The deeper (and truer) version of "conservation of matter" is conservation of energy. And energy is conserved in many worlds. In fact, that's one of the advantages of many worlds over objective collapse interpretations, because collapse doesn't conserve energy. You can think of it this way: in order for the math for energy conservation to work out, we need those extra worlds. If you remove them, the math doesn't work out.
Slightly more technical explanation: The Schrodinger equation (which fully governs the evolution of the wavefunction in MWI) has a particular property, called unitarity. If you have a system whose evolution is unitary and also invariant under time translation, then you can prove that energy is conserved in that system. In collapse interpretations, the smooth Schrodinger evolution is intermittently interrupted by a collapse process, and that makes the evolution as a whole non-unitary, which means the proof of energy conservation no longer goes through (and you can in fact show that energy isn't conserved).
collapse doesn't conserve energy
This is quite misleading. Since collapse is experimentally compatible with "shut up and calculate", which is the minimal non-interpretation of QM, and it describes our world, where energy is mostly conserved, energy is also conserved in the collapse-based interpretations.
You can think of it this way: in order for the math for energy conservation to work out, we need those extra worlds. If you remove them, the math doesn't work out.
That's wrong, as far as I understand. The math works out perfectly. Objective ...
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