QM being linear doesn't make the universe linear. Schrodinger's equation doesn't work across measurements (or universes.) And if you try to weasel out of that by saying we will describe the multiverse instead, you have just created the unexplainable phenomena of being in a specific universe, with no way to accurately describe the process behind the random choice of the universe you reside in.
> unexplainable phenomena of being in a specific universe
One universe has "observer" (a bunch of variables, really) in one state, another has it in different state. Those variables encode some information about themselves, so indeed in different universes the different "versions" of the observer are different, and each perceive it as universe randomly deciding to chose their version of existence. So what?
We're parts of the physical reality so trying to describing physics from the point of view of an out-of-universe observer, while psychologically attractive, is ultimately futile: in QM, such approach breaks very quickly.
