Re: Photons and Specific Entropy
- From: carlip-nospam@xxxxxxxxxxxxxxxxxxx
- Date: Mon, 18 Sep 2006 20:18:46 +0000 (UTC)
rev.goetz <jimgoetz316@xxxxxxxxx> wrote:
Roger Penrose (1981) defines specific entropy as the ratio of photons
per baryon.
No, he doesn't. In the reference you cite, he says that the "observed
entropy per baryon" is "essentially, the number of photons per baryon"
but that "this does not take into account the possibility of an appreciable
contribution to the total entropy arising from the presence of black
holes."
Penrose is not "defining" specific entropy to be the number of photons
per baryon. It isn't. He is merely saying that if -- as it seems from
observation-- most of the entropy in our Universe is in the cosmic
microwave background (and not, say, in black holes), then the specific
entropy can be *calculated* to be approximately equal to the number of
photons per baryon. This is basically a coincidence, having to do with
the particular form of entropy that we observe.
(If you go shopping and buy a bunch of pint bottles of water, the weight
of your shopping bag in pounds is roughly equal to the number of bottles.
That doesn't mean that you've defined weight as the number of bottles.
If you throw in a couple of pineapples and find that your bag is heavier,
that doesn't imply that the pineapples have turned into bottles of water.)
For example, the universe currently has an average of 10^8
photons per baryon
Yes, as an order of magnitude estimate. This is observed.
while a black hole has at least 10^20 photons per baryon.
No! A black hole doesn't have photons or baryons at all. It has an
entropy and a mass, but these are of a completely different form than
the "photons per baryon" in a universe dominated by black body radiation.
According to this, when galaxies eventually collapse into black
holes, then the universe would average at least 10^20 photons per
baryon.
Is this correct or incorrect?
This is incorrect. If galaxies eventually collapse into black holes,
the result will be a universe with an entropy equal to that of a
different universe with uncollapsed galaxies but many more photons
per baryon than our present universe has.
(If you put ten pineapples in your shopping bag, it will weigh as
much as one with, say, forty bottles of water. This does not imply
that pineapples turn into water bottles.)
[...]
Penrose, R. [1981]: "Time-Asymmetry and Quantum Gravity", in C.J. Isham
and R. Penrose and D.W. Sciama (eds) Quantum Gravity 2: A Second Oxford
Symposium, Oxford: Clarendon Press, pp. 245-72.
Steve Carlip
.
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- Photons and Specific Entropy
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