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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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  • $\begingroup$ See Kupervasser, "The Universal Arrow of Time," arxiv.org/abs/1011.4173v5 $\endgroup$
    – user4552
    Apr 14, 2013 at 21:35
  • $\begingroup$ 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 $\endgroup$
    – Prathyush
    Apr 15, 2013 at 10:53
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    $\begingroup$ 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 $\endgroup$
    – user16007
    Apr 15, 2013 at 16:18
  • $\begingroup$ I think this is a legitimet valid question, professiona theoretical cosmologists are investigating such and similar issues. So it should not get closed $\endgroup$
    – Dilaton
    May 31, 2013 at 9:10
  • $\begingroup$ I don't think it's relevant whether these are referred to as two universes or simply two different regions of the same universe. The thermodynamic question is the same. $\endgroup$
    – user4552
    May 31, 2013 at 14:37

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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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  • $\begingroup$ You say, "Based on the article by Kupervasser...," but what you say completely contradicts the article. $\endgroup$
    – user4552
    May 31, 2013 at 14:20
  • $\begingroup$ 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! $\endgroup$
    – user16007
    Jul 10, 2014 at 0:27