# November 20, 2000 {#week160}

Anyone who grew up on science fiction in the 1960s probably read a bunch
about adventures on strange planets, and dreamt of our future in space.
At least I did. Asimov, Clarke, Heinlein... they helped get me
interested in science, but they also painted a romantic vision of human
destiny. Only later did it become clear that *for now*, the real
adventures will come from the microscopic realm: from applications of
integrated circuits, biotechnology, nanotechnology, and the like. When
you're trying to have lots of fun in a hurry, the speed limit is the
speed of light --- and this makes interstellar travel a drag.

Nonetheless, when you imbibe a romantic dream in childhood, it can be
hard to shake it it as an adult. So I still like to read about strange
planets, even if know rationally that I can have more fun at home.

So --- let me start by talking about a world where it might rain methane!

1) Ralph D. Lorenz, "The weather on Titan", _Science_ **290** (October 20, 2000), 467--468.

    Caitlin A. Griffith, Joseph L. Hall and Thomas R. Geballe, "Detection of daily clouds on Titan", _Science_ **290** (October 20, 2000), 509--513.

Titan is the largest moon of Saturn, and it's the only moon in our
solar system with a significant atmosphere. Its atmosphere is mostly
nitrogen, with a surface pressure 1.5 times that of the air pressure
here on Earths' surface. However, there is also a fair amount of
methane, and even some ethane. At the surface of Titan, it's cold
enough for these compounds to liquefy. People have even seen what look
like pitch-black oceans of hydrocarbon compounds, hundreds of kilometers
in size!

However, 14 kilometers or more from the surface, it gets cold enough for
methane to freeze. And the news is that recently Caitlin Griffith et al
have spotted things that look like methane clouds. Compared to Earth,
which is usually 30 percent covered with clouds, the cloud cover on
Titan seems spotty. There's not really enough methane for lots of
clouds. But there may be rain! The drops would be larger than
terrestrial raindrops, and fall slowly in the gravity of Titan, which is
like that of our moon. Since the near-surface atmosphere usually has a
relative humidity of at most 60%, the drops would tend to evaporate
before hitting the ground. (I've seen a similar thing in New Mexico.)
However, in a big rainstorm the evaporation of the first drops might
elevate the humidity to the point where later drops could reach the
surface. So there might even be erosion on the surface of Titan. With
any luck, the Cassini spacecraft will arrive at Saturn in 2004 and make
about 40 flybys of Titan in the following 4 years, getting a good look
at this stuff.

Now for a crazy speculation of my own. Once upon a time James Lovelock
argued that you could tell there was life on earth simply by noting that
the atmosphere contains lots of oxygen, despite the fact that oxygen is
highly reactive. This means the atmosphere is far from equilibrium. Yet
the percentage of oxygen in the atmosphere has remained fairly constant
for long periods of time! So presumably there must be some homeostatic
mechanism at work to keep it constant. Only life --- he argued --- could be
responsible! Conversely, Lovelock guessed there is not life on Mars,
because its atmosphere *is* in equilibrium.

Now, the methane in Titan's atmosphere is dissociated by sunlight, and
this process is irreversible, since the resulting hydrogen flies off
into space. At the rate this happens, the entire methane content of the
atmosphere would be destroyed in only 10 million years if it were not
renewed somehow. In the first article cited above, the author writes:
"For the methane we see today not to be a bizarre fluke, it must be
continuously resupplied from a surface reservoir or by cryovolcanism
(that is, volcanism where the molten 'rock' is just ice)." And this
made me wonder: where is Lovelock when we need him? Maybe *life* is
responsible for this out-of-equilibrium condition.

Or maybe not. After all, it really could be something else.

Next: a world where it might rain diamonds!

2) Richard A. Kerr, "Neptune may crush methane into diamonds", _Science_ **286** (October 1, 1999), 25.

    Laura Robin Benedetti, Jeffrey H. Nguyen, Wendell A. Caldwell, Hongjian Liu, Michael Kruger, and Raymond Jeanloz, "Dissociation of $\mathrm{CH}_4$ at high pressures and temperatures: diamond formation in giant planet interiors?", _Science_ **286** (October 1, 1999), 100--102.

The atmosphere of Neptune is believed to contain lots of methane when
you go 4000 kilometers or more beneath the cloud tops. And Neptune
ain't no measly moon: it's a gas giant, so the atmospheric pressure
becomes enormous as you go further in. Recently, people have been
compressing methane under ridiculously high pressures, using techniques
too fiendish to describe here. At sufficiently high pressures, it
releases hydrogen and turns into diamond crystals! --- together with lots
of other crud, like ethane and acetylene. This could happen in Neptune
at a depth of about 7000 kilometers below the cloud tops, where the
pressure reaches 500,000 times that of the Earth's atmosphere. So in
fact, there could be a steady rain of diamond crystals on Neptune! By
the way, all these Science articles are available for free online here:

3) Science Magazine, `http://www.sciencemag.org/search.dtl`

I also want to say a bit about spin foams. Papers continue to come out
on this subject:

4) Alejandro Perez and Carlo Rovelli, "A spin foam model without bubble divergences", available as [`gr-qc/0006107`](https://arxiv.org/abs/gr-qc/0006107).

A while ago, De Pietri, Freidel, Krasnov and Rovelli showed how to get
the Barrett-Crane model for Riemannian quantum gravity from a quantum
field theory on a product of 4 copies of $\mathrm{SO}(4)$ --- see
["Week 140"](#week140). This was based on earlier work by Boulatov
and Ooguri, who did a similar thing for $BF$ theory. The basic idea is to
cook up a quantum field theory on a product of copies of Lie group, with
a nice Lagrangian that encodes how simplices can stick together to form
a spacetime. If you do a Feynman diagram expansion of this quantum field
theory, the Feynman diagrams can be identified with spin foams, and the
sum over Feynman diagrams becomes a sum over spin foams.

The sum over spin foams may diverge; this paper attempts to control
those divergences. It makes some precise mathematical conjectures about
the convergence of certain sums --- mathematicians who like analysis and
representation theory should get to work on these!

5) Alejandro Perez and Carlo Rovelli, Spin foam model for Lorentzian
general relativity, available as
[`gr-qc/0009021`](https://arxiv.org/abs/gr-qc/0009021).

This paper modifies the De Pietri-Freidel-Krasnov-Rovelli construction
to get the *Lorentzian* Barrett-Crane model from quantum field theory on
a product of 4 copies of $\mathrm{SO}(3,1)$.

6) Alejandro Perez and Carlo Rovelli, "3+1 spinfoam model of quantum gravity with spacelike and timelike components", available as [`gr-qc/0011037`](https://arxiv.org/abs/gr-qc/0011037).

In the original Lorentzian Barrett-Crane model, spacetime is made of
4-simplices whose triangular faces are space/timelike --- in other words,
like little bits of the $xt$ plane in Minkowski spacetime. This model also
allows $4$-simplices whose triangular faces are space/spacelike --- in other
words, like little bits of the $xy$ plane. This amounts to using a
different class of irreducible unitary representations of the Lorentz
group to label the triangles.

7) Daniele Oriti and Ruth M. Williams, "Gluing $4$-simplices: a derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity", available as [`gr-qc/0010031`](https://arxiv.org/abs/gr-qc/0010031).

This gives an alternate derivation of the Riemannian Barrett-Crane spin
foam model starting from the Lagrangian for Riemannian general
relativity. This is good because it gives some more intuition for the
relation between classical general relativity and the spin foam approach
to quantum gravity.

Finally, if you're hopelessly confused about spin foams and other
approaches to quantum gravity, you might enjoy the following little
history of quantum gravity. It explains how many different approaches
were tried, leading up to the research directions that people pursue
now:

8) Carlo Rovelli, "Notes for a brief history of quantum gravity", presented at the 9th Marcel Grossmann Meeting in Rome, July 2000. Available as [`gr-qc/0006061`](https://arxiv.org/abs/gr-qc/0006061).