So let me begin this talk with a question.
Take a look around you or contemplate all
of the experiences you’ve ever had, and
think of something that you’ve found to
exist in our world.
Just throw something out, name something you
see right now, yell it out.
iPhone, me, anything else?
Okay, chairs, pencil sharpeners.
What do all of these things have in common?
They are made of atoms.
If we are a little bit more open minded, we
might even add to the list things like the
air.
Sure, I can’t see it, but I certainly feel
it with my hand.
Again, made of atoms.
I might say, oh I experience sound, but this
is just pressure waves or motion of atoms.
Essentially everything we have first-hand
experience of in our universe is atoms, and
maybe light.
So we’ll say light and atoms.
The idea that the universe might be made of
individual things, like atoms, goes back a
long time.
This is an ancient Greek philosopher named
Democritus.
As far as written records go anyway, he was
the first figure to prose that maybe, if you
could break matter up matter into small enough
pieces, you’d reach a point where you couldn’t
break it up anymore.
So if I take a piece of wood, I could chop
it and make into two pieces of wood, I could
chop those pieces and make four, and I could
chop those and make sixteenths and etcetera,
but eventually I will get down to individual
carbon atoms inside of that wood that I just
won’t be able to break up any further.
This was an idea that Democritus proposed
and advocated throughout his long career,
but of course, in his day, we have no evidence
that it was true; it was just speculation.
A couple of thousand years later we came up
with this picture of the modern atom.
We’re in a chemistry building, you all are
familiar with the periodic table, but it’s
a remarkable achievement; the idea that we
could find out, approximately at the smallest
scales, what all of those things we experience
in the world is made of is a mind-boggling
achievement.
Of course, today we know that these are not
Democritus’ atoms.
Why not?
What’s different between what Democritus
had in mind and these things?
I can break these up.
I can take that carbon atom here, it turns
out that it’s just 6 protons, 6 neutrons,
and six electrons.
Even those protons and neutrons aren’t really
Democritus’ atoms, because they’re made
up of quarks and gluons  if you look even
more closely at them.
So we have a modern idea and the bottom picture
of energy and matter which consists of something
Democritus would have called an atom.
And there’s things like quarks and electrons
and so on, but here’s why it starts to get
strange and here’s where it goes from stuff
we do
understand to stuff we don’t.
This pie chart depicts what we currently understand
our universe to be made of, and the first
thing you’ll notice about it is all of those
atoms on the periodic table are a very small
piece of the cosmic pie.
So four percent of our universe, by total
energy or mass density, is made up of hydrogen
and helium.
Hydrogen and helium out in space, not even
stuff in stars, just floating out there in
clouds and space.
About a half a percent are mostly just hydrogen
and helium, but some other stuff is in the
form of stars, and then a very small amount,
point zero three of things heavier than that.
So basically all the stuff we listed at the
beginning falls into that little tiny sliver
of the cosmic pie.
And you can throw in a few other things, there
are these little particles called neutrinos,
you can’t even see it on there, but there
is a little sliver made up of light and the
vast majority, about ninety five percent is
made up of this stuff we don’t understand;
dark matter and dark energy.
Over the next hour, or so, I’m going to
try to give you a flavor for what these things
are, or not actually what they are because
we don’t know what they are, but I’m going
to try to give you a flavor for why we know
they’re there and what we do know about
them.
This is very much research in progress, I
hope that if I were giving a lecture like
this ten years from now, I might have more
answers, I’m actually pretty optimistic
we will, but for the moment this is a very
speculative topic, but one where we are well
on our way to making progress.
The story of dark matter and its story focuses
among others, these two folks, Fritz Zwicky,
a Swiss physicist and astrophysicist, he spends
much of his career at Caltech though, and
then there’s Vera Rubin, an American.
Back in the nineteen thirties, Friz was studying
clusters of galaxies and noticed that there
seemed to be problems there and then Vera
would come along later, starting in the fifties
and up through the seventies and noticing
similar problems on the scale of galaxies,
and this work would begin to convince astronomers
that there is more to the universe than atoms.
The argument here is a little subtle, but
it’s physics 101, so I think I can walk
you through it.
Let’s say I wanted to measure the mass of
a planet like Mars.
obviously this isn’t something I can put
on a bathroom scale, yet every astronomy textbook,
if you look in the back of it, will give you
a table and it will say how heavy mars is.
The way we determine that is not by weighing
Mars directly, but by watching things orbit
around it.
In particular, its moons.
So if I have say, Mars and one of its moons,
or maybe the sun and a planet or whatever,
something that has an orbiting body, I can
match the force of gravity pulling these two
things together to the centrifugal or centripetal
force pulling them apart.
So centrifugal or centripetal force is that
thing you feel on a merry-go-round, so when
you are on a merry-go-round, it’s that thing
that pulls you to the outside, meanwhile gravity
would pull you in, and if those balance, you
end up with a stable circular orbit.
So when we solve this equation, we can find
out what the mass of the sun, or mars, or
whatever is at the center is.
This is how we weigh things in astrophysics.
But we can apply it to bigger systems too,
like an entire galaxy.
This is Andromeda, it’s the nearest large
galaxy to the milky way, it actually looks
a lot like the Milky Way, it is sometimes
called the Milky Way’s twin.
If this was the Milky Way you would find us
living kind about here on the galactic outskirts
or suburbs maybe, but if you look at the outermost
stars and see how fast they’re orbiting
around this, you can effectively weigh the
whole galaxy of Andromeda.
It’s the same thing here, except in the
middle we have the total mass of the galaxy,
and at the outskirt we have the mass of the
star doing its orbit and if you just took
where all the stars, gas, and dust are on
your telescopes and tried to predict how fast
stars should be moving around galaxies, you
would get a chart like this.
For example, you would predict that a star,
one hundred thousand light years from the
middle of this galaxy will be moving at about
seventy miles per second of velocity around
that galaxy and the farther you go out the
slower they go.
This is the same reason that Pluto moves more
slowly than Mercury around the sun.
As you move farther and farther away from
the center of this gravity, the more slowly
things are going to be orbiting, but that’s
about all we actually see when we look at
real galaxies, so this is what we would have
expected to see, and this is what we measure.
The reason they are different is because we
are making predictions that don’t include
all this extra invisible mass, dark matter.
If we want to account for this, it turns out
we need to account for extra mass, and therefore
extra gravity that explains why the stars
are moving so quickly.
So we have reached a peculiar conclusion,
a surprising conclusion that most of the matter
in our universe seems to be invisible or,
at least, seems to be faint enough that we
don’t notice it.
So back in the seventies, when astronomers
began to take this seriously, they began to
hypothesize what this dark matter might be
made of, and their first reasonable guess,
the guess most astronomers consider most likely
was that they were made up of some sort of
very faint stars or planets.
They call the MACHOS for short, or massive
compact halo objects.
There’s good reason to think that such faint
stars could exist.
This diagram tells us how stars, in most cases,
evolve.
If you start, before you have a star, you
actually have just a big cloud of gas, and
those collapse, and if they collapse into
a small thing, they make something we call
a brown dwarf, which is like a very very faint
star; it never burns much fusion, so it stays
faint.
But if it’s a little bigger it burn hydrogen
and becomes a bright star.
In the case of our sun, it will evolve this
way over the next several billion years until
it becomes a giant, and then after it’s
done being a red giant, it will shrink down
into something called a white dwarf.
Now a white dwarf is something about as heavy
as the sun, but about as big as the earth.
So a very very dense ball of carbon made of
oxygen.
As that white dwarf cools, it will slowly
fade from view and become very very faint.
For stars that are bigger than our sun, much
bigger, these massive stars begin to burn
more and more elements and create a wider
variety of stuff in their cores and then they
explode.
They explode because they run out of fuel
and gravity collapses them into such a small
volume of space that they have no choice but
to rebound out as a giant explosion.
When a supernova is done exploding, the thing
left in its core is either a neutron star
or a black hole.
Before I said that a white dwarf is about
as heavy as the sun but about the size of
the earth; well, a neutron star is heavier
than the sun.
nut about the size of this town, of Auburn.
So an amazingly dense amount of material.
I used to have some sort of analogy at my
fingertips.
It was something like one teaspoon of neutron
star matter weighed as much as ten thousand
empire state buildings, or something, but
it’s so big that you just can’t put your
head around it.
It’s an incredibly dense object.
A black hole is even more dense and gives
off no light at all.
The interesting thing about this chart is
that all these types of objects are, in many
cases, so faint that we don’t detect them
with our telescopes very easily.
So, when it became clear that there was a
lot of invisible matter, many astronomers
began to imagine that that invisible matter
was made up of these sorts of objects scattered
throughout the areas of the five galaxies.
So that was our working hypothesis.
Let me talk a little more about black holes
because they’re relevant, but also just
because they’re cool and I find that people
like to hear about black holes.
If you are on the surface of the earth, and
I take a baseball, or a football because I’m
here in Auburn, and I throw that football
upward, even if you’re, you know, the greatest
NFL player in history, it reaches a certain
height and it falls back to Earth.
Okay, so you could imagine at least, though,
some sort of football propelling cannon that
could fire, could propel this football so
fast, so rapidly upward that it would escape
the gravity of the earth and fly off forever.
Now imagine, instead of the earth, I have
something even heavier, more dense.
Say this thing.
If I make it dense enough then I can make
the gravity around that object so strong that
even something traveling at the speed of light
will fall back to the object, if you will.
So any system, anything that is so dense that
the escape velocity exceeds the speed of light,
is completely invisible because light simply
can’t get away from its gravity, and we
call that sort of object a black hole.
And like I said in the last slide, this is
the kind of thing that you would expect would
be created in certain supernova explosions.
This is where the mass is in this black hole,
and around it is a sphere that we call the
event horizon and this is the barrier that
nothing can pass through.
So light cannot escape out of it, and because
of the weirdness of the general theory of
relativity, which I understand some of you
are studying right now, nothing can get into
it either.
It’s an impenetrable barrier separating
inside from outside.
But we still see these things, although not
directly, so although light can’t come out
of a black hole, certainly the black hole’s
gravity can cause violent things to happen
around them that we can see.
So in this cartoon, you’d have a black hole
in here and then not very far away from the
black hole is this ordinary star, companion
star, and the black hole’s gravity is kind
of sucking matter off of this companion star
in toward it.
So the matter is not in the black hole but
surrounded, and gravity is causing it to form
this secretion disc and shoot out violent
jets of energy and matter along its axis.
When we look through a telescope, when we
see one of these objects in space, this jet
of material and energies, they can be very
bright and we see lots of these and they are
called active galactic nuclei or blazars,
and we see these in x-ray and gamma ray telescopes
in large numbers, and we know there are black
holes in these systems.
Another way we can look for black holes, fainter
black holes, the kind of black holes that
might have made up the dark matter, is through
a technique called lensing, this is gravitational
lensing.
So the idea here, we have a telescope here
called the observer, but some sort of telescope
and some distant objects, a star, galaxy or
something, and then in here is our black hole
or other macho.
So this is our dark matter object.
When this is perfectly aligned, the gravity
from this black hole deflects the light from
that star galaxy, bending it around at the
black hole and towards our telescope.
So in reality what’s gonna happen is this
black hole’s gonna steadily travel in this
direction and over here will have no effect,
you’ll see this object normally and then
as you fall directly into this line of sight;
this object will become brighter over a period
of time, it will steadily become brighter
as this acts like a lense and focuses the
light with its gravity, and then it will travel
on and it will become dim again, it will act
like it was before.
So in principle this is very hard to do because
you would have to watch millions of stars
at one time in the hopes that this would happen
for one or two lucky ones, but astronomers
have managed to do that.
What they do is with these ground-based telescopes,
they watch the whole sky and they train computers
to look for stars becoming brighter and dimmer
as predicted by this lensing phenomena.
Here’s the same part of the sky observed
on April 28, 1996, and then here it is observed
again in the same year, but in November, so
several months later.
Then this star becomes suddenly brighter for
a number of days in November..
Now astronomers saw this and thought that
maybe this was a lensing event but we can’t
be sure, so they told the Hubble Space Telescope
to do a follow up.
Now that we know where to look we can ask
Hubble to go look in detail and lo and behold
this was a lensed star.
A star that became brighter and dimmer just
as lensing would’ve predicted, and you could
even work out how heavy the MACHO responsible
is, and it’s about six times heavier than
the sun, and this is a black hole.
So we discovered a black hole here and you
might think from that, we’ve solved the
dark matter problem, but no.
These lensing searches found some black holes
and some white dwarfs and some neutron stars,
but not nearly enough to account for the Milky
Way’s dark matter.
Maybe you can account for a percentage or
two but not very much at all.
This is just not the answer, so even though
black holes and neutron stars are pretty exotic,
turns out that whatever it is that makes up
the dark matter is way more exotic than this.
It’s something we haven’t even thought
of yet.
So if MACHO has failed us, our next best idea
are something we call WIMPs or weakly interacting
massive particles.
To explain what a WIMP is or how a particle
can behave like a WIMP, first we have to think
about the particles that we do know about
behave the way they do.
So if I take my hand and I try to press it
through this desk, I find resistance and it
pushes back against me.
Why is that?
Does anyone know?
I heard some mumbling but I couldn’t make
out what you said.
Coolum force!
Okay, what is the Coolum force?
You’re right, the Coolum force is the attraction
or repulsion experienced between electricity
charged particles.
So in this case the electrons in my hand which
are negatively charged, and the electrons
in this tabled, which are also negatively
charged push against each other, in fact,
my hand is mostly empty space.
The table, the desk, is mostly empty space,
but those electrons push against each other
preventing them from entering the table.
I can imagine a type of matter that does not
contain electric charge and doesn’t interact
by the strong nuclear force and this sort
of material would travel straight through
my hand or straight through that table without
ever knowing it was there.
That’s what we have in mind when we’re
talking about a WIMP.
This is a chart, well I was going to say,
of all of the known forms of matter and energy
but that is not quite true, and I’ll get
to why in a little bit.
These six particles are called quarks, they
all have electric charge and they all interact
with a strong force, so they are not good
dark matter candidates; they’re not WIMPS.
Over here we have some force carrying particles,
we have a photon which are particles of light,
obviously light would not make a very good
candidate for dark matter.
The gluon is made for the strong nuclear force;
that’s not gonna work.
These guys are very unstable, they only exist
for a fraction of a second, so that’s not
the answer, and then these guys, including
the electron are charged, so none of those
work.
That leaves us with these three guys that
we call neutrinos.
The only kind of matter that we know about
that comes even close to acting like dark
matter should are these particles called neutrinos.
If I hold my hand up, and put it down a few
seconds later, in that time, literally trillions
of neutrinos have passed through it, mostly
from the sun.
We are bathed in neutrinos, those neutrinos
are harmless though and we don’t feel them
in any way, shape, or form because they are
so feebly interacting that they just pass
through us as if we weren’t there.
You can imagine dark matter is made up of
something like neutrinos, but not specifically
neutrinos because these guys are too light
and quick, and they wouldn’t form the sort
of galaxies we observe, so in light of that,
we need to imagine a new thing that’s kind
of like a neutrino, but heavier and slower,
more lethargic, if you will.
At this point, this is the point in the lecture
where I say we simply do not know what the
dark matter is made of, but a lot of my colleagues
and myself like to make guesses, in science
we call these guesses hypothesis, but they’re
religious guesses.
Hypothesis is just a fancy word.
Our single best guess or hypothesis, comes
to this particle physics theory that we call
supersymmetry.
This is an idea that says for every type of
matter, which we call a fermion, there must
be a force carrying particle that we call
a boson and vice versa, so these have to come
in pairs, according to this theory.
There are lots of reasons why we like this
theory, it solves all sorts of technical problems
and makes the math work better, but it is
just a guess all the same, a hypothesis, although
a well-educated one.
So if supersymmetry is true, then the photon
cannot exist without a fermion particle, what
we call a photino, and the electron cannot
exist without a selectron and so on, so there
are twice as many particles that is those
we know about, and these are just out there
waiting for us to discover them, and these
extra particles, the ones in the darker color
here, one of them we predict, whatever one
I lightest should be stable, and if it happens
to be weakly interacting, and it might, then
it should be abundant in our universe and
very well be the stuff that makes up our dark
matter.
It’s just a guess, but it’s probably our
single best guess.
Then, of course, when you have a hypothesis
in science you don’t stop there, you make
predictions for what that hypothesis should
imply and then you go and do experiments to
see if it’s true.
So in particular, we have a handful of ways
that we would like to test this hypothesis,
that dark matter is made of WIMPS and some
supersymmetric particles in the form of WIMPS.
One thing,  you could build little detectors
of dark matter and go and put them deep down
in mines, this is the Sudan mine in my home
state of Minnesota.
You go out, maybe a mile or so underground,
you build a very carefully instrumented and
well-designed detector and you wait for individual
WIMPs to come through and recoil elastically
off of your nucleus of your detector.
This, of course, happens very rarely, but
if you build a big enough detector and wait
long enough, in principle, you might hope
to see these indications.
We haven’t yet.
Another way that you can look for dark matter
particles is not by looking for the ones that
already exist, but by making new ones.
This is a machine called the Large Hadron
Collider.
By any relatable standard this is the greatest
engineering achievement in human history.
It’s absolutely mind-boggling complexity
and it’s, yeah, I could go on and on about
how amazing it is from an engineering standpoint,
but I’ll just tell you a few things about
it.
This underground tunnel is seventeen miles
around.
This is what it looks like inside of that
tunnel.
Around that tunnel, magnets, super super powerful
magnets accelerate protons up to speeds 99.999997
percent at the speed of light.
This is a colossal amount of energy.
Wildly higher energy than any other machine
we’ve ever been able to build like this.
So one beam is fired clockwise while another
counterclockwise and then in specially designed
places where we have these enormous detectors,
this is about the size of a gymnasium by the
way, inside of the heart of those detectors
beams are smashed head-on and the protons
are going to smash into each other and various
particles fly out and we study those collisions
to try to understand more about our universe.
This is not something where we collide a proton
here or there.
The design goals about six hundred million
of these collisions every second, and can
you imagine just the simple computing problem
of trying to measure everything about every
collision six hundred million times a second
and analyze all that data?
It’s absolutely staggering that this can
work at all, but it does.
In fact, so far we’ve got about ten to fifteen
clinicians recorded and we’re well on our
way to, when the machine starts up in another
year or so, of returning and getting even
more.
So, of course, at this point you should be
asking yourself, how do you learn about things
like dark matter or anything else by smashing
protons together quickly?
It’s not obvious if I wanted to learn about
auto mechanics, driving me to chrysler's together
as fast as they could is not a good way to
do it, but in physics it is, so it all really
comes down to this equation, probably the
single most famous equation in all of science.
Einstein’s equals MC squared.
All this equation says is that energy can
be transformed into mass and mass can be transformed
into energy.
That’s all it means.
So if I want to create particles with a lot
of mass, maybe particles that we don’t know
about yet, new particles, and particles like
dark matter, or the [inaudible] that you might
have heard about, what I need to do is put
a lot of energy at one place at one time and
the best way to do that is smashing protons
together, for example.
Let’s take another look at how the LAC does
this.
Well what this was going to do was show you
how the protons get accelerated around the
ring and show you what a collision looks like,
but my animation failed me, so I’m just
going to go on to this.
In the first year of its running the Large
Hadron Collider has not discovered any supersymmetric
particles, or anything else that looks like
dark matter, but that’s a very big yet statement,
so the machine’s currently shut down and
being upgraded , it’ll go to about twice
as much energy as it’s currently run at
for another year or two, and we have plans
of collecting literally tens of times more
data at that high energy than we’ve had
so far.
We’ve had many more collisions at higher
energy, so I’m still very optimistic that
this machine will discover many new forms
of matter and energy.
So that’s disappointing, but only for now
and there is also very exciting news, who’s
heard about the discovery of the Higgs boson?
Show of hands?
Okay, almost everyone.
It is a really big deal, and it doesn’t
really have a lot to do with dark matter or
dark energy, but I think I am going to use
a couple of minutes to kind of tell you what
that’s all about.
When particles interact with each other, physicists
like to denote those interactions with diagrams
like this, this is called a phylum diagram.
What this is two electrons coming in and they
exchange a photon which causes them to repel
each other, this is that Coolum force we were
talking about.
This photon brings into effect the force of
electromagnetism causing these electrons to
repel.
This is a brilliant theory called quantum
electrodynamics, it’s probably the single
most successful theory in all of science,
but it only works if this photon has no mass,
which it doesn’t so great.
It has not mass, so it’s a great theory,
but when we try to do the same thing with
the weak nuclear force, the force that causes
the beta decays to take place, we can write
down a similar diagram and instead of the
photon, we put something like this W boson
on it, and again, the math seems like it should
only work if this particle had no mass, but
the W does have a mass, it has a big mass.
So there seemed to be a problem with mathematical
consistency, the week four simply didn’t
seem to hold together, it produced illogical
paradoxical predictions.
That is until these guys, Peter Higgs, these
guys and others around the same time in the
nineteen sixties, came up with a new theory
that solved this conundrum, and that theory
predicted that the whole universe, all of
space, is filled with a field of particles
called the higgs boson.
Obviously, Peter Higgs didn’t call it the
Higgs boson but it got named after him later.
So throughout all space is a field of these
particles, and that field interacts with things
like the W boson, causing it to behave like
it has mass.
We don’t know for sure, but in all likelihood
we think the electrons in your body get their
mass from the Higgs field as well.
Pretty much all forms of mass, well not all
forms, but many forms of mass come from the
Higgs field.
In last July, at [inaudible] where the Large
Hadron Collider is they announced that they
discovered a  particle very much like the
Higgs boson, now we’re saying it’s the
higgs boson, we measured it so well that we’re
quite confident that it is the higgs boson
that was predicted by these guys back in the
sixties, so it’s an absolute staggering
achievement.
It took a machine like the Large Hadron Collider
to do it, it took about fifty years of effort
by tens of thousands of physicist over that
time.
So this is our new picture of the standard
model includes those quirks, those neutrinos
use force carriers electrons and his cousins
and this last remaining piece called the Higgs
Boson.
Together this is a staggering accomplishment
and it’s a complete description of all of
the forms of matter and energy we directly
know about, of course not including dark matter
and dark energy.
So going back to that picture, so far I’ve
only talked about this piece of the puzzle
, and I have neglected this even bigger piece
we call dark energy.
I could tell you everything there is to know
about dark energy in pretty short period of
time because we don’t really understand
it.
We know it’s there, but we don’t know
why, and we don’t really understand, especially
why it exists in the quantity it does.
If dark matter is a puzzle then dark energy
is a puzzle on top of a puzzle.
To begin to understand it, and how we know
it’s there, we have to go back to Albert
Einstein.
Probably the most revolutionary thinker of
the twentieth century.
He turned all of these newtonian ideas about
space and time, he said that space wasn’t
a fixed thing that objects move through, he
said it was a dynamical thing that can act
on things and be active upon by things.
Time was connected to space, you couldn’t
think of time and space as separate things.
To one observer, something that looks like
space, to another observer will look like
time and vice versa.
They are deeply interconnected.
He also said that gravity is not a force like
we normally think of it but is really just
an effect you get because of the geometry
of space and time.
So because space is curved, or warped, or
stretched or whatever adjective you prefer
to use, because of that, we feel the thing
we call gravity.
Gravity exists because of that geometry of
space.
And thirdly, he realized that space and time
can change and evolve; they’re not necessarily
static.
Revolutionary ideas.
So I have a short pet peeve that I would like
to express at this point.
Of course, everyone in this room recognizes
this picture.
When I was in colleges some of my fellow classmates
had pictures like this, maybe not this exact
one, but pictures of Einstein’s on their
walls and all this and that’s great; I’m
a big fan of making great thinkers into our
heroes and people we admire, but this picture
is one you see far less often.
Who is this?
Yeah, this is the younger Albert Einstein
in 1905.
So some people like to call 1905 Einstein’s
miracle year.
In 1905, Einstein wrote the first paper proving
atoms exist, he wrote the first paper with
equation E equals MC squared in it, he wrote
a paper on something called the photoelectric
effect that proved that light came in individual
particles or photons as we now call them,
it started the quantum revolution, and he
wrote the first paper creating the special
theory of relativity.
If any individual had done any one of those
things, they would have been considered a
scientist of the absolute top tier in history,
the absolute hero of science.
He did five things in one year, that’s absolutely
mind-blowing.
And then this guy, so about ten years later,
completed the theory of general relativity,
worked gravity into his theory, and then the
more famous picture is of Einstein much later
when he didn’t accomplish all that much.
These are the heroes and I think it’s a
disservice to the young physics students to
heroicize this guy and give the impression
that you have to look like this to do what
these guys did.
By these standards, by the way, I’m already
past doing all my important stuff, okay, so
I have very motivation to tell you this is
the hero.
Because, you know, it would be good for me
and my career, but I think there are younger
people in this room who might even do greater
things.
Alright, back to dark energy.
Alright, so those of you who have taken general
relativity now have seen this equation, and
this is Einstein’s famous field equation.
You’re not going to understand everything
in it, but there are a couple of concepts
in it that are very simple and easy to understand.
Basically, all this says is if you know where
the matter and energy is in space, so where
the stuff is, you can work out from this equation
how space should be shaped or how it should
be curved, so you can work out the geometry
of space from the energy, or the distribution
of stuff in it, and vice versa, they imply
each other.
So when he took this equation and he began
to apply it, not just to things like planets,
orbits, or the force of gravity as we experience
it on earth or something like this, he said,
let’s apply it to the whole universe.
He said, okay, well let’s do a simple case,
let’s imagine that there’s a same density
of stuff everywhere, which a margin of scales
is approximately true, that’s a pretty good
assumption.
And he said I’m going to work out what the
curvature is, and he did, but here’s the
trick, when he solved that equation, the curvature
of space, the geometry of space, the shape
of space didn’t remain the same.
It changed with time, it invariably would
evolve.
Now he hated this idea, he looked out into
the night sky and he said that looks like
it’s pretty much static to me, so obviously
this is wrong, and he added this term to the
equation, he added it to make the universe
static.
There’s no good reason to put it in there,
you could, there’s nothing about the mathematics
that prohibited it, but there was no good
reason for it to be there, but he set it to
a very specific number so that when taken
altogether it would approximately keep the
universe from changing very much, and he was
happy with that at the time.
But he was wrong, a little over a decade later,
this guy, Edwin Hubble, the guy that the famous
Hubble telescope is named after, did some
measurements of nearby galaxies and used those
measurements to show that space was expanding.
It wasn’t static, it was changing, and here’s
a sort of thing you measure, this is actually
not his data because his data turned out to
be wrong, but the basic idea was right.
These dots are all individual galaxies, and
this is how far away they are from us in this
unit called Mega parsecs, which is roughly
three million light years.
So this galaxy is roughly six billion light
years away from us, and this axis is how fast
that galaxy is moving away from us, and obviously
there’s a trend here, the most distant galaxies
are moving away from us very quickly and faster
than those nearby.
This slope tells us that the amount of space
between us and those galaxies is getting bigger
with time, they’re not just moving away
from us like in some explosion, but everywhere
throughout space, that space is growing and
it makes it seem like things are moving away
from us if they are far enough away.
It’s a pretty radical and paradigm changing
observation.
So now let’s go back to Einstein’s field
equations with this in mind.
Throwing out that extra term that Einstein
put in, there were exactly three solutions
to this equation: on one hand, the universe
could be growing, expanding now, it could
reach a plateau and then get smaller again,
or it could just get bigger forever, that’s
what we call an open universe, or it could
be getting bigger for a while and eventually
reach a plateau, and obviously we didn’t
know in Einstein’s day which of these were
true, but we are hopeful that with measurements
later we’d be able to find out, but let’s
take a sidetrack for a moment and consider
what this part of our universe history would
look like, if you go back far enough, these
equations say that the universe will reach
a point where it’s infinitely small.
Where all of the energy density that we see
in our universe around us is squeezed into
a volume of zero.
That means the temperature would be infinitely
high, the density will be infinitely high,
and we call that state the Big Bang.
So let’s see, according to this theory,
how the universe has evolved since then.
So at T equals zero, I’m going to find that
at this infinitely hot, infinitely dense state,
the big bang.
About a millionth of a second later, obviously
not much time, but a little bit, this temperature
of the universe is still very high, ten trillion
degrees or so, and at that time the universe
cooled just enough so that quarks could begin
to combine together into protons and neutrons.
The way I like to think about it, is this
number, this temperature is the melting point
of protons and neutrons.
If you could heat a neutron up to that temperature
it would fall apart into individual quarks.
Moving on, about three minutes after the big
bang, those protons and neutrons began to
combine to from the first nuclei, so here
we have a proton and a neutron forming deuterium
and another neutron coming to form tritium
and another proton still forming helium, we’ve
wound up with various types of helium, hydrogen,
and lithium, maybe a little bit of boron from
this process called big Bang nucleosynthesis,
again I’d like to think of this as somewhat
of a melting point, it’s the melting point
of these nuclei, and then a few hundred thousand
years later, the universe cooled to five or
ten thousand degrees and for the first time
electrons were able to bind to protons to
make neutral atoms, hydrogen as an atom was
made for the first time, and playing on this
theme, once again, this is about the melting
point of an atom where the electrons fall
off.
This was an important transition for observational
cosmologists because when the universe went
from a charged or ionized state to a neutral
state where atoms were electrically neutral,
it was the first time in our universe’s
history that light was able to travel through
space more or less unabated, so the universe
went to a state where it was opaque to a state
where it was transparent.
So all of that light that was built up in
the universe was suddenly kind of released
and it’s traveled through space ever since,
and we still see it today.
This is a map of that light.
We see it in microwaves, has a temperature
of about three degrees above absolute zero
and by measuring the precise patterns, a tiny
little temperature fluctuations across the
sky, we can learn things like how fast the
universe has been expanding since that time,
how much matter was in the universe at different
times, and what that matter behaved like.
So we’ve learned an enormous amount of information
from this cosmic microwave background radiation.
Moving forward, roughly a billion or so years
after the big bang, the first stars began
to form, and many millions of years later,
about four and a half billion years ago, our
solar system, and the sun, and our planets,
including our earth began to form.
So back to this picture.
If we want to tell which of kinds of these
universes we live in, we can, in principle,
learn that from the cosmic microwave background.
This is the sky in the cosmic microwave background,
it’s measured by an experiment in the nineties
called boomerang, late nineties.
It was a balloon flight and they recorded
it in microwaves, the patterns of hot and
cold spots on the sky.
Now keep in mind it’s about 2.7 degrees
above absolute zero everywhere, the hot points
are one part in ten thousand, I’m sorry,
one part in one hundred thousand hotter than
the blue points that are one hotter and one
hundred thousand colder.
So tiny little temperature fluctuations spread
across the sky.
If we found ourselves in a closed universe,
we should have expected that pattern to look
like this, and if we live in an open universe
the pattern should look like this, and if
we live in a flat universe, it should look
like this.
When you compare that to these images, it’s
pretty clear, and if you do the math correctly,
you can be very very confident that this is
the right answer.
So these experiments and others like it measured
that we seem to be on this trajectory, at
least that’s what they thought at the time,
but around the same time that those observations
were being made, others were measuring exactly
how fast the universe has been expanding,
by measuring distant objects, in particular,
supernova, and seeing how fast they were receding
from us, and they measured a line like that.
Not only is the universe expanding, but it
is expanding faster than it had been expanding
in the past, the expansion rate was accelerating,
and this seemed very very strange.
Going back to this equation, I said before,
now that we have thrown out this term, what
seemed to be the unnecessary term Einstein
had put in by hand, then there were only three
solutions, but now we know we’re not in
a universe that follows the predictions of
any of those solutions.
To resolve this, we have to put this term
back in, but with a different sign, a negative
sign in front of it, and a different quantity,
a different overall scale, but it’s a term
a lot like Einstein had originally put in
back in nineteen nineteen or so.
This term, we now call the cosmological term
or cosmological constant and it’s sometimes
called the symbol, lambda.
What this means, what this term physically
represents is that a quantity of energy that
is fixed into space itself, so if I take a
cubic meter of space and I take all of the
matter out of, take all the radiation out
of it, take everything that can be taken out
of it, out of it, there’s an energy density
left in it, and that’s represented by this
term.
We call this mysterious energy, dark energy.
We don’t know what it is, we don’t know
why it’s there, but it seems to be causing
our universe to grow faster than it used to.
One other weird thing about it is that you
can’t dilute it.
So I take that cubic meter of space, and then
I wait, I let that cubic meter expand, so
then that space grows into two cubic meters.
If this were ordinary matter or radiation
or something, the density of radiation or
matter would go down to half of what it used
to be, because you increased the volume, you
have to decrease the density, but not with
dark energy.
If I double the amount of space, I double
the amount of dark energy.
So that means in the earlier universe, dark
energy wasn’t very important, but as the
universe grew and expanded and diluted away
all of the normal matter, the dark energy
began to take over, and today it’s seventy
percent or so, and in the future it’ll be
more, and causing it to grow faster and faster
and faster.
So to kind of recap this historical story
in nineteen seventeen Einstein looked at his
equations and said, “this is nonsense, clearly
the universe is static, I’m going to add
this extra term to make it do that.”
The cosmological term.
A decade later, Edwin Hubble discovered the
universe is expanding Einstein quickly became
convinced that he was right and called this
cosmological term, including it, his biggest
blunder.
Seventy years later, late nineteen nineties,
cosmetologists found that in fact the universe
does need that term because it’s expanding
faster than it used to and that sort of term,
the one Einstein originally proposed, is the
only way we know to do that.
But of course that doesn’t answer the question
of what this stuff is.
Give me a show of hands if you’ve heard
a little bit about quantum physics; if you
have a smattering of quantum physics.
Okay, like Heisenberg’s uncertainty principle.
There’s a couple of ways we can think about
Heisenberg’s uncertainty principle.
One is that you can’t exactly know where
a particle is at a given time, or you can’t
know how fast it’s moving, you can only
know about one or the other, and the more
you know about one the less you know about
the other intrinsically.
This isn’t a matter of what we know and
what we don’t know, this is the actual state
of the particle, it’s ambiguous where it
is.
Not at one place in one time, it doesn’t
want speed, it’s smeared out over space.
The other way to think about it is in terms
of energy and time.
It says that the amount of energy a particle
has isn’t exactly well-defined and when
something happens, when an event takes place,
isn’t exactly well-defined, they’re smeared
out as well.
One consequence of this is that even in totally
empty space, stuff can pop into existence.
If the universe doesn’t know how much energy
is there, it can borrow a little, it can suddenly
have more than it used to.
So if you take an empty space, our current
understanding is that electrons and positrons
pop out and then destroy each other a short
period of time later.
This is going on all the time.
So I picture space, and if you look close
enough, to look like this.
It’s kind of a billowing soup; particles
popping into and out of existence constantly.
This is not something you can ever prevent
from happening, it’s built into space, it’s
built into the fabric of our universe.
It doesn’t matter what’s there or what
you take out or put in, this is always going
on underneath.
So our current best thinking about dark energy,
is that this going on everywhere makes it
such that a cubic meter of space just has
a certain amount of energy built into it.
There’s nothing you can do to take it away
or put more in because this is going on everywhere,
because this quantum nature of energy of space
and time, space contains energy intrinsically.
This is a pretty good picture, I’m pretty
sure all of my quantum-minded colleagues would
agree with this picture because there should
be energy tied up in space because of these
sorts of processes, but the problem is that
when we calculate how much dark energy there
should be from these processes, we get a number
that is off by 120 orders of magnitude.
I don’t know if you’ve ever been wrong
about something that badly.
It’s like, “how many siblings do you have?”
“um, three” “no you have 3 times 10
to the 120.”
You’ve got it really wrong, you’re just
not this wrong very often.
It’s a really big number, and furthermore,
if dark energy was as abundant as our calculations
said it should be, then the universe would
have started accelerating expansion right
out of the gates.
Right out of the big bang, and it would’ve
grown so fast that we never would’ve never
have had galaxies, or stars, or planets, or
even atoms, none of that would have ever formed.
Life would never have been remotely possible
in a universe where there’s that much dark
energy, so we seem to be in a universe where
somehow all the positive and negative contributions
to dark energy are very precisely cancel,
leaving with only a little bit left.
This is not a very comfortable answer, it
seems like we’re in a very peculiar, maybe
lucky universe, but maybe that’s telling
us something.
Oh, it’s worth emphasizing, it’s a really
big number.
So in this vacuum of space there are so many
processes going on and somehow these processes
balance against each other in such a way that
they give a very small contribution, but that
contribution that we noticed given to the
vacuum energy or dark energy for our universe.
One possibility that could resolve the amount
we observe is so different than this number
that we predict is that maybe there isn’t
one universe, but there are many many universes,
and some of them, in fact almost all of them,
there’s roughly ten to one hundred times
too much dark energy and life never forms,
and maybe one out of ten of them there’s
ten to the one hundred and nineteen times
too much dark energy, and life never forms,
and then maybe, ten out of the one hundred
and twenty of them there’s our amount of
dark energy and we find ourselves in that
one just because that’s the only place life
can find itself living.
This is called the anthropic principle which
basically says if a conscious observer exists
somewhere, they have to exist somewhere that
conscious observers can exist.
The idea that we can apply this sort of reasoning
to explain things we observe in our universe
is pretty interesting and a very controversial
idea.
So just to wrap up: we’re at a very exciting
time.
I feel extremely privileged to be a cosmologist
at this point in human history.
We have big questions we’re addressing,
there’s a lot we don’t know, and that’s
way better than being a scientist in a world
where you know everything.
That doesn’t sound very fun at all.
There are big discoveries to be had, I hope
I get to see them and I think I will.
Maybe we’re on the right track, maybe the
WIMPS I’ve been talking about, or the supersymmetric
particles are the right answer, but if they’re
not, then I’m thrilled to find out what
the right answer is.
I don’t have a horse in this race, and few
of my colleagues do, we just want to know
the truth, and it’s really exciting to have
these questions put before us at this grand
special moment in intellectual history where
we can ask these big questions and hope to
answer them.
That’s really what it’s about to me, thanks
for your attention, thanks for the invitation
to come here to Auburn.
I’d be happy to talk with any of you afterwards.
If there’s time for questions I can do that
or if there’s not I’ll talk with you individually
afterwards, so thank you very much.
