XPost: sci.astro.research   
   From: gerry@bindweed.com   
      
   In article , helbig@asclothestro.multivax.de   
   says...   
   >   
   > In article ,   
   > Gerry Quinn  writes:   
   >   
   > > The smooth distribution always has the same entropy.  Start with the   
   > > smooth distribution and no gravity, and increase the gravitational   
   > > constant.  Now high entropy states start to become available that were   
   > > not available withouy gravity.   
   >   
   > Sounds plausible.   
   >   
   > > To put it another way, the 'clumpy' states in the non-gravitational   
   > > universe have lower entropy than the smooth state, but the clumpy states   
   > > in the gravitational universe have higher entropy than the smooth state.   
   >   
   > Imagine a clumpy universe with no gravity.  It has low entropy (lower   
   > than the smooth universe).  Now G starts increasing from zero to, say,   
   > its current value (at which point the clumpy universe has a higher   
   > entropy than the smooth universe).  At some value of G, the clumpy   
   > universe must have the same entropy as the smooth universe (which you   
   > say has the same entropy with or without gravity).  So for this value of   
   > G, the entropy is independent of the clumpiness.   
   >   
   > Someone has made an error somewhere.   
      
   Why should it not be independent of the clumpiness?   
      
   Consider a smooth universe full of hydrogen, with non-zero density and   
   no gravity.  This universe is clumpy too, it's just that the clumps are   
   mostly H2.   
      
   You could make the same paradox by imagining a universe full of H atoms,   
   and slowly turning on atomic interactions.   
      
   - Gerry Quinn   
      
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