 OK. I would like to welcome you again on behalf of the Faculty of Science and the Albert Einstein Center for Fundamental Physics at Bern University. And it's my great pleasure to welcome Professor Barry Barish from Caltech to his second lecture. As you know, he shared the Nobel Prize of 2017 with Reiner Weiss and Kip Thorne for the direct detection and discovery of gravitational waves. For those of you who weren't here yesterday in one sentence, he basically told us about a very violent event that happened in very remote parts of the universe, two black holes of about 30 solar masses circulated each other at more than half the speed of light at a distance of about 100 kilometers and then coalesced together, emitted an enormous amount of gravitational energy in the form of gravitational waves, which then took 1 billion years to reach us here on Earth. And about 100 years before the waves reached Earth, Einstein developed general relativity. And it took theoretical physicists 40 years to understand it well enough. And then about 20 years before the waves came here, Barry put the LIGO collaboration together. And when the instrument was fully functional in its advanced form, which is thanks to him and many collaborators who are difficult to coordinate, which is also what he did very, very well, then they finally, after a billion years traveling through the most empty universe, detected these waves here on Earth. OK, thank you very much, Barry. I'll just use this. I'll do this. So as you heard, the last lecture, I more or less gave you a historical approach to how we detected gravitational waves and showed you the evidence, if you want, for gravitational waves. I've tried to keep these lectures as independent as I can and not repeat everything. So it has to repeat a little bit. I'm not going to assume that everybody here was here last night. So it'll be just a little bit of repetition, but not much. Today, I'm going to talk about, I'm an experimental physicist. And I think it's common to talk about the science, which is so fantastic for gravitational waves and the scientific achievement and so forth. But from my point of view, it's the experiment and both the detection and the understanding of what we saw that is the heart of this whole endeavor. So today, that's what I'm going to do. I'm going to try to outline for you what it required to detect gravitational waves, what we did to develop an instrument good enough to do it, and a little bit about what we can do and have to do to interpret the graph that I showed you that I'll come back to that's the detection of gravitational waves in terms of something like you just heard, what we believe was the coalescence of two black holes. Tomorrow, I'll talk again, thematically, somewhat differently, I'll talk about where this field will be going as we go into the future, both short term, where there are other gravitational wave signals that we should be able to detect here on Earth, what we have to do experimentally to do that. And beyond that, what might be done or will be done in space and other ways to use gravitational waves as a new science for the future. So tomorrow is the future science. Today is the detectors and detections, as I called it. And yesterday was kind of bringing you up to a discovery. So that's my plan. And as I say, there's just a little bit of overlap at the beginning because I'm not assuming everybody was here last night. So let me again state that this story, human story, started with Einstein in 1916, one year after he presented to the world a new theory of gravity, which is based on what we call general relativity, adding acceleration to the special theory of relativity that he introduced in 1905. Adding acceleration might sound like a simple thing, but actually it was rather complex mathematically, conceptually, and is even very complex to deal with. Because general relativity, what he introduced to put acceleration in the problem, unites time with the spatial coordinates and it's a four dimensional theoretical concept, which is very difficult. In 19, but I'm not going to, I talked about that yesterday. In 1916, one year after he presented general relativity, he wrote a paper which was the first conjecture that there would be waves associated with gravity, just as we have waves associated with electromagnetism. So he published a paper, which I show the title here, which basically was not based on fundamental principles of general relativity, but rather forming the equations for general relativity he noticed in a particular way. I'll show that in my way in a little bit, not quite the way he did it, look very much like the equations of electricity and magnetism. And being Einstein, he felt inclined to make the leap from the similarity to conjecturing that if the equations look similar, then the science must also look similar and there must be waves associated with gravity, just as there are waves associated with electromagnetism, radio waves, light waves, microwaves and so forth. That first paper is not, other than the leap to gravitational waves, which I think is incredibly impressive and incredibly like Einstein was, is a rather poorly written paper. It doesn't really give you much insight other than that he can write an equation that looks a little bit like electricity and magnetism with different letters. It also has errors. There's an error of a factor of 2, which fortunately he fixed later. But when we detected gravitational waves, of course we would have misunderstood where it came from if we had this factor of 2 error. So that was the original and initial paper and it was written in 1916, the same year, another physicist, Schwartzschild, conjectured that there were black holes. I talked about black holes last night, more than I will today, but that there were black holes. The combination of those two in 1916 make up the observation that we made almost precisely 100 years later. Einstein wrote a second paper in 1918 and the second paper was more detailed than the first paper. It showed he understood more than just the superficially comparing the equations and he corrected the error of a factor of 2 that was in the original paper. He didn't reference that it was different, he just changed it to the factor of 2. And most importantly for today's lecture, and for me as an experimentalist, he spends time talking about what the underlying source would be of gravitational waves. Electromagnetic waves were discovered in the 1880s by Hertz by taking two charges, a dipole, and oscillating them, and that makes electromagnetic waves, which he detected in the next room. In the case of gravitational waves, Einstein showed that they have to come from not a dipole source but a quadrupole source. And a quadrupole source is what we find and see and look for in everything since then. So he proposed that. I write down here, this is the most technical I'll be mathematically, my way of showing that the equations look alike. On the left-hand side here, for those who know general relativity, I tell what I did. I'm not going to reference it here. In other words, you have to set up general relativity in a particular way. And if you do that, you get the equations here, which should look to you that know electricity and magnetism like the wave equation. So in electromagnetism, we have electromagnetic waves. And with different letters, that's the wave equation from electromagnetism. The h here is the fundamental measurable quantity in general relativity. It's what's called the strain. And it's shown here as little h mu nu. It is what we actually measure in gravitational waves, much like you measure the wave function in electromagnetism. If I carry this a step further, then I see that this is the wave equation. I'll get plane waves, just like electromagnetism has plane waves. And in fact, for the same reason, there's two polarizations of the electromagnetic waves that are perpendicular to each other. I also get two independent forms of the traveling wave for gravitational waves. And the difference is my drawing here is actually correct. The two separate parts of the traveling waves are in electromagnetism perpendicular to each other. But here, they're actually at 45 degrees to each other. And the reason they're at 45 degrees to each other is quantum mechanical. It's because gravity has a spin when we measure spin of 2. And electromagnetism has a spin of 1, the photon. This is an interesting last statement, because everything that I'll do from now on, and I did so far, and I will do tomorrow, is basically classical physics. It's not quantum physics. So it's always interesting to me if I can measure something that has to do with quantum physics in a classical physics experiment, which is what we can do here. We haven't done this yet. But I'll demonstrate to you that we can separate these two plane waves from each other, in which case we basically, if we show that they're at 45 degrees to each other, prove in a classical physics experiment that gravity is spin 2, which is an interesting in the sense that our experiment is really a classical physics experiment. So that's as much as I'll do of the physics background. Another way to look at general relativity and gravitational waves is that the form of the equations, if you kind of didn't absorb the way I did at this time, are similar to the equations of elasticity. And so I can write down the equations of elasticity that some of you might be more familiar with, stress and strain, Young's modulus, and all that. And if I do that, I get a form for what the electromagnetic waves would look like. And basically what comes out of that is just like we have materials that have a Young's modulus, space is really what you would call stiff, like having stiff materials in the case of Young's modulus. And it's that stiffness that makes gravitational waves not have very much effect. So the effects that I have are real, as I'll demonstrate. And then we can measure those. But the size of them is small because space itself is just very stiff and hard to bend. And Einstein's equation has just been and distorts space itself. So the take home messages are that space, time can carry waves, that they have a tiny amplitude and that there's a huge mismatch between ordinary matter and the gravitational waves themselves, so they don't transfer very much energy or cross section or however you want to think about it. So the effect becomes really tiny. And this is how tiny it is. That little h that I showed in the equation three or four minutes ago has a magnitude that we can estimate if we look at sources that we might detect. If we look at us making our own detector, the source of gravitational waves, this little h is 10 to the minus 35. If we look at something like black holes that I talked about yesterday, it's 10 to the minus 21. That's 14 magnitudes bigger, but it's an incredibly small number still. So this h that I'll come to, we estimated before we ever went after looking for gravitational waves was of the order of 10 to the minus 21. Maybe if we were lucky, it would be 10 to the minus 20 and we would have detected gravitational waves a decade ago. Or if we're unlucky, it might have been 10 to the minus 22 to find it because we didn't really know, because it had never been seen before, and we'd still be looking. So 10 to the minus 21 was our target, and we finally got there. So what does the 10 to the minus 21, and this little h that comes out of general relativity, transform to in terms of something that's measurable? And I write that here. It basically changes, because of the curvature, changes functionally what you measure as a distance. So if I have a length L, the amount that it changes, delta L, is 10 to the minus 21 times L. So you might think about what's happened as I start talking about how we approach it experimentally as having a ring of free masses by free is a key word. It is masses that are sitting in a ring, a circular ring, but they can be moved. They're free to be moved. Nothing is holding them where they are. And so if space stretches, they'll be moved. What happens is, as I say, space doesn't stretch very much. That's what I called being stiff, but I can calculate how much it'll stretch. So if I make this circle, say one meter in size, then the amount that it'll stretch, to look like the picture I have here, this amount here, is 10 to the minus 21 meters. That's a pretty small number. We know a meter is this big. 10 to the minus 21 is pretty small. For that reason, it drives us to try to make the length that I have in this equation here as big as we can so that we can make the measurement possible. That is the big advantage of the technique we use called interferometry in that we can make that length kilometers long compared to the initial way people look for gravitational waves, which I talked about last night, which is to use an aluminum bar, which was about a meter long. So we have a factor of 1,000, more sensitivity, just because we can make a long detector. And we talk now about making not a few kilometers, but possibly tens of kilometers in the future. So that's the numbers that we have to. We might get a kilometer. So our goal now is to measure something that's 10 to the minus 18 meters instead of 10 to the minus 21. OK, let's look at the possible sources and what we would expect to see if we can measure this 10 to the minus 21. I show here a freehand drawing that I made 20 some years ago of what we might see, which is pretty much what we see in the data that I'll show. What happens here is the two objects, the one we detected were black holes. They could be other objects are going around each other in some orbit, like the moon around the earth or the earth around the sun. Those objects themselves can be spinning. So I show them spinning here. And as they go around each other, because of general relativity, they radiate away a little bit of energy and slowly inspire into each other. We could detect this, in principle, very early. But in practice, to get a big enough signal, we concentrate on the very last part where they are violently coming in, merging into one object like shown here. So we look at the last part here, the merger itself, which, by the way, is, for the future, something that we don't know, can't calculate. This part we can calculate using general relativity. This part we don't know. First, it's a very strong limit of general relativity. And then finally, there's a ring down at the end. So the physics in here is yet to be known and done, and we will do in the future, to really understand whether, for example, Einstein's theory of general relativity is the right formulation or possibly some variance which exists in the literature or ones that people haven't even conceived yet. This is the strongest place where gravity comes together. And in a sense, you could think of it as a laboratory. If we can measure it, all this detail, then it's a laboratory to study general relativity in the most sensitive way possible. On the right-hand side, I show three different known sources of gravitational waves themselves. One is the one I showed last night, which is the black hole mergers, two black holes, looking like the picture here, going around each other, and they give a signal. Black holes are the heaviest. They give the biggest signal. And we didn't know how many there were, but they're the ones that we have observed first. And in order to understand them, in other words, what this shape should be and compare them with the data, required advances in our ability to study general relativity. I'll come back to that, in that we had to learn how to solve the equations which are quite difficult of general relativity on a computer. With many different possibilities, how much are these two spinning? What are the masses of the two? When you look at it, are they head on or sideways? Is there any other effects? All what the two masses are of them. To do all that requires doing general relativity many, many times, and you have to be able to do it on a computer. We only learned how to do it on a computer less than a decade ago. So when we started building LIGO, we didn't really know how to do it on a computer, but it was one of the sources we wanted. The second source, which I'll talk about a little bit later because we've observed it now, is the neutron stars colliding with each other. And those waveforms are well described. And I'll talk about that a little bit later in the lecture and tomorrow. And the main technique that we use is to compare what we see at every point in time with what we call match templates. I'll talk about that. But those are the templates that we calculate using different spins, different masses, and so forth here. And we compare each piece of data with these match templates. And I'll talk about that a little bit. The effect is incredibly small. And I put in the numbers here of what we actually observed, and what we observed was two, as was said in the introduction, two more or less 30 solar mass objects, that is two black holes, 30 times the mass of our sun, roughly, separated from each other by the time we observed them by 100 kilometers, not very far. And going around each other about 100 times a second. To do that, they have to be very relativistic. And the distance away of the ones we observed was in astronomical terms, 500 megaparsecs, in kind of layman terms, that's 1.3 billion light years. And that made a signal that was just about 10 to the minus 21 for the delta L over L. So when we finally observed that, it was pretty much at the target we aimed for in building LIGO. The first technique, I mentioned this a little bit last night, that was used was to use a big aluminum bar by a man named Joe Weber. That technique didn't have the sensitivity. In its latest versions, it was still maybe five or six orders of magnitude away from where we finally detected gravitational waves. These devices were made much more sensitive in the intervening years from when he worked in the 1960s until we made LIGO work in 2000. Over the period of about 30 or 40 years, very clever experimentalists used the same technique of these aluminum bars, not much bigger because you can't make them much bigger, but making them much colder so that the noise was less cryogenic to reduce the thermal noise and having very clever electronics so that it could be broader than just what you expect, which is a bar rings at a resonant frequency. And we're located all over the world so that you could combine the data from all of these. This is more or less as good as they got in the end shown here, and it's about 100 Hertz wide. You'll see that what we do is thousands of Hertz wide, and that enables us to do the final detection. So this scheme was the main scheme from 1960s until we came more or less after the year 2000. So in our case, we want to make a interferometer that mocks the ability to do what nature will do. If gravitational waves come through a grid that has these masses sitting there, they'll move like I just showed, and an interferometer, which I'll show, has the ability to measure the difference between this length and this length very accurately. If the two lengths are equal, we send light down, as I'll show you from here. It splits. It goes down the two arms. If they're the same length, it comes back at the same time. We orient it so that light cancels each other, and we see no signal. That's the usual form that we have our detector. And finally, we see that if gravitational wave comes through, I've shown this a few times a second. The arms change length versus the vertical one getting longer than the horizontal one, and then you will see the light come back at different times and a signal down there. I'm going to show this a little bit more. What I want to show right now is what's the challenge. And I show that on the right-hand side. So I show that we have to measure more or less 10 to the minus 18 meters. And in order to do that, we have to do two things. And these are the two experimental challenges, if I simplify it, that we faced 20 years ago when we started doing this. And that is first we have to be able to do this scheme that I told you at a level of 10 to the minus 12 times the wavelength of the light that we used to do the measurement. We use interferometry in freshman physics labs, for example. And you see fringes. People in a freshman or sophomore physics lab that do that can see fringes separated from each other. So you can probably measure to a 10th of a fringe or a 100th of a fringe. In more sophisticated uses of interferometry, people do a 1,000th of a fringe or maybe even approaching a 1,000,000th of a fringe. But we have to be able to do 10 to the minus 12 of the wavelength of the light that we use. And that's the main challenge in interferometry. This lecture is not technical enough so that I'll show you all the tricks that go into that. But we introduced many, many concepts, some brute force, some very tricky to do interferometry at a level never done before. So that's the first challenge. 10 to the minus 12, the wavelength of light. I'm not going to concentrate on that today because we accomplished it maybe 10 years ago. It's the second one that was the hard problem for us as the one that took the longest. Probably the hard problem is the first one, but it's more natural for a physicist to learn how to make an instrument work better. The second one is that we're living here on the Earth and we're trying to measure something that's incredibly tiny, 10 to the minus 18 meters. And in that, the shaking of the Earth would kill us completely. So we have to isolate the instrument from the Earth in the energy bands or wavelengths that we're looking at, again to one part in 10 to the 12. And I'll tell you how we managed to succeed to do that. But it's the key achievement or eventual or last achievement that enabled us to make the detections of gravitational waves. So I'm not going to give you the details of interferometry very much, but let me just say a few words. So the interferometry itself, we start from a laser, a very special laser that we've developed, it works in the infrared. And we aim it toward a beam splitter that sends half the light this way, half the light that way. And as I say, they'll come back at the same time. But you notice here there's something else in the way. We make basically a mirror that transmits light in one direction, reflects it in the other direction, partially silvered mirror, which captures the light for roughly 300 cycles. We do that to basically increase the number of photons by a factor of 300. And we can do that because the wavelength of the gravitational waves that we're looking for are much longer than the length we have here. So we can effectively make the length 300 times longer by bouncing the light back and forth. This is called technically Fabry-Perot arms on the interferometer. But you can think of it as just capturing the light for 300 bounces. To do that, the mirrors have to be very special. They have to focus the light. Otherwise it'll go all over the place. And that's part of doing the interferometry very well. As I say, I'm not going to show you. So what goes through is that it looks like this picture. It gets longer in this direction and longer in this direction. I have a wavelength apart. And that's what we measure. I'm not going to go through the interferometry today. I'm going to do the other part. But I start by showing a simple picture like this, which is what I showed. Each element of this is much more complicated. We don't just put a photo detector at the end. But we have a particular way of actually taking the light that comes out and making sure that we get the piece of the right wavelength. We capture the light in these arms. And we condition the laser beam in special ways. If I go to the next level, each piece of this is quite complicated, which I'm showing here. And the final apparatus is incredibly complicated. So this is the most complicated, not conceptually, but in terms of apparatus, because we've taken and tried to refine every step of interferometry to a level that was never done before. And then the scale of it is huge. We started this project in 1994. So in 1994, we were approved and funded to build two of these interferometers. We were building two, because we wanted to make sure that we saw the same signal, or saw a signal in both sites that were separated, in our case, by 2 thirds of the distance across the US, about 3,000 kilometers. We, by meaning we, met a group at Caltech and a group at MIT who were collaborating to do this work. When the proposal was given to the National Science Foundation, we had a site not too far from Caltech at what's called the Edwards Air Force Base, MIT, had a site for the second one that was in southern Maine, not too far from MIT. We turned it into the US government. Luckily, they funded us. But they also rotated it by 45 degrees. You might guess that was a political consideration that did that. So we ended up with sites in the state of Washington and the state of Louisiana, which were not our choices, but were given to us. But we ended up with two friendly senators as a result, which we needed through the years. These two sites are separated by 3,000 kilometers. So if a gravitational wave were to come this way, it would arrive in Hanford 10 milliseconds before it arrives there at the speed of light. Or if it's coming this way, it'll arrive here 10 milliseconds before it arrives here at the speed of light. If it's coming down in between, it'll arrive at the same time. So we know that a real gravitational wave will give a signal in both of these detectors plus or minus 10 milliseconds from the nominal time that we start. One can be earlier by 10, but not 15 milliseconds, because then it wouldn't be the speed of light. So we look plus or minus 10 milliseconds. We look at the times that aren't possible to see what artificial signals we get from our detectors themselves, just from noise. Then we measure all that in the detectors. It's interesting that we made a scientific choice right away. So something like 22 years ago in 1994, we started constructing LIGO. This is an aerial view of the LIGO detector construction clearing in order to make the two arms of the interferometer in Livingston, Louisiana. You can tell that because it's forests and trees and so forth. And then we built one in Hanford, Washington. And the first question is, how do you orient these two with respect to each other? I've got two L-shaped things. Do I put them parallel to each other? Or do I maybe make them at 45 degrees to each other? What do we do? That's a scientific question, it turns out. If I put them at 45 degrees to each other, then I have the ability by comparing what the difference is in the signal at the two to do what I mentioned 10 minutes ago. And that is to differentiate, because of the difference, how much of the signal is in one polarization, how much of it is in the other, or whether we really have two signals that are at 45 degrees from each other. So all of that is what you get by putting them at 45 degrees to each other. But gravitational waves had never been detected, so the advantage of putting them parallel to each other within the 16 degree curvature of the Earth, putting them parallel to each other, then we can ask, as those of you who were here last night saw, that the two signals be identical within the air of 16 degrees to each other. Of course, if you're making the first detection ever of gravitational waves, then you want to be as sure as possible that you got what you wanted, so it's not as convincing if you have different shaped signals in the two detectors. But we argue clearly the more theoretically oriented scientists on LIGO wanted us to put it at 45 degrees to each other. And the most conservative experimentalists, including myself, wanted it parallel to each other. And I was in charge, it's parallel to each other. So what does the detector itself look like? It's actually a huge vacuum system. This is showing us making this vacuum system here. This is it in place. This is making the vacuum system itself. I'll show you why we need the vacuum system in a minute. But it's 1.2 meters in diameter. It's four kilometers on an arm. We have four arms at 16 kilometers. For a technical number, for those of you that know vacuum, we run a 10 to the minus 9 tour. That's what's called high vacuum in the lore of vacuum engineers. And this is the largest high vacuum system in the world, and the second largest vacuum system in the world, the largest being at CERN on the LHC. They don't have to be at high vacuum for the whole system. So the total amount of vacuum they have is larger, but not high vacuum. And high vacuum requires a different added technology to be able to get to 10 to the minus 9 tour. So that's the vacuum system, just to give you a sense of what we do. This is the constructed interferometers. One on the left in the state of Washington, it's high desert, so it's flat, dry, and very stable. And the one on the right is in Livingston, Louisiana, and that is basically floating on water. It swamps at that point. We didn't pick the side, as I told you. So it swamps. In order to keep ourselves from being flooded when it rains, it rains a lot there. We built this up. You can't see it very well. About six meters above the surface, that's what people do is calculate the probability of storms going to a certain level. The probability of it going to five meters was something like one in 500 years. We don't expect to be doing this for 500 years. But we still went one meter higher than that. So we basically put it up where we shouldn't be flooded. But in order to get the dirt to put it up high, like a road, we had to build a borrow pit next to it. And it immediately filled with water, bugs, fish, alligators, and so forth. So that's living there. Just to give you a sense for what the apparatus looks like and a strategy, if you don't know what you're doing, I show here the inside. If you walked into the hall, what it would look like. Each of these contains those mirrors that I talked about, or lasers, or things like that, or test beams. But you'll notice the ports everywhere. Each one of these things is a port that you can get in. We had no idea that we needed all these ports for definite plans. But we put them there in order to give us as much flexibility for the future as possible. So I basically insisted we put a port everywhere we could put it, even though it cost a little bit of money, not knowing how this instrument would evolve in time. Because doing experimental physics in general, it's much more costly to build all this infrastructure than it is the technical instruments themselves. So as we improved the technical instrument, we didn't want to be limited to it being exactly like what we built before, but better. Instead, the ability to make it more flexible. And that's a plan that I think is very important. In expensive, long-term, experimental projects is to envision and put the investment in for the future so that you're not just locked into what you build at the beginning. So this is the inside of LIGO and a little speech on why you do it. This is the optics. So this is the test masses. They get moved by gravitational waves. And they also serve as the mirrors. There are huge pieces, big pieces of fused silica. And on the surface, we put a coating, 20 layers, very thin layers, of dielectric coating that reflect the light at the wavelength of the laser beam. Our laser beam is in the infrared. It's where we chose to make where we could make the best lasers. And so if I look with my eyes, this is just the most beautiful piece of clear glass I've ever seen in my life. But for the laser beam, which is in the infrared, where our eyes don't work, they reflect on the surface. And it reflects, as shown here, the 300 times or so. So we make this coated so that it traps the light for about 300 passes. And that's the mirror in the test beam. This is a picture of the laser itself, which will go up to 200 watts. It's what's called a neodymium-yag laser. And you can see just from this that it's a lot more complicated than the one in my hand. And that's because we want to make it incredibly stable. We want to make it very powerful. We want to make it very stable so it points in the same direction all the time that it doesn't move around. That it keeps the same frequency. And so forth. In order to do that, you need a lot of special techniques to make the world's most stable laser. We devised these lasers. And then we developed them in our lab and then had them built in industry. This laser here is built at Laser Zentrum in Hanover, Germany, who finally built it for us with our help. So I'm not going to show you much more equipment. What I'll show you instead is what you have to do to make this all work. And what limits you as an experiment. So we're going to try to measure this incredibly small number. And a lot of things limit us. And this is the part that kind of gives you a sense of what we need. I've already shown some of it. So the first thing is residual gas scattering, what I showed here. That is, if I go for four kilometers this distance, there's some chance this finite that the photon on its way hits a molecule, bounces some way, maybe hits another molecule, and finds its way back. But its path is different than a straight line down and back. And therefore, it will take a different amount of time to go down and back. And so that forces us to use vacuum. And in the end, as I'll show you on a graph, actually forces us to use what I called high vacuum. In order to keep that residual gas scattering low enough so it doesn't limit the measurements. That's the first one. The second is the laser itself. I mentioned that already. And in order to, again, make the measurement, we have to go to unprecedented stability in wavelength. Although this looks like a green laser. It actually oscillates a little bit in how intense it is, the amplitude fluctuations, and the pointing, which I didn't write on there. And so the laser itself, as I said, is very special. The next is the most important for the discovery itself. So when you go home and somebody asks you what this lecture told you, this next part is where you should wake up. Then you can have the elevator speech of how they discovered gravitational waves. And that is the isolation from the Earth. And that's what I call seismic noise, the Earth shaking. And how did we isolate ourselves from the Earth well enough? I'm going to show you that in just a couple of minutes. And you'll see. First, I'll tell you what else limits us, and then I'll show you that. The next thing is that the test masses that I showed you, these mirrors, are at room temperature. And anything that's at room temperature has the ability for molecules to move around. Something we call Brownian motion or thermal noise. And basically, that can be solved in the future. It's one of the ways we'll make better detectors, but we don't know how yet by lowering the temperature. It isn't what we wanted to do in the first generation. But that's a future plan, is to lower the temperature to low temperature where that noise will be less. I'll show you where these noises come in in just a minute. And then we can get to a point where we have problems much like in quantum mechanics. And that is, in order to make the best possible measurement, we want the most possible light or the most number of photons. But if we put a lot of photons in, that makes it better in one sense. And in another sense, those photons put pressure on the mirrors if so many photons are hitting the mirrors. And that creates a problem in the other way. We call that quantum noise. So those are an example. There's other sources of noise. But you put those all together. This is the plot to look at. And it's similar to the plot when I show you data. So if we look at the left-hand side, you'll see the famous 10 to the minus 21 that I talked about. So that's our target. I want to measure something there. The frequency that I show here goes from 1 Hertz to 10,000 Hertz. That should look familiar. It's the audio band. Where I'll show you, we're sensitive is from tens of Hertz to thousands of Hertz, just like your ears. And that's not an accident. Evolution has picked the place where the earth is quiet enough so we can communicate with each other. If you go to lower frequencies, then if we tried to talk to each other, it would be too noisy. If we went to higher frequencies, then you have to sample so quickly that you need lots of signal. So basically a human, I'm not doing anything audio in this experiment, but the earth itself is basically quiet in the region of the audio band. And so if I work on the earth to do a search for gravitational waves, it's those same frequencies, the audio band, even though I'm not doing anything audio, that is accessible to us for gravitational waves. So that's shown here in that we're basically tens of Hertz to thousands of Hertz. Every line on this is these different backgrounds that I talked about. So for example, if we have 10 to the minus 6 tor in our vacuum, it would be this line here. This is the better vacuum down here. This is the radiation pressure that I talked about. It is so many photons that it hits the detector. And in the end, whatever is the highest limits us. So we're able to detect and have no backgrounds if we do everything right in this region here. And a gravitational wave, as I show you, will come in first at low frequencies and pass into this. And we watch it cross over, and that's what I'll show you. So basically, this is the sensitive region. It comes below the 10 to the minus 21. It drops at the lowest frequencies due to the shaking of the earth. And that's what limits us, and that's what I'll show you. It falls very quickly, and the shaking of the earth is very difficult to isolate from. At the highest frequencies here, we're limited by what the experts that do interferometry call shot noise, but you can just think of it as photo statistics or how many photons you have to do the sampling. And in the middle frequencies, we're limited by what I call thermal noise, or the KT noise, the fact that we're working at room temperature. And so in the three different frequencies, different things limited us, but this is basically the region that's available. Now, if I change that to looking at the data we have, it looks like this. So you'll see this looks similar. It's coming down here. This is the seismic noise. This is the thermal noise, and this is the number of photons, or the photon noise. All this down here is just drawing lines of measuring what contributed. You don't have to pay any attention to that. That's just to show you that we know where the different elements come that make this final envelope. And anything above this we can detect. This is just the basic sensitivity of the instrument itself. So the lines that are here vertically, that are here, are something that experimental physicists grapple with in almost any sensitive detector. And that is some sort of resonances in the system. We have two kinds. We have electrical ones. In the states, we work at 60 hertz. So you'll see on here a line that's at 60 hertz, 120, 360, the multiples of 60 hertz. And any mechanical thing that you build to hold up the apparatus has its own resonant frequencies. So those are the little vertical lines that come up. We know what essentially all of them are. They stay at the same frequency. We just notch those out. So you should just ignore those. But I told you what they are. And our sensitivity is this. So now the evolution of LIGO. Starting from after we built the detector and then we started using it. This was the beginning, maybe 2001. And each one of these lines in different colors is an evolution of about a year or half a year. And what we would do is take this apparatus, search for gravitational waves at whatever sensitivity we've gotten, gets better and better in time as we go down here. Each time we did not see gravitational waves. And each time we knew what we learned had limited us that we could improve in the detector or new features that we hadn't yet installed in the detector. And we would take time off, improve it, run again, get the second line. Didn't see gravitational waves. The third, the fourth, the fifth, the sixth. And this went on for almost 10 years. And we never saw gravitational waves. We ended up with the best result being here where the two colors represent just two different optical configurations, one of them emphasizing the lowest frequencies, one of them the highest. They're not very different from each other. And there's a little thin line that you see here, which is basically the ultimate limit we could reach as an apparatus. So we had reached as far as we could without doing new and better interferometry. So this brings us up to maybe 2011 or 2012. We had worked in the meantime on how to make it better through all the time we were doing this. And our goal was to improve by at least a factor of 10 everywhere. So this is a log scale on the left. We can improve the high-frequency part, that's the number of photons, by developing a higher power laser. And we did that. We can do the middle part by making quieter big masses and mirrors, better materials and heavier ones, and better coatings to improve the middle ones. And we can improve the low frequencies by better seismic isolation. And it's the low one that I want you to pay attention to as I go forward. But for completeness, I'll show you that this was quite a big project. So we intended to improve everything. This is just to impress you that it's improving the power, the mass of the mirrors themselves, the topology of the interferometry, and so forth and so on. And so we were doing all that. That was all part of a big improvement program, which costs quite a bit of money. We were down for several years. And the most important improvement in terms of making the discovery is shown next. And this is where you wake up. So this is how we isolate ourselves from the ground. What you see here is a pendulum with a mirror on the bottom. So this is what the beam, laser beam, sees. And this pendulum is actually four pendula on top of each other for reasons that I won't say exactly, but it's for technical reasons of making all the instruments off of the test mass on the bottom. But you probably realize that if I have a pendulum and I move the top of it, it doesn't move the mass very much. So that's good. If the earth shakes like that, it's not going to move the mass very much. So that's why we make it a pendulum. And then that's not good enough. If I take the pendulum and it shakes up and down, it makes the mass go up and down. So I have to isolate myself better from the earth. The technique that we used until we made the improvement that made the detection was rather simple. It was the same scheme that's used in your car to make the ride nice and smooth. So in your car, you have these things called shock absorbers. And the shock absorber works such that you go over a bump and instead of feeling it like a bump, it takes the frequency. It can't get rid of the energy. It takes the frequency and moves it to lower frequency and you feel this nice, smooth ride as you go over a bump. And we did that in four different. We made the most sophisticated car shock absorbers you can imagine. Four different layers independent of each other. So what got by the first one, you put on the second one, the third one. They're springs. They look like a spring. And they're made with just the right goopiness and so forth. We did all that in the initial LIGO detector. But you remember that I said we had to isolate ourselves from the ground by a factor of 10 to the 12. We did that with these four layers and we got 10 to the 10th is the best we ever got. And we never detected gravitational waves. We started working in, I think, 1999 on an added technique to do better than we could do with the shock absorbers. And that you can respond to also. And that is all of you or most of you have gone on an airplane. And some of you have been bothered by the noise of the engines. And so you get these fancy bows or whatever earphones and you put them on and the engine noise disappears almost. And you can talk to the stewardess and hear the stewardess. So what's happening in these magic earphones? What's happening in these earphones is that the instrument measures the ambient background. Noise, which is coming from the engines. The engines make the same kind of background all the time. And then a cancellation is made. So it cancels that ambient noise. A stewardess when she comes and talks to you, raises her voice up, and you hear her perfectly fine because that's not ambient noise. So these work very well. This is the same idea. Only it has nothing to do with earphones and noise and audio stuff, but it's the same idea. What we're left with in terms of doing better than these seismic springs that isolate LIGO is to measure what the ambient shaking is of the earth that's left when we try to use the seismic detectors. And so we do that by using seismometers. And we use seismometers such that we measure the direct. It's much harder than the engines because first the amount is very little. And we have to measure the direction that the earth is going to try to shake our mirrors. And then we push back and compensate for it. So we made what we call active instead of passive, a mirror. A passive, we made active seismic isolation much like the idea of the earphones on the airplane. And it gave us the factor that made the detection, which I'll show you. And it's kind of your story to tell your roommate or wife or son. So this is what happened. After 10 years and all the measurements we made, we were on this line up here. And then we improved LIGO, turned it on. It's designed now to go down to here. We're not there yet because we haven't put in all the features. We will over the next couple of years, but that also gives you a preview that life will get better. The two lines that are the same place but different colors are because we have two detectors, one in Hanford, one in Washington, one in the state of Louisiana, one in the state of Washington. And I've just plotted them on top of each other. And you can see that despite the fact that one is in a flood plain and the others in desert, the instruments work the same. But the improvement at high frequencies, you can see here. On this scale, which is the log scale, it's about a factor of three. And a factor of three is pretty significant. It basically is a factor of three in that little h that I put up in the beginning, the amplitude of the signal, which is what we measure. And that means that we can look three times further out into the universe looking for gravitational waves. That means we look at 27 times three cubed more volume of the universe and looking for the gravitational waves. That much improvement was enough so that we decided, instead of working very hard to bring us down to here, it was worth having a first run of the data taking with a new detector. Because 27 times the sensitivity would quickly be better than what we had accumulated over 10 years before. But at low frequency, because we added the active seismic isolation, at 40 hertz, a typical low frequency that when I show you the signal we're at, the improvement was actually a factor of 100. Remember, I said we got to 10 to the 10th for passive isolation. This now brings us to 10 to the 12th, what we needed for isolation. The factor of 100, of course, makes the rate 100 cubed, or a factor of a million higher, in terms of how much volume of the universe we look at. And so the simple answer to a question I've been asked many, many times, how could we turn on this improved apparatus and make a detection in a week when we hadn't seen anything in 10 years, is because of this factor of 100 improvement, which is a factor of a million in rate. The actual signal that we saw is at very low frequencies. This is a picture of frequency versus time. And so what you see here is low frequencies, just what I was talking about. This is the signal, which makes a so-called chirp signal. It stays at low frequency. And then it goes to higher frequency as they merge together at the very end. It goes whoop, and that's what we call a chirp signal. This is the two first detections that we saw. The first one stands out because it was very heavy black holes. We saw it very quickly. The next one, which looks dim on here, is actually much easier to detect because it was lighter and made many more oscillations in our detector, but it doesn't show on this plot so well. So this is now highlighting the frequencies that were fixed by adding the active seismic isolation just to emphasize that improvement. And again, this is the discovery signal that we saw on September 14, 2015. It looks very much like what we expect from general relativity. What I show here on the top are the signals first, just the data just shown in a different way. First at Washington and then in the state of Louisiana. And below those, I show the expected shape of the signal as expected from Einstein's general relativity if it was due to two black holes merging at something like 30 solar masses each. It's slightly different than that, but that is roughly. I subtract one from another. This is something that experimentalists need to do and should do with any data when you're comparing it with an instrument because if I subtract one from the other, I can see if there's any residual effects that aren't there in terms of how well the two look like each other. And you notice this is just random. So there basically is no evidence that there's any sort of residual effects that we have to worry about. So that was basically what we saw in September 2014. We saw it by the signal standing out, but it's not the main technique that we use to find the signals. Instead, what we use is what I called earlier the matched filter technique. And the matched filter technique is to know what the shape is you're looking for. Use Einstein's equations, just like I did to calculate that. Calculate all the possible ones that might be observed and compare each one with the data. We do that in a way that I'm showing here by having a shape. As you run it across the data, shown on the bottom, you don't see anything until you get to a place where there's a real signal and then it stands out and you see the signal. That enables you to see a long signal buried in noise when it's there for a long time. And that's the primary technique that we use to find the signals called matched filtering. And we use that as our primary method. It's shown here for that second event that I showed where the actual signal is a little hard to see at any place because this is the noise, the bigger ones, but when you go over the whole range then we see it as a signal. So that's the technique that's used. And then in this longer one, we're able to look at the different pieces of it and compare it in detail with general relativity using these calculations, what we call numerical relativity on a computer and compare them with the data first in the left-hand side before they're too close together and then when the fields get stronger and stronger, enabling you to see if there's any breakdown as you move towards stronger gravity. I've just drawn it another way on this curve of our sensitivity where these first events, how they cross them. The very first event is the biggest in terms of a signal, but it was very heavy masses and it cuts off early. The other ones go out to somewhat higher masses. Okay, let me go on to something. So that's the discovery of gravitational waves. I want to show you a little bit more about what else we've done and can do. And then tomorrow I'll talk more about the future about what we've done already. So we take the data we have from these two detectors, take when the signal arrived in each and use that to predict where to calculate and determine where the gravitational waves came through the earth. So this is a map of the earth and these are the different events that we've seen and how well we know where they were. Not very well because if you've ever done triangulation on a sailboat or something, you want three, not two. Using our two, we can tell to an accuracy of 1,000 square degrees or so where they were. These are three different or four different events that we had, but notice in the lower corner here there's one that's much better. And that came about because we were joined by the detector in Italy for our last events and I'm gonna come back to that. These shapes are very rich. This is the formula that we use called a church mass formula that we use to actually fit those shapes. From that we can tell something about the masses of the two objects, their spins, how redshifted they are, that is how far they are out cosmologically, whether there's any procession, what the spins are, the two objects, all of that can be reconstructed. I've only shown you the first term here so that the actual shape of this to be fit is incredibly rich even though you find one event. So in contrast to when we do physics at CERN or something where you see many, many events to get the features, we have a lot of information because we have even in one event these detailed waveforms. So we do that and we get the parameters of this first event. So this is the parameters that we published in the discovery of the first black hole merger event that there's two black holes, one of them 36 solar masses, even the errors are shown here, 36 times the mass of our sun, the other one 29 times the mass of our sun and the final black hole is 62 solar masses. You'll notice that 36 plus 29 actually adds up to 65, not 62. And the difference between 65 and 62 is that three solar masses of energy went away in the form of gravitational radiation during this merger. That was the brightest object energy-wise in the sky for that two-tenths of a second when we observed LIGO. So anything in the sky that was a tremendous amount of energy off in gravitational waves but because gravitational waves are so difficult to detect the fact that all that energy went away, it still was hard to detect. Then there's the other parameters, the spins and so forth. We have all kinds of likelihood of what the spin was of one, the spin of the other or the masses and so forth all by fitting that data. I just wanted to show you that that's possible. This is basically a picture of what happens then as they merge together. They start further apart like this and they give a nice smooth oscillatory curve as one's going around the other. As they get closer together, it gets a little bigger. As they merge together, it gets bigger and narrower and finally it merges together very much like that first picture I drew. This is the fit then from Einstein's equations. And if I turn that into what it's showing, first how fast are these going? They're very relativistic. At the time this enters our apparatus, it's going at about a third the speed of light and by the time it merges together, it's going more than half the speed of light. So these are going around each other incredibly fast. And the distance apart, I have in units here that are called Schwarzschild radii, but the distance is about from 150 kilometers to coming together in the period that the apparatus enters us. This is a series of ones we've detected now, we've detected them that we've reported, that we've detected over a period of a year or so since we made the discovery. And you'll see each has different characteristics, how long we see it, how big they are and so forth. That's determined by how far away it is, what the spins are like, what the masses are of the two objects and so forth. And with all this, we can test general relativity by adding these up and doing them in different ways. And for example, if gravitational waves are not what I said at the beginning, but actually do have some propagator attached to them like the photon is for electromagnetic waves, we call that a graviton in physics, I can test for that. I test for it by basically putting it this little massive object into the formulas. If I do that, I've done that formula here, but if I do that, then it'll add what we call a dispersion term or change the shapes of these a little bit. And we've tested for that, and we're very sensitive to the fact that these can't be very heavy and we set a limit, which is shown here, that a graviton, if it exists, and it's the best limit that exists on something like a graviton is less than something like 7.7 10 to the minus three electron volts over C squared. This is a very tiny number. So that's the kind of thing we've done. We've always thought, and I'll talk more about this tomorrow, that gravitational waves are a different way of looking at the sky. And so when you look at the sky with gravitational waves, you'll start seeing physics or astrophysics that's different than was expected. And that's already true. I showed on the right here in just the very first observations. So first thing that wasn't known before from all of astrophysics is that there are binary black holes that mean they come in pairs, because that's what we observed. You might have known there are black holes. Of course, that was inferred, but not that there are binary black holes. Secondly, they merge together, because that's what we detected in less than the lifetime of the universe. So we know there are black holes. We know they merge together. Those are all interesting, but you needed to be able to detect black holes to see it. It's not revolutionary. The next thing is, and that is, the black holes that we saw are much heavier than what astrophysicists thought would exist in the universe. Our black holes, as I showed you, were the first ones were 30 solar masses. They're at least 20 solar masses. And astrophysicists are now scratching their head, and we are, in how these were formed. Because the problem is that we think that black holes are formed from the death of a big star. But if we have 30 mass black holes, we have to have stars that are heavier than that. And stars that are heavier than that aren't very stable because of all the other radiation around. And so there never was the belief that you'd have black holes anywhere near this kind of mass. So now there are different conjectures. It's like the next problem in physics, to understand how these black holes come to exist. Three possibilities that people conjecture are that maybe there are parts of the universe that don't have much other than hydrogen and helium. We call that low-metallicity parts of the universe. If there are low-metallicity parts, it doesn't bombard stars. They're a little more stable, and maybe you could have heavy stars. So maybe the ones we detected are in some low-metallicity environment in the universe, and that just is how they're there. Second possibility is that they were formed in what we call dense clusters, a part of the universe where there's a lot of matter, and so you make these black holes when they're smaller, and they're close enough to each other that we've seen generations of them merge and make the heavier ones. So that's a second conjecture. The third one, which is maybe one that particle physicists would like better, is that their primordial arcane about in the Big Bang itself or before, and that somehow they might be connected to the dark matter, for example, in that case. There are ways of telling the difference in those kind of conjectures, and it's like the next step in what we'll do. If they're made primordially, the spins of the two objects coming together will be totally uncorrelated and so forth. So there's different things that we're now trying to measure to at least favor those possibilities or whatever else. But I take it as an example that with gravitational waves, you're gonna see new things no matter what you do, because we have a new and different way to look at the universe. Recently, one year ago, just over one year ago, we were joined by the Virgo detector in Italy for the first time. This is the director of the ego detector, Stavros Kastin and Avedis, and Jo van der Brand is the head of the scientific collaboration. And you can see they're not quite members, more sensitivities this way, they're not yet as sensitive as we are. Our two are the ones on the bottom, you'll see that in the signal, but all three of us are now capable of seeing gravitational waves. And last year, August, in 2017, we simultaneously saw a gravitational wave from black holes, and that's what created this better resolution. So it's an example that as we add more sophistication, in this case, another detector, we now can point much better in the sky. This turned out to be fantastically lucky because three days later, black holes, by the way, don't give any signal that the astronomers can see. So everything we're looking at because they absorb all the light. And so everything we've looked at so far, astronomers forget it, they can't see it, they try, but they never saw anything from anything we've seen. So it's nice to point better, but with black holes, it doesn't really matter. Three days later, this happened. Just after we saw the first black holes with the three detectors instead of two, we see this chirp pattern for us. It's a weaker, in the case of Virgo, but detectable. We put it all together, and what we had seen is something that lasts for tens of seconds. If you look at the scale here, this is 30 seconds to zero. You remember when I showed you the black holes, it was two tenths of one second. So it's a very different long signal because it's made by very light objects, in this case, neutron stars. And when the neutron stars came together, then we saw a merger of neutron stars. Just as a word, what's a neutron star? The neutron star is the product of the death of a star, just like black holes, but the star not being heavy enough to make black holes. We think that any star, including our own, that's lighter than maybe three times the mass of the sun, can't make a black hole. So it makes something else. One of the more popular ones, depending on the science, is neutron stars. That's nuclear matter that's primarily neutrons that came about from the fact that a star burned up its fuel, gravitationally collapsed, and is just incredibly dense nuclear matter. I'll talk a little bit more about neutron stars tomorrow, but I just want to point out what this is starting, which is what we call multi-messenger astronomy. So we saw that signal. We knew where it was that's shown here. Without the Italian detector, it's here and here. With the Italian detector added on, it's in this little region here. Luckily, doubly luckily, a satellite that looks at high energy photons are gamma rays, and they look for something called gamma ray bursts. Thought to be maybe from neutron stars, but people didn't know. Saw at the same time, two seconds after us, something in the sky in this region here. So for the first time, something was seen by electromagnetic instruments at the same time we did, and at the same place in the sky. By the way, this picture here I'm extremely proud of because I've lived for 15 years where astronomers have told us we would never be able to do what they want because we can't measure space, where it comes from as well as they did. And that may be true sometimes, but in this case, they didn't measure as well as we did. So we felt pretty good. Anyway, having the confidence that they saw something two-tenths of a second after we did, we announced this to the astronomical community. There's about 4,000 astronomical instruments in the world, and about half of them ended up pointing to the sky in that direction. So it included, of course, the gravitational wave detectors. It included even detectors that detect neutrinos, but all the wavelengths of light, visible and infrared, radio waves, x-rays, gamma rays, and so forth, and that's still ongoing because this object is still glowing at some wavelengths. This is too complicated for me to explain, but I'll say in words. Each line on here is a different wavelength optical instrument and what they've seen in time. That all, as it's developed together, looking at that place in the sky where we even were able to determine which galaxy it came out of, fits a picture that was phenomenological by a physicist named Metzger at Columbia University that when two neutron stars come together, they make a phenomenon called a kilonova. A supernova, you all realize, is when a star collapses, and this is called a kilonova, and it has different elements to what happens as it develops in time, and so far it looks pretty much like his model. I'm gonna skip this. When that comes together, then a really interesting part, physics-wise, is to understand what happens to these nuclear physics objects in these extreme conditions, highly compact nuclear objects pulling on each other and tearing each other apart as they come together. We think that that's the best way to understand the dynamics of what we call neutron stars, so this is just a phenomenological picture of after it comes together, some of the nuclear physics that might happen and be detectable in the next four or five years if we detect more of these events in the future, and again, the lines going through it are the improvements in LIGO that we'll see in time. A theme that you'll hear about tomorrow when I talk about the evolution of the detectors in time as we evolve them, opening up new science and physics possibilities, but for today we'll call it quits, thank you. Okay, thank you very much for another fabulous lecture, very clear, and to explain so clearly how many challenges had to be overcome before you could make this fantastic discovery. Okay, we have time for questions, and today we even have two microphones, so please raise your hand if you have a question. You said that the effect of a gravitational wave is to change the distance between two masses, for instance, two mirrors, but the wavelength of the light between the two mirrors is not affected. Is there an easy way to understand that? No, but I'll explain it anyway. You have to understand a little bit about general relativity. When you set up the problem in general relativity that I've shown, I refer to it by setting it up in one particular way where I change the length. I can actually, and that's how you set up the metrics and set up general relativity itself, and the effect is a certain size for a certain strength of gravitational waves. I can do the, and the reason I say it's difficult is you have to explain it through general relativity, and I have to be consistent when I set up general relativity. I can alternately set up the problem in general relativity where these masses never move at all, but the light is bent as it goes from one mass to the other because of the gravitational wave going through, and I get the same answer basically. So the strength that I get is the same answer of doing it both ways, but it requires general relativity and doing it in a consistent way to do the calculation. Okay, for other questions. You have shown some pictures from the testing stations which are located in Washington and the other one in the southern parts of the US, and my question, can you explain a little bit closer the experiment, how these waves can be detected, how this experiment works? Well, I'm not sure I know what to add without a more detailed explanation of the interferometry itself, which I didn't talk about in great detail, how we do sensitivity. I talked about two numbers that you need to do it well. An interferometer is simple. We have interferometers in college physics libraries so we're doing nothing more than that, except that we have to do two things. One, we have to do that much better in terms of the interferometry by a factor of 10 to the 10th or so better than you do in a college laboratory. And in a college laboratory, it's usually on an optical table and you tie it down. And the second thing we have to do, as I said, I'm kind of repeating myself, is we have to isolate ourselves from the ground because the ground moves too much, which you don't have to in the college lab. The isolating from the ground I talked about in some detail. We do it by a combination of shock absorbers and, secondly, actively correcting for any motion of the earth. The part that I didn't talk about much, but I'm afraid it needs a whole hour again, is how to do interferometry at that level. And that requires enough photons. We do that by trapping the light in the two arms. We take the light, for example, that comes through that doesn't go back, doesn't go toward the final detector that's going back toward the laser. And we have a mirror there that sends it back in to make yet more light. So it's a multitude of tricks and techniques that enable us to improve interferometry by roughly a factor of a million over accurate interferometry that's done in other ways. And I have to take one by one to tell you how we get the million. We've done that over a period of maybe five, 10 years ago. And we've improved it some, but that's basically not what limits us now. So we can do interferometry well enough. What we have to do is isolate ourselves from the more mundane things, the shaking of the earth, the fact that we work at room temperature and that we don't have enough photons yet and need a more powerful laser, that's what limits us, not the interferometry. Itself, we're doing that much better. So unfortunately I can't answer you much better than that without another lecture. Okay, there's another question. In the plot where you plotted the speed of the merging black holes and the separation, you used a Schwarzschild radius. Yes. Plotted against it. But the Schwarzschild radius depends on the mass. So which mass did you use there? Yeah, so this fit is for the distance for the two masses that we simultaneously fit all this, but this is for the fit to the two masses that I showed, one of them being 29 solar masses, the other one being 36 solar masses, which is what fit our data best going around each other. Then you can ask after you use general relativity with the two masses that you fit the shape with, how far apart is it? What is the Schwarzschild radius? That's all I've shown here and how fast are they going? There's a question over there. Have you got the mic? Since this tool to somehow measure this merging of stars, since you have this tool, can you get a better picture of the density of the universe? And you can see things that you couldn't see before. Is it a new tool to understand better somehow in mapping of the universe? Yeah, I'll talk about that some tomorrow, but let me say yes. I can't answer all questions, obviously, but I think that already we've seen that there's a population of black holes that we didn't know existed before. So whether we can actually tell whether these black holes behave exactly like Einstein's black holes or variants of that, we'll see in time. Can we do anything that can give us some information about dark energy, which is one of the biggest puzzles, not right away, but maybe. So there's a whole variety of things, which I'll hint at more tomorrow than I have time today, that by having a new way to look at the sky, and already I'd say an existence proof is that we saw something that wasn't there before, will give us more information on what the universe is that we can't tell yet. Everything we see so far here, by the way, is basically at close distances. We haven't yet, with improved sensitivity, one thing that we'll be able to do other than see more events, more kinds of events and so forth, is begin to do what's called cosmology, that is to go back to earlier times and see how things evolved. So far, everything that we've seen is not that far back, so that'll come in the future. Okay, there's another question. I understand that LIGO is an instrument that measures the ripples in space, right? The effects gravitational waves make on space. And I understand also that your predecessor, Joe Weber, also tried basically to measure ripples in space. But you mentioned yesterday that gravitational waves also have an effect on time. And I understand that ripples in time would probably stretch, I don't know, but stretch a second or so. Is it conceivable, as an experimental physicist, to design an experiment or a clock that could measure the effects of gravitational waves on time? Maybe, I mean, in principle, the deviations come, as I said, a mixture of space and time. We're doing spatial things. That's just what we're capable of doing. But in principle, if you wanna design a new method, the effects are in time and space together, and maybe that's something that could be done in the future. I don't know how to do it, or I've thought about it very much, but your observation's a true one, I think. Okay, there's another question. Yeah, you showed how LIGO will improve, and is there any projections of Virgo and what is the status of LIGO? Ah, that's all for tomorrow, but I'll say some words. So tomorrow I'm gonna show what we're doing, and what'll improve for sure, because it's a few years away and what might happen after that. We have a program both in LIGO and Virgo to improve by factors of somewhere between two and 10 over the next decade. So you have to take those numbers and cube them in terms of what it does for us, because of what I said, to look further out. The first thing that it'll do is enable us to be cosmological. So we'll start seeing, are there as many of these black holes that we see, for example, now in the near universe, we look out as far as a 10th of the way to the edge of the universe? If you go to the next 10th, the next 10th, are there as many, or were they made later in the universe, and what's the evolution? So that will happen over the next decade. Beyond that, and I'll talk a little bit about that, we have ideas for how to build the next, like happens at CERN or anything in other fields, is not just improving the instruments we have, but making the next generation instruments. And I'll mention that tomorrow. Probably by using the same kind of technique, maybe we don't know how to do time yet, but using this technique, you can get another factor of up to 10. So we're not limited now by nature itself. We're limited by our ability to make an instrument that's more sensitive, and that's a technical and experimental question, not that we've hit something that's gonna bound us, which is very good, but it'll take us some time. You're also asked in a very end about Lisa. I'll mention that Lisa stands for laser interferometer space antenna, and it's a mission to go into space with three, I'll talk briefly about it tomorrow, with three satellites, and that's separated by 50,000 kilometers, or 100,000 kilometers, and by looking at this triangle, if a gravitational wave goes through, it changes the length of the arms relative to each other, and you can measure gravitational waves. It's totally complementary to what we can do on the Earth's surface, because I said that on the Earth's surface, we look at the audio band, 10 hertz to 10,000 hertz basically, and in space, you look at much lower frequencies. The Lisa experiment looks at minus 0.1 hertz to 10 to the minus 4 hertz, so it'll look at a complementary place in wavelength. I'll talk a little bit about what science that might give you, but I'll use first instead today the example that astronomy has made probably its biggest strides in the last 50 years or so by looking at the same phenomena, or different phenomena, and different wavelengths. We did astronomy for 300 years looking at optical telescopes. Now we do astronomy in the ultraviolet, the infrared, radio waves, and so forth and so on, like I showed you for the neutron stars, and that's made a tremendous advance in astronomy, and in the same way in gravitational waves by being able to detect gravitational waves, which will happen at different frequencies, we open up another dimension of looking at gravitational waves, so that's my short answer. I'll talk about it a little more tomorrow. Okay, there's another question from the very back of the room. Yes, in the plot that you showed, the press release plot of the discovery event, you have residuals that are quite low, and then you showed another plot with much more noise. What is the difference between the two, and, yes? Okay, I think you're talking about this one and the next one. So this was the discovery event, and it was a big signal because they're very heavy black holes, and it could be seen just above the noise, and that's why we see it here. You can imagine that this thing, we see something like 10 oscillations, if you actually imagine that the ones on the left side of this plot are seeable. So we see the last ones in the data up here, maybe. So there's maybe eight or 10 oscillations, and that's because the masses are very heavy. It enters our frequency band, and then that's as far as it can go. If we had heavier black holes than this, we wouldn't see them because they're too much at low frequency. What I showed in the next picture was an example of how we detect gravitational waves when the signal's not so big, but it is lower masses, so stays in our detector frequency band much longer. And the example that I gave is this one here, which is, this is seeing it, this one here, which is the second event that we saw, and we do that by this match filter technique that I showed you where at any time, if I looked at only six cycles, the noise is much bigger, but if I take a known shape through this whole thing and multiply it by the noise, I get a signal that I can pull out and then fit it to this shape. So this is called match filtering. It's not invented for us, it's used in noisy environments. We know the shape we're looking for because we're looking for these binary inspirals. We actually use 300,000 templates that look like this for different masses and conditions of the incoming particles, and if we see a signal like this, then we reanalyze it very much. So the second one is our second signal, but as I say, it's different conceptually and how we have to pull it out of the noise. It turns out that this second one that I'm showing here is actually more sensitive than the first one which stood out as a big signal to test general relativity, and the reason is because of the large number of cycles which lets us test the whole change of that shape over some period of time. So as we tested the parameters of general relativity, this gave a better result than the first one. Okay, there's one, maybe last question here. It's a short question. You said that you positioned the L-shaped arms at the two sides at 40 degrees difference. How did you choose the first one? Did you have any preferences or could you have chosen it randomly? Yeah, for first we put them at 90 degrees from each other, not 45, so the two choices was do we put them at 45 degrees or do we make them parallel? Parallel as well as you can taking into account the 16 degree curvature of the earth. The plot of land that we got in Louisiana was very fixed. We could do it one direction. The plot, the piece of land that we have in the state of Washington is just big desert. It's owned by the American Department of Energy but it's part of a big nuclear facility but we're way out and part of it that they don't use for reactors and so forth and we could have done anything we wanted in terms of how we oriented it there. So the question was really whether we took the interferometer that we built in Washington and made it as parallel as we could to the one in Louisiana or we rotated it by 45 degrees. We chose to make it as parallel as we could. Okay, tomorrow there's another chance to come back at 7.30 ask more questions about yet another aspect of this fascinating field but for today let's thank Professor Barish again for this wonderful lecture.