From: goldenfieldquaternions@gmail.com   
      
   On Sunday, June 11, 2017 at 1:51:16 AM UTC-5, Gregor Scholten wrote:   
   > Lawrence Crowell  wrote:   
   >   
   > > Einstein was certain the universe was an eternal static system.   
   > > What we observe as increase in entropy and so forth are in the end   
   > > just local fluctuations.   
   > > [...]   
   > > This does not preclude the fact that star formation and large scale   
   > > structures we observe are transient. This is if you consider billions   
   > > or even trillions of years transient. Poincare recurrence is very   
   > > long for a cosmology, T ~ 10^{10^{100}} years.   
   >   
   > In a static universe, Poincare recurrence theorem applies, that's   
   > correct, but that does not mean that it would be correct to say that   
   > star formation would "continue forever". Star formation would last maybe   
   > some trillions of years and stop then, for starting again after one   
   > Poincare recurrence cycle, which would be much longer than the trillions   
   > of years star formation lasted (and will last again this cycle). So, for   
   > the most time, there wouldn't any star formation.   
   >   
      
   Poincare recurrence in general relativity is a bit hard to put a finger   
   on. It is a phase space concept, which is not always easy to quantify. I   
   sort of cheated and considered the estimated time for the stability of   
   the de Sitter vacuum.   
      
   Clearly after a trillion years or so things are going to be cold and   
   dark. There will be little heat flow and after 10^{40} years the only   
   heat flow will be from the Hawking radiation of black holes.   
      
   LC   
      
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