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 >

## Advertising

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 -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---