Good morning, those of you who could get up this morning and early. I was asked to talk about gravitational waves, even though 2 months and a day ago we were at the first launch for the new Russian space station. And I thought I’d have exciting new data to tell you about. But it took them 7 weeks to turn our instruments on. And I still haven’t heard whether the data is any good. I know they’re working but I haven’t heard any news. Sam is in the front row, he knows the frustration. However, hopefully I am ready to start. And I got at least an interesting topic where we have data that’s available, that’s to talk about gravitational wave and merging black holes, particularly through the LIGO. And so the big event was in February, on February 11th. The executive director of LIGO, Professor David Reitze, made the announcement, "Ladies and gentlemen, we have detected gravitational waves." And he couldn’t contain himself, ‘We did it." And the reason he said 'we did it' is because LIGO had been going on for 40 years, so you know there’s a little bit of frustration involved in that. On the left you see the wave form from the Hanford, which is in Washington, the North West part of the United States. And you see the wave form and you see the predicted or the best-fit sort of wave form in comparison, Livingston, which is in Louisiana, diagonally almost the opposite corner, but not quite. You can see the predicted and you can see the superposition of Hanford data and the Livingston data. The thing that had to be done is, the Hanford data is flipped over, if you look. That’s because if you look at configuration here of the interferometers, you will see they’re actually lined up at different angles. The signal came in from the direction of Florida, and there’s a time delay of just under 7 milliseconds, 6.9 milliseconds. So it had to be shifted by 7 milliseconds, and it had to be inverted so that you could compare them directly. Which you should see there’s a tremendous correlation in the wave forms. This is amazing because this is a half hour after the instrument was sort of left from engineering runs. So people went to bed and this event appeared. And this event was immediately detected by the software, in less than 3 minutes, but you can see it by eye in the data. So this is really spectacular. It turns out this is what we used to call in the old days in particle physics a 'golden event'. You show it in your paper as the typical event, but this is a golden event. So what do we think this is in the wave form? That represents 2 black holes. The black part is the black holes. The event arises from the black hole. And the green is the gravity waves coming out. They’re emitting gravity waves like crazy. They lose orbital distance, potential, and they fall in. This is the gravity wave propagating out across space. So you see the strongest part of the gravity wave is the end. The whole thing is a chirp. Here is the Earth. That’s the gravity wave going through the Earth causing it to oscillate. The amplitude goes up. The Earth oscillates a lot more. It’s exaggerated. This has to do with the question - and Einstein said it when he was trying to predict it. And so if you actually do the history of gravity waves it’s a lot of starts and stops and mistakes. There are 40 years of arguments if there were any gravity waves based on theory. And then there’s another 60 years of trying to detect them. Here, 100 years after, it got to be taken seriously. We actually have seen observations. So here is the concept. We have 2 black holes co-orbiting their centre of mass. They are radiating gravity waves. Black holes are about the only things that radiate gravity waves really efficiently. Have to be very compact objects moving very fast. As they go they inspiral. So they have a very regular frequency but the frequency is getting faster and faster. It’s what we call a chirp. So there is an analogy to birds. The signals you’ll see are done, I’ll show you one later, the same way bird calls are done by ornithologists. You hear the chirp of the bird, you time versus the frequency. So they inspiral until the black hole event horizons just touch, they merge and they then ring down back to the spherical or elliptical, if it’s a curved black hole, kind of a shape. And it happens very quickly, you see it’s not quite critically damped, but it happens incredibly fast that the thing takes the same shape. And one other thing that we know, the laws of physics that we think we know, is the surface area of the black hole always increases. So if you look carefully in the simulations and so forth, you will see the surface area of these 2 black holes - they should be, when they touch - the surface area increases but when they ring down the surface area is even bigger. So keep your eye out for that. It will be a quiz, right. So here is the regular thing. Just in honour of BREXIT, on the left side you see the size of the orbit and the size of England. If you try to get rid of England with the black holes you’re going to get Ireland too and Scotland, so that’s unfortunate. So let me go through this in detail. The distance you can figure out because there’s a binary event and you know the frequency. You can figure out where the signal strength is. You can figure out what the distance is. It's 1.3 billion light years to this event, so the red shift of 0.09. The first black hole was 36 solar masses. The second black hole was 29 solar masses within certain error bars. And the resulting black hole was 62 solar masses. Now this is really surprising. And the experiment that I would tell you about but I haven’t got the data yet: We designed to study neutron star, neutron star merging and producing gamma ray burst. That was the thing that Advanced LIGO was built to detect. That was something where we could predict roughly: the population of neutron star, neutron star binaries and predict what the rate should be. We had no idea that, by 'no idea' plus or minus at least one order of magnitude from the sort of best guesses what the number of black holes - the rate we’re seeing in black holes now is at least at the top range of what people were predicting. So there are many more black holes out there than what all the theorists would tell us. And also stellar evolution theorist would predict that there shouldn’t be so many massive black holes as these. So right away, this first event, it shows a strong gravity. It shows us too many black holes. It shows us a bunch of stuff. We are already learning a lot. The thing that’s impressive is, Einstein was right. But he was right for another reason. This is 3 solar masses of energy coming out in gravity waves. And we barely detected it with the most spectacular thing, which took 40 years to build. So they’re not easy to see, gravity waves. And just to give you an idea. This is 50 times brighter in terms of energy release or flux, luminosity, whatever you want to say, of all the stars in the known universe, that is all the stars inside of our horizon. So if you can’t see that you can’t see anything. And the other thing you’ve got to look at is this green line. It’s the black hole’s relative velocity. Its unit is slightly more than half the speed of light for that last orbit. So in order to make gravity waves you got to be really massive. You got to be going really fast. You know you have to have the quadrupole moment, third derivative, be huge. Now for the ornithology (sound), its frequency on the uprising and on the other axis time. These are the bird chirps. So you actually hear them the way they really are, and you hear them frequency-shifted. So you can hear the noise. So when they are frequency-shifted and boosted, you can hear the white noise from the instrument, and then you can hear the chirp. Now here is, if it was a beautiful star field behind it, here’s the gravitational lensing in the star field behind it. You can see the black holes orbiting. And you can see how it appears to be distorting the space. Quickly, I thought let’s do a calculation. These guys are not very far apart. You need an amazingly big telescope to see this, but it’s still a beautiful thing to see. And it extremely quickly becomes a black hole, a round black hole or a spherical black hole. Let me do a little bit of history, talk a little bit about the early attempts for detecting black holes. How did we know gravity waves exist? Because we just had a theory. And the answer is Hulse and Taylor, who got the Nobel Prize in 1993. They looked at the thing that we didn’t know about before this. That is neutron stars orbiting round each other. One of them was a pulsar that gave out a very regular beat. So you could measure the parameters of this binary system very carefully and you could see its radiating gravity waves. And in 250 million years it’s going to go down to about a third of the size the orbits are now. And it’s a fairly elliptical orbit. So you can measure the advance of the perihelion. You can also measure the time delay. There are 2 slight differences. You can measure parameters and you see the data points coming down from 1975 to 2005. And you can see the general relativity prediction, and you see how amazing it is. And that whole effect is gravity waves. You will note, they gave the Nobel Prize in 1993 – there are no data points from ’93 to ’95. I have to say to the Nobel Committee you got to be careful when you give the prize, you can disrupt it. But, fortunately, they got back to work and you can see the data points going on quite well. You know, the orbital period is very long, it's 7 hours. So think about that: 2 solar mass objects orbiting each other at a 7 hour period. And the change in the orbital period is about 76 milliseconds per year. So this is how we knew that we were really on the right track for gravity waves. If you go through the history of gravity waves you will find they were arguing about whether there are gravity waves or not. Einstein withdrew a paper from Physical Review, claiming there weren’t gravity waves, because the referee told him he made a mistake. And he never published in Physical Review again, but eventually figured out there were gravity waves. But it took even longer for people to realise they carried energy and so forth. So there’s a whole long interesting story there. However,it turned out Feynman was one of the critical people who convinced some of the other scientists. So they had a meeting in 1956 to talk about gravity. And they talked about quantum gravity and a bunch of other stuff. But there was one section on gravity waves. And they were still arguing, do gravity waves carry energy or not? And then Feynman came up with his thought experiment of 2 rings that were tied on a bar. And if the gravity waves moved them they would create friction and would cause energy, and convinced people to do it. At this meeting was a young engineer named Joe Weber, who listened to this, came around and talked to many other people. He came up with the idea of making resonant frequency bars in 1960. That is make a bar, wait for the gravity waves to come through. If the gravity wave has the right frequency it will excite the bar, the signal will build up, and you will get it. So here is Joe Weber back in the 1960s working on this huge aluminium sphere, which was supported on a tower to isolate it, and fixing the sensors to measure the waves when the gravity wave comes through. You’re looking for somebody, a gravity wave to hit the right note. The right note is this - not a very pleasant note. But since this is Germany, it's closer to the right note. So he did a lot of work and excited a lot of people. And in the 1960s he claimed he had detection. And that excited a number of people to create some more resonant bars and so forth, but also theorists to do calculations. And the first set of theory papers claims, assuming that there was waves coming from the centre of the galaxy, that the galaxy was losing mass at least 200 times the rate that you could limit from observing the fact that the galaxy didn’t fall apart. This is even before we did have dark matter. But one of the other things that’s interesting is, he was an early person doing work in masers and lasers. And he actually even thought about a laser and a ferrometer. But he gave the first public talks on gravity waves. So he was a real pioneer. He excited the field. He kept getting the wrong answer, but he still progressed the field. And it’s a classic case in the process of science where people discover stuff and so forth. They get the wrong answer, people check them and so forth but then people figure out how to do it right. So let me switch to LIGO. And I’ll only talk about 40 years of LIGO. When I was a young student - Sam and I were talking about this – when I was a young student at MIT, I met Rai Weiss. He gave a talk - Although I took the course a couple of years later from Steven Weinberg before he moved over to Harvard. But he gave a course about general relativity for the students because they wanted to hear about it. And he wrote a progress report, which I’ll show you in a second, for the idea of using a laser interferometer to measure gravity waves. Now this is an idea, it turned out, 2 Russians had proposed in 1962, Gertsenshtein and Pustovoid. And it was revived by Vladimir Braginskii, back in the days of the Soviet Union. So here’s the actual report, it was this progress report. In the old days we just had to put out a quarterly progress report to the funding agencies. So you were just stuck with the report. So there’s the diagram. That’s his original sketch. This is now historical LIGO document. But I also added a thing. This was a result of the seminar he gave when I was a student in MIT. Then he held discussion sections with the students, just like we’ll have this afternoon. He had a series of discussion sections and the students were asking questions. That’s where he eventually got the idea of making the laser-interferometer. And that’s when he wrote the notes up in his progress report. So students sometimes play an important role in science. And so, depending on how you look at the records, either 1984 or 1992, LIGO gets co-founded by Kip Thorne, Ronald Drever and Rainer Weiss. Kip Thorne actually knew the Russians and he knew Braginskii and he tried to see about hiring Braginskii but he wasn’t allowed to leave the Soviet Union. And so Rai Weiss suggested that he hired Ron Drever from Glasgow. And Ron Drever came half-time and then eventually long-time. So it started out with just the 3 of them and now it’s over 1,000 researchers. It's impressive growth but if you have 40 years you have students and they have students and so on, it gets big. So here is just a little summary. Back in the end of the ‘70s, the National Science Foundation gave a limited amount of money to Caltech and even more money to MIT to develop a laser-interferometer for gravity wave detection. That’s how Drever was able to start building one there, and Rai was making a small one at MIT. And then Rai agreed to make a study with industry and with some other people to see what it would really cost to build the gravity wave interferometer on the scale that he had calculated was necessary to do. So that is what was going to become LIGO. I saw an early version of that and it was estimated to be $30 million. By the time the proposal was put in, in October of ’93, it was $100 million. It cost $200-and-something million by the time the first generation LIGO was built. The construction started in 1992. There was a whole long history that went on. They ran from 2002 to 2010, shut down for 5 years to upgrade to Advanced LIGO. And Advanced LIGO began operating late last fall. In fact, the engineering part wasn’t over when that event came in. They just had to shut down for the day, because it was like 3 o’clock or 4 o’clock in the morning. And they had gone home to rest and the gravity wave happened to come through, the gravity wave event. The total cost so far is $620 million US. Ok, what do you get for that? Well, you get this beautiful thing in Livingston, Louisiana, and in the desert of Hanford. So that’s about as far apart considering the political situation at the time. The person who was head of the committee was a senator from Louisiana. So that’s the reason that one of them ended up in Louisiana. And the other one had to be as far away from Louisiana as could be. And somehow Ted Stevens wasn’t there yet, so Alaska didn’t make it. This is the concept. A laser beam is split and sent down a pair of long perpendicular tubes, each precisely the same length. The 2 beams bounce off mirrors and recombine back at the base. The light waves come back lined up in such a way that they cancel each other out. And you add them together you get nothing. You get a zero’. That’s Rai Weiss But when a gravity wave comes along, it distorts space and changes the distance between the mirrors. One arm becomes a little longer, the other a little shorter. An instant later they switch. This back and forth stretching and squeezing happens over and over until the wave has passed. As the distances change so does the alignment between the peaks and valleys of the 2 returning light waves. And the light waves no longer cancel each other out, when added together in the recombined beam. Now some light does reach the detector with an intensity that varies as the distance between the mirrors varies. Measure that intensity and you’re measuring gravity waves. This reminds me of the movies from the ‘50s. Now the reality is a lot more complicated. So we will talk about this at the discussion but, in fact, there was a talk yesterday morning about quantum squeezed states and so forth. Ultimately, this is limited by the uncertainty principle. And you can actually try and do better if you want to measure the binary neutron stars orbiting. You have to change the frequency a little and you have to do that. So there are tricks that go on. But it’s non-trivial to actually understand how it works. But it seems like it’s ok. So here I’m reminding you what happened. Now here’s another simulation and here you see the 2 black holes and underneath you see the potential that’s colour coded by the time delay. So there’s a time delay from the gravitational potential. There is also potential. You see them orbiting, they’re losing energy. You see the lines of free fall. You will see space is pretty well behaved. This is the incredible linearity of space time. But general relativity is now mainly at the end. And as you get closer and closer, the horizons will get together and they’ll touch. And it actually gets fairly sophisticated, so we’re slowing the movie down. If you realise this whole event takes place in a quarter of a second. They merge, all kinds of destruction. But you notice the free fall lines still go up over the hill and down into it. You see the black hole oscillates, radiates away energy, and leaves basically a spherical black hole or a curved black hole in this case. Because they had orbital angular momentum, that angular momentum has to be conserved someway. So here are the waves again, just to remind you. And from the fact there’s a time delay you should get this arch across the sky. You actually have some additional information, so you can predict where the gravity wave source was in this band, which is a pretty big fraction of the sky. No telescope has a field of view like that, no optical telescope has a field of view like that. But you can see where they thought the event might have come from. Now at the same time, from the Fermi satellite, there was a gamma ray signal, a gamma ray burst. Which is kind of surprising, because 2 black holes weren’t expected to have a gamma ray burst. But it is theoretically conceivable you could do it, although it’s kind of tricky. And here’s where the gamma ray burst was thought to have come from. And you can compare them. There’s overlap between where the biggest signal was. And so there was some - back in February there was some discussion about is the gamma ray burst associated with this event. You don’t hear about that anymore because you will see this and more stuff. So, what is going on? Hanford and Livingston are on the air. VIRGO was off the air for upgrade. So VIRGO was very similar, and it’s near Pisa. In Germany there’s Geo 600 which is on the air. VIRGO should be back on the air by the spring. They just approved making a LIGO in India. And in Japan there’s KAGRA. Unfortunately, during the time this event happened, there was only 2 of them on. So you have only a small band in the sky where you’re doing it. However, this is to say LIGO has - the original LIGO is this little red thing in the centre, the little red area in the centre. The current version of LIGO is, the one we have the results from, is this gold. And when they get to the full sensitivity it’s designed to have, it will expand out there. The first expansion was a factor of 27 with the original LIGO. The full expansion will be a factor of 1000. In our early calculations that was the level where there should be at least several events of neutron star-neutron star. But perhaps up to 100 events per year of neutron star-neutron star. We’ll find out if we’re right about that or not. Well, I got this cartoon and I thought it was too good. There’s the guy with the hammer, right? And the scientists are all excited. LIGO scientists all excited about what they’re seeing. But it turned out, just 10 days or 11 days ago, whatever it was, there was a second set of black holes announced. This is 1.4 million years light years away, it’s the second event. They spun around one another coming closer and closer together, until, finally, they collided. This dance created ripples in the fabric of space and time, also known as gravitational waves. There were a lot of waves out there that are too small to see. And then there’s the big chirp where the amplitude and the frequency increased. In December of 2015 those gravitational waves reached earth and were detected by an instrument known as the Laser Interferometer Gravitational Wave Observatory, or LIGO for short. Scientists at LIGO announced the detection of the 2 black holes on June 15th. So you see the frequency is different, it's higher frequency. This is only the second time that scientists have ever directly detected gravitational waves. The first detection, also made by LIGO, was announced earlier this year. So you learn the bird calls. Currently all other telescopes and space observatories study the cosmos by collecting light or other particles. But the black holes detected by LIGO are not expected to radiate light. So by looking for gravitational waves, LIGO is illuminating otherwise invisible sectors of the universe. That’s the PR. Ok, so here’s the event. And so you will notice something different about this. The signal noise is not nearly as good. You don’t see it by eye. Although the software saw it within 3 minutes because it does outer correlation between the 2. And you see the signal and you see the amplitude, the chirp beginning to form, the amplitude going up. But if you look really closely you will see modulation. That’s precession of the orbit. It means one of the black holes has significant spin, and you have spin-orbit-coupling. Oh my god, you guys are going to have to do atom stuff, where you have spin-orbit-coupling with gravity waves because the spins affect the angular momentum of the orbit. And if you look closely at the black curve you will see that one of them has a spin at least of 0.2 whereas 1 is the maximum black hole spin. So they are significantly spinning. This is all getting interesting. So it turns out there are 3 candidate events. Well there’s 1 candidate event and 2 confirmed events. The first one immediately after the equipment was left alone by the engineers who were testing it, one about a month later. And one about 2.5 months later, 14th of September and then the 26th of December, a late Christmas present. And you will notice the difference, because these are being shown from the time when their frequency is 30 Hz to the present. Now the smaller the black holes the faster the orbital frequency because they can get closer before they merge. And so what you see is - you saw the big ones first and you saw the little ones last and this kind of thing, although they’re not that little. Here is the primary black hole and the secondary black hole - 36 solar masses, 23 solar masses, 14 solar masses. All of these are still bigger than the average. But now we’re starting to build up a population of black hole masses that people are seeing. But we’re biased to see the big ones. You have to take that into account. And you see the secondary black hole, not much difference. And you see the gravitational wave energy. The first event was 3 solar masses. The next one was 1.5 solar masses. The last one was only 1 solar mass of energy which is about what a really big Type II super nova puts out in a month. That’s kind of the scale of what’s going on. So this is fairly impressive, even though difficult to detect, even with this $600 million instrument. Well, you want to hear the sounds again. Here is the pure sound. Listen carefully. Ah, the speaker system is better than on my computer. Here is frequency shifted so you can hear it. So frequency shifted so you can hear it really does sound like a bird call. Chirp. How do we know what’s going on? How do we know what we saw or, in this case, heard? Here is the best fit and this is a LIGO thing. They really mean GW15, but whoever typed it wrote the thing wrong. Here is the predicted wave form from a numerical general relativity model, where you have the loss, the increase in amplitude of the gravity waves. And the increase in frequency as the orbit gets closer. That’s for the December one, that’s for the September one. Here is what a binary neutron star should look like. The frequency is set by 1 over the effective reduced mass of the system. That tells you what the frequency is. Because the physical size of the black hole is proportional to the mass and that tells you what the limiting orbit size can be and so forth. Just by measuring the last minute frequency, you can estimate the mass, reduced mass of the system and vice versa. So you can tell these are not the binary neutron stars. These are really black holes just by the frequencies that you see. And here is where they appear in the sky. I showed you the one before. The first one down here in the green. The 2 others, the candidate event and the recent event that was released this month. I remind you: the range, the initial LIGO range and the bigger LIGO range, it’s 1000 times the volume that we’re heading towards. We’re not there yet, we’re 26 times the volume. We expect the event rate to go up by a factor of 10 - 40, depending on how well it is done, as LIGO is improved towards its design. And that means if we were seeing one a month, we should be seeing 10 a month. This is going to be a change in the way astronomy is done. This is not the only place, not only as more detectors so you can get the localisation better, but there are other wavelength bands in which you can look. On the bottom axis it's frequency and the top axis is the strain per square root of hertz. And you see the expected sensitivities and signal levels for the space based interferometers, what we call LISA, and for the Pulsar Timing Array. So this is something that you can do. You have pulsars that give you very good clocks. You can look at them as the gravity passes by. They should Doppler-shift back and forth. You should be able to measure their performance. So this is the kind of thing I want to show you on a different scale. On the top scale is the Big Bang, the events that produce it. Those are quantum fluctuations in the Big Bang. There was a report a year ago from BICEP that they saw that. It’s not clear because it also could have been dust. You can see the other things that might go on, and what sort of scale. I wanted to say 2 more things to conclude. We had not expected that there would be 10 to 30 solar mass black holes. But if you have 30, you have a lot of distribution in there. You can start seeing them with LISA 10 years before they merge. So if LISA is up, you can start seeing these black holes, 10 years as they start spiralling down. You are in the LISA band from 10 year to about 1 day before the collision. But certainly about 1 week, you can predict ahead by at least a week. You can predict to within 10 seconds of when it’s going to coalesce. And you can predict within 1 degree, you can tell other observers where to look. It’s not only are we testing strong field gravity. We’re doing census of black holes. We’re actually going to be doing a lot of other things. This is going to turn into a whole new field of astronomy. So I finish and only 32 seconds late.