[ben_w]

Speaking as a barely informed enthusiast, we can say they exist in the Occam’s Razor sense that the maths is much less complicated when we assume they do.

I think there’s also an experimental setup, whose name I forget, but which is essentially nested Schrödinger's cat setups: Alice is in a box, Bob is in a box which contains Alice’s box, Carol is outside; Alice goes into superposition of |Alice+> and |Alice->, Bob opens the box and Carol can now demonstrate that Bob is in a superposition of |observing Alice+> and |observing Alice-> instead of the combination of 100%|observing> and a superposition of |Alice+> and |Alice->.

[tsimionescu]

The maths is the same whether we interpret it as many worlds, wave function collapse, and others.

[ben_w]

Well of course. It they were different — or at least if they gave different conclusions — we could rule some of them out.