What is the true nature of worlds in the Many-Worlds Interpretation?

[kered rettop]

TL;DR Summary

Happy New Year to anyone asking it, but it's a bad question.

The "worlds" of MWI do not actually appear in the theory behind it. They are, so to speak, an interpretation of the interpretation. But what exactly are worlds?

The picture begins with an interaction. In general this results in an entanglement. If we decompose it into product terms, each of them develops, by further interactions, into a state which reflects one of the "possible" outcomes of the interaction. These separate (now generally accepted to be due to decoherence) into non-interacting worlds.

So the simple view would be that a world is a macroscopic state reflecting one possible outcome. Writers such as Vongehr refer to these as phenomenal worlds.

Which is fine in a controlled environment, but in nature there is no obvious basis for the decomposition, so the number of worlds is undefined.

You could even chose a basis that is the original state itself so that there is no superposition and you just have one phenomenal world.

This issue goes away if there is a preferred basis, or one set by the experimenter, of course.

Next issue: the previous was about worlds as phenomenal states - observable macroscopic states. But the states needn't be macroscopic. Each microstate, representing one particular set of outcomes for all the microscopic interactions, is derived from one or other of the original possibilities, so they can all be referred to as worlds. They are (presumably) all phenomenal to an embedded observer.

So now we can ask "when did the worlds separate?" The simple answer is that it doesn't take long for the worlds to separate "enough". But it's always possible to push back to the moment of interaction where the worlds don't yet exist. Each component of the original superposition is therefore a seed for either one of the relatively few macro-worlds or for a whole bundle of micro-worlds.

The above seems, to me, to render the question "how many worlds" specious.

 

[PeterDonis]

The "worlds" of MWI do not actually appear in the theory behind it.

"The theory behind" the MWI is just standard QM. It is true that "worlds" do not appear in that theory. But that's because the MWI is an interpretation of QM, not QM itself.

They are, so to speak, an interpretation of the interpretation.

No, they are part of the particular interpretation we call the MWI. They are not another "layer" on top of it.

But what exactly are worlds?

https://plato.stanford.edu/entries/qm-manyworlds/

 

[PeterDonis]

The above seems, to me, to render the question "how many worlds" specious.

I think it is fair to say that the issue of "counting worlds" is an open one for the MWI.

However, I think one also has to ask whether that question even needs an answer. What if we just accept that in the MWI, in general, the "number of worlds" is undefined? What bad consequences follow?

 

[kered rettop]

I think it is fair to say that the issue of "counting worlds" is an open one for the MWI.

However, I think one also has to ask whether that question even needs an answer. What if we just accept that in the MWI, in general, the "number of worlds" is undefined?

Well, yes, it's not defined. But that isn't because it's not definable, it's because there are many ways to define it. For instance you can refer to Zurek's derivation of the Born Rule (which I know you dispute) as "world-counting". But what actually gets counted is the terms in a sum-of-products decomposition, which is well-defined.

What bad consequences follow?

What, from recognising that you need to say what you mean? Not a lot.

"The theory behind" the MWI is just standard QM. It is true that "worlds" do not appear in that theory. But that's because the MWI is an interpretation of QM, not QM itself.

I meant the specific bit of theory that was kicked off by Everett as his Relative State Formulation. It did not have worlds in it until someone rebranded the RSF as MWI.

 

[PeterDonis]

I meant the specific bit of theory that was kicked off by Everett as his Relative State Formulation. It did not have worlds in it until someone rebranded the RSF as MWI.

If you want to say that the "original Everett interpretation" and the "rebranded MWI" are two different interpretations, you of course have a right to your opinion. Then of course this whole thread would be irrelevant for your "Everett interpretation" since by your definition it doesn't have worlds in it. So we can just discuss your "rebranded MWI", which does have worlds in it, and which pretty much everyone else, as far as I can see, just calls the MWI.

 

[PeterDonis]

What, from recognising that you need to say what you mean?

No, from taking the position that there is no need to have a single unique definition of "how many worlds" at all. We can just ignore the whole issue. What bad consequences follow if we do that?

 

[kered rettop]

No, from taking the position that there is no need to have a single unique definition of "how many worlds" at all. We can just ignore the whole issue. What bad consequences follow if we do that?

"We can just ignore the whole issue" does not follow from "no need to have a single unique definition." You need to be more specific about what you propose to ignore.
- edited

 

[kith]

I like to separate the measurement problem into three parts (this is inspired by Schlosshauer's book "Decoherence and the Quantum-to-Classical-Transition"):

1) The problem of subsystems (how to split the universe into subsystems?)
2) The problem of the preferred basis (given a split, how are physical quantities like position singled out compared to unphysical superpositions which should be on equal footing a priori?)
3) The problem of outcomes (given the transition of the subsystem from a pure state to an irreversibly decohered mixed state, how are single outcomes realized?)

The second problem seems to be solved by environmentally-induced decoherence (or "einselection") which is derived from the theory of quantum dynamics of open systems. The third problem is somewhat dissolved by the MWI because all possible outcomes are on equal footing. (I'm saying "somewhat" because I think the answers to questions like "when does the splitting occur" are too vague, but all in all, I think the MWI is an illuminating perspective on these issues.)

You mostly seem to be concerned with the first problem and I think this is a subtle point. In a sense, the state vector of the universe rotating in Hilbert space is a very boring object. The rich structure arises only if we leave the bird's eye view and take the frog's eye view which feels awkwardly Copenhagen-like when taking a MWI perspective. There's some discussion of the problem of subsystems in chapter 2.14 of Schlosshauer's book and this paper which has been discussed here quite some time ago.

 

[kered rettop]

If you want to say...

I don't.
Perhaps it would have been clearer if I'd said "argument" rather than "theory".

 

[PeterDonis]

"We can just ignore the whole issue" does not follow from "no need to have a single unique definition." You need to be more specific about what you propose to ignore.

Um, I am proposing to ignore the fact that there is no single unique definition? I wasn't claiming that "ignore" is logically required by "no unique definition". I was asking what the problem is with just ignoring it as a choice.

 

[PeterDonis]

I don't.

Then what was your point in bringing up the distinction at all?

 

[PeterDonis]

This thread is now closed.