John Baez
Oct12-06, 05:08 AM
Also available as http://math.ucr.edu/home/baez/week222.html
October 17, 2005
This Week's Finds in Mathematical Physics - Week 222
John Baez
Last week there was a big conference on quantum gravity at
the Albert Einstein Institute near Berlin:
1) Loops '05, http://loops05.aei.mpg.de
The focus was loop quantum gravity and spin foams, but there
were also talks about other approaches, so it was much bigger than
last year's get-together in Marseille. Last year about 100 people
attended; this time about 160 did! It was strange seeing old pals
like Ashtekar, Lewandowski, Loll, Rovelli and Smolin almost lost
in a sea of new faces. But, it was great to talk to everyone,
both old and new.
I'll say more about this conference, but first let's talk about
gamma ray bursters, a black hole without a host galaxy, the newly
discovered moon of planet Xena, and lots of other transneptunian
objects.
Actually, just for fun, let's start with this science fiction novel
I picked up in Heathrow en route to Berlin:
2) Charles Stross, Accelerando, Ace Books, New York.
Also available at http://www.accelerando.org/book/
This is one of the few tales I've read that does a good job of
fleshing out Verner Vinge's "Singularity" scenario, where the
accelerating development of technology soars past human
comprehension and undergoes a phase transition to a thoroughly
different world. This is a real possibility, and it's been
discussed a lot:
3) Wikipedia, Technological singularity,
http://en.wikipedia.org/wiki/Technological_singularity
Ray Kurzweil, The Singularity,
http://www.kurzweilai.net/meme/frame.html?m=1
Anders Sandberg, The Singularity,
http://www.aleph.se/Trans/Global/Singularity/
However, it's not an easy subject for fiction - at least not for
mere human readers! Stross makes it gripping: sometimes goofy,
sometimes thrilling, and sometimes rather sad. Characters include
a robot cat with ever-growing powers and some space-faring uploaded
lobsters.
The hero, Manfred Macx, starts out as a freeware developer, futurist
and all-purpose wheeler-dealer. Here's a scene from the beginning
of the book, before all hell breaks loose:
Manfred's mood of dynamic optimism is gone, broken by the
knowledge that his vivisectionist stalker has followed him
to Amsterdam to say nothing of Pamela, his dominatrix,
source of so much yearning and so many morning-after weals.
He slips his glasses on, takes the universe off hold, and
tells it to take him for a long walk while he catches up on
the latest on the tensor-mode gravitational waves in the
cosmic background radiation (which, it is theorized, may be
waste heat generated by irreversible computational processes
back during the inflationary epoch; the present-day universe
being merely the data left behind by a really huge calculation).
And then there's the weirdness beyond M31: according to the
more conservative cosmologists, an alien superpower - maybe
a collective of Kardashev Type Three galaxy-spanning
civilizations - is running a timing channel attack on the
computational ultrastructure of space-time itself, trying to
break through to whatever's underneath. The tofu-Alzheimer's
link can wait.
An idea a minute - and the book is free online: what more could you
want?
But right now, the big news in astronomy is *not* about a type III
civilization lurking beyond M31 (otherwise known as the Andromeda
Galaxy). It's some evidence that short gamma ray bursts are caused
by collisions involving neutron stars and black holes!
Gamma ray bursts are among the most energetic events known in the
heavens. They happen in galaxies throughout the universe; we see
about one a day, and each releases somewhere between 10^{45} and
10^{47} joules of energy. The larger figure is what you'd get by
turning the entire mass of the Sun into energy.
There could be several kinds of gamma ray bursts, but there seem to
be at least two: short and long. Short bursts last between
40 milliseconds and 10 seconds - imagine the whole Sun turning into
energy that fast! Long ones last between 10 and 100 seconds. The
two kinds seem to be qualitatively different: for example, the short
ones consist of higher-frequency gamma rays. The big news is that
they happen in different kinds of galaxies!
In "week204", I described how people caught a long gamma ray burst
in the act in March 2003. A gamma ray detector aboard a satellite
relayed information to telescopes in Australia and Japan, allowing
them to spot a visible afterglow right after the burst. The details
of this glow fit the "hypernova" theory of long gamma ray bursts.
The hypernova theory says that when a star more than 25 times heavier
than the Sun runs out of fuel and collapses, it forms a black hole
that sucks down the star's iron core before a normal supernova
explosion can occur. In just a few seconds, about a solar mass of
iron spirals into the black hole, forming a pancake-shaped disk as
it goes down. In the process, this disk becomes incredibly hot and
shoots out jets of radiation in the transverse directions. As they
plow through the star's outer layers, these jets create beams of
gamma rays.
The short bursts have been harder to catch. By the time a telescope
on Earth could be aimed at the spot where the gamma rays were seen,
no afterglow could be seen!
So, in October 2004 NASA launched Swift: a gamma-ray detecting
satellite equipped with an X-ray telescope and an ultraviolet/optical
telescope that can respond quickly whenever a burst is seen:
4) Official NASA Swift homepage,
http://swift.gsfc.nasa.gov/docs/swift/swiftsc.html
5) Gamma-ray burst real-time sky map, http://grb.sonoma.edu/
On May 9th, 2005, Swift detected a short burst and caught 11 photons
of the burst's X-ray afterglow. Another short burst detected by
HETE-II had its X-ray afterglow caught by the Chandra X-ray satellite.
Analysis of these and two more short bursts has convinced some
scientists that they're caused by collisions between neutron stars
and/or black holes:
6) D. B. Fox et al, The afterglow of GRB050709 and the nature of the
short-hard gamma-ray bursts, Nature 437 (October 2005), 849-850.
Also available at http://www.nasa.gov/pdf/135397main_nature_fox_final.pdf
Despite what the news media are saying, I don't see that this paper
"proves" the short gamma-ray bursts are caused by such collisions.
Instead, I see some good pieces of evidence.
The faintness of the afterglows suggests some mechanism other than a
hypernova. But as far as I can tell, the best evidence is that short
gamma ray bursts tend to happen near the edges of old galaxies, while
the long ones happen near the centers of young galaxies.
The center of a young galaxy is where you'd expect to find a really
huge Wolf-Rayet star, the sort that dies in a hypernova. The edge of
an old galaxy is where you'd expect to see black holes and neutron
stars collide. Why? Because such collisions can only happen long
after stars are first formed. First you need an orbiting pair of
giant stars to go supernova and collapse into neutron stars and/or
black holes. Then you need plenty more time for this pair to spiral
down thanks to gravitational radiation, and eventually collide.
By then the pair may sail off to the edge of the galaxy, thanks to
the "kick" delivered by the supernova explosions.
I hope astronomers can clinch the case for the collision theory of
short gamma ray bursts. After all, these collisions involving
neutron stars and black holes are precisely what gravitational wave
detectors like LIGO and VIRGO are hoping to see! If we know to look
for gravitational waves precisely when we see short gamma ray bursts,
and we know where they're coming from, we'll have a better chance of
finding them.
(Of course, we'll also have a better chance of *fooling* ourselves
into *thinking* we found them, until we do some double-blind tests.)
By the way, LIGO is already analysing data to look for gravitational
waves. I talked about this in "week189", but here's something new:
now you can help them by running a cool screensaver called
Einstein@Home on your computer! Check it out:
7) Einstein@Home, http://einstein.phys.uwm.edu/
Speaking of black holes, last month the Hubble Space Telescope and
the Very Large Telescope in Chile detected a quasar that seems
to have no host galaxy:
8) European Southern Observatory, Black hole in search of a home,
http://www.eso.org/outreach/press-rel/pr-2005/pr-23-05.html
HubbleSite, Quasar without host galaxy compared with normal quasar,
http://hubblesite.org/newscenter/newsdesk/archive/releases/2005/13/image/a
Quasars are thought to be super massive black holes; they're usually
found in the centers of galaxies, where they devour stars and shoot
out enormously powerful jets of radiation. However, the quasar
HE0450-2958 is surrounded only by a blob of ionized gas. Nearby, a
wildly disturbed spiral galaxy can be seen. (See the NASA website
above for a picture.)
Did this quasar begin life in this galaxy and then get kicked out when
the galaxy collided with something containing a super-massive black hole?
What could that something be?
Puzzles, puzzles, in the sky....
Closer to home, astronomers at the Keck Observatory in Hawaii have
discovered that planet Xena has a moon! They nicknamed it Gabrielle,
after this famous TV character's sidekick:
9) Michael E. Brown, The moon of the 10th planet,
http://www.gps.caltech.edu/~mbrown/planetlila/moon/index.html
If you hadn't heard about planet Xena, or you don't like the idea
of naming a planet after a TV character - even a "warrior princess" -
don't get worked up just yet. Xena's official name is currently
2003 UB313, and though she's larger than Pluto, the International
Astronomical Union has not decided whether she'll officially be
considered a planet.
If Xena becomes a planet, she'll probably be renamed Persephone,
after the reluctant queen of the underworld in Greek mythology.
But, she may have to settle for the status of a mere "transneptunian
object", like Quaoar and Sedna. Indeed, if Pluto had been discovered
more recently, folks probably wouldn't have called him a planet
either.
If you haven't even heard of Quaoar and Sedna... well, you must be
too absorbed by mundane concerns to keep track of the burgeoning
population of our Solar System. But it's not too late to mend your
ways! Impress your friends by casually dropping some of this jargon:
o Transneptunian object - any object that orbits the Sun at an average
distance greater than that of Neptune. Neptune is about 30 AU from
the Sun, meaning it's 30 times farther from the Sun than we are.
Transneptunian objects can be roughly divided into three kinds:
Kuiper Belt objects, scattered disc objects, and Oort cloud objects.
o Kuiper belt object - any object whose orbit lies in the Kuiper Belt.
This is the region in the ecliptic (the plane of the planets' orbits)
between 30 and 50 AU from the Sun. There are a bunch of planetoids
in this belt. Beyond 50 AU there seems to be a sharp dropoff in
their density. Three main kinds of Kuiper belt objects have been
found so far: cubewanos, plutinos and twotinos.
o Cubewano - A cubewano is a Kuiper belt object whose orbit is not
in resonance with any of the outer planets. The curious name
comes from "QB1", since the first example was named 1992 QB1.
One of the biggest cubewanos is Quaoar, with a diameter of about
1200 kilometers. This is about half the diameter of Pluto, or a
third the size of the Moon: much bigger than anything in the
asteroid belt! Folks believe Quaoar is a mixture of ice and rock.
It's very dark in color, but last year crystalline water ice was
detected on its surface, using infrared spectroscopy. This came
as a surprise, because cosmic rays and solar wind should convert
exposed ice crystals to the amorphous form of ice within about
10 million years. Could there have been liquid water volcanos
active on Quaoar this recently?? Or maybe meteor impacts melt
amorphous ice and then it crystallizes?
Other big cubewanos include Chaos, Varuna, and Deucalion. 2003
EL61 and 2005 FY9 are even bigger, but they haven't got nice names
yet.
o Plutino - A plutino is a Kuiper belt object whose orbit is in
3:2 resonance with Neptune: they go around the Sun twice while Neptune
goes around three times. About a quarter of Kuiper belt objects
are plutinos.
The most famous plutino is Pluto itself, though some pedants argue
that Pluto can't be a "little Pluto". Pluto is quite different
than anything else we call a planet: it has an eccentric orbit that
ranges between 30 and 50 AU, and its orbit is tilted 17 degrees to
the ecliptic. Its surface is light brown, consisting mainly of
frozen nitrogen and carbon monoxide. When it comes near the sun,
as it recently did, it also gets a thin atmosphere made of these
gases.
Other plutinos include Ixion, Orcus, Rhadamanthus, and Pluto's moon
Charon. If you know Greek mythology, you'll know these guys are all
named after deities of the underworld.
o Twotino - A twotino is a Kuiper belt object whose orbit is in 2:1
resonance with Neptune. These are rare compared to plutinos, and
they're smaller, so they're stuck with boring names like 1996 TR66.
There are also a couple of Kuiper belt objects in 4:3 and 5:3
resonances with Neptune.
o Scattered disc object - A scattered disc object is a Kuiper belt
object that has been perturbed by interactions with Neptune into
an orbit that is more eccentric or more tilted from the ecliptic.
Xena (or more properly 2003 UB313) is a highly eccentric scattered
disc object whose orbit carries it between 40 to 100 AU from the sun.
Its orbit is inclined a whopping 44 degrees, and it's locked in a
complicated 17:5 resonance with Neptune. It's probably larger than
Pluto - a reasonable rough guess is 2900 kilometers in diameter, as
compared with 2400 for Pluto. Its surface has methane ice, and we
now know it has a moon.
It's quite possible that scattered disc objects are related to
"centaurs", which are planetoids orbiting the Sun between Jupiter
and Neptune. The centaurs may be Kuiper belt objects that got
knocked towards the Sun instead of away from it! Centaurs have
chaotic orbits and will probably either collide with something or
be ejected from the Solar System.
o Oort cloud object - the Oort cloud is a hypothesized spherical cloud
of comets between 50,000 and 100,000 AU from the Sun. The idea is
this cloud consists of leftovers from the original nebula that
collapsed to form our Solar system, and comets come from this region
when they are perturbed from their orbits by the gravity of other
stars.
Nobody has seen a certified Oort cloud object. The best candidate
so far is Sedna, an object roughly 1500 kilometers in diameter with
a wildly eccentric orbit taking it between 80 to 930 AU from the Sun.
Sedna was discovered in 2004 when it was 90 AU from the Sun. It's
the farthest known object in our Solar System, but still much closer
than the Oort cloud was supposed to be! Maybe it's a drastic example
of a scattered disc object, or maybe it's part of an "inner Oort
cloud" - or maybe the Oort cloud isn't as far out as people thought.
For a great introduction to the Kuiper belt and related topics, try
this:
10) David C. Jewitt, Kuiper Belt,
http://www.ifa.hawaii.edu/faculty/jewitt/kb.html
For transneptunian objects in general, try:
11) William Robert Johnston, Transneptunian objects,
http://www.johnstonsarchive.net/astro/tnos.html
Also check out this newsletter:
12) Distant EKOs: the Kuiper Belt Electronic Newsletter,
http://www.boulder.swri.edu/ekonews/
Quaoar was discovered in 2002 by Chad Trujillo and Mike Brown of
Caltech:
13) Chad Trujillo, Quaoar, http://www.gps.caltech.edu/~chad/quaoar/
For evidence of crystalline water ice on Quaoar, see:
14) David C. Jewitt and Jane Luu, Crystalline water ice on the Kuiper
belt object (50000) Quaoar, Nature 432 (2004), 731-733.
Also available at http://www.ifa.hawaii.edu/faculty/jewitt/quaoar.html
Xena was discovered in 2003 by Trujillo, Brown and a colleague of
theirs at Yale University:
15) Michael E. Brown, Chad A. Trujillo and David L. Rabinowitz,
Discovery of a planetary-sized object in the scattered Kuiper belt,
submitted to ApJ Letters, available at
http://www.gps.caltech.edu/%7Embrown/papers/ps/xena.pdf
Brown has a nice webpage about Xena and Gabrielle:
16) Michael E. Brown, The discovery of UB313, the 10th planet,
http://www.gps.caltech.edu/~mbrown/planetlila/
The same gang of three also discovered Sedna in 2003:
17) Michael E. Brown, Chad A. Trujillo and David L. Rabinowitz,
Discovery of a candidate inner Oort cloud planetoid, to appear
in ApJ Letters, available at
http://www.gps.caltech.edu/~mbrown/papers/ps/sedna.pdf
... and Brown has a fun Sedna webpage too:
18) Michael E. Brown, Sedna (2003 VB12),
http://www.gps.caltech.edu/~mbrown/sedna/
How all these transneptunian objects got where they are is a wonderful
puzzle in celestial mechanics, but you can read more about that in
the references above, especially Jewitt's Kuiper belt webpage.
Now I want to talk about Loops '05!
Instead of trying to review all the talks - a hopeless task, since
there were 86 - I'll just mention the *two* strands of work I find
most exciting.
First, there's new evidence that a quantum theory of pure gravity
(meaning gravity without matter) makes sense in 4-dimensional spacetime.
To understand why this is exciting, you have to realize that in some
quarters, the conventional wisdom says a quantum theory of pure gravity
can't possibly make sense, except as a crude approximation at large
distance scales, because this theory is "perturbatively
nonrenormalizable".
Very roughly, this means that as we zoom in and look at the theory at
shorter and shorter distance scales, it looks less and less like a
"free field theory" where gravitons zip about without interacting.
Instead, the interactions get stronger and more complicated!
So, in the jargon of the trade, we don't get a "Gaussian ultraviolet
fixed point".
Huh?
Well, roughly, an "ultraviolet fixed point" is a quantum field theory
that keeps looking the same as you keep viewing it on shorter and
shorter distance scales. A "Gaussian" ultraviolet fixed point is one
that's also a free quantum field theory: one where particles don't
interact.
If quantum gravity approached a Gaussian ultraviolet fixed point as
we zoomed in, we could calculate what gravitons do at arbitrarily
high energies (at least perturbatively, as power series in Newton's
constant - no guarantee that these series converge). Particle
physicists would then be happy and say the theory was "perturbatively
renormalizable".
But, it's not.
The conventional wisdom concludes that to save quantum gravity, we
must include matter of precisely the right sort to *make* it
perturbatively renormalizable. This is the quest that led people
first to supergravity and ultimately to superstring theory - see
"week195" for more of this story.
But, as far back as 1979, the particle physicist Weinberg raised the
possibility that pure quantum gravity is "nonperturbatively
renormalizable", or "asymptotically safe". This means that as we
zoom in and look at the theory at shorter and shorter distance scales,
it approaches some theory *other than* that of noninteracting gravitons.
In other words, Weinberg was suggesting that pure quantum gravity
approaches a non-obvious ultraviolet fixed point - possibly a
"non-Gaussian" one.
The big news is that this seems to be true!
Even cooler, in this theory spacetime seems to act *2-dimensional*
at very short distance scales.
This idea has been brewing for a long time - I talked about it
extensively back in "week139". But now there's more solid
evidence for it, coming from two quite different approaches.
First, people doing numerical quantum gravity in the "causal dynamical
triangulations" approach are seeing this effect in their computer
calculations. This is what Renate Loll explained at Loops '05. The
best place to read the details is here:
18) Jan Ambjorn, J. Jurkiewicz and Renate Loll, Reconstructing
the universe, Phys. Rev. D72 (2005) 064014. Also available as
hep-th/0505154.
but if you need something less technical, try this:
19) Jan Ambjorn, J. Jurkiewicz and Renate Loll, The Universe from
Scratch, available as hep-th/0509010.
The titles of their papers are a bit grandiose, but their calculations
are solid stuff - truly magnificent. I described their basic strategy
in my report on the Marseille conference in "week206". So, I won't
explain that again. I'll just mention their big new result: in pure
quantum gravity, spacetime has a spectral dimension of 4.02 plus
or minus 0.1 on large distance scales, but 1.80 +- 0.25 in the
limit of very short distance scales!
Zounds! What does that mean?
The "spectral dimension" of a spacetime is the dimension as measured
by watching heat spread out on this spacetime: the short-time behavior
of the heat equation probes the spacetime at short distance scales, while
its large-time behavior probes large distance scales. Spectral dimensions
don't need to be integers - for fractals they're typically not. But,
Loll and company believe they're seeing spacetimes that are *exactly*
2-dimensional in the limit of very small distance scales, *exactly*
4-dimensional in the limit of very large scales, with a continuous change
in dimension in between. The error bars in the above figures come from
doing Monte Carlo simulations. They're just using ordinary computers,
not supercomputers. So, with more work one could shrink their error bars
and test their result.
My main worry about their work is that it uses a fixed slicing of
spactime by timelike slices. So, there's a danger that their
procedure breaks Lorentz-invariance, even in the continuum limit
which they are attempting to compute. I would like to find a way
around this problem!
Luckily, some other people are getting similar results from a second
procedure that definitely does *not* break Lorentz invariance:
20) Oliver Lauscher and Martin Reuter, Fractal spacetime structure in
asymptotically safe gravity, available as hep-th/0508202.
Reuter spoke about all this work at Loops '05. The idea is to
investigate Weinberg's original idea in excruciatingly precise
detail using "renormalization group flow" ideas. The above paper
is a review of lots of others, and you need to read a bunch to get
what's really going on. The upshot, however, is that they find
evidence for a non-Gaussian ultraviolet fixed point in pure quantum
gravity. Moreover, the spectral dimension of spacetime approaches
2 in the limit of very short distance scales.
Suppose this is all true. What does it mean?
Nobody knows yet; there are lots of attitudes one could take.
Ambjorn, Jurkiewicz and Loll could probably just plunge ahead and
use computers to calculate lots of things about quantum gravity.
(Right now they want to test their results in lots of ways.) One
good thing would be to include matter of various sorts and see how
it affects the conclusions.
Similarly, Lauscher and Reuter could just plunge ahead and compute,
if they wanted.
This is excellent. But personally, I'd like to find a beautiful theory
in which spacetime is 2-dimensional at short distance scales, which
reduces to general relativity at large scales. In other words, to
redo all these calculations "from the bottom up".
Unsurprisingly, I hope this beautiful theory is a spin foam model,
since spin foams are 2-dimensional and I like them a lot. I presented
some rough ideas on how one might invent such a model:
21) John Baez, Towards a spin foam model of quantum gravity,
talk at Loops '05, available at http://math.ucr.edu/home/baez/loops05/
But, these ideas are very tentative and only time will tell if they
amount to anything. What's more important is that pure quantum gravity
seems to exist - as a theory, that is - and people seem to be learning
actual facts about it, instead of just arguing endlessly about it.
That's progress!
The second most exciting thing at Loops '05, in my biased opinion,
was the work of John Barrett, Laurent Freidel, Karim Noui and others
on "matter without matter" in 3d quantum gravity. Simply by carving a
Feynman-diagram-shaped hole in 3d spacetime and doing quantum gravity
on the spacetime that's left over, you get a good theory of quantum
gravity coupled to matter! You can even take the limit as Newton's
gravitational constant goes to zero and get ordinary quantum field
theory on flat spacetime!
Check these out:
21) John Barrett, Feynman diagams coupled to three-dimensional quantum
gravity, available as gr-qc/0502048.
John Barrett, Feynman loops and three-dimensional quantum gravity,
Mod. Phys. Lett. A20 (2005) 1271. Also available as gr-qc/0412107.
22) Laurent Freidel and David Louapre, Ponzano-Regge model revisited
I: gauge fixing, observables and interacting spinning particles,
Class. Quant. Grav. 21 (2004) 5685-5726. Also available as
hep-th/0401076.
Laurent Freidel and David Louapre, Ponzano-Regge model revisited
II: equivalence with Chern-Simons, available as gr-qc/0410141
Laurent Freidel and Etera R. Livine, Ponzano-Regge model
revisited III: Feynman diagrams and effective field theory,
available as hep-th/0502106.
23) Laurent Freidel, Daniele Oriti, and James Ryan, A group field
theory for 3d quantum gravity coupled to a scalar field, available
as gr-qc/0506067.
24) Karin Noui and Alejandro Perez, Three dimensional loop quantum
gravity: coupling to point particles, available as gr-qc/0402111.
This is mindblowingly beautiful, especially because lots of it is
already mathematically rigorous, and we can easily make more so.
It's even related to n-categories: my student Jeffrey Morton
presented a poster on this aspect.
Together with my student Derek Wise, Jeffrey Morton and I plan to have
a lot of fun studying this stuff. So, I won't talk about it more now -
I'll probably get around to saying more someday, especially about how
the whole story generalizes to 4 dimensions.
There's a lot more to say about Loops '05, but this will have to do.
In a while, a bunch of the talks should be visible on the conference
homepage.... that should give you a better idea of what happened.
-----------------------------------------------------------------------
Previous issues of "This Week's Finds" and other expository articles on
mathematics and physics, as well as some of my research papers, can be
obtained at
http://math.ucr.edu/home/baez/
For a table of contents of all the issues of This Week's Finds, try
http://math.ucr.edu/home/baez/twf.html
A simple jumping-off point to the old issues is available at
http://math.ucr.edu/home/baez/twfshort.html
If you just want the latest issue, go to
http://math.ucr.edu/home/baez/this.week.html
October 17, 2005
This Week's Finds in Mathematical Physics - Week 222
John Baez
Last week there was a big conference on quantum gravity at
the Albert Einstein Institute near Berlin:
1) Loops '05, http://loops05.aei.mpg.de
The focus was loop quantum gravity and spin foams, but there
were also talks about other approaches, so it was much bigger than
last year's get-together in Marseille. Last year about 100 people
attended; this time about 160 did! It was strange seeing old pals
like Ashtekar, Lewandowski, Loll, Rovelli and Smolin almost lost
in a sea of new faces. But, it was great to talk to everyone,
both old and new.
I'll say more about this conference, but first let's talk about
gamma ray bursters, a black hole without a host galaxy, the newly
discovered moon of planet Xena, and lots of other transneptunian
objects.
Actually, just for fun, let's start with this science fiction novel
I picked up in Heathrow en route to Berlin:
2) Charles Stross, Accelerando, Ace Books, New York.
Also available at http://www.accelerando.org/book/
This is one of the few tales I've read that does a good job of
fleshing out Verner Vinge's "Singularity" scenario, where the
accelerating development of technology soars past human
comprehension and undergoes a phase transition to a thoroughly
different world. This is a real possibility, and it's been
discussed a lot:
3) Wikipedia, Technological singularity,
http://en.wikipedia.org/wiki/Technological_singularity
Ray Kurzweil, The Singularity,
http://www.kurzweilai.net/meme/frame.html?m=1
Anders Sandberg, The Singularity,
http://www.aleph.se/Trans/Global/Singularity/
However, it's not an easy subject for fiction - at least not for
mere human readers! Stross makes it gripping: sometimes goofy,
sometimes thrilling, and sometimes rather sad. Characters include
a robot cat with ever-growing powers and some space-faring uploaded
lobsters.
The hero, Manfred Macx, starts out as a freeware developer, futurist
and all-purpose wheeler-dealer. Here's a scene from the beginning
of the book, before all hell breaks loose:
Manfred's mood of dynamic optimism is gone, broken by the
knowledge that his vivisectionist stalker has followed him
to Amsterdam to say nothing of Pamela, his dominatrix,
source of so much yearning and so many morning-after weals.
He slips his glasses on, takes the universe off hold, and
tells it to take him for a long walk while he catches up on
the latest on the tensor-mode gravitational waves in the
cosmic background radiation (which, it is theorized, may be
waste heat generated by irreversible computational processes
back during the inflationary epoch; the present-day universe
being merely the data left behind by a really huge calculation).
And then there's the weirdness beyond M31: according to the
more conservative cosmologists, an alien superpower - maybe
a collective of Kardashev Type Three galaxy-spanning
civilizations - is running a timing channel attack on the
computational ultrastructure of space-time itself, trying to
break through to whatever's underneath. The tofu-Alzheimer's
link can wait.
An idea a minute - and the book is free online: what more could you
want?
But right now, the big news in astronomy is *not* about a type III
civilization lurking beyond M31 (otherwise known as the Andromeda
Galaxy). It's some evidence that short gamma ray bursts are caused
by collisions involving neutron stars and black holes!
Gamma ray bursts are among the most energetic events known in the
heavens. They happen in galaxies throughout the universe; we see
about one a day, and each releases somewhere between 10^{45} and
10^{47} joules of energy. The larger figure is what you'd get by
turning the entire mass of the Sun into energy.
There could be several kinds of gamma ray bursts, but there seem to
be at least two: short and long. Short bursts last between
40 milliseconds and 10 seconds - imagine the whole Sun turning into
energy that fast! Long ones last between 10 and 100 seconds. The
two kinds seem to be qualitatively different: for example, the short
ones consist of higher-frequency gamma rays. The big news is that
they happen in different kinds of galaxies!
In "week204", I described how people caught a long gamma ray burst
in the act in March 2003. A gamma ray detector aboard a satellite
relayed information to telescopes in Australia and Japan, allowing
them to spot a visible afterglow right after the burst. The details
of this glow fit the "hypernova" theory of long gamma ray bursts.
The hypernova theory says that when a star more than 25 times heavier
than the Sun runs out of fuel and collapses, it forms a black hole
that sucks down the star's iron core before a normal supernova
explosion can occur. In just a few seconds, about a solar mass of
iron spirals into the black hole, forming a pancake-shaped disk as
it goes down. In the process, this disk becomes incredibly hot and
shoots out jets of radiation in the transverse directions. As they
plow through the star's outer layers, these jets create beams of
gamma rays.
The short bursts have been harder to catch. By the time a telescope
on Earth could be aimed at the spot where the gamma rays were seen,
no afterglow could be seen!
So, in October 2004 NASA launched Swift: a gamma-ray detecting
satellite equipped with an X-ray telescope and an ultraviolet/optical
telescope that can respond quickly whenever a burst is seen:
4) Official NASA Swift homepage,
http://swift.gsfc.nasa.gov/docs/swift/swiftsc.html
5) Gamma-ray burst real-time sky map, http://grb.sonoma.edu/
On May 9th, 2005, Swift detected a short burst and caught 11 photons
of the burst's X-ray afterglow. Another short burst detected by
HETE-II had its X-ray afterglow caught by the Chandra X-ray satellite.
Analysis of these and two more short bursts has convinced some
scientists that they're caused by collisions between neutron stars
and/or black holes:
6) D. B. Fox et al, The afterglow of GRB050709 and the nature of the
short-hard gamma-ray bursts, Nature 437 (October 2005), 849-850.
Also available at http://www.nasa.gov/pdf/135397main_nature_fox_final.pdf
Despite what the news media are saying, I don't see that this paper
"proves" the short gamma-ray bursts are caused by such collisions.
Instead, I see some good pieces of evidence.
The faintness of the afterglows suggests some mechanism other than a
hypernova. But as far as I can tell, the best evidence is that short
gamma ray bursts tend to happen near the edges of old galaxies, while
the long ones happen near the centers of young galaxies.
The center of a young galaxy is where you'd expect to find a really
huge Wolf-Rayet star, the sort that dies in a hypernova. The edge of
an old galaxy is where you'd expect to see black holes and neutron
stars collide. Why? Because such collisions can only happen long
after stars are first formed. First you need an orbiting pair of
giant stars to go supernova and collapse into neutron stars and/or
black holes. Then you need plenty more time for this pair to spiral
down thanks to gravitational radiation, and eventually collide.
By then the pair may sail off to the edge of the galaxy, thanks to
the "kick" delivered by the supernova explosions.
I hope astronomers can clinch the case for the collision theory of
short gamma ray bursts. After all, these collisions involving
neutron stars and black holes are precisely what gravitational wave
detectors like LIGO and VIRGO are hoping to see! If we know to look
for gravitational waves precisely when we see short gamma ray bursts,
and we know where they're coming from, we'll have a better chance of
finding them.
(Of course, we'll also have a better chance of *fooling* ourselves
into *thinking* we found them, until we do some double-blind tests.)
By the way, LIGO is already analysing data to look for gravitational
waves. I talked about this in "week189", but here's something new:
now you can help them by running a cool screensaver called
Einstein@Home on your computer! Check it out:
7) Einstein@Home, http://einstein.phys.uwm.edu/
Speaking of black holes, last month the Hubble Space Telescope and
the Very Large Telescope in Chile detected a quasar that seems
to have no host galaxy:
8) European Southern Observatory, Black hole in search of a home,
http://www.eso.org/outreach/press-rel/pr-2005/pr-23-05.html
HubbleSite, Quasar without host galaxy compared with normal quasar,
http://hubblesite.org/newscenter/newsdesk/archive/releases/2005/13/image/a
Quasars are thought to be super massive black holes; they're usually
found in the centers of galaxies, where they devour stars and shoot
out enormously powerful jets of radiation. However, the quasar
HE0450-2958 is surrounded only by a blob of ionized gas. Nearby, a
wildly disturbed spiral galaxy can be seen. (See the NASA website
above for a picture.)
Did this quasar begin life in this galaxy and then get kicked out when
the galaxy collided with something containing a super-massive black hole?
What could that something be?
Puzzles, puzzles, in the sky....
Closer to home, astronomers at the Keck Observatory in Hawaii have
discovered that planet Xena has a moon! They nicknamed it Gabrielle,
after this famous TV character's sidekick:
9) Michael E. Brown, The moon of the 10th planet,
http://www.gps.caltech.edu/~mbrown/planetlila/moon/index.html
If you hadn't heard about planet Xena, or you don't like the idea
of naming a planet after a TV character - even a "warrior princess" -
don't get worked up just yet. Xena's official name is currently
2003 UB313, and though she's larger than Pluto, the International
Astronomical Union has not decided whether she'll officially be
considered a planet.
If Xena becomes a planet, she'll probably be renamed Persephone,
after the reluctant queen of the underworld in Greek mythology.
But, she may have to settle for the status of a mere "transneptunian
object", like Quaoar and Sedna. Indeed, if Pluto had been discovered
more recently, folks probably wouldn't have called him a planet
either.
If you haven't even heard of Quaoar and Sedna... well, you must be
too absorbed by mundane concerns to keep track of the burgeoning
population of our Solar System. But it's not too late to mend your
ways! Impress your friends by casually dropping some of this jargon:
o Transneptunian object - any object that orbits the Sun at an average
distance greater than that of Neptune. Neptune is about 30 AU from
the Sun, meaning it's 30 times farther from the Sun than we are.
Transneptunian objects can be roughly divided into three kinds:
Kuiper Belt objects, scattered disc objects, and Oort cloud objects.
o Kuiper belt object - any object whose orbit lies in the Kuiper Belt.
This is the region in the ecliptic (the plane of the planets' orbits)
between 30 and 50 AU from the Sun. There are a bunch of planetoids
in this belt. Beyond 50 AU there seems to be a sharp dropoff in
their density. Three main kinds of Kuiper belt objects have been
found so far: cubewanos, plutinos and twotinos.
o Cubewano - A cubewano is a Kuiper belt object whose orbit is not
in resonance with any of the outer planets. The curious name
comes from "QB1", since the first example was named 1992 QB1.
One of the biggest cubewanos is Quaoar, with a diameter of about
1200 kilometers. This is about half the diameter of Pluto, or a
third the size of the Moon: much bigger than anything in the
asteroid belt! Folks believe Quaoar is a mixture of ice and rock.
It's very dark in color, but last year crystalline water ice was
detected on its surface, using infrared spectroscopy. This came
as a surprise, because cosmic rays and solar wind should convert
exposed ice crystals to the amorphous form of ice within about
10 million years. Could there have been liquid water volcanos
active on Quaoar this recently?? Or maybe meteor impacts melt
amorphous ice and then it crystallizes?
Other big cubewanos include Chaos, Varuna, and Deucalion. 2003
EL61 and 2005 FY9 are even bigger, but they haven't got nice names
yet.
o Plutino - A plutino is a Kuiper belt object whose orbit is in
3:2 resonance with Neptune: they go around the Sun twice while Neptune
goes around three times. About a quarter of Kuiper belt objects
are plutinos.
The most famous plutino is Pluto itself, though some pedants argue
that Pluto can't be a "little Pluto". Pluto is quite different
than anything else we call a planet: it has an eccentric orbit that
ranges between 30 and 50 AU, and its orbit is tilted 17 degrees to
the ecliptic. Its surface is light brown, consisting mainly of
frozen nitrogen and carbon monoxide. When it comes near the sun,
as it recently did, it also gets a thin atmosphere made of these
gases.
Other plutinos include Ixion, Orcus, Rhadamanthus, and Pluto's moon
Charon. If you know Greek mythology, you'll know these guys are all
named after deities of the underworld.
o Twotino - A twotino is a Kuiper belt object whose orbit is in 2:1
resonance with Neptune. These are rare compared to plutinos, and
they're smaller, so they're stuck with boring names like 1996 TR66.
There are also a couple of Kuiper belt objects in 4:3 and 5:3
resonances with Neptune.
o Scattered disc object - A scattered disc object is a Kuiper belt
object that has been perturbed by interactions with Neptune into
an orbit that is more eccentric or more tilted from the ecliptic.
Xena (or more properly 2003 UB313) is a highly eccentric scattered
disc object whose orbit carries it between 40 to 100 AU from the sun.
Its orbit is inclined a whopping 44 degrees, and it's locked in a
complicated 17:5 resonance with Neptune. It's probably larger than
Pluto - a reasonable rough guess is 2900 kilometers in diameter, as
compared with 2400 for Pluto. Its surface has methane ice, and we
now know it has a moon.
It's quite possible that scattered disc objects are related to
"centaurs", which are planetoids orbiting the Sun between Jupiter
and Neptune. The centaurs may be Kuiper belt objects that got
knocked towards the Sun instead of away from it! Centaurs have
chaotic orbits and will probably either collide with something or
be ejected from the Solar System.
o Oort cloud object - the Oort cloud is a hypothesized spherical cloud
of comets between 50,000 and 100,000 AU from the Sun. The idea is
this cloud consists of leftovers from the original nebula that
collapsed to form our Solar system, and comets come from this region
when they are perturbed from their orbits by the gravity of other
stars.
Nobody has seen a certified Oort cloud object. The best candidate
so far is Sedna, an object roughly 1500 kilometers in diameter with
a wildly eccentric orbit taking it between 80 to 930 AU from the Sun.
Sedna was discovered in 2004 when it was 90 AU from the Sun. It's
the farthest known object in our Solar System, but still much closer
than the Oort cloud was supposed to be! Maybe it's a drastic example
of a scattered disc object, or maybe it's part of an "inner Oort
cloud" - or maybe the Oort cloud isn't as far out as people thought.
For a great introduction to the Kuiper belt and related topics, try
this:
10) David C. Jewitt, Kuiper Belt,
http://www.ifa.hawaii.edu/faculty/jewitt/kb.html
For transneptunian objects in general, try:
11) William Robert Johnston, Transneptunian objects,
http://www.johnstonsarchive.net/astro/tnos.html
Also check out this newsletter:
12) Distant EKOs: the Kuiper Belt Electronic Newsletter,
http://www.boulder.swri.edu/ekonews/
Quaoar was discovered in 2002 by Chad Trujillo and Mike Brown of
Caltech:
13) Chad Trujillo, Quaoar, http://www.gps.caltech.edu/~chad/quaoar/
For evidence of crystalline water ice on Quaoar, see:
14) David C. Jewitt and Jane Luu, Crystalline water ice on the Kuiper
belt object (50000) Quaoar, Nature 432 (2004), 731-733.
Also available at http://www.ifa.hawaii.edu/faculty/jewitt/quaoar.html
Xena was discovered in 2003 by Trujillo, Brown and a colleague of
theirs at Yale University:
15) Michael E. Brown, Chad A. Trujillo and David L. Rabinowitz,
Discovery of a planetary-sized object in the scattered Kuiper belt,
submitted to ApJ Letters, available at
http://www.gps.caltech.edu/%7Embrown/papers/ps/xena.pdf
Brown has a nice webpage about Xena and Gabrielle:
16) Michael E. Brown, The discovery of UB313, the 10th planet,
http://www.gps.caltech.edu/~mbrown/planetlila/
The same gang of three also discovered Sedna in 2003:
17) Michael E. Brown, Chad A. Trujillo and David L. Rabinowitz,
Discovery of a candidate inner Oort cloud planetoid, to appear
in ApJ Letters, available at
http://www.gps.caltech.edu/~mbrown/papers/ps/sedna.pdf
... and Brown has a fun Sedna webpage too:
18) Michael E. Brown, Sedna (2003 VB12),
http://www.gps.caltech.edu/~mbrown/sedna/
How all these transneptunian objects got where they are is a wonderful
puzzle in celestial mechanics, but you can read more about that in
the references above, especially Jewitt's Kuiper belt webpage.
Now I want to talk about Loops '05!
Instead of trying to review all the talks - a hopeless task, since
there were 86 - I'll just mention the *two* strands of work I find
most exciting.
First, there's new evidence that a quantum theory of pure gravity
(meaning gravity without matter) makes sense in 4-dimensional spacetime.
To understand why this is exciting, you have to realize that in some
quarters, the conventional wisdom says a quantum theory of pure gravity
can't possibly make sense, except as a crude approximation at large
distance scales, because this theory is "perturbatively
nonrenormalizable".
Very roughly, this means that as we zoom in and look at the theory at
shorter and shorter distance scales, it looks less and less like a
"free field theory" where gravitons zip about without interacting.
Instead, the interactions get stronger and more complicated!
So, in the jargon of the trade, we don't get a "Gaussian ultraviolet
fixed point".
Huh?
Well, roughly, an "ultraviolet fixed point" is a quantum field theory
that keeps looking the same as you keep viewing it on shorter and
shorter distance scales. A "Gaussian" ultraviolet fixed point is one
that's also a free quantum field theory: one where particles don't
interact.
If quantum gravity approached a Gaussian ultraviolet fixed point as
we zoomed in, we could calculate what gravitons do at arbitrarily
high energies (at least perturbatively, as power series in Newton's
constant - no guarantee that these series converge). Particle
physicists would then be happy and say the theory was "perturbatively
renormalizable".
But, it's not.
The conventional wisdom concludes that to save quantum gravity, we
must include matter of precisely the right sort to *make* it
perturbatively renormalizable. This is the quest that led people
first to supergravity and ultimately to superstring theory - see
"week195" for more of this story.
But, as far back as 1979, the particle physicist Weinberg raised the
possibility that pure quantum gravity is "nonperturbatively
renormalizable", or "asymptotically safe". This means that as we
zoom in and look at the theory at shorter and shorter distance scales,
it approaches some theory *other than* that of noninteracting gravitons.
In other words, Weinberg was suggesting that pure quantum gravity
approaches a non-obvious ultraviolet fixed point - possibly a
"non-Gaussian" one.
The big news is that this seems to be true!
Even cooler, in this theory spacetime seems to act *2-dimensional*
at very short distance scales.
This idea has been brewing for a long time - I talked about it
extensively back in "week139". But now there's more solid
evidence for it, coming from two quite different approaches.
First, people doing numerical quantum gravity in the "causal dynamical
triangulations" approach are seeing this effect in their computer
calculations. This is what Renate Loll explained at Loops '05. The
best place to read the details is here:
18) Jan Ambjorn, J. Jurkiewicz and Renate Loll, Reconstructing
the universe, Phys. Rev. D72 (2005) 064014. Also available as
hep-th/0505154.
but if you need something less technical, try this:
19) Jan Ambjorn, J. Jurkiewicz and Renate Loll, The Universe from
Scratch, available as hep-th/0509010.
The titles of their papers are a bit grandiose, but their calculations
are solid stuff - truly magnificent. I described their basic strategy
in my report on the Marseille conference in "week206". So, I won't
explain that again. I'll just mention their big new result: in pure
quantum gravity, spacetime has a spectral dimension of 4.02 plus
or minus 0.1 on large distance scales, but 1.80 +- 0.25 in the
limit of very short distance scales!
Zounds! What does that mean?
The "spectral dimension" of a spacetime is the dimension as measured
by watching heat spread out on this spacetime: the short-time behavior
of the heat equation probes the spacetime at short distance scales, while
its large-time behavior probes large distance scales. Spectral dimensions
don't need to be integers - for fractals they're typically not. But,
Loll and company believe they're seeing spacetimes that are *exactly*
2-dimensional in the limit of very small distance scales, *exactly*
4-dimensional in the limit of very large scales, with a continuous change
in dimension in between. The error bars in the above figures come from
doing Monte Carlo simulations. They're just using ordinary computers,
not supercomputers. So, with more work one could shrink their error bars
and test their result.
My main worry about their work is that it uses a fixed slicing of
spactime by timelike slices. So, there's a danger that their
procedure breaks Lorentz-invariance, even in the continuum limit
which they are attempting to compute. I would like to find a way
around this problem!
Luckily, some other people are getting similar results from a second
procedure that definitely does *not* break Lorentz invariance:
20) Oliver Lauscher and Martin Reuter, Fractal spacetime structure in
asymptotically safe gravity, available as hep-th/0508202.
Reuter spoke about all this work at Loops '05. The idea is to
investigate Weinberg's original idea in excruciatingly precise
detail using "renormalization group flow" ideas. The above paper
is a review of lots of others, and you need to read a bunch to get
what's really going on. The upshot, however, is that they find
evidence for a non-Gaussian ultraviolet fixed point in pure quantum
gravity. Moreover, the spectral dimension of spacetime approaches
2 in the limit of very short distance scales.
Suppose this is all true. What does it mean?
Nobody knows yet; there are lots of attitudes one could take.
Ambjorn, Jurkiewicz and Loll could probably just plunge ahead and
use computers to calculate lots of things about quantum gravity.
(Right now they want to test their results in lots of ways.) One
good thing would be to include matter of various sorts and see how
it affects the conclusions.
Similarly, Lauscher and Reuter could just plunge ahead and compute,
if they wanted.
This is excellent. But personally, I'd like to find a beautiful theory
in which spacetime is 2-dimensional at short distance scales, which
reduces to general relativity at large scales. In other words, to
redo all these calculations "from the bottom up".
Unsurprisingly, I hope this beautiful theory is a spin foam model,
since spin foams are 2-dimensional and I like them a lot. I presented
some rough ideas on how one might invent such a model:
21) John Baez, Towards a spin foam model of quantum gravity,
talk at Loops '05, available at http://math.ucr.edu/home/baez/loops05/
But, these ideas are very tentative and only time will tell if they
amount to anything. What's more important is that pure quantum gravity
seems to exist - as a theory, that is - and people seem to be learning
actual facts about it, instead of just arguing endlessly about it.
That's progress!
The second most exciting thing at Loops '05, in my biased opinion,
was the work of John Barrett, Laurent Freidel, Karim Noui and others
on "matter without matter" in 3d quantum gravity. Simply by carving a
Feynman-diagram-shaped hole in 3d spacetime and doing quantum gravity
on the spacetime that's left over, you get a good theory of quantum
gravity coupled to matter! You can even take the limit as Newton's
gravitational constant goes to zero and get ordinary quantum field
theory on flat spacetime!
Check these out:
21) John Barrett, Feynman diagams coupled to three-dimensional quantum
gravity, available as gr-qc/0502048.
John Barrett, Feynman loops and three-dimensional quantum gravity,
Mod. Phys. Lett. A20 (2005) 1271. Also available as gr-qc/0412107.
22) Laurent Freidel and David Louapre, Ponzano-Regge model revisited
I: gauge fixing, observables and interacting spinning particles,
Class. Quant. Grav. 21 (2004) 5685-5726. Also available as
hep-th/0401076.
Laurent Freidel and David Louapre, Ponzano-Regge model revisited
II: equivalence with Chern-Simons, available as gr-qc/0410141
Laurent Freidel and Etera R. Livine, Ponzano-Regge model
revisited III: Feynman diagrams and effective field theory,
available as hep-th/0502106.
23) Laurent Freidel, Daniele Oriti, and James Ryan, A group field
theory for 3d quantum gravity coupled to a scalar field, available
as gr-qc/0506067.
24) Karin Noui and Alejandro Perez, Three dimensional loop quantum
gravity: coupling to point particles, available as gr-qc/0402111.
This is mindblowingly beautiful, especially because lots of it is
already mathematically rigorous, and we can easily make more so.
It's even related to n-categories: my student Jeffrey Morton
presented a poster on this aspect.
Together with my student Derek Wise, Jeffrey Morton and I plan to have
a lot of fun studying this stuff. So, I won't talk about it more now -
I'll probably get around to saying more someday, especially about how
the whole story generalizes to 4 dimensions.
There's a lot more to say about Loops '05, but this will have to do.
In a while, a bunch of the talks should be visible on the conference
homepage.... that should give you a better idea of what happened.
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Previous issues of "This Week's Finds" and other expository articles on
mathematics and physics, as well as some of my research papers, can be
obtained at
http://math.ucr.edu/home/baez/
For a table of contents of all the issues of This Week's Finds, try
http://math.ucr.edu/home/baez/twf.html
A simple jumping-off point to the old issues is available at
http://math.ucr.edu/home/baez/twfshort.html
If you just want the latest issue, go to
http://math.ucr.edu/home/baez/this.week.html