Re: Penrose and Entropy


rev.goetz wrote:
Puppet_Sock wrote:
rev.goetz wrote:
[snip]
The context has something to do with maximum entropy in a black hole.

You should try to find a physics forum for this. It's massively
off topic here. Possibly you would get some help in
sci.physics.research. Sadly, sci.physics has changed into
something that is entirely incompatible with anything like help.

Basically though, the issue is how to get some idea of the
effective entropy of a black hole. The problem is, a black
hole classically has only its radius and angular momentum
as parameters. So if you dump stuff past the horizon, what
happens to its entropy? And how does it fit the 2nd law?

Before the discovery of Hawking radiation the notion was
that the area of the BH would be a good measure of its
entropy. When Hawking radiation was discovered then there
was a requirement to relate the entropy of the produced
radiation to this. The character of the radiation could be
estimated in fairly qualitative terms (as opposed to being
quantitative or accurate) and people worked on making this
fit into thermo. So, the notion was to try to relate the character
of the spectrum of radiation from a BH to the entropy of the
radiation, and so to changes in the surface area of the horizon.

There is quite a literature on this topic, research articles and
some chapters in texts. In order to properly understand it
you will need some fairly high powered math, some topology,
some differential geometry, some other stuff. And you will
need to be up on your stat mech. It was depressing when
I went to conferences as a grad student. Folks like Weinberg
would be able to respond to questions about such issues
"on their feet" as it were. They'd be able to come up with
things like the distribution of this and the topology of that
and the cohomology of the other. I'd be struggling about
eight pages back trying to understand the definitions.
Socks

I am also trying this in other places, but I do not like cross posting.

Do you know why the number of photons per baryon tend to increase in
the universe? IIRC, the universe now has roughly 10^8 photons per
baryon, and black holes have at least 10^20 photons per baryon.

You could try for a simple explanation. Baryons are (roughly)
conserved. Photons - well as the universe expands, they need to spend
longer and longer times in flight before they hit anything, so there
are going to be more extant ones at any given instant as time goes on.

Of course, you could pick holes in this argument - like: as time goes
on, and the distances between things increases, then surely the rate of
production of new photons will decline?

James

.

Relevant Pages

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