Yeah, I mean, at this scale you’re not going to prove how nature is from any of this. What MWI is saying is that if you admit a really difficult view of the cosmos, then you can regard the Born rule as part of Schrödinger evolution—but it is kind of only possible because you punted the details into that difficult view of the cosmos. (And then the MWI-supporters come in full force and argue that actually the view is not so “difficult” after all.)

Backing up, the problem is that you have these different approaches—depending on how you count them you could maybe group them broadly and say there are 3-4, or as large as a dozen or two—that are all mathematically identical. They all predict the Born rule, but suggest different ways that Nature really fundamentally would act to produce that rule.

Since they are mathematically identical, it is provable that there is no way to choose between them. As a result, the one which steps the most out of peoples’ ways to enable experimental results, has better “genes” for its own reproduction in the publication of papers. And that has just been the Copenhagen interpretation: you the experimentalist have a soul and when that soul measures the world the nice unitary evolution of the world comes crashing down with probabilities given by the Born rule. Contrast with pilot-wave theories where you have to work out a whole separate equation that doesn’t do anything which makes any further observational impact.

The basic issue that we are facing is that while the notion of souls seems laughable for fashionable sciencey people, it also seems in some distressing way inevitable. You take Many Worlds for instance, you admit the reality of every single possibility of the entire universe as a much broader multiverse. An equation, the Schrödinger equation, essentially works over, say, a Planck time to create a vector field on top of this, saying “This instant is followed by that instant is followed by that instant.”

In the middle of that, what uniquely qualifies my experience here and now as I know such experience must exist? I do not perceive a multiverse; I perceive a changing universe. And MWI says “well actually there are a million yous, frozen in time, all perceiving changing universes. Your experience of motion through time is actually kind of a lie.” This is not a unique problem to QM; it happened much earlier with special relativity where we discovered that you are actually a rope of worldlines thrusting through a static four-dimensional Lorentzian manifold, every part of that rope being presumably in a separate conscious state, perceiving itself as moving through time but we “on the outside” can see that there is no unique present defined such that it can wash over all of the ropes simultaneously. MWI just happens to facilitate the same basic “unrolling of time” because it has already unrolled all of possibility-space. And to fix it you need something—I’m calling it a soul, you can get fancy—which “zips along the worldline” and contains my conscious experience, or you need to argue that my experience is an illusion, or you need some “universe-soul” to act like a coherent “present moment” for all of us, or the like. It all kind of sucks.

There is a nice perspective sitting in the middle of this due to Andreas O. Tell [1], and it is pleasantly agnostic while still doing something like what MWI is doing to try and derive the Born rule from normal wavefunction evolution. In brief, he says: “use the state-matrix formalism for QM, and take a completely agnostic view of what the cosmos is and how it behaves. Still if you have a local information-processing system which is embedded in the cosmos and changing, then it receives information and must update its model of the universe. Its model of the universe must necessarily come down to a list of wavefunctions with a list of weightings, but there is a freedom-of-perspective which allows you to choose the wavefunction with the highest weight as “the” one that you think the system is in. New data just forces these weights to cross in size, causing the Born rule when you try to determine whether those weights will cross over and the system will be in the new state.”

In some sense then we can live in a very Copenhageny world where we are changing data-processors uniquely present in some space and time, but we can use Schrödinger evolution to derive the Born rule just the same as the many-worlds interpretation does, but rather than committing to its plethora of different universes we might be able to just remain non-committal about what is in the rest of the universe, beyond what I see in it.

[1] https://arxiv.org/abs/1205.0293