MWI distinguishes itself by omitting (as you say) any notion of "collapse" from its axioms. This is appealing for simplicity but the problem is how it connects to experimental results:
1. How does the Born rule arise? If the universe split into two but the measure of cat-dead is 1/pi, why do I find myself in the cat-alive universe more often?
2. More generally, how does randomness arise? MWI contains only deterministic axioms, so how can it explain the experimental observation that measurements of similarly prepared states result in different values?
Imagine instead of a single experimenter observing a billion possible outcomes, a billion experimenters observing a single possible outcome.
The hope of MWI is to produce a simpler theory by eliminating an axiom. If this forces us to axiomatize "conscious observers" then it has already failed. Though I admit it may be fun to think about.
My guess would be that they are all consciously experienced, some more and some less. The alternative seems to be to say that they are so called "p-zombies". Very similiar to us, evolving according to the same laws, but not concious. But it's really up in the air.
> 1. How does the Born rule arise?
> 2. More generally, how does randomness arise?
As you said, with Many Worlds there is no randomness. The multiverse is entirely deterministic. Randomness is a Copenhagen-like concept.
There is a "universe" with an alive cat and a "universe" with a dead cat. These universes have a certain waveform distribution.
Neither of these universe are any more real or extant than the other (they have the same magnitude).*
* Though consciousness and its observations seems to follow only one path. This is a peculiarity outside the realm of physics.
Of course physics can answer this: the human minds on the different branches can't physically interact. They can't share memories. Each one is going to remember experiencing only its own branch.
Whether this is a problem or not depends on what your conception of consciousness/identity is. I see a conflict or unanswered problem there; you may not.
Wondering why you're a specific one of them and not the other seems equivalent to me to wondering why you're you and not some another person in our own world. I think it's an interesting question, but I'm not sure what an answer to it could possibly look like (since any answer that says why you're you somehow needs to work out differently for other people to explain why they're themselves too) which implies the question is malformed somehow. (If your consciousness were ... someone else, or even switched people it was tracking somehow, it's not like anyone would notice.)
Indeed.
MWI's solution to this is to say the experiments are wrong, and the results are actually the same. It rejects empiricism to simplify the theory. But that's not good science.
> Neither of these universe are any more real or extant than the other (they have the same magnitude)
What is meant by "magnitude?" It can't be the measure of the wavefunction because those can easily be different, e.g. if the particle's decay probability is not 50%. This is the Born rule problem again.
It’s as if non-determinists aren’t sure that 2 doesn’t act like a 3 sometimes because of decoherence and so 2 + 3 = 6 as a result.
Where am I going wrong in this line of thinking? How could randomness be injected into a system without superpositioning of quarks? Is that literally the only way?
Is Hawking radiation the smoking gun we think it is?
Edit: I admit I am tired when posting but this topic is perhaps one of the most fascinating of all. I can’t stay away.
It's like matrix multiplication: yes you can wind up with more elements after the operation, but the result as a whole is entirely deterministic.
If you defined matrix multiple multiplication where you collapsed the result down to a single unspecified vector, then you would have "randomness" (according to the selection).
Many worlds says "don't choose"; keep the entire matrix, and the results will get larger and larger.
The universe is not fundamentally rolling dice, though it appears that way from your perspective since you can only see a single slice of the matrix.
So the “realm of physics” is now disconnected from empirical reality? Great.
Unfortunately, yes. Empirical reality is limited by the empiricist.
---
Consider the famous Schroedinger's Cat.
The decayed particle has two states: decayed and not decayed.
The cat has two states: dead and alive.
The researcher that opens the box has two states: sad and happy.
The waveform does not collaprse. The particle, the cat, and the researcher each have a uncollapsed waveform; i.e. are in both states.
However, these waveforms are not independent; they are entangled. The decayed particle is coincident with the dead cat and the unhappy researcher. And the undecayed particle with the alive cat and the happy researcher.
All states "exist" simultaneously, but not independently. This bifurcation in the wave function magnitudes is a "split" in the universe: every future waveform interaction will be in the context of decayed particle/dead cat/unhappy researcher and undecayed particle/alive cat/happy researcher.
"Many worlds" sounds nonsensical, but it is really just a colloquial expression for waveform entanglement.
---
Now this does present a philosophical question on how consciousness functions in light of the split waveforms.
I maintain that science -- quantum mechanics or otherwise -- has no explanation or even language to express "consciousness". It's like asking science an ethics question. And this inability applies to all science, not just quantum mechanics.