Most formulations of MWI only require a "for all practical purposes" splitting. Like thermodynamic irreversibility.
A mental picture of thermodynamic irreversibility as a directed tree is indeed an appealing one. It becomes less appealing once your tree does not have any well-defined vertices or edges due to the issues I have outlined.
According to the SE.
The SE is non-relativistic, so it has absolutely nothing to say about propagation in spacetime. It does not even describe emission or absorption, an essential part of decoherence. You have to go fully monty QFT to talk about signal propagation, but no one talks about MWI in the context of QFT, as far as I know.
Merg[e]able states are not split worlds.
In MWI [eigen]states correspond to worlds, so I don't know what it means. I also don't know what you mean by mergeable states.
Do different worlds share the same spacetime and for how long?
Presumably.
This implies gravitational interaction between non-interacting worlds, so do they interact or don't they?
See Penrose on MW.
Feel free to quote... Just not his quantum consciousness speculations.
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A list of some posts that are pretty awesome
I recommend the major sequences to everybody, but I realize how daunting they look at first. So for purposes of immediate gratification, the following posts are particularly interesting/illuminating/provocative and don't require any previous reading:
More suggestions are welcome! Or just check out the top-rated posts from the history of Less Wrong. Most posts at +50 or more are well worth your time.
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Note from orthonormal: MBlume and other contributors wrote the original version of this welcome post, and I've edited it a fair bit. If there's anything I should add or update on this post (especially broken links), please send me a private message—I may not notice a comment on the post. Finally, once this gets past 500 comments, anyone is welcome to copy and edit this intro to start the next welcome thread.