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When the comet passed, people could only interact with realities in that specific moment of time with other realities that were very similar to their own. I think of it like a petri dish containing a moment of reality (such as having a dinner party with a group of specific people at a house belonging to Mike and Lee) being sorted with other petri dishes containing moments of realities that are almost parallel, and these petri dishes are only allowed to interact with each other.
You are thinking like I did for the first couple viewings. This was my 3rd viewing. At first it appears to follow the "many worlds" doctrine which is basically what you are saying about parallel universes. Basically there is an infinite number of worlds, so there is an infinite number of you's doing stuff on those worlds. With my 3rd viewing though I'm not sure this is exactly the case. The movie centers around the idea of quantum physics.
Coherence, Decoherence, Schrodinger's Cat, these things have to do with quantum physics and specifically Superposition, the state of being both spinning or still simultaneously, or alive and dead at the same time in the case of the cat. Atoms behave in this way. It may surprise you to find out that nobody has ever seen an atom, or an electron for that matter. We have Electron microscopes but we don't really see the atom as it really is.
We know there are electrons orbiting the nucleus but we cannot know where they are. Rather than the standard model that was believed for so long, which shows an atom with a nucleus and with electrons orbiting it, like planets orbiting a star, we now know, through quantum mechanics, that the atom and its electrons is more like a cloud. Its just a cloud of infinite possibilities. It is only when we try to measur eit, or to see it, that the cloud of possibilities collapses into more of a standard model of a particle with electrons orbiting.
Cloud of possibility. The electrons could be anywhere in that cloud, all possibilities are.....possible.
So once again, this is like the cat being both alive and dead at the same time, and its only when you open the box that reality collapses into either alive, or dead. Atoms behave in that way. The electrons in the atom are everywhere, simultaneously, in a cloud of possibility, and its only when we observe this cloud that it collapses into reality and appears as a particle instead of a cloud. In the movie, all the varies infinite realities you speak of, are the cloud of possibilities. ALL possibilities are possible but once observed they collapse into single timelines.
So what is it I'm saying? You may be thinking, ok here is a universe, and here is a universe, and there are infinite universes, which is the many worlds theory, but the movie points more toward a cloud of possible universes that all exist simultaneously, like Superposition, both alive and dead, but not all of those possibilities actually happen, they are just possibilities, like an atom cloud where the electrons could be anywhere and we just see a cloud of possible positions.....until we measure it.