現実を再考する。空間、時間、重力 (Rethinking Reality: Space, Time and Gravity)

字幕表動画を再生する

[MUSIC PLAYING]
And all of you here are in for a treat today.
Sam Gralla, who I'm very impressed with,
is going to tell us about one of the most amazing things
that science has done in a long time.
And that's the measurement of gravity waves.
And he will describe it to us, and at the end of the evening
we'll have a quiz.
[LAUGHTER]
But Sam is a theorist working on gravitational physics
and relativistic astrophysics.
He's interested in the strongest gravitational
and electromagnetic fields in the universe,
which occur near black holes and neutron stars.
And you heard a little bit about this last week.
Sam applies techniques from diverse communities,
relativity, astrophysics, particle physics
to study the physical processes occurring
in these extreme environments.
His PhD is from Chicago, and his postdoctoral work
is from Maryland and Harvard.
And we're really lucky to have Sam as one of our faculty
members.
Sam, where are you?
[APPLAUSE]
Well, what a pleasure to be here in this beautiful hall,
in this great university in this wonderful city.
I'm a newcomer to Tucson.
I've been here less than two years.
So I thought I'd start by telling you
the story of how I came to the University of Arizona.
When you're a young theoretical physicist, you apply widely
and you hope you get some interviews--
which, fortunately, I did.
Now, a job interview for a professor job
is a little different from a normal job interview.
It's really more like 20 or 30 interviews right
after each other.
You meet with everybody-- professor
after professor, half an hour meetings.
You barely have time to pee.
If you're lucky, in the midst of all this
you get to meet with the dean.
Now, I had a thing I did with deans on job interviews.
The first thing I would do when I got in the dean's office
is I'd take out a book and I'd start reading it.
That would get the conversation started, usually
with something like, what are you doing?
And then I'd say, you tell me one thing--
if you're in a vehicle moving at the speed of light
and you turn on your headlights, do they work?
[LAUGHTER]
And Dean [INAUDIBLE] said the U of A
was the only one who did not immediately
throw me out of the room.
OK, I made that one up.
That's a recycled Steven Wright joke.
But the comedian Steven Wright has his interviewee in his joke
ask a really deep question.
You go at the speed of light, you
turn on your headlights, what happens?
This is a good question for two reasons.
First, it pushes us outside of our comfort zone, right?
You think you kind of know how light
works from living with light all around you,
but as soon as you ask a question involving where
you're moving like the speed of light,
you get a little confused.
Maybe you don't understand light so well,
because you're used to not moving that fast.
The second reason Steven Wright's question is a good one
is because it's reasonably precise.
It's not some vague, can you make light stop?
It's some pretty precise sequence of actions.
You get in your car, you get up to light speed,
and you pull the lever that would normally
turn the lights on.
What happens?
What happens?
These kinds of questions that are reasonably precise
yet push us outside our comfort zone
are called thought experiments.
And Einstein really was the pioneer
of the thought experiment.
He called them gedanken experiments in German.
This is not exactly the kind of thought experiment
Einstein did, but it's close.
And the answer to this particular conundrum
was given to us by Einstein.
The answer is you can't go that fast.
[LAUGHTER]
Seems a little unsatisfying, but wait.
Einstein didn't mean your car won't go that fast.
That's not what he meant.
He meant you just can't go that fast,
nothing can go that fast-- not your car, not a truck,
not a motorcycle, not a plane, not a spaceship,
not an ambulance, not a backhoe--
we have lots of those in my neighborhood right now--
not a garbage truck, not a fire truck--
I have a two-year-old, he really likes trucks.
He knows about suction excavators and so forth.
None of your favorite desert animals
can go that fast-- coyotes, road runners.
You know those wolf spiders that seem like they're
going the speed of light?
Those ones can't go that fast.
You can't hit a baseball that fast, a hockey puck.
No elementary particle can be accelerated that fast--
absolutely nothing can go the speed of light.
That's what Einstein taught us.
There's a universal speed limit.
[LAUGHTER]
Now, this speed limit is not Einstein's limit
where he'll come give you a ticket if you violate it.
This is a law of nature.
You simply cannot go this fast, no matter how hard you try.
That seems well and good.
We have the authority of Einstein to back it up.
But if you were a physicist around Einstein's time,
you might say, hey, wait a minute, mister.
That doesn't make any sense, because of the following.
I don't know about you guys, but I
have memories from when I was a kid riding
in the backseat of my car, parents
driving me on the freeway.
You're watching the scenery go by, and then
all of a sudden, whoosh, a car whizzes by you.
Of course, they're just driving 60 miles an hour or so too,
but they're going in the opposite direction.
So to you, they're going 120 miles per hour.
Then there's a formula, v equals v1 plus v2,
that if you wanted to, will tell you how to compute this.
And it's really kind of indisputable, this formula.
What is speed?
It's how far you go in how much time.
So if the car up here on the left is going 60 miles an hour,
and in an hour then he'll be 60 miles to the right,
and the other car will then in that same hour
be 60 miles to the left, so in one hour
the relative distance is 120 miles.
So they're going 120 miles an hour--
seems obvious.
The person who is skeptical of Einstein
now says, well, what if I'm going
at 75% the speed of light?
Now this obvious formula tells me
that I measured the other car, [WHOOSH] the one going
by me, moving at 150% the speed of light,
which is supposed to be impossible.
So here's another thought experiment
that seems to reveal something self-contradictory
about this universal speed limit.
We now have a situation that theoretical physics
calls a paradox.
We have two laws that we really believe,
but they're incompatible.
You can't have the universal speed limit
and the formula v equals v1 plus v2.
If you were a lesser physicist you might think,
OK, well we know v is v1 plus v2 That's
utterly trivial and obvious, so Einstein must be wrong.
But if you're Einstein, you think,
we don't really have any good experimental evidence
that v equals v1 plus v2 when you're
moving near the speed of light.
We've only done those experiments
at 60 miles an hour, which might as well be standing still
compared to light.
So which of these do we keep and which do we discard?
We keep the speed limit.
It turns out, that formula is wrong.
Now, as Professor Dienes emphasized in the first lecture
in this series, if you were here,
physics doesn't discard laws .
We don't establish laws and then find out they're false.
Instead, we realize that certain laws may not
apply as widely as we thought they did.
In this case, v equals v1 plus v2 is perfectly
true at 60 miles an hour.
But it is not true near the speed of light.
And Einstein derived the correct law.
It's now up there on your right.
You don't have to worry about the details in the law.
The point is, it reduces to the old law when you're going slow,
and it's compatible with the other law of nature.
So we've resolved the paradox.
So now, you're not going to measure 150% lightspeed.
If you did the measurement, you would in fact
get 96% lightspeed.
If you actually got your Doppler radar,
this is what you would measure, the other car moving relative
to you.
So everything is happy with the idea
that nothing can go faster than the speed of light.
So what have we learned?
Is it about cars?
Well, it would also work for trucks--
[LAUGHTER]
--motorcycles, planes, spaceships, ambulances,
backhoes, dump trucks, fire trucks, wheel trenchers,
suction excavators.
All of your favorite desert animals would observe this law.
All of your favorite balls, if you played sports,
would observe this law.
Elementary particles.
It's true for everything.
When you think about it, it's not really
about the stuff of the universe.
This law doesn't care if you're a Gila monster or a backhoe.
This law is about something more fundamental.
It's really about space and time itself.
Now, why do I say that?
Well, think about how I argued a minute ago
that this original v equals v1 plus v2 law was so obvious.
I said, well, the car up there is
going to be 60 miles to your left after an hour,
and the other car's going to be 60 miles to your right.
So they're 120 miles apart in one hour--
120 miles an hour.
That argument gives a wrong conclusion.
The only slop in that argument are
the concepts of space and time, the idea
that if one goes 60 this way in an hour and the other
goes 60 that way in an hour, they're now exactly
120 apart in exactly one hour.
That seems obvious to us, but that's not actually
the way space and time work.
Einstein taught us that you can't just
add space and time together in the simple way that you think.
The theme of our lecture series is rethinking reality.
And this was a big one.
This was 1905, special relativity.
Einstein really rethought reality in a big way.
Let me ask you another question.
If I have a feather and a hammer and I let them go,
which hits the ground first?
Well, in this room, the feather would float down
and the hammer would go wham and hit the floor,
maybe damage the stage.
But if we did this experiment on the moon,
where there's no air--
there's just gravity-- in fact, the feather and the hammer
would fall at the same rate.
Now, this is something that has actually
been known about gravity since the time of Galileo.
But the Apollo astronauts actually did this on the moon
to dramatize it.
There is actually a video of dropping a hammer and a feather
on the moon.
So this dramatizes something that's unfamiliar about gravity
but absolutely true-- that gravity, like the other laws we
have been talking about, acts on everything in the same way.
Can you guess what I'm going to put up on the screen now?
[LAUGHTER]
That's right.
I could drop a truck, a motorcycle, a plane,
an ambulance, a backhoe, a Gila monster, a bark scorpion,
and a wolf spider.
They would hit the floor at the same time if there were no air.
Gravity acts in the same way on everything.
Now, here's Einstein's perhaps greatest insight
in a life full of great insights.
Gravity, since it acts the same way on everything,
is also somehow not about the stuff it's acting on.
It's more fundamental.
It too is just about space and time.
Einstein had this idea, and five minutes later it
was still an idea, and 10 minutes later it
was still an idea.
And it took him five or 10 years,
really, to flesh this idea out and turn it into equations.
And the very first thing he had to do to flesh this idea out
was to start listening to his mathematician friend
Hermann Minkowski, who had been harping on him saying,
no, no, no, time and space aren't separate in your theory.
In your theory, Einstein, you should think of time and space
as spacetime.
They need to go together.
So Einstein got on board with this idea that there should be
spacetime-- three dimensions of space and one dimension
of time--
and that somehow, gravity should just be spacetime.
And through much hard work, he hit on the idea
that what gravity is, is the curvature of spacetime.
Now, that's a kind of weird set of words.
Why would he say that?
Well, we all kind of know what curvature
is for objects in space.
The surface of the earth is curved,
or I could take a piece of paper and curve it in front of you.
We'd all agree on what curvature meant.
And there are mathematical equations
that have been known for a long time that
describe the curvature.
What Einstein realized was that if he
uses the same mathematical equations that
describe curvature of two-dimensional sheets of paper
to the four dimensions of spacetime,
he gets a theory of gravity.
And the equation is up there on the top right.
So this little cartoon up here you've seen in other lectures
if you've been coming regularly.
This flexible fabric you see looks two-dimensional
on the board, on the screen, but it's just an analogy.
It's supposed to represent that the four dimensions, all three
of space and time, are curved.
And what makes the curvature is matter.
So the big red blob in the middle might be the Sun.
The Sun makes spacetime curve, and then the Earth
orbiting the Sun, say that white dot,
just follows the straightest possible trajectory
in this curved spacetime.
And that makes it go around the Sun, giving rise to gravity.
Well, this was the hard part.
Once Einstein had these equations
he had done the hard part and then the real fun begins.
And at some level, the fun hasn't stopped since he died.
He and many others after him, including me,
are working out the amazing consequences of that equation
on the top right.
And the consequence I want to tell you
about today is called gravitational waves.
If you really buy into the analogy,
it's actually almost trivial that there
will be gravitational waves.
Because if I wiggled that big red mass in the middle there,
clearly the fabric is going to wiggle.
Waves are going to go out, waves in gravity.
And indeed, Einstein got that equation in 1915.
And in 1916, one year later, he had gravitational waves.
Another good analogy for gravitational waves
is waves on a pond.
I don't know about all of you, but I don't float very well.
So if I go out in a pond and try to float,
I end up kind of thrashing all around
and I look a little bit like the gentleman in that picture.
There's waves going out all around me.
Now, if it was a really big pond-- maybe a huge lake--
and we're on shore and we can't see the man thrashing around,
we might still be able to learn that there
was some thrashing going on, because back at shore
we would see some waves.
So you have to imagine a really still day
where the pond doesn't have any waves on it at all.
You're sitting on the shore, then all of a sudden you
see some ripples come in.
You might be able to learn from those ripples--
you could put a bob in the water to measure the ripples--
and you might be able to learn that there was thrashing
around going on out there.
And if you're really good, you might
be able to tell certain properties, like how
big the man was, how hard he was thrashing,
what frequency, and so forth.
That's really the basic idea of gravitational waves,
except now, instead of a pond, we have spacetime.
So you have some thrashing around in spacetime.
Here we have a pair of distant black holes--
more on that later.
But they're thrashing around in spacetime.
And so gravitational waves go out, and back on Earth
you can try to measure these waves.
Well, how do we do that?
This is physics.
We clearly need lasers.
That's how you do it.
You build two machines-- one in Washington state,
one in Louisiana-- with big lasers.
I'm going to explain that in a minute.
But here's a movie, just to get you oriented to the process.
Two black holes orbit and merge.
A burst of radiation goes off across the universe.
Maybe it encounters some other civilizations on its journey,
millions or billions of years.
Finally, the gravitational radiation
reaches us here on Earth.
So we'll zoom in to Earth, and you
will see an absurdly exaggerated movie
of what the waves do to Earth.
They stretch and shrink it.
They distort it tremendously in this absurdly exaggerated
video.
Here's the burst.
[LAUGHTER]
And then the waves are gone off on their journey
across the rest of the universe.
Now, those waves were made by black holes.
But we don't need black holes to make waves.
I'm going to make some waves right now.
I am shaking my fist, and I'm launching gravitational waves.
I'm launching gravitational waves to the back of the hall.
I am launching them to the people in the front.
Can you feel the power, the awesome power,
of the gravitational waves washing over you?
I'm shaking harder.
I've doubled the strength of the waves.
I am now changing the frequency.
The waves are now in resonance with the human gut.
Soon you will feel very nauseous,
and it will get very messy.
Is anyone feeling nauseous?
[LAUGHTER]
Yeah.
So it is true that moving matter makes waves.
Any motion of matter disturbs spacetime, sends waves out.
And it is true that the gravitational waves
stretch and compress and stretch and compress.
This is among the many things that Einstein calculated.
This is what the waves actually do to you.
First you feel a little tall, then you feel a little wide,
then you feel a little tall and wide.
And you were all in fact getting stretched and compressed
by the awesome power of my gravitational waves.
But you didn't feel it.
So why is that?
Well, for the answer, we're going
to turn to Einstein himself, 1916, who gave us this formula.
You don't have to worry about the details,
but let me explain what the symbols mean.
h on the left is the strain.
The strain is the same thing an engineer would
talk about the strain on a bar.
It's a measure of how much stretching or compressing
force.
Here we're quoting the amount of fractional stretching
or compressing if the bar didn't have any internal resistance
to stretching, if it were really just a free-floating blob
of particles and the gravitational wave washed by.
If this h on the left was 1/10, then that free-floating blob
of particles would stretch and compress by 1/10 of its length.
So that's what age the strain is on the left.
And on the right, with this i double dot and this D,
you have some measure of how hard I'm shaking my fist
and how far away you are from my shaking fist.
But the elephant in the room here
is the number on this slide, 10 to the minus 44.
10 to the minus 44 is a number so small
I don't think it comes up even in physics.
I have never heard of a number this small.
This number is as if you took an atomic nucleus
and you lined up atomic nuclei all the way
across the visible universe.
That would take about 10 to the 44 atomic nuclei.
That number, that fractional stretching and compressing,
is as if the whole universe changed by an atomic nucleus.
That is not a lot of stretching and compressing.
And so when Einstein saw this, he surely
thought, well, that was a nice theoretical point I made,
but we are never going to see these.
This is far too small.
This is just theoretical physics, never
experimental physics.
Everything changed when neutron stars and black holes
were discovered in the '60s and '70s.
If you came last week to hear Professor Ozel,
you learned a lot about neutron stars and black holes.
They're unimaginably dense objects.
A neutron star has the mass of the Sun
in the size of Manhattan.
That makes the density of a neutron star
the same as an atomic nucleus.
It's like an atomic nucleus the size of Manhattan.
It's a totally bizarre object.
But if you took two such atomic nuclei the size of Manhattan
and you had them orbit each other at 100 or 1,000 times
a second-- which they can do--
that's a pretty hard fist shake, right?
That might make some gravitational waves.
That can turn that 10 to the minus 44 into a whopping 10
to the minus 21.
[LAUGHTER]
10 to the minus 21 is also an extremely small number.
And if you're me, you give up.
But if you are one of the ingenious experimenters
and theorists who thought up the experiments I'm
going to tell you about next, you say, wait a minute.
10 to the minus 21--
if I build a kilometer-scale device,
that's distance changes of less than a proton radius.
But I think I might be able to do that.
And Ray Weiss at MIT drew this sketch
on the bottom left in an internal MIT journal,
and together with Ron Drever, Kip Thorne,
and many, many other important players,
they put together the Laser Interferometer Gravitational
Wave Observatory, LIGO.
Now, it's a little glib to do this in one slide
and say 40 years, a billion dollars, and 1,000 scientists.
So I want to take some time to really emphasize
how amazing this project is.
As I'm going to describe in the rest of my lecture,
this experiment has made a real breakthrough the likes of which
comes along in my opinion, once every 100 years at most.
This is a real breakthrough.
And this experiment really was 40 years in the making,
and the National Science Foundation
and research universities in the US
provided all the seed funding for the initial prototypes.
The NSF picked it up and funded it starting in 1994.
And over 20 years, they kept it going over changes of Congress,
changes of administration, changes
of NSF program director.
Everybody had the vision to see this risky but high-reward
project through.
And we should be proud, as American taxpayers,
that through our elected and appointed representatives
we supported this project.
So what is LIGO?
There's two LIGOs.
There's one in Washington state.
There's one in Louisiana.
And you can kind of make out that there's a lot of tubes.
In those tubes are lasers.
It's the Laser Interferometer Gravitational Wave Observatory.
Let me tell you why.
This device is called a Michelson interferometer.
This is something that here at the U of A
we teach our undergraduate physics
majors in the second year of their study.
So it's not something I can fully
explain in the next three minutes,
but I can give you the gist.
The basic idea is you shine laser light out,
you split it up, and then it bounces off mirrors and gets
recombined.
And then as a wave wiggles those mirrors, the amount of light
read out changes.
The reason you can do this is because light is a wave.
Light has peaks and troughs.
And when two beams of light meet,
if those peaks and troughs line up, then you get more light.
It's brighter.
But if those peaks and troughs anti-align,
as shown here on the right of your screen,
you get no light at all.
So whether the peaks and troughs are aligned or not
is a very sensitive function of the distance
the light has traveled in this setup.
And so as the wave comes through and wiggles those mirrors,
the peaks and troughs change their alignment and the light
read out on the right of your screen changes in time.
That is the light that LIGO actually measures in order
to measure the changes in distance of the mirrors
as that gravitational wave washes through.
Here's LIGO in a kind of CAD drawing.
It's the same concept, but with lots of bells and whistles.
These tubes are in vacuum--
it's a very large vacuum--
and there's all kinds of tricks they
play to increase the power in the interferometer
and to isolate it from sources of noise.
That's really the hardest part of this whole business.
You're trying to measure distance changes
of less than a proton diameter.
How do you do that when a truck could drive by
and wiggle your mirrors by way more than a proton diameter,
or an earthquake could happen?
What do you do?
You need to be isolated from environmental noise somehow.
And the way they do it is as follows.
They have this amazing gizmo, this four-stage pendulum,
which you see the design for on the left
and some photos on the right.
And this provides two kinds of isolation.
There's active and passive.
Passive isolation is like the shock absorbers in your car.
When you drive over a bump, the bump hits your car pretty hard.
But you don't feel much of that bump,
because there's springs in your car that damp that out
and give you a smooth ride.
They use that kind of passive noise isolation.
And they also use active isolation,
which is like your noise-cancelling headphones.
When you put them on and turn on the power,
they actively cancel out incoming sound waves.
Similarly, they actively drive this system
to cancel out any incoming vibrations in the ground
that it's attached to.
Now, this talk has a lot of eye candy,
a lot of really nice pictures, movies.
But I have to tell you, this is the slide
that still gives me goosebumps.
I remember vividly, almost a year ago
exactly, when this slide was released in a press conference
at the National Science Foundation, which I streamed
here at the U of A for students and faculty and anyone who
was interested.
And when I saw that signal, I thought,
oh my gosh, that's a gravitational wave.
Now, for you, it may not jump out
to be a gravitational waves so obviously.
But let me explain to you why.
But before I do that, the most important thing about this plot
are those numbers on the top left, GW150914.
That is 2015, September 14--
my birthday.
The gravitational waves arrived on my birthday.
[LAUGHTER]
Thank you, universe, for that birthday present.
OK, that's only the most important part
of that slide to me.
To the rest of you, let me take you through it.
First, look at the vertical axis.
It says "strain."
That's that fractional stretching and compressing,
and it says 10 to the minus 21.
This is from the scientific paper.
They did it.
They measured those wiggles that you
see in red are changes in distance of a part in 10
to the minus 21, less than a proton diameter.
The x-axis, the horizontal axis, is time.
Notice, all this happened over just a fraction of a second.
And now let's look at the red signal.
The red signal is what the device in Washington state
measured.
That's the readout, which represents the changes
in distance of the two mirrors.
Is that a gravitational wave?
Is it a truck driving by?
Is it an earthquake?
How do we know?
Well, on the second slide, you see that same data on the right
over-plotted with the data from the other observatory
in Louisiana, all the way across the US.
And they line up perfectly.
There's no way that this same truck drove in front of Hanford
and drove in front of Louisiana at exactly whatever
it is, three milliseconds apart, the time
for the gravitational wave to come from one to the other
in exactly the same way.
They did a bunch of fancy statistical analysis
to put some numbers to say that, yes, that's not what happened,
and yes, that's really a gravitational wave.
But this is why I knew right away
when they put it up on screen that this
was a gravitational wave.
This signal was so loud that you didn't
have to do any of that fancy statistical stuff.
It just says, wow, gravitational waves from outer space.
When we physicists try to understand these signals,
we often convert them to sound.
It's a quick way to get all the information
about amplitude and frequency.
So now I'm going to play the sound for you,
and you're going to hear a bit of a thump.
That's what it sounds like if you just
take the frequency of the wave and convert it
to a sound wave at the same frequency.
You're going to hear that thump twice,
and then you're going to hear the same sound
but upshifted into a frequency range
where your ear is more sensitive to the features.
[SOUND PLAYS]
Hear it again.
[SOUND PLAYS]
So that little whoop--
we have a name for that.
We call it a chirp.
[LAUGHTER]
That chirp's going to come back in about 10 minutes,
so let's remember that name.
Let me play it for you again in case you missed it.
Again, the first thing you hear is a kind of thump.
That's the actual signal.
And you're going to hear that twice.
Then you're going to hear an upshifted version,
then you're going to hear the whole thing again.
[SOUND PLAYS]
Those are the waves from a binary black hole,
two black holes that merged 1.3 billion years ago,
1.3 billion light years away.
The waves came all the way across the universe,
they came to the LIGO experiment,
and they made that sound.
How do we know these are actually merging black holes,
like I said?
Well, again, they did a lot of fancy statistical analysis.
But for this signal, it was so loud they really
didn't have to.
Again, this is a snapshot from the scientific paper.
On the top line, you see the same two plots
that I showed you before--
the data from one interferometer on the left,
and the two stacked on top of each other on the right.
On the second line, you see a theoretical prediction,
a calculation from Einstein's equations
of what the waves look like if two black holes merge.
And then what do you do?
You subtract the two.
You subtract the prediction from the model, and what's left
should just be noise.
And that's on the bottom.
So you see right away that, what is this?
It's the normal noise in the interferometer plus a signal,
which is merging black holes.
Now, the way these theoretical calculations are done
is by a supercomputer.
We take the equations that Einstein wrote down in 1915,
and we solve them on the state-of-the-art super
computers.
Here's a simulation of the orbiting
and merging black holes of the same size and distance
from each other that was measured
by the LIGO experiment.
Now, you see the black blobs and the tracers.
That's just to orient your eye as to what's going on.
All the interesting information is in the arrows and the colors
and the shape of the sheet below them.
That's representing the curvature of spacetime.
You'll see now the simulation will slow way down near merger
so you can see just how distorted spacetime is getting.
It's like a storm in spacetime as the black holes finally
merge, and there's really some cusp-y sharp features.
There's a burst of radiation, and then the waves
are off on their journey across the universe to LIGO.
Here's another fun video.
This is the question, suppose we were actually
near these black holes and we were watching them
in a spaceship.
What would you see?
Well, mostly you'd see the stars behind you.
And you don't see any stars from where the black hole is,
because all the light has been swallowed up by the black hole.
But you also see a very distorted pattern of stars,
because the black holes bend light.
So the stars don't look like their actual positions.
They look very distorted.
And I think we'll just watch the end of this beautiful movie
together.
Let me tell you what they actually
measured for this system.
It's not about just detecting gravitational waves.
It's also about doing astrophysics, finding out
what's out there.
So how heavy were these black holes?
How big were they?
The larger black hole was 36 solar masses,
meaning it had the mass of 36 suns.
So I've drawn 36 dots to represent that.
This was reported in the scientific paper.
The other black hole was slightly smaller.
It had the mass of 29 suns.
And then they also measured the mass
of the final merged black hole, which was 62 suns.
So everything hangs together.
If you take 36 and you add 29, you get 62.
It's simple arithmetic.
[LAUGHTER]
Wow, you guys are good at arithmetic.
Yeah, 36 plus 29 is not 62.
It's 65.
What happened to those three suns of mass?
Where did they go?
Believe it or not, all of those three suns of mass,
the weight of three suns, was radiated away
in pure energy carried by those gravitational waves.
This is e equals mc squared energy,
Einstein's other equation.
Right?
Except if you think about the normal way we use e equals
mc squared energy-- you know, something really impressive,
like atomic weaponry-- atomic weaponry releases
some tiny fraction of the e equals mc
squared energy inside your warhead, which
is not the mass of the sun.
Here you're releasing all of the e equals mc
squared energy of three suns.
That is a ton of energy.
And you're releasing that in just a fraction of a second.
And in fact, during that fraction
of a second when these black holes merge,
they're releasing more energy per unit time.
They're brighter than the whole rest of the universe combined.
As theorists, we knew this.
Einstein's equations are well-established.
We know how to solve them on computers.
We can calculate that when you merge a 36 and a 29
solar mass black hole, you radiate away
three solar masses of energy.
And we talked about this, but now we've actually
observed it happen in nature.
It's fantastic.
Another really fun part of LIGO's story
is this amazing signal I've been telling you
about which arrived on my birthday, September 14,
we almost missed.
The LIGO experiment decided to start their observing run
on September 12.
And the founder of LIGO, Ray Weiss, was dragging his feet.
He said, oh, it's not quite calibrated.
We don't want to start.
Let's get it perfect.
But the younger crowd convinced him to go for it.
And we're glad he did, because two days after they turned it
on--
this thing's been in the works for 20, 40 years--
they measured this spectacular signal.
They saw something else in October,
which was probably a signal-- they're not sure yet--
and then another confirmed one in December.
Then they took the experiment down,
upgraded some of the optics, improved the seismic isolation,
and they're observing again now.
Already, just from one measurement,
we learned a little astrophysics.
First of all, we learned that black holes can find each other
and merge.
That's not obvious.
Predictions for how many black holes there would be
and how often they would merge were all over the map.
Now we have tight constraints on that.
And we really discover a new type
of black hole, because previously, from x-ray studies
there in the purple, we knew there were black holes
of around 10, 15 solar masses.
And from other studies, like what Professor Ozel told you
about last week, we knew there were giant black holes
of a million solar masses.
And now we know that there are also 40
and 60 solar mass black holes.
So that's the weight of these black holes.
What about the size?
Well, to set the scale, I'll give you a map
of the Eastern United States.
I think that's the part I'd like to blot out with black holes
right about now.
[LAUGHTER]
There's the signal I've been telling you about.
That's how big those black holes are.
There's the candidate signal, and there's
the smaller black holes that were also measured.
So these are state-sized objects with the mass of 30, 40, 50,
60 suns.
LIGO is just the beginning.
We have two detectors, LIGO Hanford and LIGO Livingston.
Those are the ones that made the detection,
but there are many more detectors around the world,
either operational, coming online, being built or planned.
And in five to 10 years, we should have all six
of these detectors working.
In Germany, the GEO detector; Virgo in Italy;
LIGO India in India, and KAGRA in Japan.
It's great to have more detectors,
because gravitational waves are a little bit like sound.
You don't really know where a sound is coming from.
If you have two ears, you can sort of
tell where it's coming from, but not very precisely.
If you have three ears or four ears,
you could start to tell more precisely.
And if you have six ears, you can really
start to get a good handle on where
that sound is coming from.
So if we have six detectors, we can really
tell where in the sky the gravitational wave is coming
from, and we can tell our astronomer friends, hey,
go point your telescopes over there.
You might see something interesting.
When we have these six detectors--
and even before-- we have a lot of fun ahead of us.
We're super excited about the first signal
we saw, merging black holes, but we're going to see a lot more.
I'm sure LIGO has already seen more black holes, although they
don't tell people who aren't officially
in the collaboration.
But I've heard rumors.
There are supernova explosions.
When stars end their lives and explode,
they make these giant explosions.
That probably makes some gravitational waves.
We'll hope to observe those.
My personal favorite is merging neutron stars.
Again, a neutron star is matter at
the density of an atomic nucleus.
We don't know very much about matter
at the density of an atomic nucleus.
So we're going to learn a lot of nuclear physics
if we can start seeing a lot of merging neutron stars,
because those waves carry information
about the process of merging.
We'll see rotating neutron stars.
And perhaps most excitingly is the question, question,
question mark on the right, because we've really
opened a completely new window on the universe
here with gravitational waves.
And every other time in the history of astronomy that we've
gotten a new way of looking at the universe,
like when radio astronomy started or x-ray astronomy
started, every time there were expectations,
and there were huge unexpected discoveries.
So perhaps most exciting are the things
we don't know about that we will discover with this new way
of seeing the universe.
I'm going to change gears a little bit
and tell you about my own research.
I work a lot on gravitational waves,
and one question we asked recently
was, what if a black hole spins really fast?
You can spin a black hole, and you can spin it really fast.
You can't spin it at the speed of light.
Nothing can go faster than light.
But you can get it really, really, really close,
at least in principle.
So here's the sound of a wave form
that is from a normal black hole.
This is theoretically generated.
We just made this on our computers
as part of the research.
But this is just a comparison signal
for what a normal black hole merger sounds like.
[SOUND PLAYS]
Right at the end there, there's that [SOUND EFFECT].
That's the chirp.
Chirp is the hallmark, the calling card,
of merging black holes.
All the theoretical predictions have always predicted chirps.
And that's what LIGO measured.
But when we got one of these black holes
spinning really fast, when we finally cracked the mathematics
to let us explore this regime, something very interesting
happened.
It starts the same, but you're not
going to hear a chirp from this rapidly spinning black hole.
[SOUND PLAYS]
It just sits on a single note, and it fades away.
We call that a song.
[LAUGHTER]
It's very different.
It's not [SOUND EFFECT].
It's [SOUND EFFECT].
[APPLAUSE]
So why is this exciting?
Well, in astrophysics, we don't have
great ways of measuring how fast these black holes spin.
But now we can tell that if you hear
a sound that doesn't chirp--
it just sings-- you're looking at a black hole
spinning really, really, really fast.
Now, we gave this black hole a nickname.
And our scientific paper has a funny title
up there on the right, "Inspiral into Gargantua."
If you've seen the movie Interstellar,
there's a black hole called Gargantua.
And it turns out, for the plot of Interstellar
to make any sense at all, that black hole Gargantua has
to spin very rapidly.
It has to spin with 99.999999999999%
the speed of light, 14 nines.
So, is Gargantua out there?
How would we know?
Well, if the next thing LIGO hears, or some other experiment
in the future, if the next thing they hear is this song,
then we've discovered Gargantua.
When I started thinking about this problem,
I wasn't thinking about astrophysics at all.
Rapidly spinning black holes turned out
to be a really good theoretical testing
ground for the following sort of pure theoretical physics
question that I'd like to describe for you.
It's called the black hole information paradox.
At the start of the talk, I gave you
a paradox involving the speed of light being the upper limit
that you can physically go, and this formula, v is v1 plus v2.
That paradox was resolved 100 years ago.
This paradox is still with us today,
and it's really driving theoretical physics,
I'd say more than any other paradox.
In its simplest form the question is,
can you tell what was thrown into a black hole?
So these are thought experiments, not
real experiments.
But we used to do them with cats.
We would throw the cat into the black hole.
And then we started feeling bad about that,
so now we use graduate students.
[LAUGHTER]
That seems to go over a little better.
But in these thought experiments--
not real experiments--
we either throw a cat in or a graduate student in,
and then we ask you to come back later
and look at the black hole.
And can you tell--
in principle, not in practice--
if it was a cat or a graduate student that I threw in?
Einstein's theories say no.
The black hole-- anything that goes into it
is, for all intents and purposes,
gone from the universe.
You will never be able to tell, in principle, whether I threw
in a cat or a graduate student.
But there's another theory of physics
that you'll hear about a lot more in two
weeks with Professor Cheu's lecture, which
is quantum mechanics.
And all the formulations of quantum
mechanics that we know about have a fundamental law
that information is preserved.
In quantum mechanics, you have to be
able to tell, in principle if not in practice,
whether it was a cat or a graduate student.
So there's a fundamental tension here.
And it's really Stephen Hawking who first pointed this
out after discovering some fantastic
properties of black holes that made it very apparent.
His paradox is really still with us today.
Now, I did not solve this paradox, alas,
when I was thinking about rapidly spinning black holes.
But it led to a new prediction in astrophysics,
which just shows the interconnectedness of science.
In the last few minutes, I want to take a step back and think
about where in the history of science and astronomy
this gravitational wave discovery lies.
You may know that light is just one
wavelength of electromagnetic radiation,
and radio and microwave and infrared and ultraviolet
and x-ray and gamma ray are other wavelengths
of electromagnetic radiation.
There's a whole electromagnetic spectrum.
Astronomy really began when Galileo first
turned his telescope to the heavens,
and among other things, discovered
the moons of Jupiter.
You can see his sketches there.
There's Jupiter with four little moons that he observed.
Since that time, we now have astronomy in all
of these different wavelengths.
In radio astronomy, we've discovered incredible things.
That was the discovery of neutron stars, in fact.
Up there in the top left, that speck there is a whole galaxy.
That galaxy is shooting out particles
moving near the speed of light in a straight line for hundreds
of times the galaxy's size until they make this beautiful plume
that we see in the radio.
Some of my other research is aimed
at trying to understand what the heck is going on there.
In the microwave, we can see light left over
from after the Big Bang.
13 billion years ago when the universe was just
a hot plasma--
no stars, no planets, just hot plasma, no elements even.
In the infrared, we can see galaxies,
learn about their structure, trace them through cosmic time.
In the visible, well, we've come a long way since Galileo.
Now if we look at Jupiter with our best instrument, the Hubble
Space Telescope, we get that beautiful image.
That's not a painting.
That's a picture of Jupiter.
In the ultraviolet we can see the storms
on the surface of the Sun and learn about plasma physics
at high temperature.
These coronal mass ejections that wipe out communications
here on Earth-- we can study those, among other things.
And in x-ray and gamma ray, we see the high-energy events
in the universe.
The gamma rays sky looks like that big image
on the upper right there, except every once
in a while when there's a bright flash called a gamma ray burst.
Those gamma ray bursts were actually
first discovered by military satellites
looking for Soviet nuclear tests.
But they pretty quickly figured out
that the gamma rays they were measuring
were actually coming from outer space.
The origin of those gamma rays is still pretty much a mystery,
and it's a mystery LIGO might help unravel.
But that's the electromagnetic wave spectrum.
Gravitational waves also have a spectrum.
And where are we in observing this spectrum?
Well, we're just like when Galileo first pointed
his telescope to the sky.
We've made one observation.
It's tremendously exciting, these merging black holes,
but it's one observation at one tiny frequency
band in this whole spectrum.
As LIGO becomes more sensitive, we'll
start to hear higher frequency things--
maybe supernovae and merging neutron stars.
There are space-based detectors in the works that
will measure the monsters of the universe-- supermassive
black holes, black holes with millions or billions of times
the mass of the Sun.
There are other detectors that get us
to even lower frequencies, where we might hear cosmic strings--
or if we're very lucky, gravitational waves
from the Big Bang itself.
Let me summarize.
I started the evening telling you
about how a century ago Einstein discovered
a deep new reality of interconnected space, time,
and gravity.
He discovered new things about physics.
Those consequences of Einstein's equations were revolutionary,
and they are still with us today.
And 100 years later, one of those consequences
has now been turned into a tool.
We are now using Einstein's gravitational waves
to hear the universe in a completely new way.
And in closing, I want to leave you with two questions.
What will we learn in the next 100, 200
years with this new astronomy?
And what will be the next revolution in space, time,
and gravity?
Thank you very much.
[APPLAUSE]