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Viliam_Bur comments on Open thread, Nov. 24 - Nov. 30, 2014 - Less Wrong Discussion
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I don't quite understand this topic, but maybe this could be useful:
The problem with "converging / mangled worlds" is statistical. To make two worlds interact (and become the same world, or erase each other, depending on mutual orientation of their amplitudes), those worlds must have all their particles in the same position. In usual circumstances, this seems unlikely. Imagine the experiment with the cat, where in one world the cat is dead, and in other world the cat happily walks away. How likely is it that at some moment in the future, both universes will have all particles in the same positions?
So, in usual circumstances two worlds interact only if a moment ago they were the same world, and the only difference was one particle going two different paths. (Yes, there are also all the other particles in the universe, also splitting all the time. But this happens the same way in both branches, so it cancels out.)
My intuition is that this "single state" was never literally one point, but always a small interval (wave? hump?). An interval can break into two parts, and those can travel in different directions. There is no such thing as a single point in quantum physics.
(Disclaimer: I don't really understand quantum physics; I am just interpreting the impression I got from looking at Eliezer's drawings. If you have better knowledge, feel free to ignore this.)
What forces the worlds to be same in order to interact? You could also have merely adjacent worlds where the "collisions angle" could compensate for small differences. It is just a little harder to imagine how worlds of unrelated state would interact. Maybe dark energy is the sum total of gravity from other worlds?
It's also that two worlds won't long stay singular, but branch all the time into subworlds. The probability of some of the pairwise worlds being close enough is higher.
edit: Also there are settings where splitting doesn't mean lack of structure. For example in the mirror experiements the two paths will systematically intersect and this is a pretty stable result of the mirror positionings.