STEPHON ALEXANDER: I'm
going to ask this
question, why parity?
Why do we care about parity?
And of course, what is parity?
OK.
Why do we care about
that question?
But to motivate all this, I want
to make sure that we're
on the same footing here.
I know we have some physicists
in the audience.
So this talk is not really
geared for you.
It's geared for really smart
people who want to get some
footing on what the standard
cosmology is and how that
jibes with observations.
Why could we make statements
like the universe is expanding
at this given rate?
Do we have observational wiggle
room to make any other
statement about the universe
as it stands today?
But then part of this motivation
is to show that our
standard cosmology works
pretty well.
It really works well--
meaning the theory that I'm
going to talk about here,
works really well in the
face of the precision
data that we have.
But there are problems.
And these problems are actually
mainly theoretical problems.
And then I'll talk about
something that you've all
probably heard a lot about--
cosmic inflation.
And how cosmic inflation
alleviates
some of these problems.
But I'll point to yet another
problem with cosmic inflation.
And then I will bring
in this original
question here, why parity?
And then hopefully there'll be
time to talk about this.
I will talk about the Baryon
Asymmetry Problem.
In a sense, that's
the problem.
OK.
So what do we mean by this
Baryon Asymmetry Problem?
I'll introduce that idea.
And then I'll provide a
mechanism that will be related
to this question about
why parity.
And then I will end, not with
necessarily a conclusion, but
with some open-ended
questions.
So first of all, why do we care
about parity violation?
Well we have to go back
to like 1956.
Before 1956 we knew from
experimental data that the
electromagnetic interaction and
the strong interaction,
for example, basically had
the following feature.
If I study the physical system
in a given frame of reference,
in this case--
if I study, for example, the
decay of a particle called the
pion so the pion is a particle
that's made up of two quarks.
It's a balancing
of two quarks.
And this pion has zero spin.
And hence, it doesn't have
a preferred handedness.
So when we talk about the
handedness of a particle,
we're really talking about
throwing a football.
If I throw a football with my
right hand, and it spins and
goes in the same direction to
you, versus throwing it with
my left hand, and this goes in
the same direction, this
quantity, the product of the
spin and its momentum towards
you is a quantity
called helicity.
So I can have left-handed
helicity and
right-handed helicity.
And that's what we mean
by handedness here.
So now the pion is a particle
that actually has no spin.
But when it decays it produces
two particles with a spin.
So a pion could decay into a
heavy version of the electron,
call a muon.
And that has a given spin.
And the other particle we'll
produce is something called a
neutrino, which is a
chargeless particle
with spin as well.
And so because the spin is
conserved, meaning that it had
zero spin, the product of the
spin of these two particles
that are left have to
add up to be zero.
And it turns out that if I look
at this particles that
have zero spin and decay into
particles with opposite spin,
the electromagnetic interaction
and a strong
interaction will produce
particles of equal
spin all the time.
That's what we mean by
parity symmetry.
The handedness of the system--
if I change it from a
left-handed system to its
mirror image--
the probability of those
particles decaying in one
handedness is this is the same
as it decaying in the other
handedness.
OK?
That's what we mean by
parity symmetry.
And so all of the interactions
were thought to actually obey
this basic symmetry of nature.
For any laser physicists here,
you understand that also in an
atomic system, this is
the case as well.
These are what we call
selection rules.
Now Lee and Yang realized that
when they looked through the
data, there was no statement
about the weak interaction.
This is the interaction that's
responsible for something
called beta decay.
And what they realized was that
since there was no data,
they should not assume that
parity is violated.
And they propose
an experiment.
And the result of that
experiment, done by Madame Wu
at Columbia, won them
the Nobel Prize.
So let me explain what
the experiment is.
So what we're looking
at here--
where's the pointer?
I guess I don't need it.
So what we're looking at here
is the following thing.
We're looking at a
neutron that's
made up of three quarks.
It's made up of an up quark
and two down quarks in a
balanced state.
And this neutron would
decay into a proton.
And in doing so it releases, it
emits, the carrier of that
force, which is something
called a W boson.
It looks like the photon of
a the weak interaction.
And also produces an electron
and an anti-neutrino.
So let's look at this
interaction here.
We have an up quark that
becomes a down quark.
So that's here.
Once that happens, the neutron
becomes a proton.
And when the up quark becomes
a down quark,
it emits this photon--
this W boson--
and then produces an electron
and an anti-neutrino.
This is a mistake.
This should be a bar here
for the anti-neutrino.
If I do this experiment, and I
look at these electrons being
produced as pions as a neutron
becomes a proton--
and this experiment's really
carbin 60 becoming nickel 60.
OK?
If I look at this process, and I
look to see the mirror image
of this process, it'll now
produce a right-handed
electron and a left-handed
anti-neutrino, I never see this.
I only see this result.
So the mirror image of
this interaction--
here is the mirror image--
does not exist in nature.
And at the time, we didn't
have the theory for that.
And the triumph of the standard
model of Glashow
Weinberg and Salaam,
was figure out
what that theory is.
OK.
So everything you hear about the
Higgs particle, that's all
part of the story.
Why is it that nature
does not have this?
So today we find ourselves in a
similar situation that, when
I was a post-doc, we realized
that we never did this test
for gravity.
So we now have to ask ourselves,
what are the
experimental situations that
we find ourselves in?
And gravity-- or apply general
relativity, which is
cosmology, to explain this.
And that's sort of
the motivational
aspect of this talk.
So for those of you who are
string theorists in this
audience, there are some aspects
of this talk that does
hinge on String Theory, but
it's not necessary.
OK.
So I'm here to tell you that
I'm a friend of the String
Theories, but I'm also a friend
of other people, other
approaches as well.
You've got to be friendly
to everybody.
Hi, my friends out there
in string land.
OK.
All right.
So now I want to put everything
in a cosmological
context, so let's move on.
So the thing I want us to take
away here is that cosmology is
nothing more than applied
general relativity.
So I'm going to explain
that to you.
So the discovery of general
relativity basically says that
we should no longer think of
space and time as this empty
stage that we move about.
It is dynamical as
we are dynamical.
We move--
we are able to be attracted
to objects gravitationally
because space does bend.
So because of the dynamics
of space, this happens.
And this happens because of
something called the Einstein
field equations.
I guess I can't write
it [INAUDIBLE].
So the Einstein field equation,
which is a set of
field equations like
electromagnetism--
electromagnetism tell us how the
electric and the magnetic
field bends in the presence of
electric or magnetic sources.
Likewise matter and energy
sources, like planets and
stars and black holes, likewise
there is a set of
fields that bend.
And that field is a field
of space and time.
Sometimes we call that
the metric field.
OK.
So there are consequences for
this in cosmology because we
can apply the Einstein equations
to the entire
space-time of our universe if
we know the distribution of
matter in the universe itself.
So the big game in cosmology
is to first of all measure
that and make a couple
of assumptions.
And I want to tell you what
these assumptions are.
So what is standard cosmology?
Standard cosmology are
these three pillars.
Two of these pillars are
observational, and one is
theoretical.
The first pillar is a
cosmological principle which
basically is a beefed-up
version of
the Copernican principle.
We are not special.
Every point in the universe
looks the same.
Every direction in the universe
looks the same.
That's basically a symmetry
principle.
And we now have observational
evidence of this principle.
And we'll talk about
that in a second.
Is it really the case that the
universe does look the same at
all vantage points?
And then the second principle is
the Hubble Law, which tells
you that if I look at galaxies
far away from us, galaxies
further away from us
move faster than
galaxies closer to us.
And they themselves move at
rates proportional to their
distance from each other.
And if I combine these two
ideas, these two principles,
and I use Einstein's field
equations for the dynamics of
space and time, which
are ten [INAUDIBLE]
non-linear differential
equations, I find that that
theory, this mother theory,
spits out one unique solution,
[INAUDIBLE]
topology.
So there's one unique solution
for the space-time for these
two pillars.
And that's an expanding or
contracting homogeneous and
isotropic space-time.
So let's turn to this
little cartoon here.
Imagine at the surface of this
balloon, I tack on a
coordinate system at every
point on the surface.
So I have XYZ coordinate
system at every
point of that surface.
And then someone starts blowing
up this balloon at a
constant rate.
So if I'm a galaxy here, and I
look at this other galaxy, and
this is the radius--
this thing I would call a of t,
if a of t starts growing at
some rate, I will
actually see--
even though I feel that I'm
fixed in my own coordinate
system I will see another galaxy
move away from me.
And I will see another galaxy
that's further away from me
move faster because of
the angular velocity.
The tangential velocity at the
point of the surface here.
And what I've just shown you
there is nothing more than the
solution of the Einstein
equations.
What I've shown you there is
the fact that Einstein's
theory predicts actually
that our universe
actually is this situation.
It's expanding in
four-dimensional space-time.
Or three-dimensional surface
embedded in the
four-dimensional space-time,
where a of t is what we call a
scale factor.
And it's expanding.
And the natural consequence of
this is that we are co-moving
with this expansion.
And the natural consequence is
that we will see other objects
moving away faster the further
they are from us.
So that was the first triumph
of the Einstein equation.
Physicists immediately jumped
on the bandwagon and started
doing more calculations.
They realized that actually
there's a thermal bath there.
So the universe is very
hot and dense.
And therefore the hotter it got,
then all of the matter
will ionize.
All of the atoms, including
hydrogen, will ionize.
And the universe will find
itself in a state.
In fact if you do this
calculation, 300,000 years
after this initial time,
that you should
actually see the formation.
The universe cools.
And then I'll see at some time,
as the universe cools,
I'll reach the ionization
energy of hydrogen.
An electron will bind
to the proton.
It will scatter photons.
And that photons will
actually be in
equilibrium with that situation.
And there should be a
relic thermal energy
associated with that.
And so it predicts something
that we call the cosmic
microwave background
radiation.
So physicists were looking for
this background radiation as a
consequence of this expanded
space-time.
And lo and behold--
1967.
So before I tell you
about 1967--
so the picture we should
have now is that at
some earlier time--
I won't talk about this
T is equal to zero.
That's another talk.
I could come back and talk about
that in future, if you
want me to.
But what this theory does
predict is that a universe
filled with radiation
will form hydrogen
for the first time.
And there'll be a relic
background radiation that we
can look for.
And this actually has a
particular spectrum.
And it's a perfect black
body spectrum.
Two things to keep in mind.
As the universe continued to
cool, some of that stuff
clusters and forms galaxies.
So in 1967 this was measured.
The Nobel Prize was
given to it.
And this was what was measured,
where like a chicken
inside of an egg, we've
cut the egg in half
and opened it out.
And we're looking at at that
time, 300,000 years.
And we see exactly
this radiation.
And of course we saw
more things.
We saw deviations from that
average temperature.
Hot and cold spots correspond
to troughs and peaks in the
sea of this radiation.
Because there's an average
temperature, and then there
are these fluctuations.
Today we're going to talk a lot
about that fluctuation.
This is the WMAP satellite.
I was fortunate enough last year
to hang out with the WMAP
group at Princeton on sabbatical
and got intimate
with this data a little bit,
although I'm a theorist.
What we're looking at here is
a prediction from inflation.
We'll talk about inflation
in a second.
So the red line is the power
spectrum, or basically the
Fourier transform of those
dots, those undulations.
OK.
This is wavelength.
So we're looking at the relative
sizes of these
fluctuations.
And we're comparing them to
each other in the sky.
And we are looking at how
similar or different they are
from each other.
And the prediction of inflation,
which we'll talk
about in a second.
And the black spots
is the data.
So this is the best fit to the
data using four parameters.
And this is something called
the power spectrum of the
polarization of the photons.
So this is kind of cute.
You can actually
associate these
fluctuations with acoustics.
So this is literally an acoustic
peak, if you think in
terms of sound, for those
you who are more
comfortable with sound.
If I play an instrument, the
instrument resonates at
different frequencies.
But there's always an acoustic
peak associated with the
length of a flute,
for example.
I bought my soprano sax here.
And it turns out that the
universe has that
characteristic size.
So from that peak we can
deduce the size of the
universe at that time.
Coincidentally it's just an A
note 50 octaves below middle
C.
And this is the latest
and greatest,
the Planck data satellite.
And we are currently analyzing
that data as we
speak, we the community.
And the Planck data is
consistent with the standard
model that we have.
There are some anomalies,
but that's not the
purpose of this today.
But it is interesting.
So what do we learn
from this data?
We can look at this data, and
we can see that some weird
things happen.
What we thought that was
so special about us
turns out to be--
so I always like to tell people
if you ever felt like
you were never a minority, this
is the time to feel like
you're a minority.
Because this is you,
all right.
We are a minority.
We share that in common.
We're a minority in the scheme
of the universe.
These dark guys here
are the majority.
And we have no idea
what this is.
People say various things.
There's "Discover" magazine
article that came out on dark
energy this month.
And I was quoted at the end
with my own crazy theory.
I regretted actually
interviewing with "Discover"
because now all my colleagues
think I'm
even more of a crackpot.
OK.
[LAUGHTER]
STEPHON ALEXANDER: OK.
And so I won't talk about
these things today.
I'm going to talk
about actually--
I'm going to give you
the Minority Report.
So who ordered that?
I mean, who gave us this
kind of universe?
So my friend and colleague Sean
Carroll wrote a book, a
paper called "A Preposterous
Universe" because it is
preposterous.
We always thought that we
were the main stuff.
So as I said, we have this
standard picture of the
universe that, as I said, these
three pillars predicts
an expanded universe with the
features that we see in this
cosmic microwave background
radiation.
It predicts that relic
background radiation.
We went and looked for it.
All right, this was
done by Gamow--
George Gamow and Fred Hoyle
and people like that way
before the '60s.
And we found it.
So we had a model that explained
the Hubble Law but
also predicted this cosmic
microwave background radiation.
But what it did not predict
were these fluctuations.
What it predicted was the
smooth and featureless
universe that's expand.
But unfortunately we are those
very wrinkles in the universe
that made the standard cosmology
a limited model.
We need to explain
observationally why these
fluctuations exists.
Because those are the things
that grew into the structure
that we see today, meaning
galaxies, clusters of
galaxies, so on and so forth.
But there's actually a much
more serious problem.
So we can summarize the
expansion history of the
universe with this
Penrose diagram.
So a Penrose diagram is a
conformal map that allows me
to freeze out the time expansion
and look at the
expanding universe as
a set of forward and
backward light cones.
So in other words, let's look
at it the following way.
If I'm looking back at the past,
it's like me shining
light on the back.
Because meaning, the fastest
anything can travel is with
these photons.
These photons will
disperse out.
OK, I'm just giving you an
analogous picture here.
And so there'll be a limitation,
at the end of the
day, how far those photons
went back.
If they're traveling at the
speed of light, they can only
cover but a certain amount
of distance.
OK.
What is that distance?
That distance is its velocity,
which is the speed of light
divided by the time of flight.
I'm sorry, the velocity--
the time of flight
is the distance
divided by the velocity.
OK.
So in other words, there's a
limitation as to how far back
we can see.
So when we look back at this
cosmic microwave background,
we're looking far back as light
could travel to us.
And we see something
very weird.
What do we see?
We see that the temperature
at antipodal
points of the sky have--
the photons have exactly
the same temperature.
Well those who took thermal
physics know that for
something to reach equilibrium,
you must have
scattering.
You must have interaction.
But we know that interaction
are limited by causality.
OK.
You need causality for
me to bump into you.
But we're talking about
photons here.
So that means that any other
point at the back, the light
cones is of maximum distance
this photon can travel.
So this photon has the same
temperature as this one.
But there's no way they could
have been in causal contact.
And this is actually an internal
inconsistency with
the expanding space-time.
So while it predicts this one
thing, it has the seeds of its
own destruction.
And cosmologists basically
swept this under the rug,
until Alan Guth came along.
Alan Guth is actually
one of my mentors.
And coincidentally occupied the
same office when he was at
[INAUDIBLE] and came
up with inflation.
So I had this idea, I have
to live up to his legacy.
And I never did.
I just happened to work
on his theory more.
So the basic idea of inflation
is to solve this problem.
This is what we call the
horizon problem.
OK.
How it is that these photons
can communicate with each
other when they didn't
have time to do that?
They need to do that because we
see that they have the same
temperature.
So Alan Guth had a really simple
idea-- that assumes
that the expanding universe
expanded at the
same rate at all times.
So Alan just said, oh, we
can fix this problem.
Let's start off with a tiny
patch of space-time, very
tiny, microscopically tiny.
OK.
I don't know, very tiny.
Sub-Fermi scale.
Less than 10 to the minus
15 centimeters.
A little tiny piece
of space-time.
And let's assume that that
space-time had something with
the same property, some
form of energy
with the same property.
So there's no horizon
[INAUDIBLE].
Again this is an assumption.
And let's assume that stuff is
so weird that it endows the
space-time with negative
pressure.
So at some point, boom!
This piece of space-time
expands exponentially.
And like economists, when you
actually do inflation you
actually have exponentially
expanding functions as well.
So likewise the universe
actually becomes a very, very
expensive--
it's on its way to a bubble.
OK.
Actually, I have colleagues that
work on bubble inflation,
so I'm looking forward to
writing a paper about that.
Bursting a bubble.
If that happens, then what
happens is that all of these
regions actually become
encapsulated.
And you saw the horizon
problem.
If you can manage to set up a
set of initial conditions with
the same properties.
We've got to figure out
how to do that.
How to order that, OK?
Do we have the physics
to do that?
If that's the case,
life is good.
Dandy.
But there's a bonus
out of this.
But before I say, I want
to talk a little
bit more about inflation.
What makes inflation happen?
What is the stuff
that will do it?
It turns out it's actually
dark energy.
But before I actually tell you
what it is, I want to get
something straight here.
So we like to think about fields
as things that are the
carriers of forces, like the
electromagnetic field.
But as a person that's trained
in field theory, as a field
theorist, we know that
the paradigms, that
everything is a field.
OK.
When we write the standard
model down, all of these
things are presentations
of fields.
It's just that these fields
are localized
because they have mass.
OK.
But there's one electron
field.
We're just different states
of the electron field.
And likewise we must
look at the
paradigm, the field paradigm.
So again, if we try to do
inflation we are required to
use a field because that's
all we're left with.
But it cannot be these
other fields.
These other fields don't work.
Because these fields screen.
They screen, and they
like to cluster up.
We need something that's
homogeneous and isotropic
everywhere.
So it must be a field
that has no spin.
And we call these feel
scalar fields.
OK.
So they're simple
field theories.
Like the electromagnetic field
have spin one, and they have
two polarization states.
I could never do it
properly, but.
So yeah, field like this.
So you really think
about a field.
So how does inflation work?
The basic idea of inflation
is that you have a field.
The field has potential
energy, just like the
electromagnetic field could
have potential energy.
And if something has potential
energy, is like
sitting on top of a hill.
And that potential energy could
redistribute itself into
kinetic energy at the end
of the day for the
conservation of energy.
But in inflation,
the field has a
very interesting property.
Meaning, the potential
is very special.
Potential is very--
what's the word for--
has a very low gradient.
There's an easy word for that.
Flat.
It's a very flat potential.
So that means a field
rolls very slowly.
So a field rolling very
slowly is like
something that has friction.
There's friction that's
slowing it down.
OK?
And it turns out that
that situation--
if I give you a scalar field
where the potential is flat,
and I plug that into the
Einstein equation, you have to
believe me that the solution
you generate is this
expanding, this rapidly
expanding space-time.
You just have to believe
me on that.
If you gave me 20 minutes of
your free time, I could
actually walk you through
the calculations.
They are very simple
calculation.
OK.
So I hope that.
AUDIENCE: [INAUDIBLE] potential
in different parts
of space or?
STEPHON ALEXANDER:
That's right.
This field takes values at
every point in space.
But it takes the same value.
And then now the
field evolves.
So the field evolves differently
than, it's like
this potential is now not
becoming flat anymore.
So the fact that the potential
remains roughly flat, it
guarantees that this field
remain constant at different
points in space.
And that's exactly the
situation we want for inflation.
So we have to--
you can actually set this
up as a Markov chain,
believe it or not.
No pun intended.
So if that was the case,
cosmologists
would not really care.
I wouldn't care.
But why I care, I remember when
I was a grad student, and
I went to the very first
cosmology conference in
Morocco in 1993.
I saw a young cosmology post-doc
doing a calculation
for inflation where he was
calculating the perturbations.
So in other words, this
field is rolling down.
But it's a quantum field.
So there are quantum
perturbations.
These quantum perturbations are
nothing more than-- think
of a little oscillator.
The field is rolling down.
And then there are little
oscillators fluctuate because
of the uncertainty principle.
Is a quantum mechanical
system.
And so these things, you
can't run away from.
You must deal with it.
It's a quantum field theory.
So check this out.
If you actually calculate these
fluctuations of this
field, in this rapidly
exponentially expanding
background, you get a spectrum
of these oscillators, these
fluctuations.
And the spectrum has the
following property.
If inflation begins at some time
that I give you because
I'm God-Physicist--
I don't mean to sound
like that.
I mean, I'm not.
Anybody wants to
kill inflation,
talk about this, OK.
This piece here.
So inflation is a very special
situation in which the region
that sets causality--
which we called the horizon, OK,
all of the perturbations
get generated in this region
of causal contact.
Because we're doing a local
quantum field theory.
Nice.
But the rapid expansion takes
these fluctuations, stretches
it, but also amplifies it.
So it turns this quantum thing
into a large classical
fluctuation with energy.
So this gravitational dumps
itself into these large
quantum fluctuation that
becomes classical.
And they get stretched
out of the horizon.
Kind of magical.
OK?
Inflation ends and
now we have an
ordinary evolving cosmology.
These modes, these fluctuations,
become frozen.
And they come back into the
horizon now as classical
perturbations.
And they're nice and ready
to source structures.
And if I calculate this, and I
calculate the spectrum, that's
the red curve that
I showed you.
So what inflation does in
solving the horizon problem,
it provides a causal
micro-physical
mechanism for structure.
So we can now come take a
theory of inflation, do
calculations and make
predictions for these
fluctuations of the CMB and
compare it to the distribution
of galaxies and clusters of
galaxies today and come back
to the drawing board and
build better theories.
So this is what it
allows us to do.
It allows us to do physics.
But there are some
caveats here.
And I won't get into it now,
but we should not drink the
inflation Kool-Aid
theoretically, yet.
It's a paradigm that is the
winning paradigm right now.
OK?
No doubt about that.
But as a theorist, I
still worry about
this question here.
So I want to leave it for the
Google geniuses here.
Maybe one of you can come and
help me out with this.
Here's a problem.
You see those nice little
fluctuations that I
calculated?
They're quantum mechanical.
I go get Peskin and Schroeder.
He teaches me how to do
these calculations.
I do the calculation.
Boom!
I get this beautiful
spectrum, right?
Life is good.
Well these fluctuations not only
affect the spectrum of
the perturbation, they
affect the potential.
The potential also gets
quantum corrected.
Well those very same things
that do a nice job for the
fluctuation can spoil the
condition of the flatness of
the potential.
So many models of inflation
suffer from this problem.
There are some models
that get around it.
We can do a little dance.
But keep that in mind, that
inflation is not a perfect
theory as yet.
So I want to now move on to the
second third of the talk.
What's the time?
AUDIENCE: One-thirty.
STEPHON ALEXANDER: Perfect.
I'm right on time.
So, OK.
This is good.
So inflation, as I said, does
its night job, solves
[INAUDIBLE] problem, gives
us structure formation.
All right.
Let's do the dance.
I'm going to quit my job at
Dartmouth and come and hang
out with you guys
at Google now.
But unfortunately I have to stay
and continue working on
this stuff because it turns out
that these fluctuations
that are generated during
inflation, if you look at the
formalism, couples to
something called a
gravitational potential.
Remember this inflation field
is the energy that's driving
the space-time.
The space-time itself
is a field.
The inflaton field couples to
the gravitational field.
A piece of this gravitational
field is the good
old-fashioned gravitational
potential.
You know, the one that
the sun has on us.
So the universe has a
gravitational potential.
And that's the thing that's
really sourcing the infall of
matter into what have you.
But you see, if we're going to
do that, we got to do it
democratically.
We can't say that the
gravitational potential is
this guy chilling
out here, right?
And the inflaton field falls
into it because of the
gravitational attraction.
The gravitational field too
must also democratically
undergo fluctuations.
You can't do one and
not do the other.
OK.
Anyway, I'm not going to bring
up any analogies for
relationships.
The metric field also undergoes
a fluctuation.
And the fluctuation of the
metric field is something
called a gravitational wave.
So I want to talk a little
bit about that.
And just like how the inflaton
field gave us a picture of
what structure might look like
in the early universe, how the
primordial structures are
formed, we want to ask a
question about what is the
physical role of these
gravitational waves?
And yes, it will be connected
to parity.
So that's kind of where
we're going here.
Just to reorient you to that.
I don't want to take
you too far.
So what is a gravitational
wave?
What we're looking at upstairs
there is a wave--
this wave has an amplitude.
And I'm calling this
amplitude "h".
And as amplitude oscillates,
in this case as
a function of time.
And this is a gravitational
wave.
So it's the fluctuation,
it is the modulation
of space-time itself.
OK.
And so if I look at the second
line down here, I'm looking at
a schematic of the LIGO, a
LIGO gravitational wave
detector, which are two ohms
interferometer with laser
light going back and forth,
being reflected.
And as a gravitational wave
passes through, it actually
stretches the space.
And therefore the arms
will stretched.
And they'll get stretched in a
way that as a gravitational
wave passes through, there's a
compression in the horizontal
direction and a refraction in
the vertical direction.
So it does this, and this,
as you see here.
So if you're a tall person, you
get taller a gravitational
wave passes through.
But as the gravitational wave
undergoes an undulation, a
refraction, it makes you
a little bit chubbier.
So that's what a gravitational
wave does to objects in
space-time.
The space-time itself stretches
and compresses as a
gravitational wave
passes through.
OK.
And that intuition should
be consistent with
space-time as a field.
Because electromagnetism is a
field that propagates through
space-time.
It needs space-time to
propagate within.
But the metric is space-time
itself.
So it supports its
own fluctuation.
So it must contract and
expand space itself.
So that's a gravitational
wave.
And what I'm showing you here
is a first equation that I'm
going to have.
I'm going to have a few
equations now from here on.
But this equation is
quite illustrative.
What we're looking at here
is a wave equation.
Actually if I solved the
Einstein equation for a
gravitational wave,
normally you see
that middle term there?
If I ignore that term, set it
to zero, in flat space a
gravitational wave would just
be these two terms, which is
nothing more than a wave moving
at the speed of light.
But you see that middle
term there?
You see that you have "a",
which is a scale factor.
And in an expanded
background, da dt
divided by a is a constant.
That's the Hubble parameter.
So that Hubble parameter's quite
large, due to inflation.
So what ends up happening, if
I solve that wave equation,
what starts off as an ordinary
wave gets squeezed.
Meaning that the phase
of this wave--
I produce a distribution of
these waves at different
frequencies.
And they all get
the same phase.
And is a phenomenon called
quantum squeezing.
And this is exactly how
inflation surmises to amplify
and stretch the gravitational
waves.
This is quite important.
Because that means inflation
predicts a spectrum of
gravitational wave.
And that's what we're
going after now.
When we say the smoking gun
of inflation is to find
gravitational wave.
This is really a big
part of story.
That middle term is the thing
that's creating special phase
relationships between the
spectrum of all the
gravitational waves.
So another place that you can
imagine seeing gravitational
waves are if I look at binary
systems of neutron
stars in this case.
This is a computer simulation.
Credit goes to LIGO,
I believe.
So maybe we can corrected
later on.
But anyway what we're looking at
here is how a gravitational
wave changes the space-time as
a strongly gravitating binary
system goes around each other.
So notice you see the
swirl in motion.
But there's a problem here.
As I told you, if we are to
really believe this picture of
structure formation and
inflation, we need to
understand not only the
fluctuations of the inflaton
field, we also need
to understand
the following problem.
The universe is not
just inflation and
gravitational waves.
The universe is us.
It's made up of electrons
and protons and
all these nice things.
But one of the things we know
about our standard model of
particle physics is that there
are equal amounts of matter,
of electrons and anti-electrons
and positrons.
So for every particle,
we know that there's
equal amounts of both.
So what do I mean by that?
If I look really far back, and
I try to find where the equal
amounts of what we are
is, we don't find it.
We don't see any antimatter.
In other words, we don't
see anti galaxies.
OK.
So here's a problem.
The galaxies are the structures
that are formed.
So why am I not seeing
anti galaxies?
If the universe starts off in
a symmetric state, and I
believe the story of inflation,
I have to confront
the biasing of matter
over antimatter,
either due to inflation.
Or something special happens
after inflation where I got
rid of all the antimatter.
And so when I was at Slack,
me and my boss and another
post-doc, Mohammad
Sheikh-Jabbari, thought about
this problem in the context
of inflation.
We said, maybe there's something
special about
inflation that could
do the job.
And maybe the gravity
waves are the
hidden part of the story.
So the story begins
really in 1967.
What we're dealing what is
the genesis of leptons.
So remember, electrons
and neutrinos and
muons are all leptons.
So if you can form leptons
over anti-leptons, you
actually can produce Baryons
much later on.
So this is called
leptogenesis.
And so the name of the
game here is to
not explain the asymmetry.
That's not enough.
You have to explain
that number.
What is the difference between
leptons over anti-leptons
divided by the density of
photons in galaxies.
So this number is a universal
number in every galaxy.
And this number also-- so you
could measure this number just
by looking at galaxies.
Or you could measure this
number in the WMAP data.
And you get the same number.
So the name of the game is to
not explain the asymmetry, but
to explain the number.
And that's the number
right here.
So even if you have a mechanism
to explain the
asymmetry, your theory
could still be wrong.
You have to explain
this number.
So 1967, Andrei Sakharov, in
a home prison-- that's the
legend, that a picture
of him right here.
He came up with the three
necessary conditions to
explain this asymmetry.
So let me walk you through this
because this is actually
very important to understand
the rest of the talk.
So in our standard model, the
statement that you have equal
amounts of matter over
antimatter is really a
statement of the current.
So every bit of matter, the
electrons, all the fields,
actually have a current.
And the current is really-- in
particle accelerator, that's
what you're looking at.
You're looking at the
current-current interactions.
And there's an equation
for those currents.
And the equation is that
the rate of change of
the current is zero.
So the vacuum, the ground state
of the standard model,
all the currents
are vanishing.
The rate of change.
So if I start with a situation
like in the early universe,
where the current is zero,
because it's vacuum, then the
rate of change of the current
is going to remain zero.
So the standard model doesn't
have the physics to produce
more current, or number
density of particles.
So that's really the problem.
But the standard model has
another statement, that you
have an equation for
the anti-current.
And that is also zero.
So the first thing you need to
do is to come up with new
physics that says that
the change of the
current is not zero.
You have to figure out how to
speak to the standard model or
extend it in a way that that
is no longer the case.
But that's not enough to produce
a matter asymmetry.
You need to also bias the
amount of current over
anti-current.
So if I produce current, if
I produce more matter and
antimatter--
imagine I can do that if I'm
producing the same rate of
matter and antimatter,
they annihilate.
So I need to simultaneously do
something called CP violation.
Which is, notice the word
"parity" is in there?
I need to bias, I need to have
something like the weak
interaction going on
for the leptons.
OK.
The interchange of the charge
and the handedness of the
system has to bias one
production channel of matter
over antimatter.
And while that is happening, the
other degrees of freedom--
the photons and all these
things, the radiation has to
be out of equilibrium with that
production mechanism.
Because you learn from
thermodynamics that if a
system is in equilibrium with
its environment, it will
equilibrate back to its time
reversal, which is matter
becoming equal to antimatter.
So this is the only page of
equations because this is
actually what we're doing
in our model.
So the theory that we're working
with here is a theory
of gravity that encodes parity
violation naturally.
What I mean by this is that
this theory takes gravity,
which is parity symmetric--
it doesn't care about a
left-handed system and a
right-handed system, it treats
them the same mathematically.
And therefore its predictions
will be the same.
And what I mean by that now is
that gravitational waves--
I'm going to produce
a left-handed
gravitational wave.
I throw a gravitational
wave in my left hand.
And a right-handed gravitational
wave-- it will
produce both of them at
the same amplitude.
But it turns out that I can
do something to general
relativity that biases that.
And this is done by the great
mathematicians Chern and
Simons So this term here
is Chern-Simons term.
And this term seems
to be very robust.
And most approaches to quantum
gravity has this term in it.
String theory, loop
quantum gravity--
so this seems to be a natural
extension to general
relativity.
And what I'm going to show you
is that if I solve for a
gravity wave with this theory,
something really cool happens
due to inflation.
And that's all I want
to say about that.
This theta thing here is the
inflaton field that's coupling
to this Chern-Simons term.
Think of this Chern-Simons term
as chopping off one hand
and throwing the football
with the other hand.
So this is how the idea works.
What I'm now going to say is,
we're now going to talk about
the possibility of producing
leptons over antileptons and
trying to see if inflation can
give us all three Sakharov
conditions in one shot.
So here's the basic idea.
If you guys get this, I'm
going to be so happy.
So I'm going to try.
The basic idea is
the following--
inflation is driven by a
field called inflaton.
This inflaton takes the same
value at every place in space.
But that's the amplitude
of the field.
It's a field, so the field
also has a phase.
And it turns out that the phase
of the inflaton is that
thing that couples to the
Chern-Simons term.
So if the phase couples, that
means that phase is going to
affect other waves that are
produced, in this case,
gravitational waves.
So what happens is that
the inflaton field
has the same value.
It couples to gravity through
this Chern-Simons term.
And as a result, the inflaton
field, which drives
inflation--
that means it's puting my system
far out of equilibrium,
because nothing can catch up
with that rate of expansion.
So you get out of equilibrium
very naturally from just the
environment of inflation.
That same inflaton field sources
gravitational waves.
But it sources a gravitational
wave in a way that biases the
production of left-handed
over right-handed
gravitational waves.
Biologists call this
circular dichroism.
Or physicists call
it birefringence.
It is the preference of
one-handed of a wave over
another one in the amplitude.
So I have to show you
that is the case.
But it turns out that it also
does something really cool.
I believe in page 199 of volume
two of Weinberg, it
turns out that the standard
model has something called a
gravitational anomaly
that people didn't
pay attention to.
Well, people did pay
attention to it.
They just couldn't find
a use for it.
And that gravitational anomaly
is actually the statement that
d of the current is not zero,
but is proportional to the
Chern-Simons itself.
So if I have a non-vanishing
Chern-Simons term due to
inflation, I will naturally
get the possibility of
producing more leptons
over antileptons.
So what I'm saying, if you buy
the story, the inflaton field
does all three things at the
same time, all through the
Sakharov conditions.
So let's see in detail
if it works.
For the rest of the talk, the
picture you should have in
your mind is that inflation is
like this cup of coffee.
And as you stir the coffee
around one direction of over
other, I can produce gravity
waves that stir in one
direction over another
direction.
And that stirring can pop matter
out of the vacuum.
And it does it in a way that's
out of equilibrium.
Well, it's a rapidly expanding
cup of coffee.
So if you want to put Starbucks
out of business, you
do inflation with coffee.
So this is a statement.
Remember I told you, you have
[INAUDIBLE] of the J?
J is the lepton and
antilepton number.
It's proportional to this
Chern-Simons term.
So if this Chern-Simons is
non-vanishing, the left hand
side is going to be
non-vanishing.
But remember, this Chern-Simons
term is related
to r, as a gravitational
curvature.
Right?
So to calculate that thing I
have to solve a modified wave
equation for the gravity wave.
Now this is very important.
And it's also a very
beautiful equation.
It's the left hand side, if the
right hand side was zero,
I have the normal situation
for inflation for gravity
waves, that first equation
I showed you?
And so I'm going to produce
equal amounts of left and
right-handed gravity waves.
But because of the presence of
this Chern-Simons term, what
happens is that the left-handed
gravity wave is
soft by itself and the
inflaton field.
So I notice here there's
a minus sign here.
So I'll get a wave with an
amplitude that's proportional
to this Chern-Simons term.
So I can get an exponentially
amplified, sorry, right-handed
gravity wave, and at the same
time an exponentially damped
left-handed gravity wave.
And that is a source of the
left-right asymmetry.
That is a statement of
parity violation.
Left and right no longer
evolve in the same way.
Well that's nice because if that
is the case, then I find
h left and h right--
if I plug it in, or RR dual,
because RR dual depends on h
left and h right, I find that
RR dual is non-vanishing.
So the parity violation
immediately sources a
production of leptons.
So I can actually
calculate that.
All right, so the statement here
is that the solutions I
get are exponentially
grown and damped
gravitational waves.
And it's parity violating
because parity
takes left into right.
But in this case, because the
amplitudes are different, it
doesn't happen.
All right, so these are some
colleagues at work.
Last slide.
So I can now calculate this
RR dual and plug it in.
And I get this the answer.
And guess what?
It only depends on two things.
So there's very little fine
tuning in this model.
And what I find is that it
depends on Hubble over
m-Planck which is actually an
observable measured in the
fluctuation spectrum of the
WMAP and Planck data.
And then it depends also on
the value of the inflaton
field, which is something that
we can measure by measuring
the ratio of the amplitude of
gravity waves over the power
spectrum of the scale
of fluctuations of
the inflaton field.
It also depends on--
you can say, well, if I produce
a full spectrum of
different wavelengths of gravity
waves of left and
right-handed amounts, which ones
contribute the most to
the production of leptons?
So the picture you should in
have your minds is that I have
these gravity waves that are
interacting with the leptons
in the vacuum, and
they're popping
them out during inflation.
And they're popping them out so
quickly that it catches up
with the dilution
of inflation and
actually presents by expanding.
So if I calculate that number,
and I plug in the value of
Hubble of m-Planck, and if the
gravity waves that contribute
are roughly 10 to the 12 giga
electron volts, which is
perfectly fine--
so it's a very high energy
process --I could get the
observed Baryon asymmetry.
So what I've presented here is
a theory that seems to be
quite minimal if we believe
in the standard model of
inflation, and we believe in a
standard model, and we believe
that gravity interacts with the
standard model the same
traditional way that we expect
as a field theory, then this
seems to do the job.
And what we've done is we've
found a nice job for the
gravity waves.
It's not just hanging
around there.
Nature made use of it.
So can we test this idea?
So I should have about
five minutes left.
OK.
And the answer is yes.
So two ways to test this idea.
So some colleagues of mine
on the gravitational wave
astronomy side are looking to
see the effects today of these
birefringent gravity wave--
and these are some of
my colleagues that
we've worked on this.
And the basic idea is that
when I look at a binary
system, and I look at the
distribution of gravity waves
that we detect, I will see
a bimodal distribution.
I'll see two different
distributions for the left and
right gravity waves.
If I look at a binary system,
what happens when I look at a
binary system that produces
gravity waves, I can never
find one that's completely in
line with my line of sight.
So there's always an inclination
angle that I'm
going to measure.
So something really
cute happens when
you have parity violation.
And this statement
summarizes it.
In the same way that we say
that the curvature of
space-time bends like
[INAUDIBLE]
close to a strongly gravitating
body, we may say
that the effect of a
gravitational parity violating
correction is to rotate the
apparent inclination angle of
the binary system's orbital
angle momentum axis either
towards or away from us.
So it changes the apparent
inclination angle as opposed
to its true inclination angle.
All right.
And the other way that we can
potentially test this is using
this cosmic microwave background
radiation.
And yes?
AUDIENCE: [INAUDIBLE]
would you be detecting the
difference in inclination
angle as measured by gravity
[INAUDIBLE] optical?
STEPHON ALEXANDER: Exactly.
Thanks for bringing that up.
You have to also measure an
optical inclination angle and
then compare the deviation
from the expected.
Now the other way that I think
is much cooler if we can do
this-- and it will win
my friend Brian
Keating the Nobel Prize--
I'm just going to
be the theorist.
I just--
Hans goes to Stockholm because
he's going to build the
experiment.
So what the cause
of microwave--
what inflation predicts
is this red
curve for gravity waves.
OK, this is what we call
a B-mode polarization.
What any theory that has a
parody violating gravity waves
produces a different curve, an
order of magnitude larger than
the red curve.
I'm sorry, which is that
black curve up there.
So it produces a stronger
signal, a signal that's more
detectable.
And right now my friend
Brian Keating--
he's good buddies
with Jim Simons.
Jim Simons gave him like a crap
load of money to build a
satellite to actually look
for this effect.
Because, notice, it's
a Chern-Simons term.
So thank you Jim for
funding Brian.
Maybe you can fund me one day.
He's a great guy, by the way.
So this is the Simons
Array telescope
that my friend Brian--
you should invite him out here
to talk about that design.
Very cutting edge bilometry
technology.
Detectors that are way beyond
anything available anywhere.
You might want to use
some of that tech.
I don't know what you guys
can do with detectors.
So here are the stats on that.
And I want to conclude.
So one of the biggest questions
in particle
cosmology is a question
of barrier genesis, or
leptogenesis.
It's not sufficient to just talk
about structure formation
without talking about how matter
won over antimatter.
It's a real observational
question.
And what I presented to you was
a model that requires very
little new physics, no extra
dimensions, minimal
fine-tunings.
Of course you need to drink
the Kool-Aid of inflation.
And it may be testable by
measuring anomalous parity
violating power spectra--
last slide I showed you.
And LIGO, or maybe one day LISA,
if it flies, might be
able to see these waveforms in
binary mergers, like black
holes and neutron
stars and such.
And this is a great opportunity
to test a
fundamental issue using cosmic
microwave background
polarization.
And I want end to make my string
theorist friends happy.
Because the story actually
started with a string theory
investigation, looking at
the Chern-Simons term.
That it's possible that if you
find this effect, we might be
closer to actually making model
independent statements
about string theory or theories
of quantum gravity.
Thanks for having me out.
[APPLAUSE]
AUDIENCE: The parity violation
depends on the Chern-Simons
term, which depends on
the inflaton field.
Wouldn't it have vanished by now
and only be apparent close
to the Big Bang?
STEPHON ALEXANDER:
That's right.
So one thing-- there are two
effects that could happen.
One is a propagating effect,
which is that you can look at
a gravitational wave
travelling to us
from the CMB to us.
So it was affected by this
field back then.
And it propagated to us.
And it turns out, as
it propagates that
effect becomes stronger.
And another one is a source
effect, that if the field
exists today, it may source.
And you're correct that there
are cosmological constraints
that tell us that this
field cannot exist.
And if it does exist,
at the very most
it's the dark energy.
And we know that it has to
be like 10 to the minus 3
electron volts.
Good question.
AUDIENCE: What is the current
state of the gravity wave
detection experiments.
And it seems like those have
been online for awhile now.
Are there any results
coming out of it?
STEPHON ALEXANDER: know they
are very optimistic.
I mean I was just visiting my
friend Nico Yunes and Neil
Cornish who are heavy
into that game.
And they're very optimistic.
They are optimistic that they
will detect a gravity wave.
But the question is the
background noise.
Like, they have to always figure
out how to get rid of
the things that may appear
to be a gravity wave.
But because we already saw the
binary pulsar, we know that
there should be a gravity
wave out there.
It's not a question of--
so I'm optimistic.
I'm obviously not privy to the
real technical challenges that
they're dealing with.
Because it's not my pay grade.
But the part of my community
that deals with gravity wave,
we're very optimistic.
AUDIENCE: [INAUDIBLE]
CERN, you'd really detected a
real gravity wave as opposed
to just some truck passing
by, like--
STEPHON ALEXANDER: Yes.
And this is exactly the issue.
They have to figure out what
that signal to noise is.
So the question is how do
you characterize that?
So they have to understand what
those foreground are.
And so a big name of the game
is to figure out what a fake
signal is and then model
it, to subtract it off.
AUDIENCE: [INAUDIBLE]?
STEPHON ALEXANDER: That
I don't know.
I think advanced LIGO and LISA
would be designed to do that.
Because if you had LISA flying
and LIGO, and you saw the same
event, then you'll have two
different locations.
AUDIENCE: Yes, the
answer is yes.
[INAUDIBLE]
LIGO because there's some
several of them scattered
around the earth.
STEPHON ALEXANDER: The
answer is yes.
Yes.
AUDIENCE: Do we have any idea
what kind of interactions the
inflaton might have, whether
we'd be able to produce it in
an accelerator?
STEPHON ALEXANDER: That's
a good question.
So the answer is that we should
be able to do that.
And that's why last year me
and David Spergel and my
post-doc worked on a new model
of inflation that is not based
on a scalar field.
But it's based on something
that looks very similar to
quantum electrodynamics.
And in that case, inflation is
actually driven by ordinary
fields in nature.
And so we're working now--
that paper was recently
published in JCAP.
So you can look for
that paper.
It's called--
it's a model based
on vector fields.
So the photon and fermions
are driving inflation.
And so you could, for example,
try to recreate that situation
at the large Hadron Collider,
the ILC and see if you see
something that smells
like inflation.
I mean that's a forward-thinking
idea.
But we did that to show that, as
a proof of principle, that
you can do inflation with
ordinary fields in nature.
So part of that was to ask this
question that you're asking.
AUDIENCE: If an anti-galaxy were
to exist, what would be
the observational--
STEPHON ALEXANDER: Yeah.
There is-- that's right.
Around every galaxy
there's gas, like
hydrogen, for example.
So you would see a lot of
annihilation going on, if
there was anti-galaxy.
So you basically see huge
flux of photons.
So we can imagine that we do
have anomalies in the sky.
We have things called
cosmic rays.
And we have very high-energy
cosmic rays.
Maybe it could be that is a
result of some huge amount of
antimatter out there.
It's not my pay grade, but so
far every galaxy person I've
spoken to tell me that there's
no evidence of huge
anti-galaxies out there.
But I tend to keep an open mind
about things that I'm
ignorant about.
So far I've been able to answer
everybody's questions.
This is scaring me.
This is Google.
I'm just kidding.
AUDIENCE: In one part of the
talk it said, one of
[INAUDIBLE]
part of the talk.
You showed a factor of ten
ratio between matter and
antimatter.
So I'm a little bit confused.
STEPHON ALEXANDER: OK, good.
I'm glad you brought that up.
We saw a factor of 10 difference
in ordinary left
and right symmetric gravity
waves produces inflation and a
left-right asymmetric
gravity waves.
So that's a factor of 10.
But it's interesting that that
factor of 10 may be the same
factor of 10, to give you
the Baryon asymmetry.
So what we're looking at is
really the gravity wave power
spectrum, the distribution of
the frequencies that are
gravity waves.
And what we see is that we have
higher power for larger
wavelengths of gravity waves,
if they are left-right
asymmetric, and lower
power if they
were left-right symmetric.
I don't have an intuition as
to why that is the case.
But it's good to think about.
Yes.
AUDIENCE: Why is parity an
almost perfect symmetry?
Why is it a symmetry at all?
I'm curious.
If physics is just a whole
bunch of these
near-symmetries, which are
symmetries that are slightly
broken, but [INAUDIBLE].
Parity is one of these things.
Why does it exist at all?
STEPHON ALEXANDER: I think what
you mean by that is in
the weak interaction,
parity of course
is maximally violated.
We never see the other thing.
But that's right.
In terms of all the forces
combined, the weak
is the odd man out.
OK.
It's the one that
violates parity.
And the other is, if it violates
parity, it's just
like very weakly
or not at all.
And so to be honest with you,
there is no good answer to
that question.
We don't know the
answer to that.
Part of why I pursued this
line of research was to
understand--
to use gravity as a diagnostic
theoretically to understand
that question.
Because in this case parity
is just weakly violated.
It's in between.
The talk I was really going to
give you guys was a partial
answer to your question, which
was to show that actually
gravity and the weak interaction
are really the
same theory.
And the parity violation is
a consequence of parity
symmetric theory that includes
gravity in the weak
interaction.
But that talk had--
a friend of mine warned me to
not give that talk here
because, well, there were
no words in the talk.
[LAUGHTER]
Or very little words
in the talk.
AUDIENCE: [INAUDIBLE]
the weak interaction can be
unified into the [INAUDIBLE]
weak theory.
STEPHON ALEXANDER:
That's right.
AUDIENCE: [INAUDIBLE].
STEPHON ALEXANDER:
That's right.
So it's a very good point.
I notice your question.
So the electroweak
interaction--
that's a very good point.
The electroweak force actually
includes both electromagnetism
and the weak interaction.
OK.
But what happens is
that the Higgs
field breaks that symmetry.
That's what the Higgs
does, right?
It's like a magnet.
It points in a given
direction.
That's what the Higgs field is,
like a magnet pointing in
a given direction.
And that aligns the weak field
now to actually disassociate
itself from the electromagnetic
field and the
weak field.
And actually the way that it's
done is quite artificial, if
you look at the details.
And this is called
a Weinberg angle.
So what sets the Weinberg angle
to be what it is, is
kind of an input that you-- you
kind of put that answer
into the dynamics.
What we would like
is to actually--
see, the answer to your question
is related to the
origin of the parity
violation.
AUDIENCE: What are your views on
the existence of firewalls
around black holes?
STEPHON ALEXANDER: You guys
know what a firewall is?
Put a wall of fire,
you fall into it.
So there's this idea that the
Hawking radiation actually
organizes itself-- when a
black hole emits Hawking
radiation into a wall of fire
for an observer falling into
the black hole.
I would say that even if
firewalls exist or it doesn't
exist, there's still a more
fundamental question of
information loss.
And so I don't lose sleep over
firewalls, unless I find
myself near one.
Why did you ask that question?
AUDIENCE: Just curious what
your stance on it is?
I guess you don't think
either way?
STEPHON ALEXANDER: No,
it's a good question.
I think it's a really good
question of, do holes only
emit Hawking radiation,
or does it
absorb Hawking radiation?
