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

[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.

 

[kered rettop]

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)?

I think the putative issue lies upstream of probability theory itself. And yes, I think a tossing an ideal coin is a good model where we can simply postulate that there is true randomness which overrides any deterministic evolution. (Just like collapse of the wave function!)

 

[kered rettop]

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.

So it would seem

 

[kered rettop]

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

Essentially because one of the claimed merits of MWI is that it does derive the Born Rule.

 

[martinbn]

Esesemtially because one of the claimed merits of MWI is that it does derive the Born Rule.

Where?

 

[pines-demon]

Imagine the tree I added in the beginning with much more branching per node. This kind of model can indeed be used to derive a probability, isn't? I feel that users here are claiming that something more fundamental that needs to be defined in order to define a probability but I do not get what. The same idea works for a classical Galton board.

Who cares if the branching is deterministic or not to define a probability? What matters is what most observers see at the end of the branch.

Also of course a single measurement does not suffice.

 

[kered rettop]

Where?

Seriously? Why don't you Google it or even look at the topic list here on PF?

Edit: Derivation of the Born Rule is precisely why names like Zurek and Carroll are so well known.

 

[kered rettop]

I feel that users here are claiming here that something more fundamental that needs to be defined in order to define a probability but I do not get what.

Me too. Which is precisely why I launched this thread.

 

[pines-demon]

I am maybe repeating myself too much but I am not convinced by the following. Let me make a strawman argument :

1. Classical mechanics has a unique outcome
2. We cannot have full information about the system
3. Then we can define probabilities to try to predict that outcome

but then we go blind and go for something of the sort

1. Quantum mechanics does not have a single outcome
2. If you know all worlds, you know everything
3. Then we cannot define probabilities

Is the conclusion coming from point 1 or point 2 or both? Point 2 bothers me, obviously we do not have information about the other worlds. So maybe the conclusion comes from 1? In MWI we do not have single outcomes. However for the observer in a given world there is only a single outcome still.

 

[gentzen]

The second to last point is what is bothering me, obviously we do not have information about the other worlds. So maybe the conclusion comes from the idea that in MWI we do not have single outcomes? For the observer in a given world there is only one outcome still.

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.

Maybe analyzing the paradoxical situation described by the "typicality" argument helps you see why there could be problem: Even so in BM the probability measure given by the Born rule is defined on the configuration space for the positions of the particles for any fixed given time, you basically have just a single configuration drawn based on that probability measure. But what should be the role of the probability measure, if in the end you just have a single configuration? Yes, but it is a "typical configuration" is the start of the "typicality" argument. But that it is not enough, you also need to invoke the fact that the exact configuration is unknown to you, and can try to bring back some role for the probability measure somehow. Does it work? I don't know. But at least the BM proponents are aware that there might be a potential problem here.

 

[kered rettop]

At least for essentially non-repeatable scenarios, like the history of the universe itself. But for MWI, I get the impression that many proponents don't even realise that there might be a problem.

MWI starts with deterministic QM. So any need for the concept of probability only becomes apparent as you work through the theory. As such you do need to test the concept to make sure it makes sense in every scenario of interest. If you discover it works everywhere except a few special cases, then just don't try to use it there!
That said, I don't see why the main history of the universe should be such an exception. The initial singularity might be. But the main history branches through self-decoherence. Even assuming that the very early universe was unbranched, the universe today has branched gazillions of times and is now a superposition of exponential-gazillions of world-states.

 

[gentzen]

That said, I don't see why the main history of the universe should be such an exception.

It is not repeatable.

 

[pines-demon]

But what should be the role of the probability measure, if in the end you just have a single configuration? Yes, but it is a "typical configuration" is the start of the "typicality" argument. But that it is not enough, you also need to invoke the fact that the exact configuration is unknown to you, and can try to bring back some role for the probability measure somehow. Does it work? I don't know. But at least the BM proponents are aware that there might be a potential problem here.

The typicality argument might not give you the Born rule, but it gives you a probability if that is what were are looking for...

 

[jbergman]

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)?

I think this whole discussion is kind of pointless. Really the discussion should be about the Born rule which we have experimentally verified. And the question is how does MWI entail the Born rule that we observe.

 

[martinbn]

I think this whole discussion is kind of pointless. Really the discussion should be about the Born rule which we have experimentally verified. And the question is how does MWI entail the Born rule that we observe.

To me this is a strange question! MWI is an interpretation and the Born rule is a part of QM. Interpretations do not change the theory, they only interpret it. So the answer to the question "How does MWI entail the Born rule?" is "The way it is entailed in QM."

 

[pines-demon]

To me this is a strange question! MWI is an interpretation and the Born rule is a part of QM. Interpretations do not change the theory, they only interpret it. So the answer to the question "How does MWI entail the Born rule?" is "The way it is entailed in QM."

The interpretation that I know of MWI is that "Schrödinger's equation is all there is" and "there is no collapse". I do not know where does the Born rule enters here... Is there a canonical bible of MWI to check if BM is there?

 

[jbergman]

To me this is a strange question! MWI is an interpretation and the Born rule is a part of QM. Interpretations do not change the theory, they only interpret it. So the answer to the question "How does MWI entail the Born rule?" is "The way it is entailed in QM."

Your answer doesn't make sense to me. Let me phrase it another way. Why do we experience outcomes in agreement with the Born rule given that there is only unitary evolution?

As others have already explained much research has been made to try and answer this with Zurek, Carroll, Vaidman and Wallace all trying to answer this question.

To just assert this is so doesn't really offer any explanation.

 

[martinbn]

The interpretation that I know of MWI is that "Schrödinger's equation is all there is" and "there is no collapse".

This is only about the evolution part of the theory. Obviously a theory consists of more than that. For example what about observables? How do they fit? Do they have to be derived in MWI?

I do not know where does the Born rule enters here... Is there a canonical bible of MWI to check if BM is there?

Probably Everett's thesis. What is BM?

 

[martinbn]

Your answer doesn't make sense to me. Let me phrase it another way. Why do we experience outcomes in agreement with the Born rule given that there is only unitary evolution?

As others have already explained much research has been made to try and answer this with Zurek, Carroll, Vaidman and Wallace all trying to answer this question.

To just assert this is so doesn't really offer any explanation.

MWI is not the only interpretation without collapse. Does any of the others derive the Born rule?

 

[pines-demon]

This is only about the evolution part of the theory. Obviously a theory consists of more than that. For example what about observables? How do they fit? Do they have to be derived in MWI?

Probably Everett's thesis. What is BM?

BR, Born rule sorry.

My question was a bit rethorical, clearly BR is not there in the ingredients if not we would not be having this discussion nor there would be a whole section on BR in Wikipedia's article on MWI.

If the BR is not an ingredient, then it has to be justified. Of course we can add BR to MWI, but most criticism seems not to be focused on that version of MWI.

 

[pines-demon]

MWI is not the only interpretation without collapse. Does any of the others derive the Born rule?

You are right, Bohmians and superdeterminists do not have a collapse either.

I do not think any interpretation derives it conclusively, the best we have is Gleason's theorem from contextuality (but that is not a specific interpretation but a requirement).

 

[martinbn]

BR, Born rule sorry.

My question was a bit rethorical, clearly BR is not there in the ingredients if not we would not be having this discussion nor there would be a whole section on BR in Wikipedia's article on MWI.

If the BR is not an ingredient, then it has to be justified. Of course we can add BR to MWI, but most criticism seems not to be focused on that version of MWI.

Is BR part of QM? I would say yes. Then it is a part of every QM interpretation. Why should any interpretation derive it!

 

[jbergman]

MWI is not the only interpretation without collapse. Does any of the others derive the Born rule?

Bohmian interpretation offers an explanation, I believe. I'm not an expert on it but as I understand it the distribution of the hidden variables is assumed to be as such that when measured you end up with probabilities compatible with the Born rule.

In addition, collapse is also explained. See, https://plato.stanford.edu/entries/qm-bohm/#QuanRand

 

[PeterDonis]

Is BR part of QM? I would say yes. Then it is a part of every QM interpretation. Why should any interpretation derive it!

BR is a part of QM in the sense that it is needed to make predictions that match observations. QM in itself just takes it as a postulate.

However, whether a particular QM interpretation can just accept it as a postulate depends on the interpretation. The whole point of QM interpretations (or at least most of them--see further comment below) is to explain, at least to some extent, why the machinery that QM uses to make predictions works. Just accepting every postulate of QM as a postulate doesn't do that. (Which is exactly why many people complain about the Copenhagen interpretation--because it basically amounts to saying that there is no explanation beyond just accepting every postulate of QM as a postulate.)

In the case of the MWI, since the Born Rule depends on having a meaningful concept of probability, if the MWI cannot support such a concept, then the Born Rule can't be given any meaning in the MWI. So "deriving the Born Rule in the MWI" really means "formulating a meaningful concept of probability in the MWI and then showing how the MWI explains why the Born Rule works using that concept".

 

[kered rettop]

It is not repeatable.

Nothing is repeatable. Your point?

 

[pines-demon]

In the case of the MWI, since the Born Rule depends on having a meaningful concept of probability, if the MWI cannot support such a concept

why we cannot have a meaningful probability in MWI? See post #43