epistemic: they are there because we don't have accurate enough knowledge of initial conditions to make a deterministic prediction of the single outcome that will actually occur. But that doesn't work in a deterministic scenario where all outcomes occur, like the MWI, or like your simulation scenario. In those cases there is no uncertainty about initial conditions contributing to uncertainty about outcomes. So the ignorance interpretation doesn't work, and there is no other one available.

 

[PeroK]

But the simulation part of the scenario did reproduce the key aspect of the MWI, which is that all possible outcomes occur--every possible sequence of 33 coin flips happens. And that is a key obstacle to any attempt to "deterministically produce effective probabilities": if all possible outcomes happen, it makes no sense to talk about the "probability" of any outcome, unless you want to say that the "probability" of any possible outcome is $1$.

The MWI argument is that any observation is of only one world and that's where the effective probability comes from. A single observer of an experimental outcome is effectively allocated to a world randomly.

The difficulty for MWI is to explain the Born rule. Whereas your argument seems to be that MWI is conceptually a non-starter.

My scenario didn't work because the MWI analogy statistically dominated the single-world analogy. It wasn't my intention to prove MWI, which is what I inadvertently did. If I were an MWI proponent I might have been happy with my thought experiment.

 

[PeterDonis]

The MWI argument is that any observation is of only one world

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. That is what the MWI says.

and that's where the effective probability comes from.

That's the part I have not seen any convincing argument for.

your argument seems to be that MWI is conceptually a non-starter.

If one believes that the lack of a meaningful concept of probability makes it a non-starter, yes.

 

[PeterDonis]

A single observer of an experimental outcome is effectively allocated to a world randomly.

No, that is not what the MWI says.

The MWI says that, deterministically, every outcome with a nonzero amplitude in the wave function happens, and the "observer" observes every such outcome, each one in its own world (where "world" means "decohered branch of the wave function"). There is no randomness whatever. The "observer" that observes one particular outcome does not do so randomly; it is guaranteed that there will be an "observer" who observes that outcome. That is why I said earlier that the only way to talk about the "probability" of an observer observing any particular outcome is to say that "probability" is $1$.

 

[kered rettop]

Did this post get cut off halfway through unintentionally?

Yes, Or posted prematurely. I expect I slumped onto the keyboard when I fell asleep.

I know I'm going to regret this, but could you put your Moderator hat on and get rid of it, please? Thanks.

 

[PeterDonis]

could you put your Moderator hat on and get rid of it, please?

Done.

 

[pines-demon]

@PeterDonis you seem to insist on a non-starter, so I will insist on trying to get your point.

But the simulation part of the scenario did reproduce the key aspect of the MWI, which is that all possible outcomes occur--every possible sequence of 33 coin flips happens. And that is a key obstacle to any attempt to "deterministically produce effective probabilities": if all possible outcomes happen, it makes no sense to talk about the "probability" of any outcome, unless you want to say that the "probability" of any possible outcome is $1$.

This makes me say that is the "multiple outcome" which is key here. But I hope that you also agree, that an observer at the end of the branches cannot interact or see other branches. This observer is no longer the same themselves that ended in the other branches.

Do you agree that (1) by consensus preferential observers with exceptionally unlikely probabilities exist in MWI (2) multiple branches with different weights (postulate the Born rule if you will) would effectively simulate QM for the observers at the end of each branch?

 

[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?