I don't know enough of the underlying physics to conclusively comment one way or another, but it seems to me defining "total mass" as the integral of "local mass" over all worlds wrt the world probability measure implies that an object in one world might be able to mysteriously (wrt that world) gain mass by reducing its mass in some set of worlds with non-zero measure.
We don't actually see that in e.g. particle scattering, right?
This would manifest as non-conservation of energy-momentum in scattering, and, as far as I know, nothing like that has been seen since neutrino was predicted by Pauli to remedy the apparent non-conservation of energy in radioactive decay. If we assume non-interacting worlds, then one should not expect to see such violations. Gravity might be an oddball, however, since different worlds are likely to have difference spacetime geometry and even topology potentially affecting each other. But this is highly speculative, as there is no adequate microscopic (quan...
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