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SPEAKER 1: It's my pleasure to welcome you to the Hans Bethe Public Lecture this evening. Before we begin, please take note of the exits. In case of an emergency, please proceed calmly to the nearest exit, taking care for yourself and others.
The Bethe Lectureship was endowed by the university in 1977 to honor and commemorate the service to Cornell of Hans Bethe. Hans was one of the giants of 20th century physics. He was on the physics faculty here from 1935 until he retired in 1975 and remained an active leader in research for several more decades, until his death in 2005 at the age of 98.
Before World War II, he did groundbreaking work on the theory of energy production in stars, for which he would win the Nobel Prize in 1967. During the war, he was a key figure at Los Alamos as the head of the theoretical physics division. And after the war, he played a key role in transforming the Cornell physics department into a top-ranked department, hoping to attract some of the outstanding young physicists of that era, including Robert Wilson, Edwin Salpeter, and Richard Feynman.
His research spanned many areas of physics, from nuclear physics to condense matter physics to astrophysics to his famous first computation of the Lamb shift, performed on a train from New York City to Ithaca, which paved the way for the revolution of quantum electrodynamics. He wrote reviews of nuclear and atomic physics that became the Bible for a generation of researchers.
Even in his 90s, his unique mastery of such diverse subjects as thermonuclear processes, shock waves, and neutrino physics kept him at the forefront of research in astrophysics. The Bethe Lectureship is intended to bring to Cornell distinguished researchers in physics in order to enrich and stimulate the intellectual atmosphere of the university in the manner that Bethe did throughout his career.
It's a great pleasure for me to introduce this year's Bethe lecturer, Saul Teukolsky, who is very fittingly the Hans Bethe Professor of Physics and Astrophysics here at Cornell as well as the Robinson Professor of Theoretical Physics at Caltech. Professor Teukolsky received his undergraduate degree in physics and applied math from the University of Witwatersrand in South Africa and his PhD in theoretical physics from Caltech.
He's been on the faculty here since 1974 and also served as the chair of the physics department from 2003 to 2009. He has had a major impact on the fields of theoretical astrophysics, gravitation physics, and computational physics. He is the co-author of several very well-known textbooks in these fields, including The Problem Book in Relativity; Black Holes, White Dwarfs, and Neutron Stars-- The Physics of Complex Objects; and Numerical Recipes-- The Art of Scientific Computing.
He developed a formulism for describing the perturbations of black holes that is now very widely used, and he founded and leads the collaboration which leads the world today in numerical supercomputer simulations of the coalescence of black hole binaries. His achievements have been recognized by many awards and prizes, including his election to the American Academy of Arts and Sciences in 1996 and the National Academy of Sciences in 2003.
The discovery of gravitational waves in 2015 was a groundbreaking event in physics and astronomy and signaled the start of a new era of gravitational wave astronomy. In 2016, the Special Breakthrough Prize in Fundamental Physics was awarded for this discovery, a prize which Professor Teukolsky shared with others in the worldwide LIGO scientific collaboration.
We are delighted that he is here today-- with us today-- to share this exciting story with us. The title of his talk is "Black Holes, Neutron Stars, and Gravitational Waves-- Was Einstein Right?" I'd like to close by quoting for you a response received from a former Cornell faculty member in response to our invitation to attend this lecture. This quote, I think, illustrates the extent to which Professor Teukolsky is respected and appreciated by his colleagues and also how Hans Bethe's legacy continues in our department today.
The faculty member said, "I am, of course, tremendously pleased that Saul is being honored with the Bethe Lectureship. During my 25 years at Cornell, I gained enormous respect for Hans Bethe's sense of responsibility and balance, even as he was attempting to solve some of the most difficult problems in the physics of the 20th century. Saul very much walks in these same footsteps we so rarely encounter." So please join me in welcoming Saul Teukolsky.
[APPLAUSE]
SAUL TEUKOLSKY: So I'm the prototype of the absent-minded professor. I forgot to hook up to the microphone. Is that good for the back? So I was very privileged to be able to know Hans. I was a beginning assistant professor when I arrived here just at the time that Hans was retiring. In those days, it was forced retirement by age.
And so I was very lucky to know him. I mean, he was sort of a real inspiration. And just to-- I mean, there's so many stories about him. But I heard one I hadn't heard before the other day from Rose Bethe, his wife, who described how, you know, living with him was-- she was talking about how he was always doing physics. Thinking about it and all this kind of stuff.
And the day before he died, there was an article in the New York Times about some discovery in astrophysics where, according to the article, nobody knew how to explain this. And so he read this and he called her and said, call up Jerry Brown. Jerry Brown was his collaborator. Call up Jerry Brown. I think I know what's wrong with their observations.
So right up to the end, he was doing this. And so it's really a great honor for me to be able to give this Hans Bethe Public Lecture. So I'm going to be talking about these rather exotic concepts. So this doesn't like having sat here for so long.
All right, so the computer seems to have frozen. OK, there we go. OK, so what's a black hole? All right. So suppose I take my keys and I throw them up in the air. All right? So we know they go up, they pause, and they come down. And the faster the speed with which I launch the keys, right, the higher they go.
If I could throw the keys at 25,000 miles per hour, they would keep going and not fall back to Earth, right? We would say that 25,000 miles per hour is the escape velocity to escape the effects of the Earth's gravitational field.
Now imagine I could take the Earth and squeeze it down. So I get the whole mass of the Earth, and I squeeze it down to about the size of a golf ball. Now, we know from Newton's law of gravity that the strength of the gravitational force depends upon the distance between the masses. So if I were on the surface of this squeezed-down Earth, the distance between me and all the matter in the Earth would have gotten much smaller, so the gravity that I would now feel would be much bigger.
And so the escape velocity-- for me to throw my keys up-- would get higher and higher. And in fact, when the Earth is about that big, the escape velocity would be equal to the speed of light. And since nothing can travel faster than the speed of light, that would mean nothing could escape from the Earth. So, in fact, we would have transformed the Earth just by compressing it into a black hole. Because all that a black hole is is a region of space and time from which nothing, not even light, can escape.
Now of course, we could never perform this experiment of actually squeezing the Earth down. You'd have to assemble much too much energy. You know, even if you tried millions and millions of nuclear bombs you couldn't do it. But nature can do it. The way nature does it-- one way, for example-- is if you take a star and you ask what holds a star up against the gravitational attraction of all that matter? Well what holds it up is it's hot. Right? There are nuclear reactions in the core of the star, and they provide a thermal pressure that holds the star up.
But eventually the star will have used up all of its nuclear fuel-- it will have transformed everything into heavier elements-- so that no more energy can be released. And then the star will start contracting under its gravitational pull. And if the star is massive enough, then what happens is the star collapses all the way. Nothing can prevent the collapse. And you end up with a black hole.
So this has been, if you like, a theoretical prediction or expectation of Einstein's theory of gravity-- general relativity-- for many, many years. And astronomers have built whole theoretical edifices based on this idea. But the punchline of what I want to talk about is that up until these recent gravitational wave detections, we've been unjustified in a certain sense from assuming that everything worked this way. We did not have direct experimental confirmation.
So let me say a few words about general relativity. So general relativity is a terrible name. It doesn't-- it should be called Einstein's theory of gravity. OK? That's what it is. And in this theory, gravity is not the force that Newton told us it was, that was exerted between any masses in the universe. Rather, gravity is a manifestation of the curvature, the warping, of the geometry-- the very stuff of space. Not just space but space and time.
And it's a bizarre idea, right? I mean, we're all used to the idea. We don't even think about geometry in our everyday life, right? I mean, you know, angles in a triangle add up to 180 degrees. You prove it in high school, and it seems kind of obvious. And if you don't believe it you could draw triangles and measure angles, right? We all know that, right?
And Einstein says no, the geometry is determined by the distribution of matter and energy around you. And it's only on very small scales, like the neighborhood of the Earth, for example, where these manifestations, where gravity is so weak that we don't see-- unless we look with very precise measurements, we don't see the curvature, the fact that geometry is not Euclidean and that time is wrapped up in the geometry in a way as well as space.
So Einstein wrote down specific equations, quite complicated equations, to describe how the distribution of matter and energy would produce the curvature. The trouble is those equations are so complicated that, except in very special cases, we haven't been able to solve them. They're beyond the reach of our standard mathematical techniques.
And so a new discipline has arisen called numerical relativity. It's a branch-- it's just computational physics. It's this idea that if you can't solve a problem that you want to solve by traditional pencil and paper techniques, you have to resort to some kind of way to put it on a computer and get a solution.
So let's talk a little bit about these objects that I'm going to describe. So I've mentioned the black hole. The surface of the black hole is called the horizon, basically the idea that if you pass the horizon you disappear from view from the outside. And the geometry affects the space and time. So, for example, time slows down compared with clocks far away from the black hole.
Now you might say that that's crazy, right? But in fact, if you-- I'm sure that many of you have one of these phones, right? And this has a GPS system in it. And I can use this GPS to find my way all over Ithaca. Or I can get my location. There's a way to read out my location to within a few meters, and so on. How does this thing work?
The way that the GPS system works is there is a system of satellites orbiting the Earth in such a way that at any instant at least three or four of them are visible to my phone. And these satellites broadcast signals where the signal comes from the satellite with the time of a very precise clock that was in the satellite.
And also the satellite is tracked and knows its position very accurately. So the chip in this computer receives that information, the time of transmission and the location where the signal came from. And if you get three or four signals like this you can use basically simple trigonometry-- you know, the speed of light, how long the signal took to reach you, and so on. You can work out the position very precisely.
But the clock in the satellite is moving at about 18,000 miles per hour. According to special relativity, a moving clock runs slow compared with one that's not moving. So in that GPS calculation, you have to put in a correction factor for that moving clock relative to the clock on the ground. Then on top of that, the satellite up there is further from the center of the Earth than the phone is.
So, according to Einstein, according to general relativity, the ticking of that clock is a little faster than the clock that's deeper in the gravitational potential well. You need to correct for that. Now you might say this is absurd. This must be such a tiny effect. Well, in fact, if you did not put these corrections in, the whole GPS system would stop working in about 20 minutes. It would go completely out of phase. So even in your everyday life, you didn't know it, but Einstein was helping you out.
OK, now I'm going to also talk about neutron stars. So a neutron star is produced by the collapse of a normal star, as I described it makes a black hole but of a slightly lower mass. So if the mass is not too big, then the endpoint of that collapse is when all the matter in the interior of the star gets compressed to the density of a giant atomic nucleus. And that provides a pressure, which can now support the star.
So the star doesn't shine in the traditional sense. It has some residual heat, and we can detect sometimes x-rays from these stars. But it's basically a dead object in the sense that it's not producing new energy from nuclear reactions. And a neutron star is on the verge of being a black hole. So the gravity around it is not quite as strong as a black hole. But, nevertheless, it's extremely strong.
OK? And then I'm going to connect these by talking about gravitational waves. So what's a gravitational wave? So imagine you drop a stone-- a pebble-- in a pond, and the water waves travel out, little ripples on the surface of the water. So you can think of a gravitational wave as coming from some disturbance. You know, I clap my hands, and in principle the motion of my hands, right, is a motion of matter and energy and it produces a perturbation, a little ripple, in space and time, which propagates out as a gravitational wave.
Now clapping my hands makes such an infinitesimal wave that there's no hope of ever measuring it. In fact, there's no conceivable experiment we can do on the Earth that could generate a gravitational wave strong enough for us to also detect it on the Earth. But again, nature comes to our rescue. So we expect there to be-- if you ask what would be the theorist's dream of the strongest source you could imagine for gravitational waves?
Well, the strongest gravity would be to take black holes. And you take two of them and you smash them together at the speed of light, OK? That would be wonderful if we could do that. All right? So just remember that thought.
OK, so I've listed these objects-- neutron stars and black holes-- and I've divided them into two classes, namely quiescent, just sitting there doing nothing, and wildly dynamical. And the quiescent neutron stars and black holes have been understood theoretically for quite a long time. The wildly dynamical ones, these require the numerical solutions that I mentioned. So that's why I put "partially understood."
Quiescent neutron stars have been observed as radio pulsars, for example. They conveniently emit a nice regular radio signal as they rotate around. And we've studied these for a long time. Quiescent black holes, I put a "no" there with a question mark. You might say, well, why does he say no? I mean, you used to read in the paper all the time, black hole discovered at the center of our galaxy and so on.
Well, actually that's not true. OK? What those observations told us is there are places in the universe with a lot of matter in a small volume. But we have not had direct evidence by sort of measuring-- you know, that these were actually the black holes of Einstein's theory, that there was this horizon that acted like a one-way membrane where stuff could go in and couldn't get out, where the geometry was highly curved and so on.
So this was a shorthand, if you like, to say that these objects were there. The best guess is they were black holes, but we didn't know for sure. And then the excitement of the past couple of years has been wildly dynamical black holes and wildly dynamical neutron stars have been observed. And that's what I'm going to talk about.
All right, so just to say again, the observed black holes that you've heard about before the LIGO events, we couldn't really be sure that they were the true black holes of Einstein's theory. Right? We need this-- we need black holes to really test these aspects.
OK, so how should you think about a gravitational wave? So one way is to think about the effect of the gravitational wave on a detector. So imagine you put a bunch of little particles in a circle, like this, and then a gravitational wave comes through towards you.
Then what happens is the forces that the gravitational wave exerts on this ring of particles deforms it in shape so that, say, this axis stretches and this axis squeezes. And then half a cycle later, this one stretches and that one squeezes. OK? And that's what's shown over here, the stretching and squeezing.
And then I've also shown there are two different polarization states, just like in electromagnetism there are two different polarization states. And if you ever played with your Polaroid glasses you may have some idea about how this works.
So the effect on a detector, the stronger the amplitude-- so H here stands for the amplitude of the wave. The stronger the wave is, the bigger this deformation is. So if the size of the circle is originally L, then when the wave comes by you get a stretching by delta L. And so this fractional change in length is a measure of the strength of the wave.
So if you want to detect a gravitational wave, first of all what you want to do is you want to make L as big as you can afford, because then for the same size H, the delta L that you need to measure is bigger than it would have been if you used a small L. And then, as we'll see, the H is so small, it's so tiny, because we're getting signals from astrophysical events far out in the galaxy-- far away from our galaxy even-- that the delta L we're trying to measure is extremely small.
So here is a picture of LIGO. So it's an L-shaped detector, like this. Each arm here is about 2 1/2 miles long. And inside this-- so this is actually a concrete protective shield, which is about, I don't know, from maybe the width of these two tables. No, actually a little bit bigger. From there out to about here wide. And inside it, there is a steel pipe about that wide, which has been pumped down to a very high vacuum.
And laser beams travel back and forth down to the end-- there's a mirror at the end here-- and come back and similarly down this end. And these beams interfere, make an interference pattern. And if a gravitational wave were to come down, say, vertically, it would stretch one arm and squeeze the other and then alternate that. And the interference pattern that's measured in here, where the corner mirror is, that interference pattern would change.
And by monitoring that very precisely, the scientists-- so LIGO is Laser Interferometer Gravitational Wave Observatory. This is in Hanford, in Washington. And by monitoring this very precisely, they can hope to try to measure these small signals. And so the scientific collaboration that's responsible for this experiment is very big. It's about 1,000 scientists from all over the world who participated in this.
The size-- the delta L-- that they are trying to measure is about 1/1,000 the diameter of a proton. That is-- it's preposterous. I mean, it's a crazy number. You could never imagine that people would have the nerve to try to measure such a small-- another way of saying it is imagine trying to measure the distance from the Earth to the nearest star to a precision the width of a human hair. That's what they're doing. OK?
Most physicists, when they're told this, are completely skeptical. They feel some law of physics must be violated here. Now if they measured something, of course nobody would believe them. They would say, oh, you know, car door slamming in the parking lot or something like that. So there's a second detector that they built. You can see again the L here. This is in Louisiana.
The detectors were originally-- there was a first observing run starting in the early 2000s. Then the machine was shut down. An upgrade of the lasers and mirrors was made. And in September 2015 was the first science run in this upgraded detector. And this run was a few months long. And then last year there was another run almost a year in length.
And then there will be-- the machine is shut down now for another upgrade, and there'll be a third run towards the end of this year. And the sensitivity will improve by about a factor of three from where they are now. That's their goal.
Now let's talk a little bit about a computer simulation. So traditionally, physics and physicists have been divided up into theory and experiment, right? The two branches of the theory. Computer simulation is something relatively new that sort of fits in between. So the idea of a computer simulation is, instead of doing a real experiment with smashing black holes together-- I'm not sure how we would try to do that-- you use the theory to model what the experiment would-- what would happen in the experiment to model it using a computer.
Now there are many, many examples of this in science and engineering these days. For example, in the old days, if you wanted to design a new airplane, you would take parts of the airplane-- say the wing-- you would make a scale model so that you could fit it in a nice wind tunnel, and you'd blow wind over it at high speed and measure the lift and the drag and all of these kinds of things. And in that way you would design your airplane.
Today, the way airplanes are being designed is you make a model of the wing-- in fact, in some cases the whole plane-- that you put on the computer. So you have little grid points where you sample different locations on the plane. And you use the equations of fluid flow to tell you, you know, if the speed of the wind is 200 miles per hour at this point and, you know, 198 at that point, and so on. You calculate what the lifts and the drag and all of the important parameters are for the plane.
In fact, the Boeing 787 Dreamliner was the first airplane that was designed completely-- no wind tunnels at all. It was completely done on the computer. So, you know, if any of you are now nervous about flying on a 787, don't be. Probably the wind tunnel was less reliable than these things.
OK, so, what we do in our group is we use these techniques to model the gravitational waves that would come from interesting astronomical events. So here is a drawing-- a sketch showing the in spiral of two black holes. So these tornado-like things around the black holes are supposed to represent the idea that the black holes can be spinning about their axis, and this angular momentum of a black hole can drag space and time around with the object.
When the black holes are relatively far apart, then gravity is close to Newton's theory-- just some small corrections-- and so we can use perturbation theory technique to actually calculate what the signal should be, what the gravitational wave form should look like, from such an event. So that's why this part is labeled "known." Thanks. That's better.
Similarly, after the black holes merge, you have a single black hole, and it kind of oscillates a little bit, emits a last gasp of gravitational waves, and then settles down to a nice, quiet, single rotating black hole. And so this part you can actually also calculate analytically, because this is perturbation theory again, because the oscillations of the black hole are small. And you do perturbation theory about the analytic solution that describes a single black hole. So, in fact, my PhD thesis was to do that part.
Now in between, everything is very complicated. Right? There's no-- this picture was drawn before we knew actually how to do this calculation here. So this is the part that's labeled super computer. OK, so the goal from the theorists' point of view was to be able to predict this whole stretch of signal.
OK, so how do you do this? Well, you start with two black holes that are relatively far apart in orbit around each other. You set up a grid so that you can have a finite number of grid points to represent in the computer. You record the values of the curvature or the warpage or the strength of the gravitational field at each point. You choose a small increment in time.
And then Einstein's equations tell you very precisely how to update the curve, how to get the new value of the gravitational field-- that delta-t later. So the black holes move a little bit, a little bit, a little bit-- right-- all on the computer like this. And then you follow them all the way until they smash together and merge to a single black hole.
And then at the outermost limits of your grid, you measure the gravitational wave signal as it propagates out. And that's the prediction that you're making for what the observers should measure.
So why is it important to be able to do these calculations? Well, first of all, you actually in a sense improve the sensitivity of the experiment, right? Because you're looking for a very weak signal. And this signal is typically buried in all the disturbances, all the noise in the detector. So, for example, the ground is continually shaking, even when we don't-- you know, it seems pretty solid to me.
If you have precise enough instruments, you can easily detect the motion of the ground-- right-- from everything from distant earthquakes to ocean waves hitting the shore 200 miles away to thunderstorms. Everything causes disturbances. And these are big enough to drown out any possible signal.
So the first thing experimenters do is they try to isolate their equipment as much as they can, but still some noise gets in. But if you know ahead of time the shape of the signal you're looking for, then what you can do is you can take the output of the detector and you can look at different times whether that signal is present in the output of the detector.
And if it's present, then it will show up, right? Because the noise is just random-- going up and down, up and down, up and down. So on average it cancels out. But if the signal is there, when the signal goes up your model of the signal goes up. And so you get a positive thing. When the signal goes down, when the signal goes negative, your model is also going negative.
So when you multiply them together you get a positive contribution. It doesn't cancel out. So by using a template for the wave form, you can detect very weak signals that you wouldn't otherwise be able to detect in the noise. So this has got fancy names. It's called matched filtering, and there's a whole technology. It's important in all kinds of terrestrial applications. So that's one thing you can do.
The second thing is, after you've made a detection, by comparing the template that fits the signal with the signal-- you know which one it is-- that tells you what the source properties are. If you did a simulation with a mass of 28 solar masses on one hole and 24 on the other, and that's the one that gives the best fit to the data, you have measured the parameters of the-- you know what the masses are of that source.
And then the third reason that we would like to do this is, from a point of view of fundamental physics, we want to test whether general relativity is the correct theory of gravity. And so do the wave forms actually agree with what Einstein's theory predicts?
So here is just an example. This is a particular case of a big black hole and another black hole that's only one-sixth the mass. These arrows are supposed to represent spins of the black hole. So that's the spin axis. And this big black hole has a big spin. And this one has a smaller spin.
And these are the wave forms. So the two colors are those two polarizations I talked about. And you can see it's quite a complicated thing-- you know, the amplitude gets bigger and smaller, and the frequency is changing. And this information encodes the information about the masses and the spins of the source.
OK, so we have a big collaboration. It's called the SXS collaboration. It stands for Simulating eXtreme Spacetimes. It started here at Cornell and also at Caltech. And then, as many of you know, students have an annoying habit of graduating and moving to other places, so in order to keep these people connected to the collaboration we've now expanded to a bunch of other institutions.
And these are just some of the people who've been at Cornell over the years. Some of them are still here. Some of them are in the audience. People who have worked as part of this collaboration. OK. So just to say again, right now the state of the art with LIGO is you can't use the numerical simulations directly to do the signal processing. The reason is, in order to do this template matching business, you need millions of different trials-- different values of the masses' spins, angles, and so on.
Each numerical simulation, even on the biggest supercomputers in the country, takes a couple of months to do. So the prospect of doing millions of these simulations-- I mean, you can't do that. So instead, we have models right now, analytic models, that are a combination of theory-- you know, some idea of what it should look like. And then these have been calibrated against the numerical simulations that have been done.
So right now the models that LIGO actually uses are best when the spins are small and when they're nicely aligned, when things are going around like this. Of course, what you worry about is if that's the model you use to search for these objects, then you shouldn't be surprised if that's what you find. Because maybe the reason you're not finding highly spinning objects where the spins are at funny angles and so on is because you don't have models that model those wave forms very well.
So a lot of the research that is going on is to do these simulations of large spins, and I'll talk about precessioning in a little while to try to improve the models. OK, so here's just a little picture movie to show you about precession. So this is that example of the six-to-one mass ratio, where the big hole has quite a big spin compared with the small hole.
And you'll notice already you can see that the orbit is not lying in a plane the way we're used to in Newtonian gravity. Here, the spin on the black hole drags the space and time around in such a way that the orbit does not stay in a plane. And we call this precession. It's like the spinning of a top, where the axis of that top rotates around like this. Same thing is happening to this orbital plane.
And now we're going to slow things down to show the merger of the event horizon. I really love that. It's like they kiss each other. What distinguishes this movie from many others you may have seen is that this one is a precise calculation of the actual surfaces of the black hole. Because if you stop and think about it, you might say, well, how do you do that?
If the black hole surface is defined as the region from which nothing can escape, and you do a numerical solution where you start at some initial time and then you go forward in time, you don't know until you're finished whether some particular point whether a light ray could get out or not. You can't tell, down here, what the future is going to be, whether this light ray is going to get trapped in the black hole or will get out to large distances.
So to do this particular movie, what was done was actually we saved all the data that was produced during the simulation, and then afterwards sent out light rays in different directions to figure out exactly where the surface of the black hole was. So the competitors' movies are cheats. Just remember that.
All right, so here is the front page of the New York Times a couple of years ago. And we're going to talk more about this movie, but "Cosmic Chirp From Black Holes Colliding Validates Einstein-- Vindicates Einstein" and then, all over the world, Germany, all over Europe, these things. So what was the fuss about?
So this is from the first figure in the detection paper. And what's shown is this is the actual gravitational wave signal that was measured here at Hanford. This red thing. You see these oscillations going up and down. You can see the noise present there. There's a little bit of filtering that's been done on here. But we'll just call it the signal. And this is Livingston, Louisiana, in blue.
And then what's done is they've taken this signal and superimposed it on this one, shifting it to allow for the light travel time between the two sites, which are about 2,000 miles apart. And you don't have to do any fancy statistics, all right? It's the same signal.
So the first thing that we can say from this is this is the direct measurement of the strain channel of the detector. They also have about 100,000 other channels that they monitor everything from barometric pressure to Earth's magnetic fields to seismic noise-- all kinds of things. Nothing unusual happened in any channel except this one. OK?
So we believe it's a gravitational wave signal. And the fact that we see this same signal 2,000 miles apart on the we have confidence it's from outer space. Now in the lower panel what's done is we've taken this wave form. It's been smoothed a little bit. And then superposed on top of it is a wave form from our collaboration-- right-- SXS wave form. And, again, you don't need any fancy statistics, right? It fits extremely well.
So from that we conclude that this particular gravitational wave came from two black holes. Because that's how we made the wave form. Not only two black holes, we know the masses to within a few percent of these black holes. They were nice, big, fat, heavy black holes, around 30 solar masses each. Right?
So you remember I mentioned the theorist's dream? What would we like to see? This is exactly it. Right? By the time they merge here, they're going to, I don't know, half the speed of light or something. And this was the first event, the first detection.
Some people had a more relaxed reaction to this. This was outside the National Academy of Sciences building in Washington. All right? And then the labeling-- so that was 150914. This is 151226. So December 26, for those people in Britain otherwise known as the Boxing Day event.
And you can see this one looks very different. So, again, you can tell from the fact that there are many more cycles here, this means that this pair-- this binary-- came into light. Light you can only measure from about 30 hertz up to about a kilohertz in the frequency range. So what this is telling you is at the low frequency end, this came in and stayed in-band for quite a long time. So that means it must have been lower mass. All right? Because lower mass, turns out it gives you a lower frequency. And so it's detectable at a wider separation.
So we learned all about that there were more of these things. And last year's Nobel Prize in Physics went, in fact, to three people who were very instrumental in bringing LIGO into being. Barry Barish, Kip Thorne, who was my thesis advisor, and Ray Weiss.
In the second observing run that lasted through last year, several more of these black hole binaries were found. So here is just the charts of the size represents the masses. So this is the first event, producing one of total mass of a little bit bigger than 60. And this was that Boxing Day event. And then there have been three more. And there'll be a catalog paper coming out in a few months for describing the end of the first observing run. I'm allowed to say that there will be some additions to this thing that will come out in that.
OK, now, something completely different. Some of you will get the reference. Some of you won't. A long time ago in a galaxy far, far away-- many of you will get that reference. But, in fact, we can be more precise. Exactly 130 million years ago, in NGC 4993-- OK, what happened? So I'm going to now talk about mergers with neutron stars.
So neutron stars typically have a mass a little bit bigger than a solar mass-- maybe 1.4 roughly-- but much lower than these 30 solar mass black holes I was talking about. So we expect, if we're going to detect these things, there should be many more cycles visible in LIGO's frequency band. And that's good because it's lower mass, so it's a weaker signal. But because we have more cycles, our templates are much better at lining up and pulling that weak signal out of the noise.
But the most important difference is because there's matter, when you smash matter together at high density and high speed, it's fun. You get lots of fireworks. OK? So the matter can produce an electromagnetic counterpart. For example, theorists have speculated for a long time there are these mysterious things called short gamma ray bursts. They're called short gamma ray bursts so you won't confuse them with the long gamma ray burst, right?
But these are very powerful sources, bursts of radiation, at very high energy-- gamma rays. So this is an artist's conception of the merger of two neutron stars making this hot fireball thing. And these jets somehow are supposed to produce the gamma ray bursts. And another theorist's speculation was that this fireball would produce sort of some ejected material, which would be the decompressing nuclear material.
And as this decompressing nuclear material undergoes various kinds of nuclear reactions, radiation would be produced of a very particular kind. It would start very bluish, like this, and then gradually, over a period of days, become redder. And this was called a kilonova. If you want to know where the name comes from you can ask me afterwards. But anyway, we'll call it a kilonova.
And so this was actually what the LIGO experimenters thought was going to be the first thing they would see would be the merger of two neutron stars. Because being good experimenters, they never listen to the theorists. They knew that pairs of neutron stars exist, because they've already been observed in our own galaxy with radio emissions. The pulsars that I mentioned. Some of them are in binary systems.
So this was a known source. You could then extrapolate out in the universe, say how far do you have to go so that you might see one of these merge every couple of months or something like that. And that's what they were all looking for. And, of course, they said to themselves, since the volume of a sphere increases as the cube of the radius, the most likely place that you're going to see an event-- well, where is all the volume? It's at the edge of your sphere.
So it would be very unlikely to see a nearby event. There's just less volume there. So we're going to see a weak signal from two neutron stars merging. So that was their expectation, all right? So we know they're never wrong, they never listen to people like me who told them you must be ready for black holes. No, they say, they'll-- anyway, we proved them wrong on that one.
And of course you wouldn't see a gamma ray burst coincident with the neutron star, because we all knew the gamma ray burst requires a jet, like this. And so what are the odds that the Earth-- you know, this just happens to be pointing at the direction of the Earth from the first event we see. Not going to do it, right? And this kilonova business, well, that's theorists doing these numerical calculations. You can't trust them, right?
So then you can see this one. Last year, August 17. So this is a plot of frequency against time in the gravitational wave detector. So you can see this trace of the gravitational wave's signal. As time goes on, you can see it going up in frequency, just as predicted for those signals of the binary as it spirals in and goes faster and faster.
And so this is the merger time. So these are traces from three detectors of gamma rays up in two satellites orbiting the Earth. And if you look 1.7 seconds after the gravitational wave merger, there was a gamma ray burst. Here.
So if we assume that this gamma ray burst was coming from this event, then just-- for example, this is the kind of thing you can do. From the fact that it's 1.7 seconds and you estimate the distance of the gamma ray signal from the intensity, for example, you can say that the speed of a gravitational wave has to be the same as the speed of an electromagnetic wave-- the gamma ray burst is just like a light ray at a higher frequency-- to a part in 10 to the minus 16. So here I'm using units where the speed of light is one. OK?
So already a prediction of Einstein, that gravitational waves travel at the speed of light, is confirmed to a part in 10 to the 16, just from this. Now how do I know that this gamma ray burst came from this merger? Well, there are various ways to localize the source on the sky. So first of all, in blue, these are the localization areas on the sky that you get from the gamma rays, right?
So just from the fact that the time of arrival of the gamma rays at the different detectors is different. You can do triangulation. And then also by knowing something about the direction as it travels through the detector you can infer these signals. So this is the combination-- you know, this was sort of the error bar over here.
The light green banana-shaped things are the localization estimates you get from the gravitational wave detector from the different arrival times at the two detectors. About three weeks before this event, the third gravitational wave detector, the Italian-French collaboration called Virgo, which is in Italy near Pisa, came online. Its sensitivity is not yet as good as LIGO, but it's good enough to measure this particular event.
So by combining three detectors they got this relatively small error box here, the dark green one. So you see it's much better than you got from the gamma ray thing. And so there were a whole bunch of optical astronomers who were part of the collaboration who had arranged ahead of time to get alerts any time there was a gravitational wave signal like this, especially one that was likely to have an electromagnetic counterpart.
And so here you can see-- so they searched, then, in this error box. And they can do not just the two-dimensional search but a three-dimensional search, because the gravitational wave signal gives you an estimate of the distance. Because we know the strength of the source. And here you can see this little thing that's in the cross-hairs here is the galaxy. Well, this is the galaxy. And you see the little dot that's there. Well here is the same galaxy seen 20 days earlier. And there's nothing there.
So within-- this was taken about 10.9 hours after the event. They had to wait for it to get-- it was still light in South America where these telescopes were that could see this. So they actually had to wait a few hours before it got dark enough to actually look for it. And there it was.
So this is very exciting, because now we have an optical counterpart. We know this galaxy, where it is. And the directionality of the gamma ray burst was somewhere in here. And you can estimate what is the probability by chance of getting within 1.7 seconds a gamma ray burst in such a small region of the sky.
You know, that-- in other words, what's the probability this was by chance, and it's infinitesimal. It's a part in 100 million, something like that. So we are confident the gamma rays came from that.
And now all kinds of new physics can be studied. For example, when two neutron stars get close to each other, each one raises a tide-- a tidal bulge-- on the other one. And the energy that it takes to do that comes out of the orbit. And so it speeds up the rate at which they spiral together.
So we can see-- in the gravitational wave form, we can tell whether these two objects were black holes, which don't raise much of a tide, or whether they're neutron stars, which have this extra dissipation in them.
And so already limits are being set. You don't have to worry about these axes. This is the measure of how puffy a star is. And so you have to be to the left of this line to be consistent with the data. And these are some equations of state that nuclear physicists have proposed for high-density nuclear matter. And by this means we can now rule them out. We can say no, you're wrong. Maybe these guys are right. We don't know. But you've definitely got to do something else.
Here's another kind of application we can do. So you remember Hubble's law-- which was actually discovered by Lemaitre; that's why it's called Hubble's law-- says that in the nearby universe galaxies are receding from the Earth with an average expansion, or the velocity, and the velocity is proportional to the distance. So the way we measure that velocity is by the red shift of the spectral lines emitted by the stars in the galaxy.
So the z here stands for red shift. And if you multiply by c you get a velocity. So this equation is just saying velocity. And if I bring the d up here-- the d is the distance-- velocity is proportional to distance, and the proportionality is called the Hubble constant. So this is a central ingredient. Knowing the precise value of this number is an essential ingredient in cosmology today.
And so here are the two best independent determinations, as of about a year or two ago. So the thicker one here represents measurements made by studying distant supernova explosions and calibrating the light from them and then getting the distances. And so this is supposed to represent different amounts of probability. So there's some value-- 70 something and some units-- and, you know, these are error bars. And this is, like, two standard deviations, the light error box.
The thinner one comes from a satellite experiment called Planck, which looks at the microwave background radiation and, independent of these supernova measurements, get an independent measurement. And as you can see, the way the observers like to describe it, there is a tension between these two measurements because they lie outside their respective error bars, right? So it's not clear how that will be resolved.
Hubble was in 1930, right? So, you know, almost 90 years of optical astronomy to get to this level of precision. The microwave background was discovered in 1965. So, again, more than 50 years before we were at this stage. This is from the very first neutron star-neutron star merger. Only one event in gravitation waves.
So what's done here is, since we know we've identified the host galaxy that this merger took place, we can measure the red shift of that galaxy. So we know the z. We get the distance to the event from the strength of the gravitational wave signal. Right? Because the further we are away from it, we know what that source is. We know the masses and everything. We know how much energy went into the gravitational waves. And we know what energy was received by the detector. So we get the distance.
You take the ratio, and we have an independent measurement-- completely independent of anything else-- of the Hubble Constant. And this is the plot of the probability. And again, you see the peak is nicely in the neighborhood of these previous measurements. Unfortunately, the error bars are rather wide, but you can extrapolate. I think if we had about a few dozen of these measurements, then this kind of procedure will become competitive with these other two methods, and hopefully we'll try to settle what the true value is.
All right, so I mentioned the kilonova. OK? So here's the plot. Here's gravitational waves. Here's the gamma ray bursts. And these are various measurements made, you know, x-rays, ultraviolet, optical, infrared, radio, and the times in which all these detections were made. So there's a lot of information there that's irrelevant.
The main point is this event was seen all across the electromagnetic spectrum. And it started in the-- after the gamma ray burst and the x-rays, it started in the blue, ultraviolet and optical, and gradually got redder as time went on. It was exactly following the kilonova model that had been predicted.
So we can say something now about where the elements come from. So this is the periodic table. And the color coding is supposed to represent where these elements are actually made in the universe. So for example, the hydrogen is the sort of primordial stuff that you start with in the Big Bang. Everything is protons and electrons. And most of the helium is produced actually in the Big Bang, in the first three minutes of the universe.
Most of these other elements are produced in supernovae. And when the supernova explodes, that distributes those elements out into the universe, and some of that finds its way into planets like our own. And so that's where the carbon and oxygen and all these things that are important for us come from.
For a long time, the heavier elements were a bit of a mystery. What was their origin? So we understood sort of what kinds of nuclear physics you needed in order to make them. The question was, where in nature is that done? And at first it was thought that these were also done in supernova explosions. But then as the models got better it turned out that it was increasingly difficult. And the proposal was they were made in these kilonovae.
And the spectra of this that were taken with the optical and infrared light from this particular event, I won't say that they-- you know, you can identify particular elements in the spectrum. But the picture is now broadly consistent that this is where all these elements were made. For some reason the newspapers, I don't know, got get carried away. You know, every account I read of this the first thing was they've detected this thing. And then the second line was always, the gold and the platinum are being made in there.
I don't know whether they had this vision of tons of this material spewing out. But you can see it's buried with all these other dozens of other elements. OK, so I'm going to conclude just by showing a little movie, which you've probably seen before. This is this iconic picture of the two black holes spiraling around each other. What you're seeing is the shadows cast by the black holes on an imaginary star background.
So the star background is a real background from a catalog of stars. The stars are all colored according to their intrinsic properties. And the way the picture is made is by propagating light rays on a computer through the time they're in gravitational field of those black holes. And the light rays get bent by the gravitational attraction of the black holes. And that's what causes all that bizarre moving around and imaging and so on.
There's a lot of complicated physics in there. And I just want to point out that this movie was made by three graduate students here at Cornell in collaboration with the simulations done by our collaboration.
So we've come-- if you think about it, it's 100 years roughly since Einstein's paper was published where all the equations were laid out. And in that 100 years, we have learned how to solve the equations on a computer. And we've learned how to build detectors that can detect signals from these events. And, you know, who knows-- even though this is a computer picture, maybe 100 years from now our observers will have observatories where we can actually see real pictures like this. Thank you.
[APPLAUSE]
AUDIENCE: I'm curious. You mentioned how many months it takes to do these simulations, and you said it's very hard to do them for high spin in a black hole. So I'm curious, is it a question of our misidentifying events or just missing them entirely? Because it seems like the coincidence between two-- you should still see something, even if you--
SAUL TEUKOLSKY: Yes. So you can have an inaccurate template, which nevertheless, when you convolve it with the signal, there's enough of a response, enough of an overlap if you like, that you know something is there. But of course, since you don't have the optimum matched filter, you're losing signal to noise. So you may not make a detection, which you could have made if you'd have had the right template for that event.
AUDIENCE: But presumably, you have something that looks promising, then you'd try to--
SAUL TEUKOLSKY: Oh, yeah, obviously you would do that.
AUDIENCE: Then do you simulate that?
SAUL TEUKOLSKY: Absolutely, yes.
AUDIENCE: Sir, my question was-- I'm very curious about it. My question was whether the template is more important or the coincidence between--
SAUL TEUKOLSKY: No, because you don't-- for a typical event, if you just looked at the signal output, you won't see anything by eye. The signal is buried in the noise.
AUDIENCE: But you have two signals. So why don't you just look for a coincidence of the two signals from--
SAUL TEUKOLSKY: You get the false alarm. That's what they do for estimating the background. How do you know if you have a significant event? And so that's what they actually do, you know-- the problem is you get spurious coincidences. The noise is very non-Gaussian in these detectors. And so if you just take random signal streams and you do overlaps, you'll get many, many events.
AUDIENCE: You told us that you do the numerical calculations by setting up a lattice in space, which makes sense. Now once space gets twisted up to this degree, how do you keep track of where your lattice is?
SAUL TEUKOLSKY: Cleverly.
[LAUGHTER]
No. I mean, that's a good question, right? A lot of the difficulty in the early days of doing these calculations was finding a good way to keep track of the coordinates. Right? If the coordinates twist up too much and the coordinate lines cross, you get coordinate singularities like all the lines of longitude at the North Pole. So you have to avoid that. Yeah.
AUDIENCE: Does it matter that the time is also getting distorted?
SAUL TEUKOLSKY: Yes.
AUDIENCE: You're updating the time.
SAUL TEUKOLSKY: Yes. So we have a simulation time, a coordinate time. And part of the choice of good coordinates is to have a good time coordinate that doesn't get you into trouble.
AUDIENCE: Where do the two-- the gray elements on the periodic table appear?
SAUL TEUKOLSKY: Where does the what appear?
AUDIENCE: Two gray elements.
SAUL TEUKOLSKY: Oh, those two? So I know technetium is made in stellar atmospheres. So I presume the other one-- what does Pm stand for?
AUDIENCE: Is it possible they're radioactive?
SAUL TEUKOLSKY: Yeah, they're radioactive. So they don't--
AUDIENCE: There isn't any.
SAUL TEUKOLSKY: There isn't any on the Earth typically, unless you make them artificially in a reactor. They've been detected by spectral lines in some star, stellar atmosphere, so presumably made in some way there.
AUDIENCE: Technetium has a half-life of five hours.
SAUL TEUKOLSKY: Right.
AUDIENCE: Do you have any way to estimate how many of these events you should see in the unit of time. You know, like, you have a certain amount of time-- just how many events theoretically have to be observed--
SAUL TEUKOLSKY: So there were estimates before the detection. So, for example, in order to get $300 million out of Congress in the 1990s to build these, part of the proposal was that they had to have credible chances of seeing something. But if you look at those-- so before the detections those estimates ranged by over a factor of 1,000 in uncertainty.
Just because-- I mean, how would you know? What's the rate of making two black holes? Well, since we don't see black holes directly, you have to then do modeling of binary systems where, you know, each star would explode in a supernova and end up with two black holes in such a way that it didn't disrupt the system.
And so all of this complicated physics was done. And quite honestly, I mean, I don't think you could believe, really, those numbers. But there were numbers, and they were uncertain by a factor of 1,000. So I think, in fact, it's the other way around. I think we're getting to the point now where the measured rates are going to be used to calibrate those population synthesis studies that were done.
AUDIENCE: So in the out of equilibrium event horizon, near the moment of coalescence, do you ever find a black hole with a different topology than a sphere?
SAUL TEUKOLSKY: Good question. Yes.
AUDIENCE: What is it like?
SAUL TEUKOLSKY: So there was a mathematician who proved the theorem-- Steve will like this story. A mathematician proved the theorem that the topology of the event horizon as the black holes merged should be temporarily toroidal, not as it looked in that picture, like a sphere. You know, even as it joined, there was no hole in it.
And many, many dozens of simulations were carried out, and none of us saw a torus, ever. But then one of the graduate students here in my group, for his thesis-- he graduated a year ago-- he took on this problem. He, by the way, made that particular movie of event horizons going.
And what he showed was that the topology depends upon how you choose your time coordinates. Because what you're looking at is a spatial picture at some time. But the time is flexible, what you use as the time coordinate. And by changing the slicing of the time, he was able to make that picture, where there's a little hole right as the two necks come together. It's a torus. So the mathematician was correct.
AUDIENCE: Is it too early for estimates of the frequencies that these cause when events happen?
SAUL TEUKOLSKY: Well, so already-- I mean, with half a dozen events for the black holes, you know, you certainly get to within-- you know, 20% or 30% you can get a rate. Right? Because we know sort of-- we know what distances they are at, so we have a sense of the volume.
And we know how many galaxies are in that volume, so you can estimate a rate, which by astronomical standards, I mean, that's, you know, factors of two are fine. Then we don't care. Right? So we know the event rate for black hole mergers already quite well.
The neutron star mergers, even though we only have one-- from one event you can make a rate. The error bars are large. But, you know, another run is going to start up towards the end of this year. And hopefully-- you know, whichever way it is. If they don't see more, that will tell us information about the rate as well.
AUDIENCE: I want to know if one of these happened nearby, or 93 million miles away, say the black holes, would we know it?
SAUL TEUKOLSKY: Very much so. Yes. Yes. 93 million miles we'd know about. But luckily we have very strong observational evidence that there are no big black holes that close to us. I mean, I have mixed feelings about it. I actually wouldn't mind if there was one close enough that we could kind of study. But anyway--
AUDIENCE: So in the last film that we saw, there was-- it seemed like everything stopped moving except for a certain ring was moving. Why did that happen?
SAUL TEUKOLSKY: Yeah. So what's happening in that ring is-- that ring comes from stars that were almost on axis behind the black holes, right? And so, if you think about those light rays coming around the black hole, then they can come-- anywhere around that circle, a light ray would get to us.
And any small change in the position of that star or any fluctuation in the field, in the gravitational field-- you know, some residual perturbation that's settling down-- would give a small distortion. And that shows up as a flickering, a large flickering in the image.
AUDIENCE: Saul, the technology of the detectors seems like such a tremendous leap. And it was such a tough thing to build. But have there been-- are there other applications of the detector that might be-- have people thought about that?
SAUL TEUKOLSKY: So there has been some spin-off technology in lasers and expansion and so on. But from a physics point of view, I think the most interesting other application is that even though these mirrors weigh, you know, 50 pounds or something-- they're this big-- they are already functioning almost at the quantum limits. You almost have to worry about the Heisenberg uncertainty principle.
Because you are trying to measure an x. And as you know from elementary quantum mechanics, you know, there's a delta p. You influence-- you give a little kick to the mirror when you're trying to measure its position very accurately. And probably not in this particular upgrade, this factor of three, but in the next upgrade after this, this is an important thing that has to be taken account of, how to do the measurements taking account of the uncertainty principle.
And it can be done. I mean, basically what you do is you-- well, if you're interested, I can tell you. It can be done.
AUDIENCE: Is it known how the elements that are produced in the merging neutron stars are dispersed to the rest of the universe and could end up here on Earth?
SAUL TEUKOLSKY: Well, presumably, if you have the ejector-- for example, in an event like this, the ejector goes out at whatever it is-- 10,000 kilometers a second, some appreciable fraction of the speed of light. So if you just wait long enough, you know, that can travel over a substantial fraction of the galaxy.
So you can distribute those elements out in such a way. And then if you have multiple events occurring at different times in different parts of the galaxy, you build up-- you know, you have to check if the numbers work out, but I'm told by my colleagues who do this for a living that the numbers do roughly kind of work out-- they can account for the measured abundances of these elements that we do measure [INAUDIBLE].
AUDIENCE: As you do additional numerical simulations for different masses or different spins and you get a new filter, can you go back to the data you already collected and see if it fits. Or do you have to--
SAUL TEUKOLSKY: So that is done to some extent. So, for example, in a few months the collaboration will publish what they call a catalog paper, which is an ensemble of all of these detections that have been made over the last year. So that's like the definitive statement of all the properties. And to do that they actually rerun all the analyses with all the latest best models and fits and so on. So that does get done. Yeah. Usually the changes are very small.
SPEAKER 2: OK, well let's thank Saul again.
[APPLAUSE]
Nearly a hundred years ago, Einstein published the General Theory of Relativity, which predicted the existence of black holes and gravitational waves. Despite much circumstantial evidence gathered by astronomers, these bizarre deviations from Newton's theory of gravity have had no firm experimental confirmation until now.
This year's Nobel Prize in Physics went to the founders of the LIGO experiment for the detection of gravitational waves from a pair of orbiting black holes, verifying Einstein’s predictions—one of the most exciting scientific discoveries of the past fifty years. What are gravitational waves and how were they detected? How have Cornell researchers used supercomputers to establish that the waves did in fact come from black holes? How does this experiment confirm that space and time are distorted by strong gravity, just as Einstein predicted? And why is the recent detection of waves from colliding neutron stars causing such a stir?
Saul Teukolsky explained gravitational waves and other phenomena during his Bethe Lecture on March 28, 2018. Teukolsky is the Hans A. Bethe Professor of Physics and Astrophysics.
