From: Jeff L Jones (jeff@spoonless.net)
Date: Fri Mar 21 2008 - 15:35:02 MDT
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.
> That is not the same thing. My question is how do you derive the mass of a
> proton from c, h, and G if it is not a coincidence? Why do you need the age
> of the universe?
You *cannot* derive it from those, as it depends on completely
different physical constants from those (such as the fine structure
constant, lots of electroweak parameters, the QCD scale, etc.). If
you are putting in those numbers and getting something close to the
proton mass, then it is purely coincidence... you haven't done
anything meaningful, you've just put a bunch of random numbers
together. It seems to me that no matter what you got when you divided
V by S, you would have claimed it was an interesting coincidence. I
mean, if you had gotten the size of an atom, you would say "oh wow, 1
bit per atom"... if you had gotten the size of the solar system, you
would have said "wow, 1 bit per solar system!" But bits per volume
means nothing. There is nothing significant about that quotient
coming out near the proton mass. There are plenty of other masses of
particles that it could have come out near.
Jeff
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