I just finished Sean Carroll's Something Deeply Hidden, and found it the best explanation of MWI I've ever seen, and even find that I have no good arguments against it; the parts I understand seem plausible (there are certainly parts I don't understand). One point I find problematic, however, is his p170-1 suggestion that we can see "world splitting" as either "globally instantaneous" or as propagating through space at the speed of light, since either gives the same predictions. This is unsatisfying since, given relativity, there is simply no such thing as globally simultaneity. So it must be the former, but it was not explained how this works with non-local correlation. I have an idea about this and want to hear back from MWI-supporters to tell me if I'm on the right track, or how to better think about this.
Say Alice is near Earth measuring a particle whose spin is correlated with one measured by Bob near Jupiter. According to MWI each measurement splits the world into one where they measure it spin up, another spin down. But as these measurements must be correlated, there are not four possibilities, only two. This leads me to the following picture: that as they speed toward each other or share signals about their results, the two copies of each (Alice-up, Alice-down, Bob-up, Bob-down) are in a sense separated from each other in Hilbert space so that they only "see" or meet the other which has "moved" to the same part of Hilbert space, so Alice-up meets or gets a message from Bob-up, Alice-down meets Bob-down. Each of the new up-up/down-down pairs has, in a sense, made the same shift to a different part of Hilbert space--and when they or their signals meet in physical space, can interact--but Alice-up is radically shifted away from Bob-down and so cannot interact with him. Or, to put it another way, the particle measurements made by Alice and Bob each split the world, but this split can only interact with things within its light cone, and when its effects interact in physical space they only do so with things in the right location in Hilbert space. Or, to put it a third (?) way, the split propagates at the speed of light, but these two splitting-waves are correlated in such a way that, whenever or wherever the Alice-split-wave meets the Bob-split-wave, the two up-split waves neatly meet and merge, same with the two down-waves, each merging occurring, but each merging now becoming just a single split (in the future light cone of the merge). But maybe this is again just a restatement of my first point, if the "propagating split" is simply the propagation of particles and signals which can interact, but occurring in one or another part of Hilbert space.
I'm also trying to picture this with a kind of altitude analogy, seeing height as a kind of dimension in Hilbert space separate from (and much bigger than) physical space, or rather defining many different versions or levels of otherwise similar "physical" spaces. It's as if Alice and Bob, initially at 20K feet, are hurtling toward each other from, say, east and west, but Alice & Bob "up" have both been shifted to 30K feet and so see each other as they pass; Alice & Bob "down" have been shifted to 10K feet, and see each other, but neither pair approaches the other pair, even though looking from straight down it looks like their planar geographical coordinates are the same. So all four can head to, say, "Mars," but the Mars-up that A-up and B-up meet at is not the same Mars that A-down and B-down meet at, though they otherwise look a lot alike.
My summary question: do these various different ways of explaining it (or various different ways of stating a single explanation?) make sense in terms of the MWI? Are some better than others? If any are close to right, I'm tempted to say that MWI actually explains the "before-before" and other correlation experiments better than anything else I've read, and discards "action at a distance" because while all four measurement results occur, none caused each other, and the observed correlation between the particles is manifested by the fact that each observer can only interact with the post-measurement version of her partner which saw the same result.
I'm not a professional physicist, just an interested outsider and eager to attain greater clarity on this, or correction if what I'm saying is incorrect or misleading. To that end, please don't answer merely with criticisms of MWI unless they relate directly to my question, as I'm most interested in first understanding MWI properly.
