Many Worlds locality and EPR experiment I've read in Sean Carroll's book (Something Deeply Hidden) that the Many-Worlds interpretation of quantum mechanics might be the only way to avoid instantaneous effects of entanglement, by having the branching expand from the branching-event at the speed of light. This makes sense to me, observers far away are still "single-copy", until the branching reaches them.
But if we think of the experiment with Alice and Bob and their entangled particles far away (which must have opposite spins), I'm not sure what to make of it. When A or B measures the electron, there's the branching and we have the two worlds with the two possible outcomes (feel free to correct me, that's just how I understood it).
Now from the measurement event we then get the branching expanding at the speed of light.
What I don't get is: if they both measure their electron at -almost- the same time (whatever that means, let's say before light can travel between them anyway), then how can we think about branching? We have 2 particles with 2 states each, but only 2 possible combinations (=>worlds), either up/down or down/up.
So if Alice measures up and Bob measures down, that's two measurements and two branching events, but the outcome is related (the "Alice up" world can only go with the "Bob down" world), so do the branches "join" halfway through? Is that two branching events in two different places for the same branch?
And even then, I'm not sure how this solves the problem of "how does the particle immediately know which state to take/which world to join", that still seems completely non-local to me.
Note: I'm aware that "worlds" are just a puny human interpretation, but I definitely don't have the mathematical skills to understand the rules at the bottom of it, therefore I'm just asking for "a way to think about it".
 A: I'm not sure what Carroll said, but I do not think that Many Worlds avoids non-locality in entanglement, at least not in this way you're talking about it (one can debate just what locality means). Since branching is ultimately an 'arbitrary' way of splitting a wave function as a sum of (practically) non-interacting terms, I don't believe there's much precise meaning in statements like "the branching expands from the branching event at the speed of light".
In the EPR case, imagine we have the combined two-particle system in the state (ignoring the normalization for simplicity)
$$|\uparrow \rangle_A |\downarrow \rangle_B + |\downarrow \rangle_A |\uparrow \rangle_B $$
where the subscripts $A,B$ stand for Alice and Bob's particles. If Alice measures the spin of her particle, the universal wave function describing the situation really is
$$ |\text{Alice's detector measured} \uparrow \rangle |\uparrow \rangle_A |\downarrow \rangle_B + |\text{Alice's detector measured} \downarrow \rangle |\downarrow \rangle_A |\uparrow \rangle_B $$
The content of the No Communication theorem is that the information locally accessible to Bob (who has no access to $A$ or the dectector) has not changed. In this way locality is preserved -- you cannot use entanglement for communication.
However, the description is still non-local. It only makes sense to speak of the state of both particles at once (that's what entanglement is about). It's not that Bob's particle "knows" the result of Alice's measurement and won't contradict it. They have a combined state, and in that combined state there simply isn't a possibility of finding both up or both down.
There's still an uncomfortable non-locality here and it cannot be wished away - it ultimately becomes the violation of Bell's inequality, and this has been experimentally confirmed. Crucially, however, you can only attest that Bell's inequality has been violated once you compare the measurements of Alice and Bob, and so information must have had time to travel (respecting the speed of light limit). In this way quantum theory maintains a curious, but ultimately consistent, middle-of-the-road position between locality and non-locality.
A: Let's say physicists on planet x choose randomly a positron or an electron and send that particle up to space from the north pole. Then they send that particle's anti-particle up to space from the south pole.
Now an important thing is that the sent particle carries quite a lot of information about the planet.
If people on planet y observe that a positron was sent to their direction, then they know that in their branch the history of the planet x is such that an electron was sent to the opposite direction, at least if they discussed about the experiment with the people of the other planet.
So the planet y becomes entangled with the planet x. The way the two planets branch becomes correlated.
speed of propagation of branching = speed of propagation of information
