On Friday, November 7, 2014 5:07:01 AM UTC, Bruce wrote: > > LizR wrote: > > > > (Another way to look at this is that the expansion is producing more > > available states for the universe to move into, effectively raising the > > entropy ceiling. This means an expanding universe can never reach a > > state of equilibrium - this is particularly clear during the BB > > fireball, which I would say is very near to equilibrium for a lot of the > > time.) > > > I thought I remembered that someone had written that the idea that the > expansion produces more states so the entropy ceiling increases with the > expansion of the universe is mistaken. I have found the reference, it is > Roger Penrose in 'The Road to Reality' in Section 27.6 (p. 701ff) > > He writes: > "There is a common view that the entropy increase in the second law is > somehow just a necessary consequence of the expansion of the universe. > This opinion seems to be based on the misunderstanding that there are > comparatively few degrees of freedom available to the universe when it > is 'small', providing some kind of low 'ceiling' to possible entropy > values, and more available degrees of freedom when the universe gets > larger, giving a higher 'ceiling', thereby allowing higher entropies. ... > > "There are many ways to see that this viewpoint cannot be correct.... > ...The degrees of freedom that are available to the universe are > described by the total phase space. The dynamics of GR (which include > the degree of freedom defining the universe's size) is just as much > described by the motion of our point x in the phase space as are all the > other physical processes involved. This phase space is just 'there', and > it does not in any sense 'grow with time', time not being part of the > phase space. There is no 'ceiling', because all states that are > dynamically accessible to the universe (or family of universes) under > consideration must be represented in this phase space....." > > I recommend Penrose's book for a lucid explanation of these things. >
I think the phase space conception is a very good approach. But....on the terms of the phase space there are dynamical histories that correspond to entropy increasing at parity with expansion, that happens to arrange states just about right to get a big pile of sand. and I rest my case with that. I'd be an impoverished attorney, and not that, being the case > > Bruce > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
