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I just finished readying Sean Carroll's book, "From Eternity to Here", and have a question about reversibility and inflation:

Assume inflation allows random quantum fluctuations to produce high energy density regions that pinch off from the original spacetime and grow into disconnected baby universes. If we slice spacetime a while after this disconnection has occurred, how would the time-reversed dynamics know to spontaneously connect the two separated regions of spacetime together? Would this situation necessarily violate time reversibility (or render it undefinable)?

In particular, assuming that the entire multiverse is infinitely large, and each baby universe spawning can be described by a finite number of variables, there would be an infinite number of completely indistinguishable spawning events. Slicing spacetime a short while after each one, they could be reconnected arbitrarily without violating the dynamics.

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I think it's a very good question. In general, physics of the last 20 years was showing that all such "processes that should be irreversible" are ultimately microscopically reversible in principle but they don't happen in the opposite way in practice because that would require the entropy to decrease and such violations of the 2nd law are unlikely. Possible but insanely unlikely. That's how we explained that black holes may devour matter but they never "spit" stars etc. It's much more likely for them to spit the energy in the form of the Hawking radiation. – Luboš Motl Apr 13 '13 at 6:33
For splitting Universes, it's tougher because we don't have a well-defined enough quantum description of such forking Universes yet. There's another trouble here - the microscopic processes we deem "possible in principle" seem to be able to merge an arbitrary baby universe that is flying somewhere - and therefore influence the predictions in a region by some properties of a baby that was "totally elsewhere" to start with: a big new violation of local predictivity. – Luboš Motl Apr 13 '13 at 6:35
However, one must be careful before he screams "a contradiction". When only the local doable observations in the original parent universe are concerned, it's still plausible that the effect of all the baby universes that may suddenly merge into the parent universe is a calculable modification of the predictions. Sidney Coleman had described some potentially eternally splitting/joining baby universes as a factor that makes some constants of physics variable. There are various interesting observations but no complete theory here. – Luboš Motl Apr 13 '13 at 6:37
Thanks for the interesting comments. One possibility that occurs to me: in the same way that wave function collapse is reversible if you take into account the practically unreachable information from the other worlds created by decoherence, maybe baby universe spawning is reversible if you take into account the other worlds in which the baby universe didn't spawn, but stayed topologically connected in a way that implied that a separate universe spawned off. – Geoffrey Irving Apr 13 '13 at 20:04
Moreover, my pigeonhole argument doesn't show anything, since if you were to reconnect the distinct but identical baby universes in a different way, the resulting spacetime would be unchanged. – Geoffrey Irving Apr 13 '13 at 20:10

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