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

[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

 

[pines-demon]

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

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 ?

 

[gentzen]

Nothing is repeatable. Your point?

To answer your request for clarification:

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

Maybe you should think about how unbelievably small the probability for the one actual history of the universe will be: 10^-1000? Which is fine, as there are a correspondingly huge number of other potential histories of the universe. But there is no way to perform or observe an experiment which could yield any of those alternatives, and certainly no way of repeating such an experiment arbitrarily often.

With respect to "Nothing is repeatable", see the beginning of my first post:

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.

 

[PeterDonis]

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

I've already discussed that in some detail in my previous post. Nothing in your post #43 addresses any of the issues I raised.

 

[pines-demon]

I've already discussed that in some detail in my previous post. Nothing in your post #43 addresses any of the issues I raised.

Which previous post?

Which point (1) and (2) of the argument of post #43 is the one making you say that probabilities cannot be defined properly. I just want to narrow down the issue.

 

[PeterDonis]

Which previous post?

All of my posts in this thread before your post #43.

Which point (1) and (2) of the argument of post #43

The posts of mine I was referring to were made before your post #43. I'm not sure I accept the framework you are using in post #43 anyway. But in any case that post doesn't address any of the issues I raised, as I said.

 

[PeroK]

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

Consider, as an analogy, a Markov chain modelling multiple tosses of a fair coin. One interpretation of the Markov chain is a schematic of possibilities, where probabilities at each branch are fundamental. And, only one actual path through the schematic actually occurs.

Another interpretation is that the Markov chain represents all things that happen. There is no fundamental probability at each branch but a split into multiple worlds. In this case, probabilities reappear in each world. For example, there is more chance of getting a total of three heads and three tails than all six heads. Because there are more worlds in one case than another.

In this case, these probabilities come from a counting of worlds.

One problem for MWI is that this interpretation of the Markov chain only coincides with the probability interpretation under strict conditions. Essentially a homogeneous branching into equally likely events at each stage. Otherwise, the numbers don't add up to the probabilities.

In any case, that would be an attempt to generate effective probabilities in a deterministic, everything actually happens model, where probability is not fundamental.

 

[jbergman]

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 ?

It has an evolution that behaves effectively like a collapse. Again, this is discussed in detail in https://plato.stanford.edu/entries/qm-bohm/

 

[PeterDonis]

In this case, probabilities reappear in each world. For example, there is more chance of getting avtotal of three heads and three tails than all six heads.

No, this is not correct. You have relative frequencies in each world, but each world only has one set of relative frequencies. If I am in the world with six heads, I have no way of knowing that there is only one world like mine, while there are multiple worlds with three heads and three tails. (Note, though, that these worlds are not identical: the sequence of individual results is different in each one. They just all have three heads and three tails.) So I have no way of making sense of the statement that "three heads and three tails are more probable than six heads". I only know that in my world there were six heads.

In fact, if I am in the world with six heads, my natural conclusion from that data will not be that there must be other worlds with different relative frequencies and my world is very improbable. My natural conclusion will be that the coin is biased towards heads. Which points to another issue with formulating a meaningful concept of probability in the MWI: observers in different worlds with different relative frequencies will not agree on what the probabilities are. And since they can never detect the other worlds, let alone compare data with them, there is no way to even make sense of the notion that they should take other worlds into account in making their probability calculations.

 

[gentzen]

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

Even in classical mechanics, we have to make some assumptions (like ergodic hypothesis) and then show that those assumptions allow us to define probabilities.

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

It is not the claim that "we cannot define probabilities". But you have to define the meaning of probabilities in your scenario, especially if you want to prove something about those probabilities, like that they follow BR.

 

[pines-demon]

It has an evolution that behaves effectively like a collapse. Again, this is discussed in detail in https://plato.stanford.edu/entries/qm-bohm/

Sure I agree that you can replace collapse with Bohmian arguments but that does not tell me anything about the Born rule. Where in that link discusses the Born rule derivation?