Once decoherence has occurred I don’t think it’s meaningful to say that the system exists in a superposition of states. The multiple decohered branches of the wave function can no longer interfere with each other and so there’s no way for them to affect each other, which is why we call them separate worlds. Within each decohered branch there’s an experimental apparatus and a human that sees one specific outcome. This was Everett’s main insight that each observer in each branch experiences what looks like a collapse but is really just their brain becoming entangled with one or other of the measurements.
According to quantum mechanics, they can no longer interfere with each other.
But we are bringing gravity into the mix. Gravity works differently than the other forces. Do space-time structures also exist in a superposition of states? Or does QM work against an essentially classical gravitational space-time background?
Without a theory combining quantum mechanics and gravity, the answer is not obvious. The fact that the superpositions do NOT interfere gravitationally means that either there was no quantum mechanical superposition (collapse actually happened) or that gravity can also exist in superimposed states. If you believe in the Everett interpretation, then there must have been a quantum mechanical superposition, and this tells us something non-trivial about a quantum theory of gravity.
