No, at least not in a technical mathematical-physics sense. “Conservation of matter”, in mathematical physics, translates to the Hamiltonian operator being conserved, and that happens in quantum physics and a fortiori in all its plausible philosophical interpretations. In concrete, operationalist terms, this implies that an observer measuring the energy of the system at different times (without disturbing it in other way in the meantime) will see the same energy. It doesn’t imply anything about adding results of observations in different MWI branches (which is probably meaningless).
For example if you have an electron with a given energy and another variable that “branches”, then observers in each branch will see it with the same energy it had originally, and this is all the formal mathematical meaning of “conservation” requires. The intuition that the two branches together have “more energy” that there was initially and this is a conservation problem is mixing pictorial images used to describe the process in words, with the technical meaning of terms.
No, at least not in a technical mathematical-physics sense. “Conservation of matter”, in mathematical physics, translates to the Hamiltonian operator being conserved, and that happens in quantum physics and a fortiori in all its plausible philosophical interpretations. In concrete, operationalist terms, this implies that an observer measuring the energy of the system at different times (without disturbing it in other way in the meantime) will see the same energy. It doesn’t imply anything about adding results of observations in different MWI branches (which is probably meaningless).
For example if you have an electron with a given energy and another variable that “branches”, then observers in each branch will see it with the same energy it had originally, and this is all the formal mathematical meaning of “conservation” requires. The intuition that the two branches together have “more energy” that there was initially and this is a conservation problem is mixing pictorial images used to describe the process in words, with the technical meaning of terms.