From: goldenfieldquaternions@gmail.com   
      
   On Thursday, June 15, 2017 at 9:14:49 AM UTC-5, Gerry Quinn wrote:   
   > In article ,   
   > goldenfieldquaternions@gmail.com says...   
   > >   
      
   > >   
   > > 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.   
   >   
   > If we believe in Poincare recurrence, don't we have to believe in   
   > Boltzmann brains?   
   >   
   > - Gerry Quinn   
      
   We have a number of subtle issues. The first is what is meant by   
   equilibrium. With quantum black holes for instance we can demonstrate   
   there is no equilibrium. A black hole of mass M has a temperature   
   T =3D 1/8pi M. Assume this black hole is a region with a background   
   having the same temperature. Assume the black hole emits radiation   
   so M ---> M - delta m or absorbs a photon from the background so M   
   ---> M + delta m. The temperature of the black hole increases or   
   decreases and this makes the black hole removed from equilibration   
   with the background. Over time this will increase and either the   
   black hole will quantum evaporate or grow arbitrarily large.   
      
   There is not clear idea of what is meant by equilibrium in the   
   thermodynamics of general relativity or black hole radiance. This   
   also means questions concerning Poincare recurrence are not easily   
   addressed. We might give an estimate for the phase recurrence of   
   10^{90} particles as some idea of this T ~10^{10^{10^{90}}}, where   
   a classical Poincare recurrence is the log of this. Yet in a way   
   we are sort of shooting in the dark.   
      
   With Boltzmann brains there is a bit of a problem that the time for   
   the assembly of such by random events should be shorter than the   
   time it would take a universe to appear, or maybe equivalently the   
   Poincare recurrence time. Sean Carroll sees this as a problem, for   
   we are left with the uncertainty we might be Boltzmann brains. I   
   see this as more of an annoyance than a problem. If we were Boltzmann   
   brains it would then be questioned how the level of complexity we   
   observe in the exterior universe also came about. This is also   
   connected in some ways to the quirky question over whether we are   
   a simulation. I think these things are unlikely, for it would imply   
   some tight limitation on the level of complexity in the outside   
   world, and so far at least that has not been found.   
      
   --- SoupGate-Win32 v1.05   
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