At this point the two wavefunctions cease to be the same (the spin of the particle becomes entangled with its position).
So it seems that you define the degree of separation of worlds as the spatial overlap of the spin-up and spin-down components of the wave function, probably the inner product of the two normalized terms. I did not follow your musings on “displacements of every particle in the universe between the two worlds”, however.
M2: In the experiment given, any single particle is essentially returned to exactly the same superposition of states it was in before it entered the fields.
Are you saying that the screen with the two holes has no effect whatsoever? Just wondering.
(Also, I hold that I can still use density matrices to deal with my subjective uncertainty, even about single particles).
You sure can, but it seems unnecessary for a pure state. Or maybe I misunderstand what you mean by “subjective uncertainty”.
So it seems that you define the degree of separation of worlds as the spatial overlap of the spin-up and spin-down components of the wave function, probably the inner product of the two normalized terms. I did not follow your musings on “displacements of every particle in the universe between the two worlds”, however.
Are you saying that the screen with the two holes has no effect whatsoever? Just wondering.
You sure can, but it seems unnecessary for a pure state. Or maybe I misunderstand what you mean by “subjective uncertainty”.