December 29, 1999

This Week's Finds in Mathematical Physics (Week 143)

John Baez

Since this is the last Week of the millennium, I'll make sure to pack it full of retrospectives and prognostications. But I'd like to start with an update on something I discussed a while back.

By the way, please don't give me flak about how the millennium starts in 2001. I use the CE or Common Era system, which starts counting at the year zero, not the AD system, which starts at the year one because it was invented in 526 CE by Dennis the Diminutive, long before the number zero caught on. In my opinion, the real "millennium bug" is that anyone is still using the antiquated AD system!


In "week73", I mentioned a theory about why molecules important in biology tend to come in a consistent chirality, or handedness. For example, there's lots of dextrose in nature - this being the right-handed form of the sugar sucrose - but not much of its left-handed counterpart, levulose. It's no surprise that one or the other would dominate, but you might guess that which one was just an accident of history. After all, there's no fundamental difference between right and left, right?

Or is there? Actually there is: the weak nuclear force distinguishes between the two! So some people theorized that very slight differences in energy levels, due to the weak force, favor the formation of left-handed amino acids and right-handed sugars - which is what we see in nature.

Recently people have found evidence for a somewhat different version of this theory:

1) Robert F. Service, Does life's handedness come from within?, Science 286 (November 12, 1999), 1282-1283.

When radioactive atoms decay via the weak force, the electrons they shoot off tend to have a left-handed spin. Could this affect the handedness of molecules or crystals that happen to be forming in the vicinity? Sodium chlorate is a chemical that can form both left-handed and right-handed crystals, so researchers took some solutions of the stuff and let them crystallize while blasting them with electrons formed by the decay of radioactive strontium. Sure enough, this biased the handedness of the crystals! Blasting the stuff with right-handed positrons favored formation of crystals of the opposite handedness. The strangest part was that the effect was even bigger than expected.

I still think the whole business is pretty iffy - after all, the flux of radiation in this experiment was a lot bigger than what we normally see on earth. But it would sure be neat if the origin of chirality in biology was related to the deeper mystery of chirality in particle physics.

Okay, now for a little retrospective. Don't worry - I won't list the top ten developments in mathematical physics of the last millennium! Instead, I just want to recommend two papers. First, an old paper by Poincare:

2) Henri Poincare, The present and future of mathematical physics, Bull. Amer. Math. Soc. 12 (1906), 240-260. Reprinted as part of a retrospective issue of the Bull. of the Amer. Math. Soc., 37 (2000), 25-38, available at

This article is based on a speech he gave in 1904. After a fascinating review of the development of mathematical physics, he makes some accurate predictions about quantum mechanics and special relativity - but closes on a conservative note:

In what direction we are going to expand we are unable to foresee. Perhaps it is the kinetic theory of gases that will forge ahead and serve as a model for the others. In that case, the facts that appeared simple to us at first will be nothing more than the resultants of a very large number of elementary facts which the laws of probability alone would induce to work toward the same end. A physical law would then assume an entirely new aspect; it would no longer be merely a differential equation, it would assume the character of a statistical law.

Perhaps too we shall have to construct an entirely new mechanics, which we can only just get a glimpse of, where, the inertia increasing with the velocity, the velocity of light would be a limit beyond which it would be impossible to go. The ordinary, simpler mechanics would remain a first approximation since it would be valid for velocities that are not too great, so that the old dynamics would be found in the new. We should have no reason to regret that we believed in the older principles, and indeed since the velocities that are too great for the old formulas will always be exceptional, the safest thing to do in practice would be to act as though we continued to believe in them. They are so useful that a place should be saved for them. To wish to banish them altogether would be to deprive oneself of a valuable weapon. I hasten to say, in closing, that we are not yet at that pass, and that nothing proves as yet that they will not come out of the fray victorious and intact.

The same issue of the AMS Bulletin also has a lot of other interesting papers and book reviews from the last century, by folks like Birkhoff, Einstein and Weyl.

The second paper I recommend is a new one by Rovelli:

3) Carlo Rovelli, The century of the incomplete revolution: searching for general relativistic quantum field theory, to appear in the Journal of Mathematical Physics 2000 Special Issue, preprint available as hep-th/9910131.

Let me just quote the abstract:

In fundamental physics, this has been the century of quantum mechanics and general relativity. It has also been the century of the long search for a conceptual framework capable of embracing the astonishing features of the world that have been revealed by these two ``first pieces of a conceptual revolution''. I discuss the general requirements on the mathematics and some specific developments towards the construction of such a framework. Examples of covariant constructions of (simple) generally relativistic quantum field theories have been obtained as topological quantum field theories, in nonperturbative zero-dimensional string theory and its higher dimensional generalizations, and as spin foam models. A canonical construction of a general relativistic quantum field theory is provided by loop quantum gravity. Remarkably, all these diverse approaches have turn out to be related, suggesting an intriguing general picture of general relativistic quantum physics.
Now for the prognostications. Since we should never forget that the towering abstractions of mathematical physics are ultimately tested by experiment, I'd like to talk about some interesting physics experiments that are coming up in the next millennium. These days more and more interesting information about physics is coming from astronomy, so I'll concentrate on work that lies on this interface.

In "week80" I talked about how Gravity Probe B will try to detect an effect of general relativity called "frame-dragging" caused by the earth's rotation. I also talked about how LIGO - the Laser Interferometric Gravitational Wave Observatory - will try to detect gravitational waves:

4) LIGO homepage,

If all works as planned, LIGO should be great for studying the final death spirals of binary black holes and/or neutron stars. When it starts taking data sometime around 2002, it should be able to detect the final "chirp" of gravitational radiation produced a pair of inspiralling neutron stars in the Virgo Cluster, a cluster of galaxies about 15 megaparsecs away. Such an event would distort the spacetime metric here by only about 1 part in 10^{21}. This is why LIGO needs to compare oscillations in the lengths of two arms of an interferometer, each 4 kilometers long, with an accuracy of 10^{-16} centimeters: about one hundred-millionth of the diameter of a hydrogen atom. To do this will require some very clever tricks to reduce noise.

As the experiment continues, they intend to improve the sensitivity until it can detect distortions in the metric of only 1 part in 10^{22}, and second-generation detectors should get to 1 part in 10^{23}. At that point, we should be able to detect neutron star "chirps" from a distance of 200 megaparsecs. Events of this sort should happen once or twice a year.

Since it's crucial to rule out spurious signals, LIGO will have two detectors, one in Livingston, Louisiana and one in Hanford, Washington. This should also allow us to tell where the gravitational waves are coming from. And there are other gravitational wave detection projects underway too! France and Germany are collaborating on a laser interferometer called VIRGO, with arms 3 kilometers long, to be built in Cascina, Italy:

5) VIRGO homepage,

Germany and Great Britain are collaborating on a 600-meter-long one called GEO 600, to be built south of Hannover:

6) GEO 600 homepage,

The Japanese are working on one called TAMA 300, which is a 300- meter-long warmup for a planned kilometer-long interferometer:

7) TAMA 300 homepage,

In addition, the Brazilian GRAVITON project is building something called the Einstein Antenna, which uses mechanical resonance rather than interferometry. The basic principle goes back to Joseph Weber's original bar detectors, which tried to sense the vibrations of a 2-meter-long aluminum cylinder induced by gravitational waves. But the design involves lots of hot new technology: SQUIDS, buckyballs, and the like:

8) GRAVITON homepage,

There are also other gravitational wave detectors being built... but ultimately, the really best ones will probably be built in outer space. There are two good reasons for this. First, outer space is big: when you're trying to detect very small distortions of the geometry of spacetime, it helps to measure the distance between quite distant points. Second, outer space is free of seismic noise and most other sources of vibration. This is why people are working on the LISA project - the Laser Interferometric Space Antenna:

9) European Space Agency's homepage on the LISA project,

NASA's homepage on the LISA project:

The idea is to orbit 3 satellites in an equilateral triangle with sides 5 million kilometers long, and constantly measure the distance between them to an accuracy of a tenth of an angstrom - 10^{-11} meters - using laser interferometry. (A modified version of the plan would use 6 satellites.) The big distances would make it possible to detect gravitational waves with frequencies of .0001 to .1 hertz, much lower than the frequencies for which the ground-based detectors are optimized. The plan involves a really cool technical trick to keep the satellites from being pushed around by solar wind and the like: each satellite will have a free-falling metal cube floating inside it, and if the satellite gets pushed to one side relative to this mass, sensors will detect this and thrusters will push the satellite back on course.

I don't think LISA has been funded yet, but if all goes well, it may fly within 10 years or so. Eventually, a project called LISA 2 might be sensitive enough to detect gravitational waves left over from the early universe - the gravitational analogue of the cosmic microwave background radiation!

The microwave background radiation tells us about the universe when it was roughly 10^5 years old, since that's when things cooled down enough for most of the hydrogen to stop being ionized, making it transparent to electromagnetic radiation. In physics jargon, that's when electromagnetic radiation "decoupled". But the gravitational background radiation would tell us about the universe when it was roughly 10^{-38} seconds old, since that's when gravitational radiation decoupled. This figure could be way off due to physics we don't understand yet, but anyway, we're talking about a window into the really early universe.

Actually, Mark Kamionkowski of Caltech has theorized that the European Space Agency's "Planck" satellite may detect subtle hints of the gravitational background radiation through its tendency to polarize the microwave background radiation. You probably heard how COBE, the Cosmic Background Explorer, detected slight anisotropies in the microwave background radiation. Now people are going to redo this with much more precision: while COBE had an angular resolution of 7 degrees, Planck will have a resolution of 4 arcminutes. They hope to launch it in 2007:

10) Planck homepage,

What else is coming up? Well, gravity people should be happy about the new satellite-based X-ray telescopes, since these should be great for looking at black holes. In July 1999, NASA launched one called "Chandra". (This is the nickname of Subrahmanyan Chandrasekhar, who won the Nobel prize in 1983 for his work on stellar evolution, neutron stars, black holes, and closed-form solutions of general relativity.) The first pictures from Chandra are already coming out - check out this website:

11) Chandra homepage,

On December 10th, the Europeans launched XMM, the "X-ray Multi-Mirror Mission":

12) XMM homepage,

This is a set of three X-ray telescopes that will have lower angular resolution than Chandra, but 5-15 times more sensitivity. It'll also be able to study X-ray spectra, thanks to a diffraction grating that spreads the X-rays out by wavelength. And in January, the Japanese plan to launch Astro-E, designed to look at shorter wavelength X-rays:

13) MIT's Astro-E homepage,

Taken together, this new generation of X-ray telescopes should tell us a lot about the dynamics of the rapidly changing accretion disks of black holes, where infalling gas and dust spirals in and heats up to the point of emitting X-rays. They may also help us better understand the X-ray afterglow of γ ray bursters. As you probably have heard, these rascals make ordinary supernovae look like wet firecrackers! Some folks think they're caused when a supernova creates a black hole. But nobody is sure.

Peering further into the future, here's a nice article about new projects people are dreaming up to study physics using astronomy:

14) Robert Irion, Space becomes a physics lab, Science 286 (1999), 2060-2062.

In 2005 folks plan to launch GLAST, the Gamma-Ray Large Area Space Telescope, designed to study γ-ray bursters and the like, and also the Alpha Magnetic Spectrometer, designed to search for antimatter in space. But there are also a bunch of interesting projects that are still basically just a twinkle in someone's eye....

For example: OWL, the Orbiting Wide-Angle Light Collector, a pair of satellites that would trace the paths of super-high-energy cosmic rays through the earth's atmosphere. As I explained in "week81", people have seen cosmic rays with ridiculously high energies, like 320 Eev - the energy of a 1-kilogram rock moving at 10 meters per second, all packed into one particle. OWL would orbit the earth, watch these things, and figure out where the heck they're coming from.

Or how about this: The Dark Matter Telescope! This would use gravitational lensing to chart the "dark matter" which seems to account for a good percentage of the mass in the universe - if, of course, dark matter really exists.

15) Dark Matter Telescope homepage,

Anyway, there should be a lot of exciting experiments coming up. But as usual, the really exciting stuff will be the stuff we can't predict.

© 1999 John Baez