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

[kered rettop]

Sorry @kered rettop I will go back to topic soon.

Don't bother, nobody else does!

 

[PeterDonis]

you've switched to talking about outcomes of the initial measurement.

No, I haven't "switched" (but see further comment at the end of this post). The different decohered outcomes are the "worlds" in the MWI. So those are the relevant things to be looking at.

I was talking about the product terms when you do a fine-grained decomposition of the decohered state. (Down to every degree of freedom if necessary.) Is not such a term a state?

They aren't "worlds" in MWI-speak. If decoherence spreads entanglement through, say, $10^{30}$ degrees of freedom in the environment after I measure the spin of a qubit, that doesn't mean the number of "worlds" goes from $2$ (one for each outcome) to $10^{30}$. It's still just $2$ worlds.

At some point the term "state" appears to have entered the discussion, but unless it is taken to be a synonym for "world" in MWI-speak, I'm not sure what relevance it has. If I am partly responsible for the inadvertent switch in terminology, I apologize.

 

[Demystifier]

There is no collapse for Bohmians.

Can you provide some source to show that Bohmians derive the Born rule? Where is the house Bohmian @Demystifier ?

There is no true fundamental collapse, but there is effective apparent collapse, Bohmian mechanics explains it in a rather simple way. It explains easily the Born rule in arbitrary space (momentum, energy, spin etc. space) from the Born rule in position space, see e.g. my https://arxiv.org/abs/1811.11643 . For the explanation of the Born rule in position space itself, see https://www.mdpi.com/1099-4300/20/6/422 .

 

[PeroK]

Here is explicitly how a probabilistic model can be simulated by a deterministic model.

Take $2^{33}$ people, each in a sealed room. That's approx the current Earth population, so it seemed a good number to choose.

In the probability model, pick one of them. Toss a coin 33 times on their behalf and give them the string of heads and tails.

In the simulated model go through all possibilities for strings of 33 heads or tails and give each one to someone. In this model, every person has a different string ranging from 33 heads to 33 tails and everything in between.

The point is that each person in the simulated model cannot tell which experiment is being done. Likewise, the person in the probability model above, cannot tell which experiment they are part of.

In particular, the person with 33 heads and the one with 33 tails cannot conclude they are in the simulation.

This, in terms of probability theory is clear. There should be no argument that probabilities can be simulated in this way.

 

[PeterDonis]

In particular, the person with 33 heads and the one with 33 tails cannot conclude they are in the simulation.

Why not?

 

[PeroK]

Why not?

For the same reason that the person in probability scenario cannot conclude they are in the simulation. They were subject to the unlikely one in $2^{33}$ probability of being chosen.

 

[PeterDonis]

For the same reason that the person in probability scenario cannot conclude they are in the simulation. They were subject to the unlikely one in $2^{33}$ probability of being chosen.

Sorry, I don't see the connection here. Every person in the experiment knows that there is only one person in the probability scenario, while there are $2^{33}$ people in the simulation (i.e., all of them). So each person would conclude that it is overwhelmingly likely that they are in the simulation, even before seeing the data they are given. Seeing 33 heads or 33 tails just makes it even more overwhelmingly likely that they are in the simulation, since in the simulation it is guaranteed that someone will see those data sets, whereas in the probability scenario they are overwhelmingly unlikely.

 

[PeterDonis]

For the same reason that the person in probability scenario cannot conclude they are in the simulation.

And also cannot conclude that they are not, correct? You said they can't know which experiment they are part of.

But what is the reason for that? It is because the data set the person in the probability scenario will see will be one that doesn't give them any useful information about which scenario they are in. Since every data set occurs in the simulation, the only data sets that don't give any useful information about which scenario one is in are data sets that are likely to occur in the probability scenario. A data set that is overwhelmingly unlikely to occur in the probability scenario, like the ones with 33 heads and 33 tails, does give useful information about which scenario one is in, since such data sets are not unlikely to occur in the simulation--they can't be, because they are guaranteed to occur in the simulation.

 

[PeroK]

Sorry, I don't see the connection here. Every person in the experiment knows that there is only one person in the probability scenario, while there are $2^{33}$ people in the simulation (i.e., all of them). So each person would conclude that it is overwhelmingly likely that they are in the simulation, even before seeing the data they are given. Seeing 33 heads or 33 tails just makes it even more overwhelmingly likely that they are in the simulation, since in the simulation it is guaranteed that someone will see those data sets, whereas in the probability scenario they are overwhelmingly unlikely.

It's true that in this thought experiment everyone can guess they are in the simulation. Knowledge of the other people is a flaw in how I've set it up. I'm sure that can be fixed.

 

[PeterDonis]

It's true that in this thought experiment everyone can guess they are in the simulation. Knowledge of the other people is a flaw in how I've set it up. I'm sure that can be fixed.

If you're sure, then please fix it. I'm not at all sure it can be fixed. You are struggling with an issue that MWI proponents have been struggling with for a number of decades now, and IMO none of them has fixed it. The basic problem, as I said, is that in the MWI all possible outcomes are guaranteed to occur. Nobody has come up with a meaningful concept of probability in that context, and it's not for lack of trying.

 

[PeroK]

If you're sure, then please fix it. I'm not at all sure it can be fixed. You are struggling with an issue that MWI proponents have been struggling with for a number of decades now, and IMO none of them has fixed it. The basic problem, as I said, is that in the MWI all possible outcomes are guaranteed to occur. Nobody has come up with a meaningful concept of probability in that context, and it's not for lack of trying.

They have the problem of extending it beyond the simple equally likely scenarios. There may be some deeper issues even there.

 

[pines-demon]

If you're sure, then please fix it. I'm not at all sure it can be fixed. You are struggling with an issue that MWI proponents have been struggling with for a number of decades now, and IMO none of them has fixed it. The basic problem, as I said, is that in the MWI all possible outcomes are guaranteed to occur. Nobody has come up with a meaningful concept of probability in that context, and it's not for lack of trying.

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

Why is so bad that some people get impossibly unlikely odds? Quantum suicide and all that, these are very exceptional cases and these observers will not able to derive the right probabilities, but the more coins throws and people you add the less exceptional cases there are relative to the majority. There is consensus in MWI that these exceptional cases must exist but are not important.

 

[Fra]

As there appears to be no consensus about the meaning of probability in a deterministic model, I am asking what the sticking point is?
That's all really.

fwif, I rarely engage in mwi discussions, but if I were to make a comment to your original question, from another (agent/qbist centered view) I would like to describe it like this.

To give both descriptive or normative probabilities a real meaning we need to have an observer or agent that is either collecting and processing the data to infer the descriptive probability(statistics) in some limit, or an agent that uses his incomplete knowledge to place bets.

Mwi attempt to do away with obsevers, is to me like denying that observers are real physical systems, and to say that "any possibility" always occurs, is to suggest that all possible physical observers actually exist. This makes no sense to me. Everything that is possible, does not necessarily actually happen, especially if you take the normative interpretation of probability.

But one you start to think about this, which I have done, mwi seems not interesting to me at least.

A similar situation can appear in a agent-centered kind of "solipsist" view, where you can argue that there is always some "strange agent" that can have a particular biased inferred normative view of the future. BUT the thind is that if you take seriously that agents/observers are not just fictions but real objects (having mass!) and not just a "coordinate system" that is fictive, then it seems reasonable that the population of agents in the universe is not arbitrary, therefore, everyone that seems possible, in a remote future, does not actually happen.

/Fredrik

 

[pines-demon]

fwif, I rarely engage in mwi discussions, but if I were to make a comment to your original question, from another (agent/qbist centered view) I would like to describe it like this.

To give both descriptive or normative probabilities a real meaning we need to have an observer or agent that is either collecting and processing the data to infer the descriptive probability(statistics) in some limit, or an agent that uses his incomplete knowledge to place bets.

Mwi attempt to do away with obsevers, is to me like denying that observers are real physical systems, and to say that "any possibility" always occurs, is to suggest that all possible physical observers actually exist. This makes no sense to me. Everything that is possible, does not necessarily actually happen, especially if you take the normative interpretation of probability.

But one you start to think about this, which I have done, mwi seems not interesting to me at least.

A similar situation can appear in a agent-centered kind of "solipsist" view, where you can argue that there is always some "strange agent" that can have a particular biased inferred normative view of the future. BUT the thind is that if you take seriously that agents/observers are not just fictions but real objects (having mass!) and not just a "coordinate system" that is fictive, then it seems reasonable that the population of agents in the universe is not arbitrary, therefore, everyone that seems possible, in a remote future, does not actually happen.

/Fredrik

Everything, that is consequence of a quantum superposition, happens according to MWI. Why the observer cannot be the one at the end of each branch? Do you agree that if you accept that there are strange agents, then the probability could be defined?

 

[kered rettop]

They have the problem of extending it beyond the simple equally likely scenarios. There may be some deeper issues even there.

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.

 

[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?