Re: Philosophy specifies: organisms process information


<carlip-nospam@xxxxxxxxxxxxxxxxxxx> wrote in message news:f17sd2$g14$1@xxxxxxxxxxxxxxxxxxxxxx
Perplexed in Peoria <jimmenegay@xxxxxxxxxxxxx> wrote:

<carlip-nospam@xxxxxxxxxxxxxxxxxxx> wrote in message news:f10a8k$5de$2@xxxxxxxxxxxxxxxxxxxxxx
Perplexed in Peoria <jimmenegay@xxxxxxxxxxxxx> wrote:


[...]
It isn't the initial 'order' of the universe which requires explanation.

Sure, it is. The initial entropy of the Universe -- in the technical sense
of the word -- was tiny; a highly inhomogeneous early Universe would have
had a much higher entropy. Homogeneity is a very special initial condition,
which does not occur as a natural outcome of any previous evolution.

I don't see how you can say this. Homogeneity is the ultimate *high entropy*
generic situation, and it is the natural outcome of any evolutionary process
taking place at high enough temperatures. High enough to overwhelm the enthalpy
term in the Gibbs free energy definition.

Inhomogeneity has lower entropy than homogeneity, almost be definition.

This is true in a situation in which there are no long-range, unscreened
forces. Gravity changes everything.

I'm told that the modern discovery of the thermodynamic peculiarities of
self-gravitating systems began with a 1962 paper by Antonov, but it was
published in an obscure Russian journal, and I confess I haven't read it.
The results were rediscovered by Lynden-Bell and Wood in a famous paper
(well, famous in some circles), "The gravo-thermal catastrophe in isothermal
spheres and the onset of red-giant structure for stellar systems," Mon. Not.
R. Astr. Soc. 138 (1968) 495.

The basic feature that makes a self-gravitating system strange is that it
has a negative specific heat -- as it radiates energy, its temperature
*increases*, causing faster radiation. As a simple one-body analogy, consider
a satellite in low-Earth orbit. As it loses energy to friction, its height
decreases, increasing its orbital velocity and speeding the loss of energy.
The same kind of phenomenon is generic in systems dominated by gravity. For
systems with negative specific heat, ordinary intuition about equilibrium
breaks down, and the behavior can be quite different from what you would
expect from more ordinary thermodynamic systems.

Consider a cloud of gas in a spherical container, with either the temperature
fixed at the walls (canonical ensemble) or the energy fixed (microcanonical
ensemble). In the absence of gravity, the highest entropy configuration will
be one in which the gas fills the container homogeneously. If you turn on
gravity and the density is low enough, this will still be approximately true,
although there will be a density and temperature gradient as you move inward.
If you increase the density, though, you will reach an instability, basically
the Jeans instability, and the gas will start to collapse. The collapsing
region will not head back toward the initial equilibrium (negative specific
heat!), but will radiate and continue to collapse.

[third attempt to post this]
Ok, I understand that negative specific heat overthrows my intuitions.

Incidentally, in the question period after a lecture, I once asked Chandrasekhar
(believe it or not!) "Doesn't the fact that an observer just outside the event
horizon measures the temperature of the 'microwave' black body radiation to
be very high - doesn't that prevent a black hole from forming." His reply
was that there were so many things wrong with my assumptions that he couldn't
be bothered to correct them all. ;-(

My thinking had been based on the thought experiment described by Wheeler in
the 'telephone book'. Take a self-gravitating cloud of gas and let it keep
radiating away energy. My point was that if the sky becomes as hot as you
are, you can't radiate away energy. But now I see that it doesn't matter once
you reach the negative specific heat stage.

If the temperature of the
walls is high enough and is kept constant, or if short-range forces start to
dominate, the collapse may eventually stop; if the temperature is too low, it
will continue until you have a black hole.

Or until you have a neutron star, or white dwarf, or maybe a sphere of liquid
hydrogen and helium, or some other phase of matter. The negative specific heat
is only guaranteed for ideal gases and plasmas, as I understand it. But probably
I am still wrong.

The collapsing region of gas must radiate away heat to its surroundings, of
course. In normal situations, it does so through electromagnetic radiation,
and the rate of collapse depends on how strong the gas couples to light.
But even in a purely gravitational system, with no other interactions, the
same thing happens, though on a slower time scale; the collapsing region
"radiates" by ejecting small numbers of high-velocity particles (which pick
up their energy through complicated many-body interactions), and you still
end up with a compact lump surrounded by a thin, hot gas.

What happens to entropy during this process? The second law is not violated;
the entropy increases. This is true even if your boundary conditions allow
no heat flow out of the system. (This should not be surprising: gravitational
collapse is a local phenomenon, and won't suddenly stop because of boundary
conditions very far away.) So the conclusion is that the final state, a hot
lump surrounded by radiation, has higher entropy than the initial, uniform
state. In a large system, the collapse will typically happen locally, and
you will end up with many lumps; the entropy is still higher than that of the
initial homogeneous state.

This can all be confirmed by explicit calculations, as well as by numerical
simulations. The simplest illustrative calculation I know of is given at
the beginning of chapter 5 of Zeh"s book, _The Physical Basis of the Direction
of Time_. Note that the basic phenomenon is already present in Newtonian
gravity -- no GR needed -- and does not require any assumptions about the
large-scale cosmology.

So it really is true that the initial entropy of the Universe (or, at least,
the part of the Universe we can see) was very low, and that this is something
that we need to explain.

Well, only if the temperature and density were within the Jeans instability
limits. Were they? I see that I should probably read Zeh before popping off
on this subject again.

I see no need to summon a "God of the gaps" -- there
are a number of interesting ideas floating around, for example from eternal
inflation models of cosmology, and there's no reason to believe we'll never
have an answer. But for now, it's an open problem.

(This should be a cause for celebration -- think how boring life would be if
we had no interesting questions that we didn't yet know how to answer.)

Steve Carlip

Thanks for the response.


.

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