[MUSIC PLAYING]
[APPLAUSE]
STEVEN S. GUBSER: Hi, folks.
My name is Steve
Gubser, and this is
my colleague, Frans Pretorius.
We are the authors of "The
Little Book of Black Holes,"
which is really hot
off the presses.
And there is some
copies over there.
I hope there's a few left.
And we'll be sticking
around to sign if you
want a version that's signed.
So our book is about
black holes and about
Einstein's theories of special
and general relativity.
And what I wanted
to do to start is
to talk about how time
behaves in special relativity,
because when we get to general
relativity in black holes,
it'll help us a lot to
have warmed up with the way
special relativity works.
So let's just do a first
demo, which I have to admit
is a bit of a fake.
These stopwatches, if they
were accurate to a femtosecond,
would be just right
for this demo.
But somehow, I couldn't get
hold of the more accurate ones.
Anyway, so we're going
to do the twin paradox
as it's normally understood.
I'm going to run across
the room and come back,
while Frans stays still.
And we're going to each run
our stopwatch, starting on 3--
1, 2, 3.
[WATCH BEEPS]
I'm going to go like this,
a some constant velocity,
more or less, and
then come back.
And 1, 2, 3.
FRANS PRETORIUS: Oops, shit.
[LAUGHTER]
I'm 7 seconds.
STEVEN S. GUBSER:
And I'm 6 seconds.
That's good.
Because of time
dilation, I managed
to have less time elapse.
I say just kidding, because
the actual difference
between our times was
approximately 1 femtosecond.
I'm actually now younger than
Frans by about a femtosecond.
And so when we commuted
to New York City,
we actually gained a
little bit more youth.
Or if you maintain a regimen
of jogging every day,
it does actually keep
you slightly younger.
So let's just see this
same thing in an animation.
I've got, now, me, I suppose,
running the other way across
the stage-- go for it, Frans--
holding a stopwatch.
And then I accelerate
to run backward.
Meanwhile, I've got Frans with
a fictitious friend Fred here.
And I suppose that I go
for a full 60 seconds.
But you can see here
I've arranged things
so that I'm moving really fast,
which I can't in the demo.
I'm moving at a significant
fraction of the speed of light.
And so my clock really does
run significantly slower.
You can really see it.
Now, the first thing
that people tend
to say when they
see the twin paradox
is if motion is really relative
the way Einstein taught us,
why can't we look
at it another way?
Let's go to the next animation.
Why can't we look
at it this way?
Go ahead.
Where I consider myself to
be stationary and I consider
Frans to be the one who's
moving back and forth.
Why can't we look at it that
way if motion is relative?
And the answer is, yes,
motion is relative,
but acceleration
is something real.
Because when I got to
the end of the room,
I had to actually work at it
to turn around and come back.
While I'm actually moving
at a constant velocity--
OK, if I were like frictionless
or something like that,
I could just coast and
my motion would be, then,
physically equivalent
to standing still.
So it's really the acceleration
which distinguishes between me,
the guy whose clock runs
slow, and Frans, who's
clock runs at the normal time.
This is wall time,
namely the time
that some distant
observer would receive.
OK, so let's understand
a little bit more
of the physics of why
time has to do this.
And the claim is that if you
think about it just right,
you can not only see
that time must run slower
for the accelerating
observer, you
can even derive one of the main
formulas of special relativity.
So let's now think about this
particular demo or animation,
where instead of an
ordinary stopwatch,
Frans and I are going to
carry little photon clocks.
And we measure the way
time passes according
to how many times the
photon goes up and down
and up and down.
And so for the moment,
I've got a stopwatch also
so that you can compare and see
that these are two equivalent
ways of measuring time.
Only the stopwatch,
this stopwatch,
who knows how that works?
It might have
gears or something.
The way the photon clock works
is actually closely related
to the way atomic clocks work.
So it's what really is sort
of physically transparent.
And so far we're not having
me or Frans move at all.
But now let's see,
indeed, what happens
if I do my little
dance of running
across the stage
with my photon clock.
And the claim is that my photon
clock does get out of sync with
Frans's.
As you saw, the photon is
going up and down more slowly.
What's transparent about that?
Well, let's look at
two more animations
that I hope it
will become clear.
I'm now going to trace the
path of the photon as it goes.
And what you can notice,
if you look closely,
is that the overall velocity of
the photon, the overall speed,
is actually constant.
It changes its direction.
The velocity changes direction
and goes across and back and so
forth, but its
speed is constant.
It's always the speed of light.
And it's the same speed
that Frans's photon
experiences going up and down.
But Frans's photon makes
it up and down more times,
because all it's doing
is going up and down.
Whereas my photon has to do
the left-right motion too.
And so that keeps it from going
up and down as many times.
The point is that
encapsulates time dilation,
because time is nothing
more than how many times
the photon goes up and down.
Nothing more or less.
So if we buy into that, we buy
into that picture, like I said,
we can actually derive
one of the main equations
of special relativity,
but see it in the demo.
Now I'm just going to
move across stage in--
whoops, we've got a
little software problem.
FRANS PRETORIUS: Oh, sorry.
I forgot to reset.
My problem.
STEVEN S. GUBSER: This is the
sin of using global variables
when you should use
local variables--
[LAUGHTER]
--because the path is
in a global variable.
OK, never mind.
I'm a physicist, not
a computer scientist.
So I write sloppy code.
Anyway, here is a
photon doing what
it ought to do, following
me going across the stage.
And I decided to have
a simpler trajectory
where I do not
accelerate, I just
run at a constant
velocity across the stage.
And as a result, the
photon's trajectory,
my photon's trajectory
is straight,
and it follows the hypotenuse
of a right triangle.
It has a rightward
component, where
it's going at a velocity v,
which is my velocity running
across the stage,
obviously somewhat
less than the speed of light.
Although in this illustration,
I made it actually
nearly the speed of light.
And then there's a
downward component
of the photon's
motion, which I define
to be c times the time tau
that I perceive as elapsing.
This is the crucial
point, that I
define my time, my proper time,
in terms of how much distance
the photon manages to
track in my own frame.
And that's why this side
of the right triangle
is the speed of light times tau.
And now we get to
the point where
we can do just a little bit of
math and come to the punchline.
I say, Pythagoras's
theorem says the sum
of the squares of the two
sides of the right triangle
equals the square
the hypotenuse.
Now, this unknown mysterious
thing was my proper time.
We can solve this Pythagoras
equation for my proper time.
And you get the time
dilation equation,
just as Einstein
derived it in 1905.
So the point that I'd
like to make here,
the takeaway message, is that
special relativity is simple.
Once you make the one assumption
that the speed of light
is the same in all frames,
as measured by any observer,
provided they're
moving at a constant
but relative to other observers,
once you make that one
assumption, just
ordinary plane geometry
is sufficient to derive
pretty much the whole subject.
And so, for instance,
in our book,
one of the things we do
with a very similar setup,
like a photon clock setup,
is we explain how to derive E
equals mc squared
with similar logic.
Now obviously, you can't do
that all with plane geometry,
because there's a little bit of
physics in telling you what e
is and what M is and so forth.
But if you just follow
your nose in understanding
what the physics concepts
are, then a little bit
of plane geometry is
enough to get even
into the main depth
of special relativity.
But general relativity
is quite a bit different.
And I'm going to
turn it over to Frans
to have a first go with that.
FRANS PRETORIUS: OK,
so now we want to--
eventually, the goal is to
explain what black holes are.
And the black hole
solutions that were first
discovered by Schwarzschild very
soon after Einstein discovered
general relativity, it's
surprisingly simple.
The geometry is so incredibly
beautiful and simple.
But what it implies is very
bizarre and very confusing.
In fact, Einstein didn't
accept a lot of the aspects
of those solutions.
He never believed
in black holes,
even until the day
he died in 1955.
So Steve introduced one
aspect of special relativity,
time dilation.
So relative motion introduces--
observers perceive different
time based on relative motion.
So I'm going to
explain one aspect
that we would describe black
holes from the perspective
of time dilation.
So now we have to go
to general relativity.
And what is new about
general relativity,
so as special relativity is a
theory about space and time,
or spacetime, but where
as in special relativity,
space time is flat.
It's given by this thing
called the Minkowski metric.
Now, in general relativity,
spacetime can be curved
and it can be dynamical.
And what produces curvature in
spacetime is matter and energy.
So for example, this cartoonish
picture of the Earth, I mean,
the Earth has a lot of matter.
It's a very heavy object.
And so in general
relativity, Earth
is curving spacetime around it.
We're sort of
representing it here
with this-- imagine the
curvature of spacetime
to be the surface.
And so you can imagine that
the Earth is denting it.
So the Earth produces
curvature in space and time.
One aspect of that curvature
connecting to the time dilation
is curvature produces
time dilation regardless
of relative motion.
So in special relativity,
when we were moving relative
to each other, that we
perceive time dilation.
But now, what the
Earth is doing is
if you had a clock, someone
that's just sitting there
on the surface of the
Earth, like we are,
and someone very, very
far away, the clocks
near the surface
of the Earth will
run a little bit slower due
to the curvature of spacetime.
OK, so we're going
to use this idea
that curvature introduces time
dilation to get to black holes.
You can go to the next slide.
So as I mentioned, in
general relativity,
it's matter and energy
that produces curvature.
To produce more
curvature, the theory
says you need to take a certain
amount of matter and energy
and make it as dense--
denser and denser,
or more compact,
and you will produce
more curvature.
So let's take,
again, the same idea
of characterizing curvature by
the sort of denting the surface
and just take now a star here.
Say, imagine the sun.
Of course, the sun is much, much
more massive than the Earth.
About 10 to the 32 kilograms.
And it's about a million
kilometers across.
At the surface of
the sun, there's
quite a bit more curvature.
And so more time
dilation than here
at the surface of the Earth.
But now what relativity
says, if we could somehow
compress the sun down to
a much smaller radius,
so where the surface used to be,
it would be exactly the same.
But now we're taking all
this matter and energy,
compressing it into a
much smaller volume.
And so now if we get closer to
that higher curvature region,
there's going to be
more time dilation.
And that's sort of what
this sequence is showing.
Now, a star like the
sun, when it uses up
all of its nuclear
fuel, it's eventually
going to go supernova.
And the core, the
remnant, is going
to collapse to something
called a white dwarf, which is
almost as massive as the sun.
But now it's much
more compressed.
It's about the
size of the Earth,
a few thousand
kilometers across.
So if it goes near the
surface of the white dwarf,
there's going to be
quite a lot of time
dilation, a lot of curvature.
And now we can say,
well, can we go further?
How much time dilation, in
principle, could we get?
Well, for stars
that are, perhaps,
10 times the mass
of the sun, when
they go through the
nuclear burning phase,
they lose all of the
energy to prevent--
to hold them up against gravity.
When they collapse down,
they won't collapse down
to a white dwarf, but
to a neutron star, which
is an incredibly dense object.
Again, these things weigh
around the mass of the sun,
but a typical
neutron star might be
10 to 20 kilometers in radius.
So something the mass of the
sun compressed down to something
the size of Manhattan.
It's almost absurdly
dense to think about it.
Now, for neutron
stars, the curvature
is so strong near the surface
that the time dilation
becomes significant.
Things that we could
easily think about.
It might be a factor
of 20% to 30%.
So if you were on the
surface of the neutron star,
your clock would run
slower by 20% to 30%
compared to someone
that's far away.
[INAUDIBLE] let's go further.
We don't think that there's
a form of matter that's
more dense than neutron
stars, but suppose there is.
Supposed we could contract
a neutron star even further.
Like what this image
is suggesting is
the more we pressurize, the
stronger the curvature becomes.
So you can think, well,
can we compress it down
to a kilometer?
Can we compress it
down to a centimeter?
So the curvature
becomes very, very large
and the time dilation can become
an arbitrarily large factor.
And the answer is no.
In relativity, something
very, very interesting
happens when you try
to compress it to
within what's called
the Schwarzschild
radius of the object.
So for something like
the mass of the sun,
that's about a radius
of three kilometers,
or a diameter of six kilometers.
So if you try to take
all of that matter
and compress it
down, when it reaches
to a point of that
Schwarzschild radius,
this character of
spacetime starts to change.
And spacetime undergoes what's
called gravitational collapse.
And surprisingly, at that
surface, which isn't really
a surface, it's a
place in spacetime--
so don't think of
it as a surface.
We define it as a surface.
It's a sphere of
a certain radius.
There, time dilation
goes to infinity.
So if you were at
that finite radius,
your clock would stop relative
to an observer's at infinity.
But if you imagine trying
to compress something,
actually, that's a
bit of a misnomer
to think that time
is actually stopping.
But spacetime is really
changing character.
The matter collapses, collapses
down to a singularity,
and that's a black hole.
So now you can explain--
Yeah, let me use a
couple of my simple demos
to reinforce what Frans is
saying out time dilation.
What I've got here
first is an illustration
of how time runs at different
elevations in a Schwarzschild
geometry.
And this is even relevant
right here in this building.
So let's watch it again.
You see that my clock,
being relatively high
up in the
Schwarzschild geometry,
runs faster because
I'm experiencing
less gravitational redshift.
And Frans's runs slower.
But then Schwarzschild geometry
is really all around us.
It is an excellent approximation
of the spacetime geometry
that we experience above
the surface of the Earth.
So if this Frans on the
first floor of this building,
and here we are
on the 10th floor,
then it really is true that
our clock runs a little faster.
In other words, the
people on the 10th floor
can get more work done
in a day, but the price
is they age quicker
in the process.
No free lunches.
And you see now,
wall clock time here
is an arbitrarily
distant observer.
And such an observer's clock
runs even faster than mine.
After all, I am still
fairly close to the horizon.
And everything is so
simple, just because I'm
not up to drawing
these beautiful funnel
shapes for Schwarzschild,
but otherwise, it is actually
a mathematically accurate
depiction of the Schwarzschild
metric.
Now, let's have one
more thought experiment
where Franz and I start
at the same elevation
in the Schwarzschild
geometry, and I jump.
But we're assuming that I'm
a tremendously good jumper.
So even though I'm close
to the black hole horizon,
I can still do it.
I move up at nearly the speed of
light and then I come back down
and land.
OK, so now, a striking feature
is that my clock has gone
through more ticks than Frans's.
And if you remember that the
twin paradox that we started
with, that might seem
very odd, because when
we did the twin paradox,
the accelerating observer,
namely me, the guy who ran
across the stage and back,
was the one you had
fewer ticks on his clock.
But now it seems like it's
the accelerating observer who
has more ticks on his clock.
That is a secret to another
pillar of relativity
theory, which is that the
natural motion of objects
is the path that maximizes the
time elapsed for that object.
So actually, Frans,
in this animation,
is doing a very unnatural thing.
He's somehow hovering at a
fixed elevation in a black hole
geometry.
So we'd have to have
like a rocket ship,
or he has to be standing on some
surface that's very unnatural.
Whereas I can just
boost off, and then
for the entire duration
of the animation,
I am following a perfectly
ballistic trajectory
with no force at all.
So most properly, I
should think of myself
as the free falling
observer and Franz
as the less natural observer
who manages, therefore,
to stay younger.
OK, and just for
entertainment, I
modified this demo while waiting
to come upstairs so that I
would not stop when I got
back down to Frans's level.
Let's just say I keep
going toward the horizon.
OK, so what's happening
there, something extreme
happened there.
Let's make sure it's
really clear on the screen.
Time dilation got
extremely intense.
See, my clock is running
and running and running.
And I got more
ticks on my clock.
But now it's slowing
down tremendously.
And this is because I'm getting
close to the black hole horizon
and my gravitational
redshift becomes extreme.
OK, so now we're
going to just explain
a little bit about what
I mentioned before,
where the character of
spacetime changes completely
once this gravitational
collapse happens.
So what I mean by that
is outside a black hole,
like this spacetime is
what's called static.
So current there is
a strong curvature,
but it's not changing with time.
And in particular, one
way to describe it,
if you're some distance
away from the black hole,
you just experience
the same curvature.
And so let's measure distance
by radius from the black hole.
So the Schwarzschild radius,
that's the event horizon.
Again, for something
the size of the sun,
that will be the radius would be
about three kilometers-- sorry,
the mass of the sun.
So if you're some
distance away, you
experience strong
curvature, but the spacetime
doesn't change at all.
Now, if you approach
the horizon,
and then when you
cross it, spacetime
changes character completely.
And in particular,
what you thought of as,
at this distance, radius, and
what you thought of as time,
the time coordinate,
completely flip character.
They completely switch roles.
And so as you cross the
horizon, spacetime suddenly
becomes intrinsically dynamical.
And all of space and
time is being swept down
to the singularity,
r equal zero.
And what's sort of
alarming about that,
well, first of all,
that's also one
way to think of why the surface,
this area of the Schwarzschild
radius is an event horizon.
You can never go back.
If we postulate, well,
you can't go faster
than the speed of
light, or another way
of saying that is you
only go forwards in time.
There's a natural direction,
which is forwards in time,
and you can't go
backwards in time.
So let's say there's a
black hole over here.
I've read our
book, so I know you
shouldn't cross the horizon.
But somehow I accidentally
wander and I cross the horizon.
And again, the horizon
isn't like a solid surface.
It's really just this
point in spacetime.
And so, oh dear,
what's happened?
Well, I've gone
from larger radius
to smaller radius
crossing the horizon.
And I'm going forwards in time.
And now I've said, suddenly,
when you're inside the horizon,
radius is actually
measuring time.
And so by continuity, the
forward direction in time
is going to smaller radius.
So suddenly, once you're inside,
spacetime has become dynamical
and this flow of
spacetime is taking you
from larger to smaller radius.
So now I panic,
because I've heard
that there's a singularity
inside that black hole,
and say, OK, how can I get out?
Well, getting out means you want
to go to a larger radius again.
But you can't,
because that would
mean going backwards in time.
And so you're doomed, right?
Because of the nature of time,
you can't escape the horizon.
Why are you doomed?
What's bad about being
caught up in this flow?
Well, there's a
singularity to the geometry
at what was r equal zero.
That's sort of the origin.
And again, when you're
outside the black hole,
you can say, OK, r equal
zero, that's where.
I can avoid it.
But now you've cross
over and suddenly it's
like, where's the singularity?
What can I do to avoid it?
Which direction should
I accelerate in?
But that's the wrong
question anymore,
because r doesn't measure
radial distance anymore.
It measures time.
And so the right question
is, when is the singularity?
And the answer, it's in your
future, so you can't avoid it.
And in fact, it doesn't matter.
again, so it doesn't
matter which direction you
accelerate in, you're going
to get to the singularity.
And in fact, there's this
principle that Steve mentioned,
that the natural path,
you maximize the time
that you take.
So if you want to survive for as
long as possible, just let go.
Just relax and freefall
into the singularity.
Don't accelerate.
OK, let me just
also mention this.
This also tells us
why the singularity
is such a bad thing.
Because this r coordinate
that outside is radius,
inside is time,
serves two purposes.
One is it also tells
you what the area
of a sphere of that
particular radius, right?
So it'll give you some sense
of how large space at a certain
radius.
It's the same
outside and inside.
So inside it's also measuring
the area of the sphere.
So now you cross the black hole.
You're at a certain radius.
But now time going
forward means radius
decrease, so that
means space is really
collapsing down to a point.
And even worse, what
was time outside
is now a coordinate that
represents distance.
And that distance is
being stretched out.
So this radius-- the
area of the spheres
are being squashed down to
zero, and the radius diverges.
So this is a sort of
spaghettifying singularity.
Just by the nature
of space and time,
everything gets
stretched and squeezed
into an infinitely thin line.
So very bad place.
OK, so with all of that
description, you say,
that sounds bizarre.
It sounds kind of ridiculous.
And that's perhaps why
people like Einstein
never really bothered
to take this aspect
of the Schwarzschild
solution seriously.
He accepted that it describes
things far outside of bodies
like the Earth, but the
material in the Earth
means that inside, it's not
the Schwarzschild solution.
It's something different,
which is perfectly fine.
So he didn't really spend too
much time thinking about it.
He dismissed it as unphysical.
But then over the last 40, 50
years, essentially starting
in the '60s and '70s,
through a combination
of theory and
astronomical observation,
we started to think
that there actually
are these things out there,
that black holes actually
might exist in the universe.
As I've just explained, it's
a very bizarre prediction.
So you want to say, if we're
going to say that there really
is something so bizarre
happening out there,
that there's someplace
out there where
this gravitational
collapse is happening,
where time completely
flips on its head
and drags everything
down to a singularity,
to paraphrase Carl Sagan,
it's an extraordinary claim.
We need extraordinary evidence.
So we can go the next slide.
What evidence do we have?
Until a couple of
years ago, when
LIGO made their historic
discovery, which
we'll talk about a
little bit later,
I said the evidence was
getting very, very strong,
but it was all circumstantial.
And here are a
couple of examples
of the good evidence that
there was, but circumstantial.
This is a picture of looking
towards the dynamical center
of our galaxy.
So it's about 30,000
light years away.
And so this-- it's a
very small frame of view,
just a fraction of
a light year across.
And this is showing
that astronomers--
so these bright
objects here are stars.
And so it's showing astronomers
over the past 20 years
have been tracking the
positions of these stars.
And you can see,
well, they're orbiting
what looks like the dynamical
center of our galaxy.
But there's nothing there.
So they orbit-- there's
obviously something
that's keeping them in orbit.
And if you just
apply Kepler's laws,
you can deduce
that there must be
something that's 4.4 million
times the mass of the sun.
So that is astonishing.
So here's something that's
the mass of the sun.
It's bright.
But there is something that's
four million times the mass
of the sun and we don't see it.
What could it possibly be?
So that doesn't show
it's a black hole,
but if it were a black hole,
that would be consistent.
Because a black hole that
large would have a radius
of about 12 million kilometers.
So at 30,000 light
years away, it's
going to be subpixel
size on that disk.
Another example
with good evidence
that's been gathering
over the years
is in the so-called
stellar binary systems.
So this is an artist's
depiction of a star in orbit
around a putative black hole.
And again, similar to this,
what is observed is-- well,
the black hole isn't observed,
but this star is observed.
And so this star is wobbling
back and forth with time,
but its companion isn't seen.
And again, you can
apply Kepler's laws,
that for these stellar
mass black holes,
there are many
candidates where it's
inferred that the companion
is 10, 15, 20 times
the mass of the sun.
And again, the puzzle, what
could possibly be that massive,
composed of ordinary matter,
and that we don't see it?
So again, it's not proof
that it's a black hole,
but it's consistent.
If it were a black hole,
that's exactly what
it would look like.
So over the years, the
evidence has been gathering.
But as you can see,
it's circumstantial.
We're not seeing the
black hole, we're
seeing the effects of the black
hole on surrounding stars,
or the start in this case.
Now, that all changed
a couple of years ago.
And you've probably
all seen this.
I hope you have.
This was the first
gravitational waves
detected by the
LIGO collaboration
that represents the in-spiral
and merger of two black holes.
So briefly, stars can be binary.
Stars can collapse
into black holes.
So black holes can
be in binaries.
So two black holes can
be orbiting each other.
If it's, again, a single
isolated black hole,
it's like from outside,
it's a static spacetime.
Nothing happens.
But if you have two
black holes in orbiting,
you've essentially got
masses and energies
that's accelerating.
And general relativity says
that when that happens,
you can actually produce
gravitational waves, which
all these ripples in the
geometry of space that
propagate out at
the speed of light.
So two black holes in orbit are
producing gravitational waves,
but that's carrying away
energy from the system.
And so the way that that
reacts back on the binary
is that they spiral in.
So the system is losing
energy to gravitational waves.
The closer they get, the
faster they start to spiral,
the more they emit.
So it's sort of a
runaway process.
Initially, it starts
out very, very slowly.
So these black holes probably
formed a binary billions
of years before they merged,
but it slowly ramps up.
And then it's a runaway process.
And we're seeing
the last few orbits
of the life of this binary
as the two black holes
orbit, spiral into each other,
and form a larger black hole.
Why this-- in terms of showing
that this is black holes, why
it's different, sort of
qualitatively different
from before, I said
before was circumstantial.
Because we're
seeing other things.
We're seeing photons and
inferring they're black holes.
But here, this pattern,
the structure of the waves
is really coming
from the whirling
motion of spacetime about
these horizons of a black hole.
So it's really telling
us what geometry
is doing in the vicinity
of the horizons.
Of course, it can't tell
us what's going on inside,
so that's always
going to be a mystery.
And if relativity
is right, nothing
can escape the
black hole, not even
information in
gravitational waves.
But at least up until these--
from outside towards this point
where gravitational collapse is
presumably happening,
this is really
a signature of what spacetime
is doing right at that point.
So I'll briefly, just
in words, describe
what gravitational waves
are and how LIGO actually
detected them.
So again, they're ripples in
the geometry of space and time,
and they propagate outwards.
And one property
of them is, say,
if you imagine a
gravitational wave that's
moving directly into the
screen, it's changing distances.
It's a rippling geometry.
But it changes distances
in a very particular way.
So there are what are
called two polarizations.
One polarization-- if
the gravitational wave
is moving, at one instant
it'll stretch the screen
in a horizontal direction,
while simultaneously
squeezing it in the
vertical direction.
And as the cycle happens, it
will oscillate back and forth.
So stretching and
squeezing in what's
called the plus configuration.
Sort of just by the geometry.
The other polarization is
called the cross polarization.
It's just rotated by 45 degrees.
So the key thing is, as that
gravitational wave propagates,
it transfers to the
direction of propagation.
It's inducing this [INAUDIBLE]
change in distance.
And so to measure a
gravitational wave,
we want to measure
changes in distances.
We want to construct a ruler.
It turns out that it's an
incredibly sensitive ruler
that we have to construct.
And that's what LIGO has
been doing over the last--
since the '60s it was planned.
It's been under funding and
construction since the '90s.
And now Steve is going
to demonstrate that.
STEVEN S. GUBSER:
OK, so first, let's
see it with yet one more
animation, where what I've done
is I've taken a picture
of an interferometer
directly from the
LIGO collaboration.
I think this will play
better if I change size.
OK, let's see how this goes.
So first, I want to
show this plus pattern
of gravitational radiation,
what it would do to this device
that I'm showing on the screen
if it hits the screen, just
as Frans described.
So it's stretching and
squeezing the device itself.
And I tried to animate
it in such a way
that that beam
splitter in the middle
stays more or less stationary.
But what we mean by stationary
in a dynamical space time
is a little bit up for grabs.
Anyway, what we
definitely can know
is what is the relative
length of the two long arms
of the interferometer.
And the way we measure it
is we have some laser here
which shoots coherent photons.
Half of them go through the
beam splitter straight on
and half of them
go the other way,
but it's a quantum phenomenon.
So really, every photon
explores both paths.
The photons bounce
back off the mirrors
and they recombine
at the beam splitter.
Each photon recombines with
itself, because remember,
it explored both paths.
And depending on whether
those paths are exactly
the same length or
slightly different lengths,
the photon might
either reinforce itself
or cancel itself
out as it travels on
to the readout device.
And so we have a little
demonstration scale
model of LIGO which is really
working just as I showed.
Let's get the houselights
down a little bit.
This is a little bit dim.
And the reason it's
dim is that we're
using a teeny weeny little
laser, like a laser pointer.
We have bigger lasers
or more powerful
lasers in the
physics department,
but they wouldn't let me
take one to New York City,
because you walk through
Penn Station with one
of those things and you're
really taking your chances.
So you see that these stripes
are drifting down the screen.
The reason that's happening
is the whole device
is warming up a little
bit, and so all the angles
and so forth are just
changing very, very slowly.
It has nothing to do, really,
with the main physics.
To illustrate the main physics,
first let me block one beam.
So if I block one beam, you see
the stripey pattern is gone.
And what's left is
just some dim pattern
with a little bit
of features and such
which only have to do with
the particular optical devices
that I have in here.
So any flaw in the
mirror will show up
as a little feature
on the screen.
So if I block the other
beam, you can see,
again, the pattern goes away.
It's only when the two
beams recombine that you
get this quantum
interference between the two,
just as I described.
And then it's thrown up on the
screen with a defocusing lens.
OK, so now that the thermal
expansion has pretty much
settled down, if I joggle
this thing in any way,
you can see that the
interference pattern responds
a lot.
And the reason that
it's responding
is that just a light
touch on the base
is causing the relative length
of these two arms, this one
and this one, to change by just
enough, like micron size is
enough, in order for
the interference pattern
to shift by about one stripe.
See how just a light
tap is about enough
to cause the interference
pattern to shift by one stripe.
Whereas what LIGO's
really seeing
is it's seeing something
that's more vibrational.
Like if I do this, you can see
that it does ring a little bit.
You can see these things
go brrrr, like that.
That is what LIGO is actually
watching, except they watch it
a heck of a lot better
than we can watch it here
with this eensy weensy little
demonstration scale model.
I can measure
differences in length,
of relative length
in these two arms,
to about the micron scale.
LIGO, with four kilometer
arms and similar light,
although far more intense, is
able to measure relative length
differences that are less
than the diameter of a proton.
So it's an exquisitely
sensitive device.
I still don't understand,
quite honestly, exactly
all the tricks that
allow them to measure
things that are such small--
length that are so much
smaller than the wavelength
of light that they're using.
So it's quite an achievement
that, as Frans mentioned,
was decades in the making.
And there's certainly more games
we could play with this device,
but let's save it
until afterward
and go back to the
question of, what
are these gravitational waves
and how is a black hole really
producing them?
FRANS PRETORIUS: OK, so I
think the next thing would just
be an animation of
what I described.
This is a computer simulation
of two black holes merging.
And these are
parameters that are
similar to the first
event that was detected.
So you can play it.
So these are two black holes.
They're orbiting each other.
These green-- this
haze that's going out,
this is a representation
of the gravitational waves.
And so what you'll notice
is as they're orbiting,
the amplitude is increasing.
So that's because they're
actually slowly spiraling in.
Say this is runaway.
The closer that they're
getting, the faster they're
starting to move, the
more energy they emit.
And eventually, it gets
brighter and brighter.
They coalesce.
When two black holes meet,
they form a larger black hole.
And then you see this little
burst of radiation at the end.
And what's left is sort of
this perfectly stationary
rotating black hole.
Now, so there's a
lot of things that
are fascinating
about this one event.
Again, representative--
this is another depiction
of the waveform.
So from the way that
LIGO saw that little path
and became properties
of the black holes,
they were both about 30
times the mass of the sun.
One's a little bit bigger
than the other one.
This is slowed down
tremendously between real time.
And Steve will show
a demo which almost
demonstrates that in a second.
But if they were in
real time, they'd
go, again, a sizable fraction
of the speed of light.
20, 30 times the speed of light.
And this scale is about 1,000
kilometers for this thing.
So that's incredibly fast.
And what's perhaps
more astonishing
is the energy that's
released in this final burst.
So it happens in a few
milliseconds, this final burst
that you saw.
And in that one
instant, if you just
compute the energy in
gravitational waves,
it's brighter than all
the visible starlight
in the universe combined
at that one instant.
That sounds like a ridiculous
statement, but it's true.
So in gravitational waves,
it outshines all the stars
in the universe at
that one instant.
STEVEN S. GUBSER: Frans, I
think we're about out of time.
Why don't I show this.
FRANS PRETORIUS: Right,
so now I think, yeah.
STEVEN S. GUBSER:
OK, so this last demo
is aimed at showing you
analogous mechanical system.
Let's see if we've
got this playing.
You know, I have to
restart QuickTime.
It always does this.
So what I've got is a spinning
disk which settles down
to a stationary state.
It's not really quite like a
black hole merging, of course,
with another black hole,
but it's in the same spirit,
because for starters, it's
exhibiting similar frequencies
of output for similar reasons.
It looks like I'm not going
to have any cooperation here
from QuickTime.
One more try and
then I'm just going
to go straight to the demo.
OK.
There we go.
All right, so this is nothing
more than a spinning coin.
[COIN SPINNING]
It's called Euler's
disk for no good reason.
It's just a spinning coin.
It's settling down.
And you can hear
already that it has
some characteristic frequencies.
And what we've got
over here on the right
is a sound analyzer, which
is picking up everything
that this microphone hears.
So for instance, it's
hearing my voice.
And if I use a tuning
fork, you can get--
[TUNING FORK DINGS]
--a peak, you see,
at about 128 hertz.
So it's noisy.
You can still see that peak.
If I stop talking you
can see it better.
[TUNING FORK DINGS]
And this Euler's disk
takes a little while
to settle down, but
in its final stages,
what I like about it
is that it's exhibiting
the same behavior as
merging black holes in that
the point of contact is whipping
around faster and faster.
And it's emitting,
therefore, a similar kind
of chirp, only in sound that
colliding black holes emit
in gravitational radiation.
And now I'll stop talking
so you can see the waveform
on the spectrum analyzer.
[SOUND OF COIN SPINNING RAPIDLY]
OK, that chirp is very
like the sound of two
merging black holes.
What's not so much
like it is that you
see many overtones here.
You see some down
at about 30 hertz
and then all the way up to a
strong one at about 100 to 150.
That's because it's a
dirty mechanical system.
Just for contrast, let's go
back to one of Frans's slides,
and you can see what a much more
beautiful system these swirling
black holes are.
Let's show it.
So this is what LIGO saw.
Their picture is tilted
90 degrees from mine.
And you see this
is the waveform.
There's the chirp,
same chirp that I saw,
but there's no
overtones, because this
is a very pure tone coming
from the colliding black holes,
but at a rather
similar frequency.
You remember, I was
at about 150 hertz.
They're at about 150 hertz.
So if you could hear
the black hole merge,
it would sound
kind of like that.
So a great discovery.
It really convinces
us that black holes
are in the universe.
And I think that's a good
place to stop for questions.
Thank you.
FRANS PRETORIUS: Thank you.
[APPLAUSE]
SPEAKER 1: Hi, folks.
We have a mic here.
There's no mic set up,
so if you have questions,
I'll just pass this around.
AUDIENCE: So you told us
that close to the event
horizon, the time dilation,
time runs slower compared
to an outside observer.
So essentially, all of the
physical processes at the event
horizon are running slower.
Does that apply also
to the contraction,
meaning ultimately,
does the black hole
actually even form in the
lifetime of the universe,
since the time is essentially
slowing down to a standstill
at that point?
STEVEN S. GUBSER: So
there's a strange kind
of answer to that, which is it
depends on whose clock you're
talking about.
When we look from
outside, as we say,
wall clock observers,
what we can definitely say
is that once a black
hole is formed, then
from our perspective
as outside observers,
nothing manages to fall in.
It all kind of settles
down into the horizon
ever more gradually.
But in terms of black
holes really forming,
that's a bit different, because
the gravitational collapse
isn't complete until
it's really happened.
So I would say that, in fact,
yes, black holes really do
form.
It's best answered
with spacetime.
You have to draw something
like a Penrose diagram
and say that on any
respectable time slice,
yes, there is a black hole
that really has formed.
It's just that the signals move
so strangely in the black hole
geometry that the distant
observer can never
see the signal from at
or inside the horizon.
So that's the way I
try to balance the two
answers, that yes, it happens,
but you can never actually see
the signal from the black
hole, because that's
what a black hole is.
AUDIENCE: So you started
with an explanation
of how time dilation, it
depends more on acceleration
than actual velocity
of the observer,
but then when you got into
the Pythagorean theorem
explanation, that made perfect
sense to me if you were just
thinking about velocity
and ignoring acceleration.
So I got a little
confused about which way
I should be thinking
in terms of changing
velocity or constant
velocity, and how
that affects the dilation.
STEVEN S. GUBSER: Yeah,
the reason for this
is that it feels more
valid to compare clocks
at the same place.
So if I ran across the stage
and stopped my clock over there,
I could manage it with
constant velocity.
But then you might doubt that
my notion of time over there
was the same as
the one over here.
And so that's why I felt obliged
to go there and then come back
a couple times to
illustrate that there was
something real going
on here and that
necessitates the acceleration.
But when we get to this
business of actually deriving
the formula, then
it's a heck of a lot
simpler to idealize
and say, look,
let's consider a perfectly
straight velocity.
What I could have done to
bridge the gap between the two
is I could have said, when
I get across the room,
then I turn back
instantaneously.
And then I would
have a perfectly--
my photon would go down
like this, like I showed,
and then it would
just go right back up.
So I could manage it at the
cost of infinite acceleration,
and then my geometry would
have been perfectly correct
and I would still be able to
measure time at the same point.
Yes.
AUDIENCE: I'll just go with it.
So when we look at
atomic theory and what
Einstein and Oppenheimer and
guys were doing with atomics,
right, we did something with
that, either creating the bomb
or creating nuclear
fusion reactors.
You're talking about
quantum mechanics.
And even Google's Explore are
using that for computation.
From an application and
exploitation perspective,
has there been
research in what we
might do with this as a
species or something like that?
Did that question make sense?
STEVEN S. GUBSER: I
have the GPS answer.
AUDIENCE: [INAUDIBLE].
FRANS PRETORIUS: Yeah, did
you mean with black holes
or with general relativity
or gravitational waves?
Yeah, GPS is a good answer.
STEVEN S. GUBSER: Yeah, so
gravitational positioning
satellites are way up
there in some elevation
so high above the Earth that
the gravitational redshift
effects matter.
And in order to make
GPS work as well
as it does within
a few feet, you
have to have timing in those
satellites figured out really
well to, I guess, it's about
the few nanosecond level.
And that's done with
atomic clocks, by the way.
But it's also done by
understanding the Schwarzschild
metric.
Now, as for really practical
applications of black holes,
per se--
maybe you should tell them
about the Penrose process.
FRANS PRETORIUS:
So really, if we
did happen to have a black
hole that came wandering nearby
and didn't run into us, in
principle, if it was rotating,
we could go to that
black hole and mine it
for rotational energy.
And in summary, that's probably
one of the most efficient forms
of energy that we could get.
If you think of nuclear fusion,
if you think of like the rest
mass equivalent of energy
that you get from that,
that's less than
a percent, or it's
like a fraction of a percent.
In theory, if you had a very
rapidly rotating black hole,
you could get upwards of almost
30% of its rest mass equivalent
in energy extracted from it.
So for example, if we formed a
back hole the mass of the sun,
there'd be a whole sun's
worth, E equals mc squared,
of energy in that black hole.
If it's rapidly rotating, about
30% of that can be extracted.
It's like taking a
third of the sun,
E equals mc squared, and
converting it to energy.
But that would
require us finding
one of these black holes.
And I mean, there've
been science fiction,
and even Freeman
Dyson has sort of
imagined advanced
civilizations powering
themselves using black holes.
AUDIENCE: So I have a
kind of weird question.
We were billions of light years
away from this collision when
it happened, and
so we detected it
with this exquisite detector.
Presumably, if you
were closer to it,
I mean if you were
like close to it,
you'd be destroyed by this
enormous energetic event.
But there must be
at some distance
where you would feel it.
What would it feel like?
FRANS PRETORIUS:
That's a good question.
So I can imagine--
so the thing is
that you're going
to be stretched and squeezed.
And let's say if you're about
100 times the Schwarzschild
radius of this thing
away, so for this event,
say you were about
10 kilometers away,
then the amplitude,
the fractional change
is going to be something
like 10 to the minus 3.
So you might be stretched and
squeezed by a few millimeters.
So that's actually, I think--
I mean, you'd feel it.
A few millimeters over
the length of your body
isn't too bad.
The thing where I'm a
bit more concerned about
is the frequency is very high.
So this thing,
like at 100 hertz,
being stretched and
squeezed at 100 hertz,
that might mess up
with some things.
But for example, you'd
probably hear it.
Like it will affect
your ear drums.
They'll be stretched
and squeezed,
so they'll probably be a thing.
But I mean, you'd feel it.
You'd feel this very
rapid vibration.
Yeah, but you'd have to get
very, very, very close to it.
AUDIENCE: Thanks.
AUDIENCE: My question's
about the detection
of the gravitational waves.
It seems like if you kind
of rotated the instrument,
like 45-- if you had it
originally at the ideal angle
and then you rotated
it 45 degrees,
you wouldn't see
it at all maybe.
And also, you were
saying it was like--
like the time was very short.
Like if the machine had
turned off for a millisecond,
would you have just
totally missed it?
And how frequently do two
rotating black holes collide?
I guess, how lucky were
they that they saw it,
or was it pretty likely that
they would see something?
FRANS PRETORIUS: I think
it was quite likely.
One thing is we didn't know how
frequently these black holes
mergers could happen.
And there was actually a lot
of doubts in the community
that LIGO would actually work.
So there's a whole story about
that that goes back decades.
But you're right, if it
hadn't been on at that time,
we would have missed it.
And presumably, these
things are happening
in a galaxy the size
of the Milky Way,
once every million years.
And so that's why LIGO
has to be sensitive enough
to, at least in its
range, sweep up at least
about a million galaxies.
So we have a chance of
seeing like one per year.
But those rates are uncertain.
But you can imagine,
say hundreds of billions
of galaxies in the universe,
so every day, there's
several dozen or
several hundreds
of these mergers happening
somewhere in the universe.
And the waves come.
They cross the Earth
very, very rapidly.
So if LIGO isn't on when
it passes, we've missed it.
So I think-- we're
running out of time.
I mean, I can talk
about this for a lot
if you were
interested, but there's
a lot of things
about this event that
was very fortunate the
way that they had--
they had just turned
the instruments on.
They actually didn't think they
were ready for a science run.
Because of that, they
didn't [INAUDIBLE]..
It took them a long
time to understand
that it really was a signal.
Someone thought
they were playing
a joke or hacking the system.
And it took them a long
time to convince themselves
that this was a real signal, and
then just nature being lucky.
Like we actually didn't
expect such heavy black holes.
We had no idea about the rate,
so there was a lot of luck,
both from nature and the
way the experiment worked.
STEVEN S. GUBSER: Let
me add a quick answer
to this business of
being insensitive
to the other polarization.
You're quite right that if you
got only the cross-polarization
when you were ready for plus,
then you wouldn't see it.
And each detector in LIGO
is sensitive to only one
polarization.
However, the signals
that we can imagine
have a mix of both
polarizations present,
and so you're going to see it.
That's not a problem.
FRANS PRETORIUS: Right.
So yeah, the intensity is going
to depend on the orientation,
but you won't miss it
completely because of that.
AUDIENCE: So a question on that.
How do we know
these are actually
like a binary black
hole system and not
dilation of spacetime ether
or some other explanation?
FRANS PRETORIUS: Right, so
because of the very particular
shape of the waveform, this
is what's equal to chirp.
So it increases in amplitude
and it reaches a maximum
and then decays.
So the exact shape is very
characteristic of black holes.
So if I you want to play devil's
advocate you can say, well,
is there something
else in the universe
that might produce this?
And well, so far we don't know.
I'd say that there's nothing
that we know of that could
produce a signal like that.
Another side of the question
is, could it be noise?
Because are these things,
they're measuring distances.
They're incredibly sensitive.
So I mean, they can take
the tiniest earthquakes that
happen anywhere in the world.
One example, they can
detect just regular waves
crashing on the oceans
around the United States.
An incredibly
sensitive instrument.
So you have to also
make sure that noise
wasn't responsible for that.
And incidentally, that's
why there actually
are two detectors, one in
Hanford, Washington State, one
in Louisiana, separated by
a few thousand kilometers.
And so one way that they
can vet for noise sources
is they have to see the same
thing separated by most--
the light crossing time.
So if the gravitational
waves happen
at a certain orientation,
they'll sit instantaneously.
The maximum time
difference could
be if it first hits one and then
travels and hits the other one.
So the time that light--
so 10 milliseconds or so.
So yeah, some very
good questions.
And the thing is this looks
exactly like what we--
when we saw the Einstein
equations for black hole
mergers, it looks exactly
like a black hole merger.
But yeah, those are things
that need to be considered.
SPEAKER 1: Cool.
Thank you.
We are out of time,
so we'll end here.
STEVEN S. GUBSER: Thank you.
[APPLAUSE]
