[kgwgk]

While you no longer need wave functions to collapse, you need universes to branch out. The latter interpretation doesn't seem "better" than the former as far as being a reasonable description of the real world goes. And of course for all practical purposes they are equivalent.

[whatshisface]

The universes don't need an additional mechanism in order to branch out, wavefunctions will already do this if they're left alone (to be clear about what I'm saying, I mean that if you isolated some particles in a box they would start doing multiverse). The natural behavior of wavefunctions is to do multiverse, and if you want something else you have to introduce an additional mechanism that collapses them.

[kgwgk]

And what does it mean for a few-particles isolated system to start doing multiverse? Cannot you just describe it with a wave function without any branching out? The standard interpretation of quantum mechanics doesn't have any issues with the evolution of an isolated system, it doesn't require continous wave function collapse.

[whatshisface]

The isoated particles will, according to accepted physics, do everything that MV says we are doing. The discrete branches are a textbook illustration; it's really more of a continuous thing. There's still only one wavefunction, it just behaves in a way that can be compared to branching.

In a nutshell the idea of multiverse is that the entire universe evolves as an isolated system, without any wavefunction collapse.

[kgwgk]

I know, but you need to reconcile that with the universe we observe where looking at the system will find it in a definite state and not in a superposition. What is the multiverse response precisely? How is "branching magic" an improvement over "collapsing magic"?

[whatshisface]

"Collapsing magic" consists of a projection that somehow happens during the time-evolution of the wavefunction, changing it from a superposition of eigenfunctions into one eigenfunction.

"Branching," to the extent that branching is a good word for what happens, already is known to be a behavior of wavefunctions: as a Gaussian pulse moves, it spreads out (due to dispersion inherent to the Schrodinger equation), and we as humans can arbitrarily call that branching. (But, like I said, it's continuous instead of discrete like the word branching would imply.)

So, what remains is to explain why we find the universe in a definite state, if it time-evolves into something other than specific eigenvalues. But, first, I'll ask you: what happens if you put a manned capsule inside of the isolated particle box, so that the person inside the capsule starts dispersing too?

[kgwgk]

In summary, the situation seems to be:

0) quantum mechanics is great, but it can lead to quantum systems described as a superposition of states and then we need to explain why we find the universe in a definite state.

1a) one option is to say that the wave function collapses to a definite state.

1b) another option is to say that there is a multiverse... and what remains is to explain why we find the universe in a definite state.

Solution (a) may be ugly, but “solution” (b) sets you back to the starting point!

[kgwgk]

I fail to see the relation between "branching" (or however do you want to call the feature that separates the standard universe from the multiverse, I let you pick the name for it) and the unitary evolution of the wave function.

As for your question: I don't know. Let's say the Schroedinger equation is actually not perfectly linear and there is spontaneous collapse which happens quite rapidly for a system with N~10^30 particles. Now what?

[kgwgk]

Which existing mechanism gets you from that metaphysical multiverse to the physical universe?

[whatshisface]

The "multiverse" would be one big wavefunction (quite physical), and each "universe" would be a partition of the wavefunction in phase space. In this sense "multiverse" and "universe" would just be names for different parts of the wavefunction, like "The Rocky Mountains," and "Kona," would be names for features on a topo map.

[kgwgk]

Which basis is used to partition the wavefunction?

If you are going to tell me that it is according to the eigenvalues of the observable operator it's not that different from saying that there is a collapse on one of the eigenvalues of the measurement.

And the question remains for your "isolated particles in a box doing multiverse". How is the partition of the wavefunction done if there is no preferred basis?

Edit: Maybe in your interpretation the only "physical" thing is the universe described by its wave function and those infinite multiverses are just mathematical "projections" of that wavefunction. But then how can a mathematical operation without any physical substrate explain anything about the physical world?

[whatshisface]

Not every "fundamental" statement in physics is a natural law, for example the idea of grouping together like microstates into macrostates. We group together microstates into macrostates based on their macrovariables, which are selected to line up with emergent behavior that we observe on the macroscale. Temperature is well-motivated, but it's motivated in a different way than position.

In Multiverse, the projection-onto-eigenbases statistical rule (which guides the partition of the wavefunction into conceptual universes), is seen as being like thermodynamics: statistical, and motivated to compress vast microscopic information into variables that are nice for humans. Someone who thought MV was the right idea would say that projections were a way to calculate the fraction of universes in which something was true, and thereby your probability of ending up in one where it was. In that view, it's emergent, instead of fundamental - like temperature. This reduces the number of fundamental ideas necessary by allowing projection to emerge instead of being asserted.

[kgwgk]

It's interesting that you mention thermodynamics. Macrostates are not a real thing. They are a reflection of our lack of knowledge about the precise state of the physical universe. We use a statistical ensemble of microstates, all of which could be the actual one as far as we can tell. In the best case, the true microstate will be included. But thermodynamic properties are not "real", they are a construct.

I don't see the point of the analogy. In statistical mechanics we have to consider all the possible microstates because we don't know which one is real. In the multiverse approach we know what universe is real, so what is the point in keeping all the universes that "could have been but are not" around? We know they are not real! Deriving thermodynamics from statistical mechanics we get a useful theory. What does the multiverse bring us?

The wave function can be interpreted epistemologically, as the expression of our lack of knowledge of the precise state of the universe (v.g. pilot wave theory). But there is no need for parallel universes that we know are not real, if you want to have virtual parallel universes they will be just those that we could be in as far as we know (and one of them will be the true one). The wave function collapse is in that interpretation the fact of narrowing the set of potential universes compatible with the actual one, as we learn more about the universe we live in.