The experiment you liked is just a supped up version of the experiments that first showed that Bell's Inequality is violated in our reality. The experiment did

The experiment you liked is just a supped up version of the experiments that first showed that Bell's Inequality is violated in our reality. The experiment didn't really have any theoretical import. I don't think anybody really thought that Freedman and Clauser's experimental outcome was due to some "loophole" that, when closed, would let Bell's Inequality be satisfied. And despite what the experimenters seem to believe, the experiment you linked to does not show non-local effects. That's not really the way that science and experimentation work. The experimental result rules out a particular class of physical theory - specifically any theory that's local and real, but a deep assumption of the derivation (so deep that one doesn't realize one is making it) is that every measurement has one outcome, which of course Many Worlds does not assume. I don't think that anyone is hand waving about where probabilities come from -- they are the integral of the squared modulus of the wave function. Nothing ambiguous about the mathematics of the theory. If you're asking why this equation rather than some other equation, it's an open question, and an interesting one. But the Many Worlds Theory can perfectly well do its job as a predictor of experiment without justification of where the equation comes from. You may as well ask "Why the Schrodinger Equation rather than some other equation?". It's also worth pointing out that all interpretations of QM have the same open question because they all have some form of the Born Rule without justification.