>it's meaningless to ask whether those other worlds really exist or not
Dunno - if you think of something like the two slit experiment whether the worlds where the particle goes through slit one or where it goes through slit two exist or not seems to have experimental results as they produce an interference pattern.
You can also ask about more complicated situations and whether the other worlds exist may not be meaningless if they have an effect on event probabilities in ours, if only a small one.
> if you think of something like the two slit experiment whether the worlds where the particle goes through slit one or where it goes through slit two exist or not seems to have experimental results as they produce an interference pattern
Intereference is not due to the interaction between "worlds". You don't have "one world" where the particle goes through one slit and "another world" where it goes through another. (If you think that's the case, how does "our world" where the interefence can be observed fit in that description?)
You can perfectly explain interference with a single world where the particle doesn't go through any particular slit. It doesn't have to, because we're not trying to determine which slit it goes through (and if we do, the interference disappears).
In the many worlds interpretation, as soon as a world has "split"/"the wave of differentiation has hit"/"particles have been entangled"/"whatever terminology you want to use" from the observer, it has zero impact on any future results, not just a small impact. Until that split happens, we're just talking about our own world. It's never possible to observe any evidence for more than one world, that follows from the way we define what a "world" is.
Many-worlds does not try to explain why particles have a wave function, it only tries to explain the source of the apparent randomness in the way that wave function collapses, whilst removing the need for experimenters to be in some way "special" and immune from quantum effects.
Is that really true? In principle, if many worlds is the case then you could have a super machine enact a powerful unitary transformation which transforms the state of the observer such that there is interference between the two copies of the observer.
Dunno - if you think of something like the two slit experiment whether the worlds where the particle goes through slit one or where it goes through slit two exist or not seems to have experimental results as they produce an interference pattern.
You can also ask about more complicated situations and whether the other worlds exist may not be meaningless if they have an effect on event probabilities in ours, if only a small one.