From: Matt Mahoney (matmahoney@yahoo.com)
Date: Fri Mar 21 2008 - 17:18:24 MDT
--- Jeff L Jones <jeff@spoonless.net> wrote:
> On Fri, Mar 21, 2008 at 12:27 PM, Matt Mahoney <matmahoney@yahoo.com> wrote:
> > The Bekenstein bound is based on thermodynamics, an entirely different
> > approach.
>
> I'm pretty sure there is only one approach here. Here is my understanding:
>
> The entropy of a black hole is based on calculating the rate of pair
> production to see how much Hawking radiation comes out, which turns
> out to be exactly what you'd expect of a blackbody radiating at a
> particular temperature T. If you use standard thermodynamics to turn
> that temperature into an entropy S, then voila, you get S = A/4 for
> the entropy of a black hole. The Bekenstein bound is based on the
> argument that the most stuff you can fit into a region of space is a
> black hole... and on various thought experiments, which indicate that
> if you tried to put *more* stuff in, you would just get a bigger black
> hole. You don't calculate anything independently, you just quote the
> result from black holes, and say that for anything else, S < A/4. So
> yes, there is some thermodynamics involved, but it's involved at the
> stage of calculating the black hole entropy... which you need to do
> first in order to find the Bekenstein bound. There aren't two
> different approaches, because one result requires the other result to
> be computed first.
They may indeed give the same results, but that is not the approach I used. I
counted states as a function of volume and mass/energy, then set those values
to that of the universe. I only used the Schwarzchild radius to estimate the
mass of the universe.
-- Matt Mahoney, matmahoney@yahoo.com
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