Comment by mr_mitm

This is not what falsifiability means in the Popperian sense. You are confusing falsifiability of a theory’s predictions with falsifiability of an additional claim of what those theories mean. We might as well say that the simulation hypothesis is falsifiable because the laws of physics govern our simulated universe, so if you can falsify those laws you can falsify the simulation hypothesis. That being said, the concept of falsifiability is not without its weaknesses.

> Many worlds is just the Schrödinger equation without the wave function collapse.

It is not, it is the Schrödinger equation plus an extra rule that says that classical observers are only certain kinds of quantum states. There's no explanation in the MWI for why a device never reads out that a particle is 1/sqrt(2) |here> + 1/sqrt(2)|there>, even though that is exactly as probable a state as being |here>. And it turns out that this is exactly equivalent to positing wave function collapse / the Born rule.

And no, decoherence has nothing to do with this. Decoherence explains why there is no observable interference at the classical level between these states, not why you can only observe some states.

This is known as the preferred basis problem, for anyone who wants to read more about it.