I am confused about the relationship between relative state and
decoherence in the Many Worlds Interpretation of QM. My understanding of
MWI is that as the universal wavefunction evolves, components of it
decohere from each other, and when this happens we can think of it as the
world spliting into branches and treat the components seperately from that
point on because they would be unlikely to interfere with each other. 

Now how does relative state fit into this? Is relative state still an
important part of the MWI, or is decoherence sufficient for the
interpretation?

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