That's science fiction, though. The Everettian Many Worlds Interpretation is just that: An interpretation of a set of equations. And pretty much by definition the worlds cannot interact in any way. Even if there were some obscure way to differentiate between MWI and, say, the Copenhagen interpretation, I wouldn't expect it to become feasible anytime soon. But as far as I know there cannot be any experiments differentiating between the two (or other interpretations), because they're simply different interpretations of the same equations. They predict the same experimental outcomes.