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[MUSIC PLAYING] SAUL A. TEUKOLSKY: He's the chairman of the United States consortium to participate in the construction of the Square Kilometer Array, which is going to be, when it's finally completed, the largest radio telescope array in the world. On campus, he was the chair of the astronomy department for 20 years. I don't know how he survived that, but he did. And he built up the department to be one of the leading astronomy departments in the country.
He's received many honors and awards. But I'm just going to single out two that are closest to home. One of them was the university set up the Yervant Terzian undergraduate scholarships. And in 2009, an endowment was set up by Chuck Mund, who endowed these Yervant Terzian lectureships.
So that brings me to this year's lecturer, Kip Thorne, the Feynman Professor of Theoretical Physics Emeritus at Caltech. Now, most people when you hear the word "emeritus," you think winding down. In Kip's case, if anything, he's sped up. Not only has he continued to conduct research, but he's taken on a second career as a filmmaker. And I hope we'll hear something about that.
His research has covered the fields of relativistic astrophysics and gravitational physics. And his list of scientific accomplishments is far too long. We could spend the whole hour talking about them. But I'm just going to single out perhaps the most topical to today's talk.
In 1984, along with Rai Weiss and Ron Drever, Kip co-founded the LIGO Project. And he carried out many research contributions to that project. And that led to the successful detection of gravitational waves just in the past few months.
He has contributed also to science education. Many of you know about his textbook on general relativity, MTW, for the initials of the authors. This was the first new textbook on the subject since the 1923 textbook of Eddington.
It was the first book to introduce modern mathematics and modern astrophysics into the teaching of the subject. It was only 1,279 pages long, much to the distress of students with backpacks. But you'll be pleased to know that he has a new textbook coming out later this year on classical physics. And it's shorter. It's only 1,216 pages.
[LAUGHTER]
He has advised over 50 PhD students and many, many postdocs. And he's also received many awards and honors. And I'm just going to mention what I think is the most unusual combination. He may be the only person who is a member both of the United States National Academy of Sciences and the Russian Academy of Sciences. So please help me welcome Kip Thorne.
[APPLAUSE]
KIP THORNE: Thank you, Saul. Can you hear me in the back?
It's a great honor and pleasure to come to Cornell as the Terzian lecturer. I'm very fond of you, Yervant, and have watched the impact that you've had both on astronomy, and on Cornell University, and on the astronomy department-- on astronomy broadly, internationally, and on astronomy at Cornell, and on the university. Your impact has been huge.
I have spend a large amount of time over the decades here, beginning in the 1970s, through the '80s, the '90s, the 2000s. And I've come to love Cornell and love the atmosphere that you have fostered and created within astronomy here at this university. And so for that reason, I'm really very pleased to be giving this lecture.
I want to begin with Einstein 100 years ago last November, formulating his laws of general relativity. I want to give you a little bit of background on that. So I want to begin with Einstein's audacity, which goes back a little earlier. And his audacity has to do with asserting that Newton had to be wrong and he had to be right, in a period when he was a rather young man and Newton was the god of all science.
In 1687, Isaac Newton gave us a framework for the laws of nature that lasted for 218 years based on concepts of absolute space and absolute time, the kind of space and time that we experience as human beings, forces, accelerations, the things of everyday experience. In 1905, Einstein came along with a whole new framework that replaced Newton's framework. It's now been in place for 111 years. And it's based on a principle of relativity, that he formulated, that says all the laws of nature must be the same in every freely moving laboratory everywhere in the universe.
He was asserting a law that would govern all the laws of nature, those that had already been discovered and those that would ever be formulated in the future, and claiming that he knew this law that governed all the laws. And then Einstein, having formulated this and drawn a number of conclusions about it, one of the conclusions is it related to the speed of light. If I measure the speed of light by watching a particle of light, a photon, travel past me or a beam of light travel past me with some sort of signal on it so I can watch how it travels, I will measure a speed of about 300,000 kilometers a second.
If you are traveling at a very high speed, 200,000 kilometers per second pass me, and you measure the speed of light, the question is, do you get the difference then between what I measure and your speed, that is 100,000 kilometers per second, which obviously you have to? But no, you don't. According to Einstein's principle of relativity, you have to get the same 300,000 kilometers per second. That's a rather startling conclusion, which violates all of our everyday experience about how velocities work, that they have to add.
And so you ask how is this possible? And it's only possible because Einstein concluded, in his pioneering work on relativity, that we will disagree about the length of your car, really disagree about how long it takes the car to go past me. And we will disagree about what events are simultaneous. And with all of that disagreement, everything hangs together in just such a way that you'll get the same speed as I get, which makes one queasy when you think, well, something's gone wrong with all of our notions about the nature of space and time. But there's a very concrete way in which it goes wrong, which can be described mathematically. And turns out to be quite beautiful mathematics when you get into it.
Einstein then looked at Newton's laws of gravity. And Newton's laws say that the force of gravitational attraction between the Sun and the Earth is proportional to 1 over the square of the distance between them. The square distance, of course, changes as Earth moves along its elliptical orbit. So you have to say that distant when.
Well, the distance measured at some instantaneous separation, measured at simultaneous moments, the Sun and the Earth, then you get a distance. However, Einstein then asks, the separation D as measured by the Sun or by the Earth? They're going to disagree on what that distance. And instantaneous as measured by the Sun or by the Earth? They're going to disagree about the nature of instantaneity.
And so, therefore, Newton's law of gravity violates Einstein's principle of relativity. The Sun and the Earth are going to disagree about these things. And there is no objective way to formulate Newton's laws of gravity if you go to very high accuracy. Einstein's confusion then was that Newton must be wrong, just because Newton's laws of gravity violate Einstein's principle of relativity, who had a chance to control all physical laws, including Newton's laws and including all that come in the future.
And so Einstein then set out to give us a whole new description of how gravity works. And he came up with the first piece of his description in 1912. I like to call this Einstein's law of time warps. That's not what anybody else calls it. But after you hear me describe it, you'll agree that this is a much better name than anyone has ever used. So I also have some audacity, but not quite at the level of Einstein.
So what Einstein's law of time warps says is that things like to live where they will age the most slowly. And gravity pulls them there. Now, wouldn't you like to live where you will age the most slowly? And gravity pulls you there. And the more you're the location you are at has time flowing slowly then elsewhere, the stronger gravity will be. And Einstein gave us a formula that says, for a certain amount of slowing of time, how strong gravity would be.
And so as an application, the Earth's mass warps time according to Einstein. It slows time near the surface of the Earth. And this time warp is what produces gravity, according to Einstein's law of time warps.
And so if you go in and you do a little calculation by Einstein's formula, and you know how strong the gravitational pull is near the surface of the Earth, you can then compute how much time slows on the surface of the Earth compared to at high altitude. And the amount of slowing is one second in one century. That's the amount of slowing of time that's required to explain the gravitational pull that holds us on the surface of the Earth. That's not very much slowing of your aging.
But it is measurable. It has been measured. And was measured, in fact, in 1976. The first really high precision measurement by Bob Vessot, who, with NASA, flew atomic clocks in a rocket to high altitude. And then telemetered back to Earth their ticking rate and compared it with the ticking rates of atomic clocks on the surface of the Earth. And found perfect agreement, within the accuracy of the experiment, one part in 10,000 or 0.01% agreement with Einstein's law of time warps, rather remarkable.
Now, Einstein also-- oh, no. I don't go there quite yet. Near a black hole, such as Gargantua in the movie Interstellar-- and so I'm going to use Interstellar to illustrate some ideas of general relativity in this talk. Near a black hole, such as the black hole Gargantua in Interstellar, gravity is enormously stronger. So the slowing of time must be enormously greater.
And so, in particular, in Christopher Nolan's Interstellar, there's a planet that's in orbit near the horizon, near the surface of a black hole. And on that planet, one hour of time passage is the same as seven years back on Earth. So a enormous amount of slowing of time, just because gravity is so strong there, the gravity of the black hole. The planet is being held out by its centrifugal force, that prevents it from falling in. But the gravity is enormously strong.
And so you see this. A hundred million people saw this in a movie. And really came to understand in a visceral sort of a way Einstein's law of time warps, the slowing of time.
Cooper, played by Matthew McConaughey, talks to his daughter, his 10-year-old daughter. He tells her he's going to go out into the universe and may go close to a black hole and that they can compare how much time lapses occurred when he returns to Earth. And when he returns to Earth after a few years, she may be as old as he is now.
And, indeed, he goes near a black hole. Some seven years elapse-- or some three hours elapse while he's down near the black hole on Miller's planet. That corresponds to 21 years on Earth. And then when he comes back after three hours of time lapse, she has become Jessica Chastain, a famous theoretical physicist.
[LAUGHTER]
And this is of the things I like about this movie. On the red carpet, at the world premiere in Los Angeles, Jessica, all she talked about was playing a theoretical physicist, and how fun it was to write equations on the blackboard, and be tutored by Elena Murchikova, who was a Caltech graduate student, who was her technical adviser, and me. So that's some of the joys of living near Hollywood.
[LAUGHTER]
So Cooper goes down near the black hole once more. And his daughter grows to be a very old woman. He comes back and meets her in a very touching scene near the end of the movie. But this slowing of time becomes a real, very obvious thing, very powerful thing at Christopher Nolan's hands in this film.
In 1912, Einstein realized if time is warped, then space must also be warped or curved. And again, it was 1976 that one of the first really high precision measurements of this occurred, a measurement that I like very much pedagogically.
At that time, there was a Viking spacecraft in orbit around Mars. And Mars carried the spacecraft back almost behind the Sun. It went very close to being going behind the Sun. And radio signals sent from the Earth to the spacecraft, and then telemetered back to Earth, measured the round trip travel time from Earth to the spacecraft and back, as the paths went very near the Sun.
And the round trip travel time was excessively long when the paths were near the Sun, compared to where they were farther away, longer than you would expect if space was flat, longer by some hundreds of microseconds. And from that extra time delay, one could conclude that space, in here, since these light signals were traveling at the standard speed of light, space had to be warped, that distance had to be larger near the Sun than you would expect. So the shape of the space near the Sun, if you were to think of space as embedded in a higher dimension.
And so this is the two-dimensional surface made out by these radio signals or equivalently by the Earth and the orbit of the Viking spacecraft. And that two-dimensional surface, we can think of it as embedded in a higher dimension, has to be bent down, on a bowl shaped like this. So you could infer to very high precision what that shape had to be. And it agreed with general relativity, again to a part in something like 10,000. So really quite remarkable.
Now, I'm going to use these kind of diagrams. I will call the higher dimensional space in which we imagine surfaces, two-dimensional surfaces, that represent part of our own universe in which they are embedded, I will call that the bulk, borrowing a phrase that comes from modern physics, from string theory. And a phrase that also made its way into Interstellar. So in Interstellar, there is a bulk. Our universe is embedded in a higher dimensional space. And there is at least one huge macroscopic extra dimension in Interstellar.
Now, between 1912 and 1915, Einstein struggled to understand, to discover the laws that govern the warping of space and time. And in 1915, November 25, he presented those laws to us, to the rest of humanity. They are what is called Einstein's field equation, which says, roughly speaking, that the energy and the momentum that are present in spacetime, as embodied in this T funny thing, generate the curvature or warping of spacetime as embodied in that G funny thing, which is called Einstein's tensor.
And that mathematical description, with a lot of underpinning mathematics under it, is the thing that you use to compute things that are related to warped spacetime, such as gravitational waves that I'll talk about, and other phenomena that I'll discuss for you. And this warping of space, that's caused by the energy, the mass, the momentum, is present in space and time. This warping controls the motions of stars, spacecraft, light, and everything else through the universe. So that was Einstein's general theory of relativity, November 25, 1915.
So I want to describe to you a few of the things that Einstein's equation has taught us during this past 100 years. Here's a little list that I could go into. Each of these has large amounts of information and wonderful discoveries tied to it, high-precision tests; cosmology; relativistic mass; physical objects; geometrodynamics; gravitational waves; problems between quantum theory and general relativity; various speculations, like time travel, cosmic strings, and so forth; and the mathematical structure of Einstein's theory. These are all things that physicists have struggled with and made great discoveries with in the last century.
But I've chosen for this talk to focus in on things that involve pure curved or warped spacetime without any matter present. And that's a rather remarkable thing, the idea that Einstein begins with, that you have mass, and energy, and momentum that create warping. But now, I want to talk for the rest of this talk about the warping in the absence of any mass, energy, or momentum.
In particular, for example, with a black hole, I'll ask the question where does the warping come from? And so let me begin with black holes. And I will tell you now that a black hole, although black holes are created by the implosion of stars at the end of their lives, a black hole, once it's created, is made wholly, entirely, and solely from warped space and warped time.
And here is a diagram that depicts that for a non-spinning black hole. The warped space is shown, again, by embedding a two-dimensional surface. This is a slice through the equator of the black hole to get a two-dimensional surface. It's embedded in that higher dimensional bulk. And also, you can visualize it.
So the circumferences gets smaller. But not as fast as they would if space were flat, as you go down toward the horizon. The horizon is down here. The horizon is the surface of the black hole.
And so space, as seen from the bulk, is embedded in a sort of a trumpet horn shape. It has a sort of a trumpet horn shape. It's a weird shape of warped space.
Time flows in a color-coded manner. At the yellow location, time is flowing at 10% of the rate far away. Down at the black location, down here, a black circle, that's the horizon of the black hole, where time is slowed to a halt. It doesn't flow at all.
Because I've removed one dimension, that horizon is a circle. If I put that one dimension back, it would become a sphere. So the surface of the black hole is a sphere. And you can look in at it and you would see, as I will show you in a few minutes, a spherical horizon or, if the black hole spins, a flattened sphere.
Now, on Miller's planet, in the movie Interstellar, one hour on Miller's planet is supposed to be seven years back on Earth. But the closest Miller's planet could be to the black hole, according to general relativity, if the black hole is not spinning, is about here. Well, one hour would be 90 minutes on Earth, hardly any slowing of time at all. You are up in that region in terms of the colors.
And why can't it be closer? Because if it were any closer, the orbit would be unstable and the planet would spiral into the black hole and fall through. It's unstable as a pencil standing on its tip, more unstable than that.
And so after the movie Interstellar came out, there were a number of bloggers who knew a fair amount about science. And they said this is impossible because they knew about non-spinning black holes. No way that you could have Miller's planet be close enough to the black hole to have one hour on Miller's planet be seven years back on Earth.
However, if a black hole is spinning rapidly, it's a whole new ball game. Because a spinning black ball drags space into whirling motion around itself like the air in a tornado. And that whirling motion of space stabilizes orbits. So you can get an orbit, in principle, down here as close to the horizon as you wish because the orbit is held out, both by centrifugal forces and by the whirling motion of space in its vicinity.
And so one hour and seven years is possible, though it's really pushing beyond the limits of what's very plausible. So the name of the game in this movie, in Interstellar, was to have a movie that does not violate any of the well-established laws of physics. And it does not. This certainly is possible.
But you can stretch things about as far as you wish, as long as allowed. And this is allowed, but very unlikely in the real universe, that black holes spin this fast.
Now, in the movie, you see 1-kilometer-high water waves. And I'm going to show you a film clip about that and then discuss it.
[VIDEO PLAYBACK]
- How long for the engines, CASE?
- A minute or two.
- We don't have it. Helmets on.
Brand, copilot, you're up. CASE, blow the cabin oxygen through the main thrusters. We're going to spark it.
- Roger that.
- Locked.
- Depressurizing.
[RUMBLING]
Engines off.
[END PLAYBACK]
KIP THORNE: So that is a rather startling kind of a wave. And your question is, where does it come from? And the answer is related to what is called tidal gravity.
Miller's planet is down near the horizon. The gravitational pull on this side of the planet is bigger than on that side of the planet. Centrifugal forces are keeping the planet from falling in.
So in the planet's reference frame, the average of those gravitational forces is zero because of centripetal forces. And the planet just feels like it's being stretched radially. And it turns out it's squeezed from the sides. This is precisely the way that tides are produced on the Earth's oceans, precisely the same thing. The tidal forces are just a little bit larger here.
[LAUGHTER]
But they are large enough, it turns out, to be able to produce these gigantic waves. And the basic issue is this, that the planet has been deposited in this orbit, near Gargantua, by a gravitational slingshot swinging around an intermediate mass black hole, a smaller black hole. It swung around and got thrown into this orbit.
And this happened relatively recently, as seen by the planet's time. It may have been a long time ago, as seen from Earth. But there's that factor of 60,000 disparity in time.
And the tidal forces then have grabbed the planet. First, they deform it. And then they grab it and they prevent it from spinning. And so it's sitting there, oscillating back and forth, and settling down into a state like the Moon is with the Earth, with the same face always facing toward the planet. But it's in this state of swinging back and forth, back and forth, and settling down.
So you can compute how big Gargantua has to be from the fact that the planet is strongly deformed. And that says that Gargantua has to be a hundred million solar masses. It's the same mass as the black hole at the center of the Andromeda Galaxy, the nearest large galaxy to our own. And its circumference is approximately the same as the circumference of the Earth's orbit around the Sun. So it's a gigantic black hole.
Knowing that, you can then compute the swinging period for this planet as it's settling down. It turns out to be about one hour. And in the movie, there is one wave per hour. So obviously, the oceans must be sloshing back and forth. And the wave is produced by this sloshing. The analog is what's called a tidal bore on the Earth's oceans.
So they slosh. It produces a one-kilometer water wave. These water waves don't break. They're just water waves that propagate without breaking. And that's what we call a soliton. It's a wave that holds itself together, with its own non-linear self-interaction of the wave, counter-balancing what's called dispersion, which would cause the wave to come apart.
Now, it holds itself together stably. That's very much like a black hole, which holds itself together through a nonlinear self-interaction. It's the energy, in the warping of space and time of a black hole, that produces the warping of space and time in a black hole. And it all holds together stably.
These kinds of non-linear phenomena are tremendously important in modern science and technology. And you have here now two examples in Interstellar, one, the black hole; and the other is the water waves. So these are the numbers I just gave you about Gargantua.
Now, what does a black hole actually look like to your eyes if you're up close to it? Well, in Interstellar, we did a computation of that for the movie. We placed a camera in orbit around the black hole. And if you have a star there, light can come to the camera along various paths. It moves along the shortest paths that are possible, in the sense that any neighboring path is a little bit longer in this picture.
And so there's one path there. That's one light ray. Another light ray goes around the other side. Another light ray goes down and spins around the black hole once and comes up here. You can quickly imagine there are an infinite number of possible light rays. And along each light ray, the camera is going to see an image of that star.
And so I gave to the team at Double Negative Visual Effects in London the equations to compute this so-called gravitational lensing. And they computed that then, not just for one star, but for many, many stars, a field of stars. And then for a disk of hot gas around Gargantua.
In the case of the field of stars, here is a still that I'm going to turn into a film in a moment. This black is the shadow. No light can come through that region. If I go back, that's the shadow here. And all of these light rays avoid the shadow. And so none of them can come in from the direction of the shadow because the black hole's horizon is there.
And, in fact, we counted up to 14 images that we can actually see of a single star in here. So each star is producing multiple images. And you watch the images be created and destroyed in pairs. And this is a fascinating phenomenon in optics.
So you look down here, for example. Is it possible to turn the lights down for a minute? If you look down here very close to the black hole, you're going to see suddenly two star images are going to be created. And then, they will move on around the black hole. And then one of them will annihilate, with another stellar image up here.
And all those images come from the same star. It's just the vagary of this gravitational lensing. So let's goes forward.
So it's in here you'll see two images appear very shortly. There, splitting apart. This guy's going to go around and annihilate against another image. And this is a phenomenon that is quite general in physics. It's related to what's called catastrophe theory.
And this is associated with what's called a fold catastrophe. And it's a fold catastrophe or caustic for physicists, a caustic in the geometry of the past light cone of the camera. And when the star goes through a caustic, images are created or destroyed in pairs every time it goes through a caustic.
But it's really a beautiful phenomenon, the gravitational lensing produced by a black hole. But in the movie, you don't see the stars. This is what you see. And this has become the iconic image now for black holes, that you see quite frequently in the popular literature about black holes.
And the question is, why does that look like that? And the answer is what we have is the black hole Gargantua and a disk of hot gas around it called an accretion disk. The camera is just above the plane of this disk. It's a very thin disk, much like the rings of Saturn.
Light from the top, back face of the disk, the light rays go around the black hole, are bent down by the warping of space and time, and come to the camera there. So the camera thinks the top, back face of the black hole is up here. The top back face of the disk is that.
And similarly, from the bottom, back face of the disk, the light comes up to the camera. And that explains this piece of the image. And then the light from the side of the disk goes to the camera and produces that piece of the image. So a very simple explanation of a very iconic and weird looking image of a black hole. And that the black hole you see over and over again in the movie Interstellar.
Now, where do these disks come from is the black hole's tidal forces carrying a star apart. It has tidal forces strong enough to tear the star apart. But in the case of Gargantua, not quite strong enough to tear Miller's planet apart.
And so up here in this simulation, there is a black hole sitting up here in the corner, in that box, and a star that's going to go around it and be torn apart. So if you watch.
[VIDEO PLAYBACK]
OK. Here comes the star around. It was torn apart by the black hole. The black hole, now you realize is right in there.
Some of the hot gas from the star that was torn apart is getting deposited in a disk around a black hole and some of it is being thrown off in this jet. And that's basically where the disks come from for black holes.
We have a black hole that weighs 4 million times as much as the Sun, that sits in the center of our galaxy. Andrea Ghez and her group at UCLA have been monitoring the orbits of stars around that black hole for several decades. With the aid of a group at the National Supercomputer Center at the University of Illinois, they have produced this image, which shows you these orbits of these stars.
You don't see the black hole. But you quickly recognize where the black hole is by how the stars go. They're swinging around the black hole that's in here, rather beautiful.
And by looking at those orbits and applying Kepler's laws to those orbits, Andrea and her team were able to weigh the black hole and find that it weighs about 4 million times what the Sun weighs. Small, compared to the black hole at the center of Andromeda, compared to Gargantua, which is 25 times heavier. But still very, very impressive, down to the center of our galaxy.
There are great prospects to see the accretion disk in the shadow of this giant black hole at the center of the Milky Way thanks to what's called the Event Horizon Telescope. This is made by a radio astronomy, the field that Yervant has contributed so much to, where you combine data from many radio telescopes worldwide, looking at the center of our galaxy, to produce images. It's a collaboration of hundreds of radio astronomers from 34 universities and institutes. You can read about it at this location. Those are some of the telescopes.
And the prospects are excellent, within the next several years, to begin to see, actually see, the shadow of the black hole and the disk around it, much like what you see in Interstellar. I think it's just fabulous that the technology has come this far.
Inside the black holes, there are what we call singularities, which is a domain controlled by the laws of quantum gravity. I want to talk about that briefly and then move to gravitational waves.
So as I told you, at the horizon of the black hole, the event horizon, time is stopped. And so you might ask what happens inside the black hole? What's slower than stopped time?
And the answer is, it turns out that time inside the black hole is flowing downward in what you would have thought was a spatial direction, toward singularities inside the black hole. It's flowing downward. And that's another reason why when something goes inside a black hole, it cannot get back out because the forward flow of time drags it on downward. And nothing can move backward against the forward flow of time.
So there's that reason. The second reason, of course, is because the gravitational pull at the surface of the black hole is infinitely strong if you're trying to resist it, if you're trying to avoid falling in.
Now, in Interstellar, Cooper, played by Matthew McConaughey, plunges into Gargantua, for reasons I'll comment on briefly. And as he plunges in, he tells you when he's crossing the event horizon. And then the camera turns around and pans upward. And you see what it looks like to be inside the event horizon of a black hole, as computed by propagating the light rays from this accretion disk down to the camera.
[VIDEO PLAYBACK]
- OK, I'm nosing down. Approaching the event horizon. Portside, dipping down beneath it, to go through it.
[END PLAYBACK]
KIP THORNE: So there's the disk. Here's the external universe. It now looks like it's inside the disk. And the black hole's shadow is covering more than half of the sky, everything from here on around, over there. And I'll let you think about why the shadow has become so huge. But it's really a lovely image to me.
When you're inside the black hole, there's no problem with the light falling in. They bring you a image of the universe above you. If you're outside, there's no way to get any light or any signals out to you. So it's a one-way process. Here, you have Matthew McConaughey looking up and seeing the universe from inside the black hole.
Now, inside Gargantua, there's a singularity, as seen from the bulk. Again, if I use a diagram, where I show you what this looks like in terms of a surface embedded in the bulk. Well, I've used some artistic license down here to depict something that is a chaotic singularity. It's called BLK singularity sometimes.
That singularity is a place that if you fall in, you get stretched and squeezed by tidal forces in a chaotic manner until you're dead. And then the atoms that your body's made from, get stretched and squeezed in a chaotic manner until they're no longer recognizable as atoms. And then, we don't know what happens because the core of the singularity is governed by a new set of physical laws, called the laws of quantum gravity.
We don't know what they are. But they are likely some variant of what it is called string theory. Though it's also possible that under some context, they're a variant of something called loop quantum gravity or other descriptions. But these laws of quantum gravity have been the holy grail of theoretical physics since 1960. And they control not only singularities inside black holes, but the birth of our universe and whether or not you can have time machines for traveling backward in time.
And so if we could get these laws of quantum gravity, we will learn wonderful things from them. In Interstellar, Cooper goes into this thing, into the black hole, in order to find the laws of quantum gravity. In order to send them back to his daughter so his daughter can learn how to control gravity and save humanity. And so that's why he goes in.
But he cannot go into that singularity. He's dead. But it turns out we've learned through theoretical analyzes in recent years that there are two other singularities created. One created by all of the stuff that falls into the universe, in the rest of the life of the universe, billions of years. It comes crashing in on top of Cooper in a fraction of a second, as seen inside the black hole. That's enormous warping of time.
And basically a shock wave, that is so quick as it hits him, that although he gets stretched by an infinitely strong tidal force, by the time he gets hit, the total amount of deformation of his body is probably enough to kill him, but not infinite. And so we don't know what happens after that.
Or, interestingly, all the stuff that fell in before, a little bit of it gets scattered back toward him, that fell in over the last billions of years since this black hole was formed. A little bit scatters back up, again in a sort of a shock wave, which he does hit in the movie. And where, again, he is deformed by a total amount that is only finite according to the theory.
So again, we don't know what happened. And we hope he survives. In the movie, he survives. And he is scooped up by something called the Tesseract and carried back to Earth. And this is all related to the end of the movie.
And I'm not going to tell you about the end of the movie. But the climax of Interstellar, I'll just tell you that in one of my first conversations with Christopher Nolan, when he joined us, working on the movie-- I'd been working on it already for about five years at that time-- he brought the ending of the movie, along with a huge amount of doubts. It's basically his story, no longer mine and Lynda Obst. We started it. But it's his and his brother's, this movie, Christopher and Jonathan Nolan.
He said to me, I want to have an ending that is as puzzling as the ending of 2001, A Space Odyssey because I've always admired that. But one that is explainable. And then, later on, in a later meeting, he said, I give you the opportunity to explain it.
[LAUGHTER]
And so if you buy my book, The Science of Interstellar, you can get the explanation. And I have to tell you that Chris and I went the rounds, many personal meetings and many telephone conversations, over the details of the explanation before we finally got onto the same page. But it's a fabulous and wildly fancible ending, that is still within the realm of possibility, but rather implausible. That's the rules of the game.
Now, I want to move on and talk for the rest of my time about gravitational waves. I had a version of this talk that I was giving last autumn. And this section did not exist. But something happened between then and now. And so this does exist. And that's what I want to tell you about.
So I want to begin with Albert Einstein in 1916, June of 1916, so a hundred years from a couple of months from now. He published a paper using his Einstein field equations, that he had devised in his general relativity, to predict the existence of gravitational waves.
These waves are ripples in the shape of space, that travel the same speed as light. And they stretch and squeeze things in directions perpendicular to their propagation. So if the waves are propagating into Miller's planet, into the screen, they'll stretch Miller's planet in one direction and squeeze it from the sides. The next half cycle of waves will squeeze vertically, stretch horizontally, and so forth. Or, if they go through you, they'll stretch and squeeze you by very small amounts.
When Einstein did the numbers to compute how strong these waves would be, he got rather disappointed. He concluded in his classic papers on this, in 1916, and then a follow-up paper in 1918, that it was hopeless to think that humans would ever be able to detect these gravitational waves. Well, it was 50 years later that Joseph Weber at the University of Maryland had the audacity to think maybe he could do it and devised the technique and built a set of detectors based on the vibrations of huge cylinders of aluminum.
I met Joe in the French Alps in 1963. We went hiking together at a physics summer school. And I got the bug. He convinced me that this was a wonderful area of research that I ought to get involved in. And so I actually owe my getting into this as a theorist to Joe.
In 1967, Rai Weiss-- when I was a graduate student at Princeton, Rai was a post-doc. And so we knew each other there. We were both associated with the research group of Bob Dicke, one of the great experimenters of the 20th century. I did also theory work with John Wheeler, which was my primary home. But I spent a lot of time with Rai and Bob Dicke's group as well
Rai went to MIT and started a research program, which included going after gravitational waves. And I went to Caltech, started a research program that included the theory of gravitational waves and their sources.
In 1972, Rai wrote what I regarded as probably the most important and remarkable technical paper about experimental physics of all time, at least that I'm familiar with, in which he described a set of gravitational wave detectors that are the sort that appear in LIGO. He invented it. But the basic idea had been invented previously in Russia by Mikhail Gertsenshtein and Vladislav Pustovoit. But Rai didn't know about that.
But they just said, here is an idea. And they didn't really know how to compute how good it could be or what the noise sources were, how you would deal with them. Rai, in this paper, he identified all the major noise sources that we would deal with. In the first generation of our LIGO gravitational wave detectors, described how they could be dealt with, and computed what the resulting sensitivity would be. And concluded that with detectors that had arm-length, as I will show it to you, of a few kilometers, you had a shot at success. And it's really remarkable.
But Rai believed at the time that you shouldn't really be publishing about this until you discover gravitational waves. And so he didn't publish this in the regular literature. He published it in an internal MIT report.
But it quickly became well-known in the field and it got spread to other experimental groups. It became the foundation for other groups to go into this particular way of doing it, including Ronald Drever, at the University of Glasgow, who invented some very important improvements on Rai's ideas, including, in technical words, the invention of making the arms of this thing into Fabry-Perot cavities. Those of you who are not physicists, forget I said that.
So the basic idea of this interferometer, or this gravity wave detector, is you hang mirrors from overhead supports by wires, along the east-west direction and along the north-south direction. When a gravitational wave comes along, it will stretch space in the east-west direction, and stretch the separation between these mirrors in the east-west direction, and squeeze in the north-south direction. Then a half cycle later, stretch in this direction and squeeze in that direction. And a technique called laser interferometry, which I won't talk about the details, is used then to monitor these changes in the separation between mirrors. And so that was the idea.
I had long conversations with Rai Weiss. I had long conversations with Vladimir Braginsky in Moscow, who is another other really great experimenters, certainly in this field, of the 20th century. And I became convinced in the late 1970s that this field was likely to succeed. And so I went to my colleagues at Caltech and said we really should get into it. We should build a group at Caltech doing it. And we imported Ron Drever to Caltech to lead the experimental effort.
And just to give you some numbers then, also, by 1970, the late 1970s, we thought we knew how strong the waves were. I and others had done a lot of work on sources of waves. We had a workshop on sources of waves in 1978. And the conclusion was the strongest waves probably have strengths in terms of the fractional stretching and squeezing of things, of one part in 10 to the 21. That's 0, point, 20 zeros, and a 1 after that, for delta L over L, the fractional change in length here.
And that turns out to be precisely the strength of the waves that were detected by LIGO last September. So we already knew in 1978 where we were going. We weren't sure-- we were quite uncertain about that number. We knew that that was the ballpark. What that means is you multiply 4 kilometers, for a separation between these mirrors and what we ultimately built, by 10 to the minus 21. You get, then, 10 to the minus 15 centimeters, which is the diameter of a proton divided by 100.
So imagine the diameter of a proton is a hundred thousand times smaller than the diameter of an atom. And an atom is-- let's see, I have to get this number straight. It's thousands of times smaller than the wavelength of the light that we're using. And so this is really remarkable to think that you can measure something to that level. But, in fact, Rai convinced me that it was possible.
And so, in 1980 to '83, Ron Drever, and Stan Whitcomb, and colleagues at Caltech build a 40-meter prototype. At MIT, Rai and his group continued to work on a smaller prototype. And they carried out a feasibility study for kilometer-scale interferometers, together with Stan Whitcomb from Caltech.
In 1984, we came together at NSF, with Richard Isaacson and Marcel Bardon at NSF. And Caltech, MIT, and NSF agreed to create the LIGO Project, led initially by Rai Weiss, Ron Drever, and Kip Thorne. We were called the troika in that era. And troika in that era was a phrase for a rather dysfunctional leadership. And that's what we were.
[LAUGHTER]
And so in 1987, in order to be able to go forward, we brought in Robbie Vogt to lead LIGO, take the leadership over from us because we were not functioning terribly well. And it was Robbie, then, who led us through the final phases of getting the groups working together well, and writing a proposal to NSF, and hopefully getting it funded.
Our construction proposal in 1989 said we would first build facilities to house the interferometers. And then we would build the interferometers in two steps, initial interferometers, at a level of sensitivity where, if we were extremely lucky, we would see something. But we probably wouldn't see anything. And then advanced interferometers, with a sensitivity where we should see a lot.
And we had to do it in two steps because the distance from the prototypes that we were operating in that era, or that Rai, and Ron, and collaborators in Europe were operating, from there to the advanced interferometers, was much too big. There was a little hope-- certainly, we couldn't have any confidence of getting here, without going through an intermediate step.
Getting approval to do it in this two-step way-- for just the first step, it was $300 million-- was not easy. We had a lot of opposition from members of the science community. But we convinced the funding agency, all review committees that we faced. And we finally got it approved by NSF and by Congress. And Congress and NSF have stood by us steadfastly all the way through, since then.
In 1994, we brought in Barry Barish, a well-known high-energy physicist, who had led one of the detector groups at the SSC, which had been canceled, the high-energy physics accelerator that had been canceled. And Barry led us through the construction of the facilities. He expanded the LIGO collaboration, from Caltech and MIT, to something approximating what it now is, a collaboration of a thousand scientists, at 75 universities around the world.
We built, under Barry's leadership, the two facilities to house the interferometers, one in Livingston, Louisiana; the other in Hanford, Washington. This is the list of the nations that are now involved in this.
And then Barry led us through the construction of the initial interferometers and their first gravitational wave searches. And then he got stolen away from us by the high-energy physicists again because they wanted to design what's called the International Linear Collider, which involves all the major nations in the world because it's so expensive. And the funding agencies of all these nations and the physicists could only agree on one person to lead that effort. It was Barry Barish. And he was told, if you don't do it, there will be no International Linear Collider. So he reluctantly left us.
And we had a series of directors after that, who did very well in carrying us through the initial searches for gravity waves between 2005 and 2010, with the initial interferometers. We didn't see anything, as expected. The team got a lot of experience with these interferometers and set interesting limits on gravity waves.
Then, 2010 to 2015, we installed these advanced interferometers that we had said we would build in our original proposal. And then on September 14, 2015, we saw gravity waves before we began our first search, while the instruments were being tuned up.
I will return to that after I make a personal comment. Around 2001, right after I had written the science case based on interactions with a lot of other people, written the science case for the advanced interferometers, I basically left LIGO. And I left LIGO because I was very worried that we did not have the community, did not have a capability to simulate the sources of gravity waves. And if you can't simulate them, you won't know what it is you've seen when you see it. And if you can't simulate them, then you also won't know what to look for in terms of shapes of waves. And so you'll have a lot harder time finding the waves.
And so I came to a Saul Teukolsky, who had built and had led a group working in numeric relativity by 2001. For how long? 10, 15, 20 years, for almost as long as I'd been doing LIGO. And said, I'd like to build a group at Caltech, working in collaboration with your group. Import some of your people to Caltech. And I think I can help get larger resources to pull this off, a successful simulation of the sources.
So that's what came to be, simulations of colliding black holes, by what began as a Cornell-Caltech collaboration. It now includes CITA, Toronto, Cal State Fullerton, Washington State University, the Albert Einstein Institute. And I left off Oberlin somehow.
This has now been a 15-year effort. The team, under Saul's leadership, has created what's called the Spectral Einstein Code. Primary authors of the code are Larry Kidder, who's here at Cornell; Harold Pfeiffer, who is now at CITA; and Mark Shields, who's at Caltech. And this is the code that was the primary underpinning for the data analysis that led to the detection of the gravity waves and the understanding of the gravity waves that LIGO saw.
So I have to say that I've gotten a lot of fame as a result of this discovery. But it's because I'm associated with a superb group of people working on the numerical simulations and a superb set of experimenters. And they really make me look good.
And so one of the things that this team set out to do is to build a catalog and dictionary of gravitational waveforms. So if you pick a black hole, pick the binary, two black holes of different masses and sizes, different spins, spinning around different axes, and they spiral together and merge, you compute what the shapes of the gravitational waves will be. The stretching and squeezing is a function of time.
And the idea was to build a catalog of about a hundred simulations, either in a catalog of waveforms, and then a dictionary that says what the black holes were doing when these waves were produced. It's become a more complicated process now that we are seeing gravitational waves going in. When you see a signal, you go in and do a bunch of simulations to pin down the properties of those colliding black holes. So Saul and the team are moving in a new direction, that will be integrated more tightly with the LIGO observations.
The discovery, very quickly. This is from a visualization by Andy Bohn. Francois, I don't know how you pronounce your last name. That's a shame. Where are you?
FRANCOIS HEBERT: Hebert.
KIP THORNE: Hebert. OK. It's truly French. OK. Francois Hebert and Will Throwe, who did a computation of what it would look like if these black holes go around each other, by the same technique as we used in Interstellar to compute what Gargantua looks like and the gravitational lensing in Interstellar. And, in fact, Andy, Francois, and Will helped us find a bug in the Double Negative code for Interstellar, when we found we had a bug in the code. And we could be sure that we had it right. We did some visualizations with the same thing. So it's been great having these collaborators here at Cornell.
So the story is that 1.3 billion years ago, a distance of 1.3 billion light years from Earth, two black holes were going around and around each other. And this is just what it would look like if you were up close to them, rather beautiful patterns due to the gravitational lensing of the light. The images of the caustics are ring here. That's a principal image of a caustic, the past light cone.
Anyway, they're going to come crashing together and merge. And there they have merged. It doesn't look all that impressive until I tell you how much power came out. The total power that came out in gravitational waves during the merger, or a small fraction of a second during the merger, was 50 times larger than the power that comes off of all the stars in the universe put together, out to the edge of the observable universe, out as far as you can see. So it's 50 universe luminosities from these colliding black holes, all coming off in gravitational waves.
Here is a visualization of the warped space and time, by Harold Pfeiffer again. This was all done with SpECT. But the visualizations were done now, in this case, by Harold Pfeiffer at CITA. So this is the shape of space around the black holes. The arrows are the dragging of space into motion or, for relativity experts, they're the negative of the shift function. And the color coding is the lapse function or the slowing of time. Red, that you will see deep down inside here, is where time is slowing enormously.
[VIDEO PLAYBACK]
And we all watch as these black holes go around and around each other. And you will see the warping of space and time, time the color coding; space, the shape of space as they merge. This is the gravitational wave form.
This is about where LIGO caught the waves, about here. So what you're watching now is what was going on. And I've slowed this down, or Herald has slowed it down, so you can watch the merger.
The merger will come at the peak of the waveform there. And Harold pauses the movie at the peak. There's the merger. Space is horrendously warped. Here's slowing of time, with the red. And then the gravitational waves that are flowing out, away from this, carrying 50 universe luminosities in gravitational waves.
These gravitational waves left the galaxy in which they were born and traveled outward across intergalactic space. And I remind you they were born 1.3 billion years ago. On Earth at that time, multicellular life was just beginning to spread over the Earth, the things that had more than one cell in them, when these waves were created.
Waves traveled through intergalactic space. They arrived at the edge of the Milky Way Galaxy 50,000 years ago, when humans were sharing the Earth with the Neanderthals. They traveled across our galaxy, arrived at Earth in the Southern Hemisphere, traveled up through the Earth. And climbing up through the Earth, they passed through the gravity wave interferometer, LIGO's gravity wave interferometer, at Livingston, Louisiana.
And then they arrived 7 milliseconds later at Hanford, Washington, traveled through. The gravitational wave shapes, with no data analysis on here at all, except moving frequencies above 350 Hertz, where the instrument is noisy, and below 35 Hertz, no other data analysis.
This is what the signal looked like in Livingston, Louisiana. This is what it looked like in Hanford, Washington. And then you overlap them. It's the same signal.
You remove the noise. And then you compare it with the best-fit waveform from the SSX collaboration, the Cornell-Caltec-CITA collaboration. The red is the waveform. The gray is basically with the noise removed. And the agreement is absolutely fabulously good.
And so then it was a particular waveform for providing the black holes that matches. You go in then and you look at what the black holes were doing that produced that waveform. And that's the movies that I just showed to you. So it's really very impressive.
You conclude that the two black holes, initial black holes, were 29 solar masses and 36 solar masses, a total of 65 solar masses. The final black hole is 62 solar masses. So three solar masses of energy. It's like taking three Suns, converting them into pure energy in the form of gravitational waves and sending it off.
But you do it so quickly that the power output, the energy per unit time, is 50 universe luminosity, at a distance of 1.3 billion light years. So all this information comes from comparing the waveform with the waveforms of the SSX simulations. So now you appreciate why I thought it was so crucial to join in with Saul and his group in order to pull off the simulations.
Looking at the future, I'm going to wind up now very, very quickly. There are a number of other sources of gravitational waves that Advanced LIGO is likely to see, pulsars, spinning neutron stars, black holes tearing neutron stars apart. This is also from a Cornell simulation.
Neutron stars colliding. Neutron stars are stars that are made of pure nuclear matter. They have a size that is something like 20 kilometers across, with something like 1 and 1/2 solar masses of material in those 20 kilometers. They're unbelievable phenomenon Two stars colliding, a neutron star being torn apart by a black hole, the core of a supernova explosion,
Cosmic strings. These are strings that stretch across the universe, that were thought to have been created by the inflationary expansion of fundamental strings, from which all matter is believed to be. According to string theory, it's all made from that. So you have these fundamental strings, submicroscopic, much smaller than the nucleus of an atom.
Some of them expanded to cosmic scale. And then they run into each other. They collide. They pluck each other. And they make gravitational waves as they interact. And so bends on the strings go running down the strings at the speed of light, producing gravitational waves.
But most importantly, we're likely to see things that we never expected. There will be giant surprises. There have always been big surprises when a new window has been opened onto the universe. And that's going to be no exception. Because gravitational waves are so radically different from the electromagnetic waves, which are the only form of radiation we've ever observed in the universe in the past.
All of the ways of observing the universe that we have up until now, X-rays, light, radio waves, gamma rays, and so forth, infrared, ultraviolet, they're all oscillating electric and magnetic fields. They're all the same thing, just different frequencies of oscillation, different periods of oscillation. Similarly, gravitational waves are expecting to have four windows, gravitational wave windows, into the universe, opened up within the next two decades. We've already opened up the first one, LIGO, which looks for gravitational waves of oscillation periods of milliseconds.
LISA, is a space-based analog of LIGO, light beams measuring distances between spacecraft, looking for gravitational waves of minutes to hours. Pulsar timing arrays, there's a significant effort here, led by Cordes, looking for gravitational waves by this technique. Timing the radio signals that come from pulsars, looking for gravitational waves with periods of years to decades. And then there's also a significant effort here at Cornell and elsewhere on looking for the imprints of gravitational waves with periods of billions of years, the imprints they place on the polarization of cosmic microwaves that came off of the Big Bang.
And all four windows are likely to be opened within the next 20 years. I predict that three of them will be opened within the next 10 years. One was opened last February.
So general relativity, we're at the end of the first 100 years. These years have been amazing in what we have learned about the universe. And the next 100 years are likely to be more amazing. Thank you.
[APPLAUSE]
SPEAKER: The question is, will you have time for some questions?
KIP THORNE: So the question is the velocity. The theoretical prediction is that gravitational waves propagate with the same speed as light. And the question is, do we have confirmation of that?
We will have very high precision confirmation soon. We do not really have good confirmation at the present. Because when you have two black holes collide and merge, they don't produce any electromagnetic waves because they're just made from warped spacetime. They produce waves that are made warped spacetime.
When a black hole tears a neutron star apart, the neutron star is made of matter. And when it's torn apart, it's going to produce a huge blast of electromagnetic waves, or when two neutron stars collide, a huge blast of electromagnetic waves, or when a supernova explosion occurs.
And so the theory says you should get the electromagnetic waves at approximately the same time as the gravitational waves. There may be some delay associated with the physics of the source, how long it takes to tear the star apart, and so forth. But if it's same time to within an hour, that's an hour out of billions of years, if you go out to the source, say a billion years.
That's enormous accuracy if they traveled together and arrived at the same time, within an hour, or within a second, or a fraction of a second. And I expect we will be doing timings, arrival timings, of electromagnetic waves and gravitational waves to that precision of order, a second or faster. We will have that confirmation, or disproof, which would be a huge surprise, before very long.
So he's asked, movies such as Interstellar, The Martian, and Gravity, which purport to have some level of scientific accuracy. There are bloggers, particularly, and columnists, who like to nit-pick and find things that they think are wrong with them, movies. Do I think that this detracts from the movies or is it a good thing?
I have to say, I think it's a good thing. It calls attention to the science that's in the movies. And I think that's a valuable thing.
In the case of Interstellar, the bloggers and columnists started nitpicking before they knew my book existed. And we weren't allowed to tell people that the book existed until the day the movie was released because there was a lot of worry. There was so much science in this movie that they-- well, particularly the lead producer, Emma Thomas, who's Christopher Nolan's wife, but others in the studios, were afraid that if one knew there's a book about the science of this movie, it's going to get labeled immediately, being a geek movie. And you wouldn't get nearly as much viewership.
[LAUGHTER]
And I think that was probably fair. And so a hundred million people did go to see the movie around the world, which was not bad. It's the only way I'll ever reach a hundred million people with something related to science.
But I think the nitpicking helped call attention to the movie, help call attention to the issue of science accuracy of the movie. And so I was pleased to see it. And I was also pleased to see some of the bloggers eat crow--
[LAUGHTER]
--after they read my book.
So if or when I go back in time to discover I'm not interested in gravitational waves, what would be my passion?
I have to say that I've found-- I've worked in many different areas of science and technology over my career. And I found that almost anything that I look at becomes really interesting when I get into the details, whether it's gravitational waves; whether it was design of solid propellant rocket engines, which I did early in my career; whether it was design of baffles to control scattered light in the LIGO beam tubes; or numerical simulations of gravity wave sources, or other things.
Science and technology are just plain interesting. But so is collaborating with artists and musicians, which I'm now doing, and film making. My philosophy has been, particularly later in my career, to watch for opportunities in unusual places and grab them if they look interesting.
And I think that's also good advice for physicists, particularly for young aspiring physicists. Look beyond the particular research problem you're working on. Look more broadly for interesting things that might somehow be related to what you're working on, but might carry you in a more interesting direction in the next phase of your career.
So I don't know what it would be. But I would find it by simply looking around myself for unexpected opportunity.
SAUL A. TEUKOLSKY: Thank Kip, again.
[APPLAUSE]
Renowned astrophysicist Kip Thorne, co-founder of LIGO (Laser Interferometer Gravitational Wave Observatory) and executive producer / scientific advisor on the movie 'Interstellar,' spoke at Cornell April 6, 2016 as part of the Yervant Terzian Lectureship Series. The talk encompassed gravitational waves—detected for the first time in September 2015—black holes, the Big Bang, the warping of spacetime and, of course, Interstellar. All of these seemingly disparate topics have a common thread: Einstein's 1915 general theory of relativity, which is his theory of gravity, and its implications for our understanding of the cosmos.
