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
>
>
>
>
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Received on Mon Nov 05 2007 - 18:35:18 PST