Most people would agree that the sun emits light in all directions, but there is no way to prove it with concrete evidence. The only thing you can prove with concrete evidence is that the sun emits light in the direction of objects in our solar system that we can see. We infer that the sun emits light in all directions because that is the best explanation that accounts for the data that we have.
Many-worlds is the same. We can't demonstrate their existence, we infer it from the current-best explanation that accounts for the data that we have.
Many-worlds is by far not accepted to be the "current-best explanation".
It's a candidate. It's not clear it's right.
I realize that's argument by authority, and that's considered a fallacy...
https://www.amazon.com/Philosophy-Physics-Princeton-Foundati...
https://www.amazon.com/Quantum-Mechanics-Experience-David-Al...
Or, if you don't feel like buying a book:
https://flownet.com/ron/QM.pdf
Or, if you prefer a video:
https://www.youtube.com/watch?v=dEaecUuEqfc
BTW, it may come as a surprise to learn that I am actually not a big proponent of many-worlds despite recognizing that it is in fact a logical consequence of the math. If so, you may find this interesting too:
https://blog.rongarret.info/2009/04/on-shadow-photons-and-re...
and a follow-up written ten years later:
https://blog.rongarret.info/2019/07/the-trouble-with-many-wo...
The chasm between my grades in linear algebra and my grades in quantum begs to differ... :(
> It's not mystical nonsense, it's a logical consequence of the mathematics of quantum mechanics.
It's an interpretation of the mathematics of quantum mechanics. It's not the only possible interpretation.
> You may find it distasteful, but it's the way the world appears to be.
Yeah? I agree that quantum appears to be the way the world works; show me your concrete evidence for many worlds. You can't do it.