This is not true, and it is one of the merits of Many Worlds to allow QM to respect locality and causality. If you want to know the details, I put it in my journal, but the point is essentially this:ShalomShlomo said:Bell showed that QM itself formally breaks causality.
ie whether QM is Classical, Copenhagen, Many Worlds, Bohmiam, etc all describe a QM that violates causality because QM itself violates causality.
when Alice performs her "measurement", with respect to Bob, she's just in a superposition, and got entangled with her photon, BUT ACCORDING TO BOB, THERE WASN'T ANY RESULT AT ALICE'S. It is only when Bob LEARNS about Alice's result that he in fact chooses in which branch he lives, but this happens of course when he's in local (causal) contact with Alice, or with a messenger of Alice.
So that's the way how many worlds gets around Bell's theorem: there simply WASN'T A RESULT at Alice's and at Bob's, so you cannot talk about the probability of Alice to have observed something, from Bob's point of view.
It is described in much more detail in my journal (collection of old posts on the subject).