[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.