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I was trying to think but cannot figure it out. For instance, if the interaction is small, for instance limited to a windows, the observers in each universe will see that the other goes in reverse. But what if they can start a more meaningful interaction? (for instance, if one observer crosses the window and moves to the other universe, will anything change? why and how fast? (at least at the beginning his thinking will move in the same time arrow than in his universe, but the physical processes around him will still violate the second law?

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closed as off topic by Chris White, Waffle's Crazy Peanut, Emilio Pisanty, Brandon Enright, Alfred Centauri Jun 11 '13 at 22:01

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See Kupervasser, "The Universal Arrow of Time," – Ben Crowell Apr 14 '13 at 21:35
Thanks! I'll read it! – user16007 Apr 14 '13 at 21:43
Its a strange question, firstly what does it mean for 2 universes to be connected. Do they share a connected space time in which case you have one universe. Also we specify a initial conitions on a given spacelike slice, and what is forward is defined as what is accessible experimentally to the observer. It is not clear in your situation how these initial conditions are defined – Prathyush Apr 15 '13 at 10:53
assume the two universes are disconnected for most of their history, and become connected at some point in the middle for a finite amount of time (trough a wormhole?). It doesn't matter if you name it a single universe or two, what matters is that the thermodynamic arrow of time is in the opposite direction between them, at least when they are not connected – user16007 Apr 15 '13 at 16:18
I think this is a legitimet valid question, professiona theoretical cosmologists are investigating such and similar issues. So it should not get closed – Dilaton May 31 '13 at 9:10

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Based on the article by Kupervasser suggested in the comments by Ben Crowell, I suspect the answer is that my hypothetical situation is impossible: in general, for a complex enough dynamical system, there is no solution to the equations is which two universes with opposite arrows of time can interact. In order to have that, your system should have to satisfy boundary condition of low entropy for both universes at their beginnings, which are most likely impossible to satisfy (that is, you must satisfy initial conditions for half of your system and final conditions for the other half, which is in most cases mathematically impossible).

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You say, "Based on the article by Kupervasser...," but what you say completely contradicts the article. – Ben Crowell May 31 '13 at 14:20
HAHA one of the paradoxes of thought! perhaps I interpreted something totally opposite of what the author meant (I only read it once) but still found it explanatory! – user16007 Jul 10 '14 at 0:27