[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?