I think many worlds interpretation is inconsistent with the EPR paradox. Quantum mechanics says that particles are really in more places at the same time and the particle is really only probability wave - otherwise the concept of probability in quantum mechanics doesn't make a sense, because everything have its own specific cause (There is no probability 1/6 that you roll the dice at the six - because this "probability" is caused as your brain controls your muscles in your hand). But the world where everything have only probable location (and everything is on more locations) makes a sense - because cause could be on more locations too (Imagine particle, what collide with another particle - if both of them have specified position, we know where the second particle will fly. But when probability wave collide with another probability wave, we don't know where they will fly, because we don't know one specific direction of this forces.). But in many worlds interpretation is in one world only one particle at the one place - otherwise we describe another interpretation, where Schrödinger's cat alive and died. So how could be many worlds interpretation possible?
What causes which world will we live in? (This does not imply that Hugh Everett was wrong - only that many worlds interpretation is incomplete.)
"But in many worlds interpretation is in one world only one particle at the one place" For the awful pop-sci version of MWI yes, but for actual MWI no. MWI is formulated with the math of quantum mechanics, and that means the Schrodinger equation. Have you read Everett's thesis? Assuming you already know some of how QM works, it's actually a fairly easy read for the most part. Basically he normal Schrodinger equation involves multiple blobs of high probability that "don't interact with each other" (this is not interpretation dependent, and just how the math works), and Everett just assumes (essentially) that 1. the wavefunction is a real physical thing, and 2. this effect bubbles up to the macroscopic level without any interference. This page, while somewhat dogmatic (the demonstration does not prove many worlds in any sense whatsoever, but is just a basic demonstration of how the Schrodinger equation works), has a more honest representation of what MWI is about.
More importantly according to MWI we live in all worlds, not just one. There is no "cause" here because there's no choosing event, there just appears to be one from the inside. If I clone you several times and place half the clones inside and half outside, asking "by what process was I selected to be inside" is asking the wrong question. A possibility wasn't 'selected' in any meaningful way. All possible options play out over several clones that have no contact with each other, and each clone looking back through its repeated cloning/placement history sees a single history and a convergence to a particular ratio of inside to outside placements, which we interpret as measurement probabilities.