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In the many worlds interpretation there is only supposed to be the wavefunction and no collapse, which puts an image in my mind of this thing waving in 3D space sort of like temperature fluctuations or something (I understand that the values are complex).

My main question is where the "branches" arise out of all of this. Is it just that there are so many things getting stacked on top of each other to make the total wavefunction that each subpart perceives itself as a separate system?

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    $\begingroup$ Just a note - to the (limited) extent that it makes sense as a concept, the wave function of the universe is not an object in 3D space. If there are $N$ particles to describe, each with 3 coordinates, then it would be an object in $3N$-dimensional space. $\endgroup$ – J. Murray Nov 6 '19 at 14:57
  • $\begingroup$ Yeah I'm going to ask a new question with that in mind. $\endgroup$ – Jeff Bass Nov 6 '19 at 15:18
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They don't "come from" anywhere, they were already there overlapping, they split from each other by interacting with the environment, decoherence; the superposition of states of a system interacting with the environment results in the superposition of environment having interacted with state A + interacted with B, etc, and after this mixing, they evolve independently of each other and never interact again. Don't know about the waving thing... in my mind the universal wavefunction is like a fat cylinder, with the big bang at the center and constantly splitting into many slices towards the edge, and my consciousness always confined on a single slice at the edge due to how it collects information/interacts with everything.

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