Level 1 Déjà Vu Speculations
Earlier in Parallel Universe - are some aliens ourselves? I discussed the parallel universe essay by Dr. Max Tegmark, Cosmologist from the University of Penn. In an infinite universe, or a sufficiently large enough one, other Earths exist far far away, with the same history - a Level 1 parallel universe. These parallel universes are regions that are beyond our cosmic horizon - regions beyond the limit of our ability to see or detect. They need to be that far so that the region can be parallel - two Earths in the same space would not be parallel since they would not have the same night sky, the same environment, and observing each other could upset the parallel developments. They exist now, in the past, and yet to be, all echoing our Earth in history. Even with true random chance and free-will, another Earth can accidentally follow ours. Infinity is an eerie thing. We have twins out there. Maybe this level 1 parallel universe explains déjà vu as we somehow in some quantum manner not yet discovered connect dimly at times with our exact duplicates. Of course that would mean at the exact time we experience déjà vu, so would our double.
I wonder, though, if it is necessarily true that parallel Earths have to be in regions beyond our comic horizon. Could a region of space, in an infinite universe, be of such special symmetry that two identical inhabited planets could orbit separate but identical stars and still see the same constellations, have the same interstellar environment? And in discovering each other, discover each other at the exact same time, in the same exact way? It may be the rarest of the rares, but in an infinite universe, could it not still happen? How weird, and frustrating, that would be for the explorers engaging in first contact: both speaking the same thing at the same time (and marveling that they both speak the same language and look and sound the same), flipping a coin to break the impasse and both saying "heads" at the same time, so go to a quantum random number generator to break the impasse (to decide who speaks first, for instance) and while both being truly random still, by chance, coming up with the same number... Probably the further apart, the more likely random effects could affect message transmissions such that the impasse would be finally broken. But I can not help but think in a truly infinite universe, there would be a place where each Earth would always simultaneously echo/parrot each other in perfect unison - hopefully, for those two twin worlds, there would be something in physical laws of the universe that would prevent the perfect parroting from being eternally true.
Breaking the Jinx
Maybe it would be better that another Earth would be similar but not the same. It would aid in establishing a real dialogue. On a theological note, can slightly different Earths be our afterlife/reincarnation (choosing, living, other paths as ourselves)?