Somehow the answer to these questions must be explicable in terms other than it "comes out of a subtle result on the structure of Hilbert spaces".Stephen says:
It would be nice, but I'm not sure that it "must be" explicable so easily. We really lack the intuitions and therefore the vocabulary here in the macrocosm. I think it would be important to be able to do it simply, but no-one has managed it to my knowledge.
@Stephen
I cannot believe that an intricate mathematical subtletly can be at the bottom of the conundrum that something about the nature of making a measurement demands a sudden re-zeroing of the state of the universe. On measurement one deterministic process suddenly ceases and a new one begins! The answer must, indeed, have a mathematical embodiment but we ask what specific character of the structure of hilbert space connects with these interminable splittings of the universe at each measurement event.