“Decoherence causes the Universe to develop an emergent branching structure. The existence of this branching is a robust (albeit emergent) feature of reality; so is the mod-squared amplitude for any macroscopically described history. But there is no non-arbitrary decomposition of macroscopically-described histories into ‘finest-grained’ histories, and no non-arbitrary way of counting those histories.”
Importantly though, on this approach it is still possible to quantify the combined weight (mod-squared amplitude) of all branches that share a certain macroscopic property, e.g. by saying:
“Tomorrow, the branches in which it is sunny will have combined weight 0.7”
There is no non-arbitrary definition of “sunny”. If you are fine with approximations, then you can also decide on decomposition of wavefunction into some number of observers—it’s the same problem as decomposing classical world that allows physical splitting of thick computers according to macroscopic property “number of people”.
You’re right that you can just take whatever approximation you make at the macroscopic level (‘sunny’) and convert that into a metric for counting worlds. But the point is that everyone will acknowledge that the counting part is arbitrary from the perspective of fundamental physics—but you can remove the arbitrariness that derives from fine-graining, by focusing on the weight. (That is kind of the whole point of a mathematical measure.)
There is no non-arbitrary definition of “sunny”. If you are fine with approximations, then you can also decide on decomposition of wavefunction into some number of observers—it’s the same problem as decomposing classical world that allows physical splitting of thick computers according to macroscopic property “number of people”.
You’re right that you can just take whatever approximation you make at the macroscopic level (‘sunny’) and convert that into a metric for counting worlds. But the point is that everyone will acknowledge that the counting part is arbitrary from the perspective of fundamental physics—but you can remove the arbitrariness that derives from fine-graining, by focusing on the weight. (That is kind of the whole point of a mathematical measure.)