Sorry the nice equation formats did not make it past the server. Anyone interested in the equations can find them at the associated wiki links.
George Russell Standish wrote: >On Fri, Nov 02, 2007 at 12:20:35PM -0700, George Levy wrote: > > >>Russel, >> >>We are trying to related the expansion of the universe to decreasing >>measure. You have presented the interesting equation: >> >>H = C + S >> >>Let's try to assign some numbers. >>1) Recently an article >><http://space.newscientist.com/article/dn12853-black-holes-may-harbour-their-own-universes.html> >> >>appeared in New Scientist stating that we may be living "inside" a black >>hole, with the event horizon being located at the limit of what we can >>observe ie the radius of the current observable universe. >>2) Stephen Hawking >><http://en.wikipedia.org/wiki/Black_hole_thermodynamics> showed that the >>entropy of a black hole is proportional to its surface area. >> >> S_{BH} = \frac{kA}{4l_{\mathrm{P}}^2} >> >>where where k is Boltzmann's constant >><http://en.wikipedia.org/wiki/Boltzmann%27s_constant>, and >>l_{\mathrm{P}}=\sqrt{G\hbar / c^3} is the Planck length >><http://en.wikipedia.org/wiki/Planck_length>. >> >>Thus we can say that a change in the Universe's radius corresponds to a >>change in entropy dS. Therefore, dS/dt is proportional to dA/dt and to >>8PR(dR/dt) R being the radius of the Universe and P = Pi. Let's assume >>that dR/dt = c >>Therefore >> >>dS/dt = (k/4 L^2) 8PRc = 2kPRc/ L^2 >> >>Since Hubble constant <http://en.wikipedia.org/wiki/Hubble%27s_law> is >>71 ± 4 (km <http://en.wikipedia.org/wiki/Kilometer>/s >><http://en.wikipedia.org/wiki/Second>)/Mpc >><http://en.wikipedia.org/wiki/Megaparsec> >> >>which gives a size of the Universe >><http://en.wikipedia.org/wiki/Observable_universe> from the Earth to the >>edge of the visible universe. Thus R = 46.5 billion light-years in any >>direction; this is the comoving radius >><http://en.wikipedia.org/wiki/Radius> of the visible universe. (Not the >>same as the age of the Universe because of Relativity considerations) >> >>Now I have trouble relating these facts to your equation H = C + S or >>maybe to the differential version dH = dC + dS. What do you think? Can >>we push this further? >> >>George >> >> >> > >I think that the formula you have above for S_{BH} is the value that >should be taken for the H above. It is the maximum value that entropy >can take for a volume the size of the universe. > >The internal observed entropy S, will of course, be much lower. I >don't have a formula for it off-hand, but it probably involves the >microwave background temperature. > >Cheers > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
