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

[kered rettop]

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.

 

[pines-demon]

In a deterministic model there is no fundamental probability, we can agree on that. In classical systems, probability arises from the lack of knowledge of all physical of factors influencing the experiment or from the chaotic evolution of the dynamics.

In MWI the probability of quantum events seems to arise from the branching of the worlds. As observers, get split into separate worlds from their own counterparts, there is a fundamental lack of knowledge as different worlds cannot interact. Thus a particular observer can never have the full picture of all the worlds, thus needs to describe their results in terms of probabilities.

As discussed in previous posts, if the amplitudes are symmetrical $\frac1{\sqrt2}(|+\rangle+|-\rangle)$ then for Alice the branching is clear, the world splits into two after measurement, let's say $\frac1{\sqrt2}(|+\rangle|A_+\rangle+|-\rangle|A_-\rangle)$, where $A_{\pm}$ represents Alice seeing a (+) or a (-).

However if the state is $\frac12|+\rangle+\frac{\sqrt{3}}2|-\rangle$ then the same happens, $\frac12|+\rangle|A_+\rangle+\frac{\sqrt3}{2}|-\rangle|A_-\rangle$ but we still seem to have two worlds? Why Alice would feel that is more probable to get $|-\rangle$ if she repeats the experiment?

Sure there would be a special Alice that measures always (+), and another that always measures (-), but in the long run the average Alice would measure (-) 75% of the time. If we are naive, and we say that the worlds split always in two like in a tree diagram, then this cannot be the case.

The average Alice at the far ends of the tree, after a large $N$ of measurements should be able to trace back her previous results and come up with the right probabilities for the state (25% +, 75% -) but a binary tree provides 50-50%.

How to make the probabilities right? Maybe the worlds split into a finite number larger than 2 to make the results make sense. But if for example the relative weight is irrational between the two states, then we have infinitely many worlds that must split in order to make the probabilities correct. So you have to introduce some continuous density weight to the worlds. Then it looks more like a fluid going down a series of pipes of different diameters. These models exist but I do not know if there is a consensus about it.

Wikipedia summarizes the attempts in Born rule:

Several other researchers have also tried to derive the Born rule from more basic principles. A number of derivations have been proposed in the context of the many-worlds interpretation. These include the decision-theory approach pioneered by David Deutsch and later developed by Hilary Greaves and David Wallace; and an "envariance" approach by Wojciech H. Zurek. These proofs have, however, been criticized as circular. In 2018, an approach based on self-locating uncertainty was suggested by Charles Sebens and Sean M. Carroll; this has also been criticized. Simon Saunders, in 2021, produced a branch counting derivation of the Born rule. The crucial feature of this approach is to define the branches so that they all have the same magnitude or 2-norm. The ratios of the numbers of branches thus defined give the probabilities of the various outcomes of a measurement, in accordance with the Born rule

 

[Lord Jestocost]

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.

The Many-Worlds Interpretation (MWI) cannot explain the probabilities, because the whole point of MWI is to reject probabilities. Thus, probabilities are “masqueraded” as “world splittings”, and all possibilities are realized in inaccessible alternate world branches. It reminds a bit of “philosophical flapdoodle”.

 

[kered rettop]

The Many-Worlds Interpretation (MWI) cannot explain the probabilities, because the whole point of MWI is to reject probabilities. Thus, probabilities are “masqueraded” as “world splittings”, and all possibilities are realized in inaccessible alternate world branches. It reminds a bit of “philosophical flapdoodle”.

No, that's not true. MWI rejects randomness. But probabilities can be, and usually are in everyday life, due to simple ignorance. Which is how MWI tries to explain them. If you think a different word is needed, or a phrase like "appearence of probability", then you might have a case, but I'd rather not get embroiled in semantics.

 

[kered rettop]

In a deterministic model there is no fundamental probability, we can agree on that. In classical systems, probability arises from the lack of knowledge of all physical of factors influencing the experiment or from the chaotic evolution of the dynamics.

In MWI the probability of quantum events seems to arise from the branching of the worlds. As observers, get split into separate worlds from their own counterparts, there is a fundamental lack of knowledge as different worlds cannot interact. Thus a particular observer can never have the full picture of all the worlds, thus needs to describe their results in terms of probabilities.

As discussed in previous posts, if the amplitudes are symmetrical $\frac1{\sqrt2}(|+\rangle+|-\rangle)$ then for Alice the branching is clear, the world splits into two after measurement, let's say $\frac1{\sqrt2}(|+\rangle|A_+\rangle+|-\rangle|A_-\rangle)$, where $A_{\pm}$ represents Alice seeing a (+) or a (-).

However if the state is $\frac12|+\rangle+\frac{\sqrt{3}}2|-\rangle$ then the same happens, $\frac12|+\rangle|A_+\rangle+\frac{\sqrt3}{2}|-\rangle|A_-\rangle$ but we still seem to have two worlds? Why Alice would feel that is more probable to get $|-\rangle$ if she repeats the experiment?

Sure there would be a special Alice that measures always (+), and another that always measures (-), but in the long run the average Alice would measure (-) 75% of the time. If we are naive, and we say that the worlds split always in two like in a tree diagram, then this cannot be the case.

View attachment 339571
The average Alice at the far ends of the tree, after a large $N$ of measurements should be able to trace back her previous results and come up with the right probabilities for the state (25% +, 75% -) but a binary tree provides 50-50%.

How to make the probabilities right? Maybe the worlds split into a finite number larger than 2 to make the results make sense. But if for example the relative weight is irrational between the two states, then we have infinitely many worlds that must split in order to make the probabilities correct. So you have to introduce some continuous density weight to the worlds. Then it looks more like a fluid going down a series of pipes of different diameters. These models exist but I do not know if there is a consensus about it.

Wikipedia summarizes the attempts in Born rule:

 

[kered rettop]

Yes, that's a good summary of the problem, but it doesn't really answer my question, which is why there's no generally accepted meaning to probability.

 

[pines-demon]

Yes, that's a good summary of the problem, but it doesn't really answer my question, which is why there's no generally accepted meaning to probability.

I think it is because the people advocating for it cannot agree on the terminology or on a single way to describe it. This is what happens with most interpretational problems, semantic disagreement kicks in very quickly.

Edit: funny enough the difference between interpretations is not sharp, it even leads to bold claims like MWI= Bohmian mechanics or MWI=superdeterminism

 

[Demystifier]

Yes, that's a good summary of the problem, but it doesn't really answer my question, which is why there's no generally accepted meaning to probability.

Because there is no natural (or convincing, or simple) explanation of the Born rule in MWI, so all explanations constructed have serious problems.

 

[kered rettop]

Because there is no natural (or convincing, or simple) explanation of the Born rule in MWI, so all explanations constructed have serious problems.

Hang on! I was asking about the meaning of probability not the derivation of the BR. The derivation obviously needs the meaning of probability if we are to know what it purports to show let alone actually validate it. However, the meaning should not depend on the validity of the derivation. In fact if it did, there would be a grave danger of circularity. And we wouldn't want that, would we?

I know you will get the point (even if you dispute it) but for the sake of anyone who might mistake this for semantic nit-picking, no it is not. Assigning meaning to probability is vital before we can talk about whether a rule for calculating it is valid. "That whereof we cannot speak, thereof must we remain silent" (Which is the sum total I know of Wittgenstein, but it's a nice aphorism.)

Physicists are a bright bunch (no I have no references to back that claim up) so I would have expected them to have arrived at a consensus. But (I'm told), they haven't and I want to know what's the sticking point. It could render MWI incoherent, which would be pleasing, but I suspect the incoherence lies elsewhere.

Thanks.

 

[Demystifier]

I was asking about the meaning of probability not the derivation of the BR. The derivation obviously needs the meaning of probability if we are to know what it purports to show let alone actually validate it. However, the meaning should not depend on the validity of the derivation. In fact if it did, there would be a grave danger of circularity. And we wouldn't want that, would we?

Well, ideally one would like first to have a well defined meaning of probability in MWI and then to derive the BR. But in reality, it doesn't work that way. The most obvious notion of probability in MWI, which a priori anyone would agree with, leads to the conclusion that any possible world has the same probability, which violates BR and observations. So the notion of probability that seems natural from MWI point of view is in fact wrong. Hence one should either reject MWI or redefine the notion of probability, and it is not clear how to do the latter. In fact, all "derivations" of BR from MWI are somewhat circular, see https://arxiv.org/abs/0808.2415 .

Physicists are a bright bunch (no I have no references to back that claim up) so I would have expected them to have arrived at a consensus. But (I'm told), they haven't and I want to know what's the sticking point. It could render MWI incoherent, which would be pleasing, but I suspect the incoherence lies elsewhere.

Physicists are smart, but they have blind spots too. MWI-ers, in particular, like the MWI idea so much that they are not able to admit that probability is a too big issue.

 

[pines-demon]

Hang on! I was asking about the meaning of probability not the derivation of the BR.

Could you clarify what kind of discussion on the meaning of probability you have in mind? Something of the sort of deciding if the probability is Bayesian or frequentist? Or some counting rule?
I think we all agree that whatever probability we assign to MWI has to coincide with the probability that Alice can infer at the end of the branch from her measurements alone.

Physicists are a bright bunch (no I have no references to back that claim up) so I would have expected them to have arrived at a consensus. But (I'm told), they haven't and I want to know what's the sticking point. It could render MWI incoherent, which would be pleasing, but I suspect the incoherence lies elsewhere.

Wikipedia article on Many-Worlds has a good chapter on discussions of probability, Born rule and incoherence if this is what you are looking for. However I do not think there is even a consensus on which sticking point everybody agrees to disagree.

 

[kered rettop]

Well, ideally one would like first to have a well defined meaning of probability in MWI and then to derive the BR. But in reality, it doesn't work that way. The most obvious notion of probability in MWI, which a priori anyone would agree with

Sorry but I insist that I fall into the category of "anyone" and I can't remember ever being likely to assume equal probabilities.

leads to the conclusion that any possible world has the same probability, which violates BR and observations.

And common sense. The equal probabilities that you say are a natural assumption can only be reached by some sort of Principle of Indifference. Which is just a recipe for assigning probability in the absense of any information that might have a bearing on it. Obviously amplitudes do have a bearing, but it's not even necessary to say that in fact they do, it is sufficient that they might, in which case the naive equal probability conclusion is illogical.

So the notion of probability that seems natural from MWI point of view is in fact wrong.

Well, no, it really does not seem natural. At least to me. Maybe I don't hold "the MWI" point of view.

Hence one should either reject MWI or redefine the notion of probability,

or gently debunk the foolish argument.

If that involves disabusing the masses of their notion of probability, so be it!

and it is not clear how to do the latter. In fact, all "derivations" of BR from MWI are somewhat circular, see https://arxiv.org/abs/0808.2415 .

Skimmed though it. I'm not asking about the Born Rule, let alone Wallace's betting-shop theory. I'm interested in defining probability a priori. The BR can't be part of the definition because, if we lived in a world without QM there would still be a need for probability.

 

[kered rettop]

Could you clarify what kind of discussion on the meaning of probability you have in mind? Something of the sort of deciding if the probability is Bayesian or frequentist? Or some counting rule?

I have no idea. I'm asking why physicists are alleged not to have reached consensus. I guess identifying the sticking point does involve nailing down what kind of probability they're looking for, but I'm not going pre-empt it.

I think we all agree that whatever probability we assign to MWI has to coincide with the probability that Alice can infer at the end of the branch from her measurements alone.

Well, yes, it would be nice to think that the definition of probability does in fact allow one to calculate and get the right answers

Wikipedia article on Many-Worlds has a good chapter on discussions of probability, Born rule and incoherence if this is what you are looking for. However I do not think there is even a consensus on which sticking point everybody agrees to disagree.

And so the infinite regress of non-consensuses begins.

 

[Demystifier]

Maybe I don't hold "the MWI" point of view.

if we lived in a world without QM there would still be a need for probability.

So you just ask what is probability, you don't really ask about many worlds, or even about QM. Am I right? I'm sure many people here could answer that question too, but perhaps your question would be more suitable to the probability subforum. https://www.physicsforums.com/forums/set-theory-logic-probability-statistics.78/

 

[kered rettop]

So you just ask what is probability, you don't really ask about many worlds, or even about QM. Am I right? I'm sure many people here could answer that question too, but perhaps your question would be more suitable to the probability subforum. https://www.physicsforums.com/forums/set-theory-logic-probability-statistics.78/

Not generic probability. Just probability in MWI. And, specifically, why is there no consensus about what probability means in MWI.

 

[pines-demon]

Not generic probability. Just probability in MWI. And, specifically, why is there no consensus about what probability means in MWI.

This looks like a Socratic dialogue, where we give answers and you say "but why?"

The central claim of MWI is that Schrödinger's equation is all there is. No Born rule. Everything should come naturally from the mathematical formalism. But if I do the most simple example as above with a binary tree it does not work. Instead if we assume the Born rule then the argument is circular.

It seems that MWI suppoters cannot have the cake and eat it.

[I know this does not answer anything but we can keep iterating]

Edit: do you have a question related to the Wikipedia entry? That might help focusing the conversation.

 

[kered rettop]

This looks like a Socratic dialogue, where we give answers and you say "but why?"

The central claim of MWI is that Schrödinger's equation is all there is. No Born rule. Everything should come naturally from the mathematical formalism. But if I do the most simple example as above with a binary tree it does not work. Instead if we assume the Born rule then the argument is circular.

Yes, of course. So best to drop them both.

It seems that MWI suppoters cannot have the cake and eat it.u

[I know this does not answer anything but we can keep iterating]

Edit: do you have a question related to the Wikipedia entry? That might help focusing the conversation.

Not really.

 

[PeterDonis]

probabilities can be, and usually are in everyday life, due to simple ignorance. Which is how MWI tries to explain them

Yes, by saying that the ignorance is ignorance of which branch we are on (or more precisely, will be on after measurement). However, there are two problems with that:

(1) The ignorance interpretation based on not knowing which branch we will be on means that the probabilities are given by the branch weightings. But we never measure the branch weightings. We never know the weights of any other branches besides the one we are on. What we actually measure are relative frequencies of outcomes in the branch we are on. That's not the same as the weightings of different branches.

(2) The ignorance interpretation of probability depends on not having sufficiently precise knowledge of initial conditions in a deterministic system with single outcomes for events; for example, we assign 50-50 odds for a coin flip because we don't know the initial conditions accurately enough to use the deterministic laws of physics to tell us which way the coin will land. But in the MWI, all outcomes occur. The determinism in the MWI is not a matter of initial conditions picking a single outcome out of multiple possibilities, and us not knowing the conditions precisely enough to know which one. The determinism in the MWI is a matter of all possible outcomes always deterministically occurring. There is no formulation of the ignorance interpretation of probability that covers that.

In the literature there are various attempts to deal with (1) above, by arguing that, under certain reasonable assumptions, the relative frequencies we observe in our branch will converge to the branch weightings with some reasonable accuracy. I personally don't find those arguments convincing (and I am not the only one), but in any case, they don't address (2) above at all, and I'm not aware of any argument in the literature that does.

 

[kered rettop]

Yes, by saying that the ignorance is ignorance of which branch we are on (or more precisely, will be on after measurement). However, there are two problems with that:
[...]
I personally don't find those arguments convincing (and I am not the only one), but in any case, they don't address (2) above at all, and I'm not aware of any argument in the literature that does.

Right. Thank you. That's exactly what I was asking about. Of course I would like to discuss the two points regardless of any show-of-hands aspect. But I'm far too brain-fogged to do it now.

 

[pines-demon]

(2) The ignorance interpretation of probability depends on not having sufficiently precise knowledge of initial conditions in a deterministic system with single outcomes for events; for example, we assign 50-50 odds for a coin flip because we don't know the initial conditions accurately enough to use the deterministic laws of physics to tell us which way the coin will land. But in the MWI, all outcomes occur. The determinism in the MWI is not a matter of initial conditions picking a single outcome out of multiple possibilities, and us not knowing the conditions precisely enough to know which one. The determinism in the MWI is a matter of all possible outcomes always deterministically occurring. There is no formulation of the ignorance interpretation of probability that covers that.

Could you expand on this? I do not get it. I mean who cares if it is deterministic, the problem is how to interpret the outcomes as seen by a post-measurement observer. The post-measurement observer cannot see (is ignorant of) the nodes and branches.

 

[PeterDonis]

who cares if it is deterministic

The OP of the thread specified deterministic. In any case, I'm not aware of any formulation of an ignorance interpretation of probability for non-deterministic dynamics.

The post-measurement observer cannot see (is ignorant of) the nodes and branches.

Yes, but that's not the kind of ignorance that appears in the only formulation of an ignorance interpretation of probability that I'm aware of. Ignorance of which branch you are (or will be) in in a dynamics in which all possible outcomes occur is not the same as ignorance of initial conditions in a dynamics where the initial conditions determine one outcome out of multiple possibilities.

 

[PeterDonis]

Ignorance of which branch you are (or will be) in in a dynamics in which all possible outcomes occur is not the same as ignorance of initial conditions in a dynamics where the initial conditions determine one outcome out of multiple possibilities.

Perhaps this will help: even the notions of "possibility" in these two cases are not the same. In the standard ignorance interpretation, the notion of "possibility" used is epistemic: the underlying dynamics are deterministic, so only one outcome is actually possible, but because we don't know the initial conditions accurately enough to know which outcome is actually possible (i.e., going to happen deterministically), we have to consider multiple possible outcomes epistemically, i.e., in the sense of our knowledge for the purpose of making predictions.

In the MWI, however, the notion of "possibility" is completely different: it is ontic, i.e., the deterministic dynamics is that all of the "possible" outcomes, i.e., all the outcomes that have nonzero amplitudes in the wave function, actually occur. The standard ignorance interpretation of probability doesn't even make sense with that notion of "possibility".

In fact, even to say that "we" are ignorant of which branch "we" will end up on in the MWI is a misstatement. "We" end up on all branches. The "we" that ends up on each branch can't detect or measure any other branches, but there is still a "we" on each branch--the same quantum degrees of freedom. Again, the standard ignorance interpretation of probability doesn't even make sense in that context.

 

[bhobba]

but I'd rather not get embroiled in semantics.

IMHO that's the problem with MWI, it inherently involves semantics:


Thanks
Bill

 

[bhobba]

Yes, that's a good summary of the problem, but it doesn't really answer my question, which is why there's no generally accepted meaning to probability.

Aside from the Kolmogorov Axioms, there is no generally accepted meaning of probability, even in mathematics. Often, in many worlds, you find it couched in terms of decision theory formulated as a kind of bet on which world you would experience. It sounds reasonable, but an interpretation of probability is part of the MWI.

John Baez thinks many QM interpretations are, at least partially, just interpretations of probability rehashed in terms of QM.

https://math.ucr.edu/home/baez/bayes.html

Thanks
Bill

 

[Demystifier]

Not generic probability. Just probability in MWI. And, specifically, why is there no consensus about what probability means in MWI.

I don't think that one can understand what is probability in MWI without first understanding what is probability in general.

 

[pines-demon]

IMHO that's the problem with MWI, it inherently involves semantics:


Thanks
Bill

Kind of off topic, but what is the "Massagon meeting"?

 

[kered rettop]

I don't think that one can understand what is probability in MWI without first understanding what is probability in general.

Indeed. Which is the root problem I'm trying to unravel here - there seems to be no agreed meaning. I'm afraid I tend to say "If it looks like probability and quacks like probability then is probably is probability" but others seem to insist on a more restrictive definition.

 

[pines-demon]

Indeed. Which is the root problem I'm trying to unravel here - there seems to be no agreed meaning. I'm afraid I tend to say "If it looks like probability and quacks like probability then is probably is probability" but others seem to insist on a more restrictive definition.

I am not trained enough in probability theory so I am failing to understand what the issue is too. What kind of "rigor" are we expecting? Can somebody provide an example of a well-defined probability (not necessarily quantum)?

 

[martinbn]

I don't think you should expect consensus about any aspect of any interpretation. Two physicists, who work on the foundations of QM, would agree only on how wrong a third interpretation is.

 

[gentzen]

Physicists are smart, but they have blind spots too. MWI-ers, in particular, like the MWI idea so much that they are not able to admit that probability is a too big issue.

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

 

[kered rettop]

Aside from the Kolmogorov Axioms, there is no generally accepted meaning of probability, even in mathematics.
It sounds reasonable, but an interpretation of probability is part of the MWI.

OK, but you can hardly expect MWI to interpret the mess it inherited from QM which it inherited from (classical) probability theory, which inherited it from mathematicians who reliably never agree about anything . I think it is reasonable to use the same working assumptions as a statistician would. Maybe any claims about probability need to be stated with a caveat or perhaps MWI should only talk about quasi-probability, but that doesn't invalidate anything. What MWI does need to do, is to make sure that its quasi-probabilty does, in fact, make the same predictions as a "real" probability would.

Often, in many worlds, you find it couched in terms of decision theory formulated as a kind of bet on which world you would experience.

Yes. I read a paper by Wallace a few years ago expounding his decision-theoretic approach. It seemed to be counter-productive, in that, by implication, it accepts that there is a problem peculiar to MWI, not common to all interpretations, or indeed all quantifiable science. But I was young then (like hell) and these days I am much more open to the idea that that there really is an issue. Whether that openness survives this thread remains to be seen.

Very glad of your reply, thank you.

 

[gentzen]

I am not trained enough in probability theory so I am failing to understand what the issue is too. What kind of "rigor" are we expecting? Can somebody provide an example of a well-defined probability (not necessarily quantum)?

If you have a well specified experiment that you can repeat as often as you want, then the probabilities for the outcomes can be considered to be basically well defined. There are still some caveats, like sufficient independence between the different actual repetitions of the experiments, but basically one is fine enough in this scenario.

But for essentially non-repeatable scenarios, like the probability of earthquakes of a certain strength in a certain region and time, it becomes hard to assign good meaning to probabilities. And for stuff like the probability of rain tomorrow (in a certain sufficiently well specified place), one is on "intermediate ground", and many different procedures to use probabilities in practice offer themselves. Some are simply misguided and lead to "wrong" results ("replication crisis"), some only allow to compare performance of different "predictors" on actual data sets without singling out a single "correct" assignment of probability values, some ...

 

[martinbn]

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?

 

[gentzen]

If you have a well specified experiment that you can repeat as often as you want

And for QM, it is simply unclear whether you are in this scenario or not. The minimal statistical interpretation is basically just happy to be restricted to that scenario, and hence can rely on probabilities being well defined and meaningful. For the Copenhagen interpretation, the assumption is also that you can always reduce its probabilities to that scenario, even so you give yourself more freedom in how you compute stuff. At least for essentially non-repeatable scenarios, like the history of the universe itself, there is basically agreement that the Copenhagen interpretation fails to apply.

But for realist interpretations like MWI or BM, you do want that they apply to the universe itself. So the question of the meaning of probability becomes relevant. For BM, one way out would be to say that it basically appies to the universe itself, but its probabilies are only meaningful for hypothetical repetitions. Of course, BM's proponents don't want this, and invented the "typicality" argument instead. But for MWI, I get the impression that many proponents don't even realise that there might be a problem.

 

[gentzen]

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.