# September 17, 2000 {#week156}

This week I want to catch you up on some of the experiments that have
been going on lately. Mathematical physics is no fun without some
experiments to think about now and then. So here's some news about
black holes, superfluid hydrogen, T violation, the $\tau$ neutrino, and the
Higgs boson.

I like black holes because they are a nice example of what general
relativity can do. Once upon a time they seemed very exotic, but now it
seems they're common. In particular, there appear to be black holes
with masses between a million and several billion times that of the Sun
at the centers of all galaxies with a "bulge". This includes galaxies
like the Milky Way, which has a central bulge in addition to a flat
spinning disk, and also elliptical galaxies, which consist solely of a
bulge. Many of these supermassive black holes emit lots of X-rays as
they swallow hapless stars. As I mentioned in [week144](week144.html),
the X-ray telescope Chandra has seen evidence for about 70 million of
these black holes!

Recently, two teams of researchers have found that the mass of these
central black holes is correlated very closely to the dispersion of
stellar velocities in the galaxy:

1) John Kormendy, "Monsters at the heart of galaxy formation", _Science_ **289** (2000), 1484--1485. Available online at `http://www.sciencemag.org/cgi/content/full/289/5484/1484`

2) Laura Ferrarese and David Merritt, "A fundamental relation between supermassive black holes and their host galaxies", _Astrophys. J. Lett._
**539**, (2000) L9, preprint available as [`astro-ph/0006053`](https://arxiv.org/abs/astro-ph/0006053).

3) Karl Gebhardt et al, "A relationship between nuclear black hole mass and galaxy velocity dispersion", _Astrophys. J. Lett._ **539**, (2000) L13, preprint available as [`astro-ph/0006289`](https://arxiv.org/abs/astro-ph/0006289).

Tight correlations are a bit rare in astrophysics, so they tend to be
important when they exist. If you look at a graph you'll see how nice
this one is:

4) Supermassive Black Hole Group, "Theory of black holes and galaxies", `http://www.physics.rutgers.edu/~merritt/theory.htm`

Ferrarese and Merrit estimate that the black hole mass grows as roughly
the 4.8th power of the stellar velocity dispersion, which they define as
the standard deviation of the radial component of the velocities of
stars in the galaxy.

But what does this correlation *mean*? Astrophysicists are still arguing
about that. But at the very least, it suggests an intimate relation
between supermassive black holes and the process of galaxy formation.

Part of the puzzle is that nobody knows how these supermassive black
holes formed. You see, until very recently, all we've ever seen are
small black holes formed by the collapse of a single star (between 3 and
20 solar masses), and these supermassive ones at the centers of
galaxies. But last year, people started seeing middle- sized ones!
Colbert and Mushotzky found black holes between 100 and 10,000 solar
masses in about half of 30 nearby spiral and elliptical galaxies that
they examined:

5) Ed Colbert's homepage, `http://www.pha.jhu.edu/~colbert/`

    E. J. M. Colbert and R. F. Mushotzky, "The nature of accreting black holes in nearby galaxy nuclei", preprint available as [`astro-ph/9901023`](https://arxiv.org/abs/astro-ph/9901023).

Ptak and Griffiths found a black hole of over 460 solar masses in an
irregular galaxy called M82:

6) A. Ptak, R. Griffiths, "Hard X-ray variability in M82: evidence for a nascent AGN?", preprint available as [`astro-ph/9903372`](https://arxiv.org/abs/astro-ph/9903372).

This is a "starburst galaxy", meaning that it's full of supernovae
going off like a big firework display. When a star dies in a supernova
explosion, that's when a neutron star or black hole is formed --- so it
seems likely that this black hole in M82 was formed by the merger of
several such black holes. Could we be seeing the gradual formation of a
supermassive black hole?

Maybe someday we'll understand the complete ecology of black holes. I
can't help but feel there's some important role they play which we
don't understand yet. (For one theory about this, see the end of
[week33](week33.html).)

Now: you've all heard how helium-4 becomes a superfluid below 2.18
kelvin and helium-3 does it below 2.4 millikelvin. But what about
superfluid hydrogen? Unlike helium, hydrogen is not a snobbish loner:
it's a friendly, sticky molecule. So usually it solidifies before it
gets cold enough to go superfluid! But in 1997, some folks at the
University of Illinois noticed a possible loophole: films of liquid
hydrogen about one molecule thick on a silver substrate should form a 2d
superfluid at a temperature of 1.2 kelvin. Here's a picture of a
computer simulation:

7) David Ceperley et al, "Prospective superfluid molecular hydrogen", `http://www.aip.org/physnews/graphics/html/h2.htm`

Since then, other people have cooked up other schemes.

Now it seems people have actually made the stuff. Tiny amounts of it!
The way they do it is to take superfluid helium and put in a bit of
carbonyl sulfide (OCS) and hydrogen. About 14 to 16 hydrogen molecules
stick to the carbonyl sulfide molecule, and when the temperature drops
to .15 kelvin, these molecules form a superfluid. The hard part is
checking experimentally that this really happens --- and even *defining*
what it means for a cluster of so few molecules to be a superfluid. I
can't explain the details; for that you'll have to read the paper:

8) Slava Grebenev, Boris Sartakov, J. Peter Toennies, and Andrei F. Vilesov, "Evidence for superfluidity in para-hydrogen clusters inside helium-4 droplets at 0.15 Kelvin", _Science_ **5484** (2000), 1532--1535, available online at `http://www.sciencemag.org/cgi/content/abstract/289/5484/1532`

Here "para-hydrogen" refers to a molecule of hydrogen where the spins
on the two nuclei are anti-parallel --- as opposed to "ortho-hydrogen",
where they're lined up. The two states have different properties and
this matters a lot in delicate situations like these.

Next: T violation. Once people thought the laws of physics were
symmetrical under exchanging either particles with their antiparticles,
left with right, or future with past. These three symmetries are called
C (for "charge conjugation"), P (for "parity") and T (for "time
reversal"). The weak interaction is now believed to violate all of
these.

Very briefly, the story goes like this: Yang and Lee won the Nobel prize
for helping discover P violation in the $\beta$ decay of radioactive cobalt
back in 1956, though in retrospect it was only the sexism of the Nobel
committee that prevented Wu from sharing this prize --- she did the actual
experiment. In $\beta$ decay, a neutron turns into a proton, an electron and
an electron anti-neutrino via the weak interaction. Since the electron
anti-neutrino only comes in a right-handed form, this process violates P
symmetry.

Cronin and Fitch won the Nobel prize for discovering in 1964 that
neutral kaons decay in a way that violates CP symmetry --- i.e., the
symmetry where you switch particles with their antiparticles *and*
switch left with right. I believe that neutral kaons are still the only
system where CP violation has been seen.

Now there's something called the CPT theorem which says that various
reasonable axioms for a quantum field theory imply symmetry under the
*combination* of C, P and T. For the math of this, the obvious place to
go is this classic text on axiomatic quantum field theory:

9) R. F. Streater and A. S. Wightman, _PCT, Spin and Statistics, and All That_, Addison-Wesley, Reading, Massachusetts, 1989.

In case you're worried, PCT is the same thing as CPT. I like this book
a lot. The only thing I dislike is how it unleashed a flood of physics
papers whose titles end with "and all that". For example:

- "CFT, BCFT, ADE and all that"
- "Quantum cohomology and all that"
- "String theory, supersymmetry, unification, and all that"
- "Anti-de Sitter space, branes, singletons, superconformal field theories and all that"
- "The modified Bargmann-Wigner formalism: longitudinal fields, parity and all that"
- "The Zamolodchikov C-Function, classical closed string field theory, the Duistermaat-Heckman theorem, the renormalization group, and all that"

Enough! Listen, guys: it was funny once, but now it's just lame. Stop
it!

But I digress. Where was I? Oh yeah: given the CPT theorem, from CP
violation we can conclude T violation. The future and the past are
slightly different --- but of all the known forces, only the weak force
notices the difference! This is bizarre and fascinating. But the way we
reached this conclusion was not completely satisfying, since we needed
to assume the usual axioms of quantum field theory to get the CPT
theorem. What if the axioms are wrong? It would be better to have more
*direct* evidence of T violation, given how important this issue is.

So in the late 1990s, people in the CPLEAR collaboration at CERN did
some precision experiments on neutral kaon decay, and found more direct
evidence of T violation!

10) CPLEAR homepage, `http://cplear.web.cern.ch/cplear/Welcome.html`

11) CPLEAR collaboration, "First direct observation of time-reversal non-invariance in the neutral kaon system", _Phys. Lett._ **B 444** (1998) 43, available online with all other papers by this collaboration at `http://cplear.web.cern.ch/cplear/cplear_pub.html`

Now we can all sit back and rack our brains even harder about what T
violation really *means*. So far, all we know is that it arises from the
darkest corner of the Standard Model: the Kobayashi-Maskawa matrix. This
is a matrix describing quarks' couplings to the Higgs. The fact that
it's not diagonal means that the "flavor eigenstates" of the quarks -
up and down, strange and charmed, bottom and top --- are not the "mass
eigenstates". Why does the Kobayashi-Maskawa matrix equal what it
equals? Why is it of a form that violates T symmetry? Nobody knows.

Another nice confirmation of what we already believed was the recent
discovery of direct evidence for the $\tau$ neutrino. If you don't remember
the particles in the Standard Model, try [week119](week119.html):
you'll see that it has 3 generations of quarks (listed above) and 3
generations of leptons: the electron, muon and $\tau$ and their corresponding
neutrinos. Of the leptons, the $\tau$ is the heaviest and thus hardest to
produce. Tau neutrinos are produced by the decay of $\tau$ particles, but
since it's hard to make these particles and hard to catch neutrinos,
until recently nobody had ever done the clinching experiment: creating a
beam of a $\tau$ neutrinos and letting it collide with some stuff to form $\tau$
particles again.

On July 21st, 2000, the DONUT collaboration at Fermilab announced that
they had successfully done this experiment:

12) Christina Hebert, "Phyisicists find first direct evidence for $\tau$ neutrino at Fermilab", `http://www.fnal.gov/directorate/public_affairs/story_neutrino/p1.html`

In case you're wondering, "DONUT" stands for "Direct Observation of
the Nu Tau", where $\nu_\tau$ is the standard abbrevation for $\tau$ neutrino.

In short, the final details of the Standard Model are all falling into
place just as expected --- except for the fact that neutrinos are doing
lots of weird stuff they shouldn't be doing! As I explained in
[week130](week130.html), neutrino physics is the big place for surprises
in particle physics these days. This is yet another reason why it was
good to directly observe the $\tau$ neutrino.

And then, of course, there's the Higgs --- the final particle in the
Standard Model. As you've probably heard, we're getting awfully close
to seeing it --- or at least definitively *not* seeing it. Right now
they're looking for it at LEP --- the big particle accelerator at CERN,
in Geneva. They're just about to shut LEP down, since it's done pretty
much all it can do, and they need to deactivate it to build an even more
powerful accelerator --- LHC, the Large Hadron Collider. But at the last
minute they decided to extend its life to November 2nd, 2000:

13) LEP shutdown postponed by one month, `http://press.web.cern.ch/Press/Releases00/PR08.00ELEPRundelay.html`

They're going for broke, boosting its power to the utter max, so that
they can see hints of the Higgs as long as its mass is 114 GeV or so. In
fact they have already seen a couple of events that suggest a Higgs of
about this mass.

Whether or not LEP sees the Higgs the folks at the Tevatron at Fermilab
should see it when they start Run II in a while, as long as its mass
below 130 GeV. And if *they* don't see it, folks at CERN should see it
with the LHC accelerator by around 2005, as long as its mass is below
180 GeV. A Higgs more massive than that would mean the Standard Model is
seriously screwed up, so at that point, even *not* seeing the Higgs
would be an important discovery.

The folks getting ready to analyze the Run II data at the Tevatron are
doing so with a few theories in mind: the Standard Model, the minimal
supersymmetric extension of the Standard Model, and a
"next-to-minimal" supersymmetric extension. This is a major project;
you can find lots of details here:

14) Higgs Working Group webpage, `http://fnth37.fnal.gov/higgs/higgs.html`

That's basically it for this week. I just have a couple of questions
about CPT. A while back on sci.physics.research I emphasized a little
theorem that says: any self-dual irreducible unitary group
representation H must admit an antiunitary intertwiner $J\colon H \to H$ with
either $J^2 = 1$ or $J^2 = -1$. In the first case $H$ comes from a real
representation; in the second case it comes from a quaternionic
representation. For more details, try this:

15) John Baez, Symplectic, quaternionic, fermionic, `http://math.ucr.edu/home/baez/symplectic.html`

Now, after I mentioned this, someone who goes by the name of "squark"
suggested that the CPT operator for massive spin-$1/2$ particles was an
antiunitary intertwiner with $(\mathrm{CPT})^2 = -1$. I'm not sure this is true,
but it's definitely antiunitary, so we have an intesting question:
which unitary irreducible representations of the Poincare group are
self-dual? Of these, which come from real representations and which come
from quaternionic ones? My hunch is that the bosonic (i.e.
integral-spin) reps are real and the fermionic (i.e. half-integral-spin)
reps are quaternionic. And then the question is: is the operator $J$ just
the the CPT operator? This would certainly shed some nice mathematical
light on the meaning of CPT symmetry.

By the way, This Week's Finds has a nice new feature, courtesy of
Laurent Bartholdi: now you can search all the old issues for a keyword
or phrase! This is very useful, at least for me. Check it out on my
website.

------------------------------------------------------------------------

Footnotes:

Squark found in Volume 1 of Weinberg's "Quantum Field Theory" that
the CPT operator on the Hilbert space of a spin-$j$ representation of the
Poincare group is an antiunitary operator with $(\mathrm{CPT})^2 = -1^{2j}$. So
indeed we do have $(\mathrm{CPT})^2 = 1$ in the bosonic case, making these
representations real, and $(\mathrm{CPT})^2 = -1$ in the fermionic case, making
these representations quaternionic.

Allen Knutson points out that Streater and Wightman's title "PCT, Spin
and Statistics, and All That" was itself modelled after that of Sellar
and Yeatman's humorous history: "1066 and all that; a memorable
history of England, comprising all the parts you can remember including
one hundred and three good things, five bad kings and two genuine
dates."

Martin Hardcastle wonders if Streater and Wightman were inspired by the
similarity of their names to those of Sellar and Yeatman!