LIGO and Gravitational Waves, III: Nobel Lecture, December 8, 2017

The first observation of gravitational waves, by LIGO on September 14, 2015, was the culmination of a near half century effort by ∼1200 scientists and engineers of the LIGO/Virgo Collaboration. It was also the remarkable beginning of a whole new way to observe the universe: gravitational astronomy. The Nobel Prize for “decisive contributions” to this triumph was awarded to only three members of the Collaboration: Rainer Weiss, Barry Barish, and me. But, in fact, it is the entire collaboration that deserves the primary credit. For this reason, in accepting the Nobel Prize, I regard myself as an icon for the Collaboration. Because this was a collaborative achievement, Rai, Barry and I have chosen to present a single, unified Nobel Lecture, in three parts. Although my third part may be somewhat comprehensible without the other two, readers can only fully understand our Collaboration's achievement, how it came to be, and where it is leading, by reading all three parts. Our three-part written lecture is a detailed expansion of the lecture we actually delivered in Stockholm on December 8, 2017. In Part 1 of this written lecture, Rai describes Einstein's prediction of gravitational waves, and the experimental effort, from the 1960s to 1994, that underpins our discovery of gravitational waves. In Part 2, Barry describes the experimental effort from 1994 up to the present (including our first observation of the waves), and describes what we may expect as the current LIGO detectors reach their design sensitive in about 2020 and then are improved beyond that. In my Part 3, I describe the role of theorists and theory in LIGO's success, and where I expect gravitational-wave astronomy, in four different frequency bands, to take us over the next several decades. But first, I will make some personal remarks about the early history of our joint experimental/theoretical quest to open the first gravitational-wave window onto the universe. I fell in love with relativity when I was a teen age boy growing up in Logan Utah, so it was inevitable that I would go to Princeton University for graduate school and study under the great guru of relativity, John Archibald Wheeler. I arrived at Princeton in autumn 1962, completed my PhD in spring 1965, and stayed on for one postdoctoral year. At Princeton, Wheeler inspired me about black holes, neutron stars, and gravitational waves: relativistic concepts for which there was not yet any observational evidence; and Robert Dicke inspired and educated me about experimental physics, and especially experiments to test Einstein's relativity theory. In the summer of 1963 I attended an eight-week summer school on general relativity at the École d’Été de Physique Theorique in Les Houches, France. There I was exposed to the elegant mathematical theory of gravitational waves in lectures by Ray Sachs, and to gravitational-wave experiment in lectures by Joe Weber. Those lectures and Wheeler's influence, together with conversations I had with Weber while hiking in the surrounding Alpine mountains, got me hooked on gravitational waves as a potential research direction. So it was inevitable that in 1966, when I moved from Princeton to Caltech and began building a research group of six graduate students and three postdocs, I focused my group on black holes, neutron stars, and gravitational waves. My group's gravitational-wave research initially was quite theoretical. We focused on gravitational radiation reaction (whether and how gravitational waves kick back at their source, like a gun kicks back when firing a bullet). More importantly, we developed new ways of computing, accurately, the details of the gravitational waves emitted by astrophysical sources such as spinning, deformed neutron stars, pulsating neutron stars, and pulsating black holes. Most importantly (relying not only on our own group's work but also on the work of colleagues elsewhere) we began to develop a vision for the future of gravitational wave astronomy: What would be the frequency bands in which observations could be made, what might be the strongest sources of gravitational waves in each band, and what information might be extractable from the sources’ waves. We described this evolving vision in a series of review articles, beginning with one by my student Bill Press and me in 1972,2 and continuing onward every few years until 2001,3 when, with colleagues, I wrote the scientific case for the advanced LIGO gravitational wave interferometers.4 In 1972, while Bill Press and I were writing our first vision paper, Rai Weiss at MIT was writing one of the most remarkable and prescient papers I have ever read.5 It proposed an L-shaped laser interferometer gravitational wave detector (gravitational interferometer) with free swinging mirrors, whose oscillating separations would be measured via laser interferometry. The bare-bones idea for such a device had been proposed earlier and independently by Michael Gertsenshtein and Vladislav Pustovoit in Moscow,6 but Weiss and only Weiss identified the most serious noise sources that it would have to face, described ways to deal with each one, and estimated the resulting sensitivity to gravitational waves. Comparing with estimated wave strengths from astrophysical sources, Rai concluded that such an interferometer with kilometer-scale arm lengths had a real possibility to discover gravitational waves. (This is why I regard Rai as the primary inventor of gravitational interferometers.) Rai, being Rai, did not publish his remarkable paper in a normal physics journal. He thought one should not publish until after building the interferometer and finding gravitational waves, so instead he put his paper in an internal MIT report series, but provided copies to colleagues. I heard about Rai's concept for this gravitational interferometer soon after he wrote his paper and while John Wheeler, Charles Misner, and I were putting the finishing touches on our textbook Gravitation7 and preparing to send it to our publisher. I had not yet studied Rai's paper nor discussed his concept with him, but it seemed very unlikely to me that his concept would ever succeed. After all, it required measuring motions of mirrors a trillion times smaller (10–12) than the wavelength of the light used to measure the motions — that is, in technical language, splitting a fringe to one part in 1012. This seemed ridiculous, so I inserted a few words about Rai's gravitational interferometer into our textbook, and labeled it “not promising”. Over the subsequent three years I learned more about Rai's concept, I discussed it in depth with him (most memorably in 1975, in an all-night-long conversation in a hotel room in Washington, D.C.), and I discussed it with others. And I became a convert. I came to understand that Rai's gravitational interferometer had a real possibility of discovering gravitational waves from astrophysical sources. I was also convinced that, if gravitational waves could be observed, they would likely revolutionize our understanding of the universe; so I made the decision that I and my theoretical-physics research group should do everything possible to help Rai and his experimental colleagues discover gravitational waves. My major first step was to persuade Caltech to create an experimental gravitational-wave research group working in parallel with Rai's group at MIT. Rai sketches the rest of this history, on the experimental side, in his Part I of our Nobel Lecture, and I recount some of it in my Nobel biography. I now sketch the theory side of the subsequent history. When Bill Press and I wrote our 1972 vision paper, our understanding of gravitational wave sources was rather muddled, but by 1978 the relativistic astrophysics community had converged on a much better understanding. The convergence was accelerated by a two week Workshop on Sources of Gravitational Waves convened by Larry Smarr in Seattle, Washington in July–August 1978. The participants included almost all of the world's leading gravitational-wave theorists and experimenters, plus a number of graduate students and postdocs: Figure 3. Some conclusions of the workshop were summarized in diagrams depicting the predicted gravitational-wave strain h as a function of frequency f for various conceivable sources:8 three diagrams, one for short-duration (“burst”) waves, one for long-duration, periodic waves (primarily from pulsars and other spinning, deformed neutron stars), and one for stochastic waves (primarily, we thought then, superpositions of emission from many discrete sources). Most relevant to this lecture is the segment of the burst-wave diagram that covers LIGO's frequency band: Figure 4. The supernova line in the figure was an estimated upper limit on the strengths of the waves from supernovae. More modern estimates predict waves much weaker. The box labeled CBD was the range in which the strongest compact-binary waves were expected. Looking at this figure, we Workshop participants concluded that the strongest gravitational wave burst reaching Earth each year would have an amplitude of roughly h ∼ 10–21; and I (mis)remember that in our enthusiasm for this goal, we had T-shirts made up with the logo on them “10–21 or bust”. However, colleagues with better memories than mine assure me we only discussed such T-shirts; the T-shirts were never actually created. The first wave burst that LIGO finally detected, in 2015, was at the location of the red star, which I have added to this figure, and was from CBD: the inspiral and merger of two black holes (a “binary black hole” or BBH). Its amplitude was precisely 10–21 and its frequency was about 200 Hz — a bit stronger strain h and lower frequency than our 1978 estimates. This agreement of prediction and observation is partially luck. Our level of knowledge in 1978 was much lower than it suggests. Although this was just a guess, in planning for LIGO it led us to lay heavy emphasis on binary black holes, as well as on the much better understood binary neutron stars. By 1989 when, under the leadership of Rochus (Robbie) Vogt, we wrote our construction proposal for LIGO9 and submitted it to NSF, gravitational waves from compact binaries were central to our arguments for how sensitive our gravitational interferometers would have to be. The estimated event rates and strengths were so crucial to the scientific case for LIGO that we thought it essential to rely on rate estimates from astrophysicists who had no direct association with our project. For binary neutron stars (BNS), those estimates10 (based on the statistics of observed binary pulsars in our own Milky Way galaxy) placed the nearest BNS merger each year somewhere in the range of 60 to 200 Mpc, with a most likely distance of 100 Mpc (320 million light years), and a signal strength as shown by the blue, arrowed line in Figure 5. (In 2017, when the first BNS was observed, its distance was about 40 Mpc — somewhat closer than expected — and its strength was as shown by the red, arrowed line in the figure.) For BBH merger rates, the uncertainties in 1989 remained so great that we did not quote estimates. (The first BBH seen, in 2015, was as shown by the red star.) In the 1990s and 2000s, astrophysicists made more reliable estimates of BBH and BNS waves, with less than a factor 2 change in the BNS distances, and with the distance for the nearest BBH getting narrowed down to a factor ∼10 uncertainty (∼1000 uncertainty in the rate of bursts).11 It is remarkable that gravitational astronomy gives us the binary's distance r but not its redshift z (fractional change in wavelengths due to motion away from Earth), whereas electromagnetic astronomy, looking at the same binary, can directly measure its redshift but not its distance. In this sense, gravitational and electromagnetic observations are complementary, not duplicative. The relationship between distance and redshift, r(z), is crucial observational data for cosmology; for example, if the binary is not too far away, r(z) determines the Hubble expansion rate of the universe today. Therefore, as Schutz emphasized, for binary neutron stars it should be possible to observe both the binary's gravitational waves (distance) and its electromagnetic waves (redshift) and thereby explore cosmology. That is precisely what happened in 2017 with LIGO's discovery of its first BNS, GW170817; see Barish's Part II of this lecture. (In 1986, having identified the gravitational-wave observables for compact binaries, Schutz then started laying foundations for the analysis of data from gravitational interferometers.13 He became the intellectual leader of this effort in the early years, before I or anyone else in LIGO began thinking seriously about data analysis. For some discussion of LIGO data analysis, see Weiss's and Barish's Parts I and II of this lecture.) As a compact binary spirals inward due radiation reaction, the strength of the mutual gravity of its two bodies grows larger, their speeds grow higher, and correspondingly, relativistic effects (deviations from Newton's laws of gravity) become stronger. This presents a problem (the need to compute relativistic corrections to the binary's waveforms), and an opportunity (the possibility that those corrections, when observed, will bring us additional information about the binary and can be used to test general relativity in new ways). The relativistic corrections are computed, in practice, using the post-Newtonian approximation to general relativity: a power-series expansion in powers of the bodies’ orbital velocities v and their Newtonian gravitational potential Φ ∼ v2. Motivated by the astronomical importance of these waveform corrections, several efforts were mounted to compute them beginning in the 1970s, and then the efforts accelerated in the 1980s, 1990s, and 2000s. I estimate that many more than 100 person years of intense work were put into this effort. The leading contributors included, among others, Luc Blanchet, Thibault Damour, Bala Iyer, and Clifford Will; and by now the computations have been carried up to order v7 beyond Newton's theory of gravity.14 As expected, at each higher order in the computation, there are new observables that can be extracted from the observed waves. These include, most importantly, the individual masses M1 and M2 of the binary's two bodies, and their vectorial spin angular momenta; and, if the binary's orbit is not circular, then its evolving ellipticity and elliptical orientation, and relativistic deviations from elliptical motion. And at each order, there are new opportunities to test, observationally, Einstein's general relativity theory — tests that are now being carried out with LIGO's observational data.15 When the relative velocity of the binary's two bodies approaches 1/3 the speed of light and the bodies near collision, the post-Newtonian approximation breaks down. This, again, presents a problem (how to compute the waveforms) and an opportunity (new information carried by the waveforms). The only reliable way to compute the waveforms in this collision epoch is by numerical simulations: solving Einstein's general relativistic field equations on a computer — numerical relativity. For this reason, in the 1980s I began urging my numerical relativity colleagues to push forward vigorously on such simulations. In the late 1950s and early 1960s, John Wheeler identified geometrodyamics as tremendously important. It is the arena where Einstein's general relativity should be most rich, and deviations from Newton's laws of gravity should be the greatest. Black hole collisions, Wheeler argued, would be an ideal venue for studying geometrodynamics. Recognizing the near impossibility of exploring geometrodynamics analytically, with pencil and paper, Wheeler encouraged his students and colleagues to explore it via computer simulations. With this motivation, Wheeler's students and colleagues began laying foundations for BBH simulations: In 1959–1961, Charles Misner, Richard Arnowitt and Stanley Deser16 brought the mathematics of Einstein's equations into a form nearly ideal for numerical relativity, and Misner analytically solved the initial-value or constraint part of these equations to obtain a mathematical description of two black holes near each other and momentarily at rest.17 Then in 1963, Susan Hahn and Richard Lindquist18 solved the full Einstein equations numerically, on an IBM 7090 computer, and thereby watched the two black holes fall head-on toward each other and begin to distort each other. Sadly, Hahn and Lindquist could not compute long enough to see the holes’ collision and merger, nor the gravitational waves that were emitted. These calculations were picked up in the late 1960s, with some change in the detailed formulation, by Bryce DeWitt and DeWitt's student Larry Smarr, and were brought to fruition by Smarr and his student Kenneth Eppley in 1978.19 In these simulations the two holes collided head on and merged to form a single, highly distorted black hole that vibrated a few times (rang like a damped bell), emitting a burst of gravitational waves, and then settled down into a quiescent state. Here we had, at last, our first example of geometrodynamics. But head-on collisions should occur rarely, if ever, in Nature. When two black holes or stars orbit each other, gravitational radiation reaction drives their orbit into a circular form rather quickly, so BBH collisions and mergers should almost always occur in circular, inspiraling orbits. The big challenge for the 1980s and 1990s, therefore, was to simulate BBHs with shrinking, circular orbits. This was so difficult that by 1992 only modest progress had been made. To accelerate the progress, Richard Isaacson (the NSF program director who had nurtured the LIGO experimental effort with great skill, see Weiss's Part I of this lecture) urged all the world's numerical relativity groups to collaborate on this problem, at least loosely. Richard Matzner of the University of Texas at Austin led this Binary Black Hole Grand Challenge Alliance, and I chaired its advisory committee. To generate collegiality and speed things up, in 1995 I bet many of the Alliance's members that LIGO would observe gravitational waves from BBH mergers before numerical relativists could simulate the mergers; see Figure 10. I fervently hoped to lose, since the simulations would be crucial to extracting the information carried by the observed waves. By early 2002, the Alliance had made much progress, but was still unable to simulate a full orbit of two black holes around each other. The computer codes would crash before an orbit was complete, and I was worried I might win the bet. Alarmed, I left day to day involvement in the LIGO project and focused on helping push numerical relativity forward. Together with Lee Lindblom, I created a numerical relativity research group at Caltech, as an extension of the group I respected most: that of Saul Teukolsky at Cornell. With the help of private funding from the Sherman Fairchild Foundation, we grew our joint Cornell/Caltech Program to Simulate eXtreme Spacetimes (SXS) to the size we thought was needed for success: about 30 researchers. The SXS program's first great triumph arose not, however, from the collaborative work of the SXS team. Rather it was a single-handed triumph by Franz Pretorius, an SXS postdoc. In June 2005, Franz cobbled together a set of computational techniques and tools into a single computer code that successfully simulated the orbital inspiral, collision, and merger of a BBH, one whose black holes were identical and not spinning.20 Six months later, two other small research groups achieved the same thing, using rather different techniques and tools: a group led by Joan Centrella at NASA's Goddard Spaceflight Center, and another led by Manuela Campanelli at the University of Texas at Brownsville.21 I heaved a sigh of relief; perhaps I would actually lose my bet! But we were still a long way from meeting LIGO's needs: It was necessary to simulate BBHs whose two black holes have masses that differ by as much as a factor of 10, and spin at different rates and in different directions. And these simulations had to be carried out with a computer code that was highly stable and robust, and had a well calibrated accuracy that matched LIGO's needs. And it was necessary to carry out a large suite of simulations that covered the full range of parameters to be expected for LIGO's observed sources — seven non-trivial parameters: the ratio of the holes’ masses, and the three components of the vectorial spin of each black hole. We estimated that about a thousand simulations would be needed in preparation for LIGO's early BBH observations. To achieve this goal, Teukolsky led the SXS team in constructing a code based on a formulation of Einstein's equations that is strongly hyperbolic and uses spectral methods — technical details that guarantee the code's accuracy will improve exponentially fast as the coordinate grid is refined. The resulting SXS code is called SpEC for Spectral Einstein Code.22 SpEC was far more difficult to write and perfect than the Pretorius, Centrella, and Campanelli codes, or codes created by several other numerical relativity groups (notably Bernd Brugman's group in Jena, Germany, and Pablo Laguna's Georgia Tech code, which grew out of Matzner's Texas effort). The other codes were perfected several years before SpEC and made major discoveries about geometrodynamics while SpEC was still being perfected. But SpEC did reach perfection a few years before LIGO's first BBH observation and then was used to begin building the large catalog of BBH waveforms to underpin LIGO data analysis;23 and now that we are in the LIGO observational era, only SpEC has the speed and accuracy to fully meet LIGO's near-term needs.24 And with great relief, I have conceded the bet to my numerical relativity colleagues. lnterfacing the output of the numerical relativity codes with LIGO data analysis was a major challenge. The interface was achieved by a quasi-analytic model of the BBH waveforms called the Effective One Body (EOB) Formalism, which was devised by Alessandra Buonanno and Thibault Damour;25 and also achieved by the quasi-analytic Phenomenological Formalism, devised by Parameswaran Ajith and colleagues.26 The numerical-relativity waveforms were used to tune parameters in these formalisms, which then were used to underpin the LIGO data analysis algorithms that discovered the BBH waves and did a first cut at extracting their information. The final extraction of information is most accurately done by direct comparison with the SpEC simulations. Just as I did not play a role in LIGO's experimental R&D, so also I did not play any role at all in formulating and perfecting the SXS computer code SpEC. My primary role in both cases was more that of a visionary. For SpEC a big part of that vision was inherited from Wheeler: Use SpEC simulations of BBHs to predict the geometrodynamic excitations of curved spacetime that are triggered when two black holes collide, and then use LIGO's observations to test those predictions. By 2011, SpEC was mature enough to start exploring geometrodynamics. To assist in those explorations, we developed several visualization tools. The first was a pseudo-embedding diagram (Figure 12), developed by SXS researcher Harald Pfeiffer. In this diagram, Pfeiffer takes the BBH's orbital “plane” (a two-dimensional warped surface), and visualizes its warpage (or, in physicists’ language, its curvature) by depicting it embedded in a hypothetical, flat three dimensional space. The colors of the resulting warped surface depict the slowing of time: in the green regions, time flows at roughly the same rate as far away; in the red regions, the rate of flow of time is greatly slowed; the black regions (not often visible) are inside the black hole, where time flows downward. The silver arrows depict the motion of space.27 These pseudo-embedding diagrams and movie have serious limitations. They depict only the BBH's equatorial plane and not the third dimension of our universe's space. The gravitational waves are not well depicted because they are essentially three dimensional. And some remarkable phenomena are completely missed, for example, two vortices of twisting space (one with a clockwise twist, the other counter-clockwise) that emerge from of each black hole, and also a set of stretching and squeezing warped-spacetime structures called tendices.29 The SXS simulations reveal the rich geometrodynamics of the BBH's spacetime geometry, and of its vortices and tendices. And the beautiful agreements between LIGO's observed gravitational waveforms and those predicted by the SXS simulations (e.g., Figure 6 of Barish's Part II of this lecture) convince us that geometrodynamic storms really do have the forms that the simulations predict —, i.e., that Einstein's general relativity equations predict. If you and I were to watch two black holes spiral inward, collide and merge, with our own eyes or a camera, we would see something very different from the pseudo-embedding snapshots of Figure 12 and their underlying movie. Far behind the BBH would be a field of stars. The light from each star would follow several different paths to our eyes (Figure 13), some rather direct, others making loops around the black holes; so we would see several images of each star. (This is called gravitational lensing.) And as the holes orbit around each other, the images would move in a swirling pattern around the holes’ two black shadows. Teukolsky's graduate students Andy Bohn, Francois Hébert, and Will Throwe produced a movie30 of these swirling stellar patterns from the SXS simulation of LIGO's first observed BBH, GW150914. Figure 14 is a snapshot from that movie. Figures 12 and 14 and the geometrodynamic phenomena that I have described give a first taste of the exciting science that will be extracted from gravitational waves in the future. To that future science I will return below. But first I will dip back into the past, and describe briefly some contributions that theorists have made to the experimental side of LIGO. A major aspect of the LIGO experiment is understanding and controlling a huge range of phenomena that produce noise which can hide gravitational-wave signals. Theorists have contributed to scoping out some of these phenomena. This has been highly enjoyable, and it has broadened the education of theory students. I will give several interesting examples: In each arm of a LIGO interferometer the light beam bounces back and forth between mirrors. A tiny portion of the light scatters off one mirror, then scatters or reflects from the inner face of the vacuum tube that surrounds the beam, then travels to the other mirror, and there scatters back into the light beam (Figure 15, top). The tube face vibrates with an amplitude that is huge compared to the gravitational wave's influence, and those vibrations put a huge, oscillating phase shift onto the scattered light. That huge phase shift on a tiny fraction of the beam's light can produce a net phase shift in the light beam that is bigger than the influence of a gravitational wave. This light-scattering noise can be controlled by placing baffles in the beam tube (dashed lines in Figure 15) to block the scattered light from reaching the far mirror. A bit of the scattered light, however, can still reach the far mirror by diffracting off the edges of the baffles. Baffles and their diffraction of light are a standard issue in optical telescopes and other devices. But not standard, and unique to gravitational interferometers, is the danger that there might be coherent superposition of the oscillating phase shift for light that travels by different routes from one mirror to the other; such coherence could greatly increase the noise. In 1988 Rai Weiss recruited me and my theory students to look at this, determine how serious it is, and devise a way to mitigate it. Eanna Flanagan and I did so. To break the coherence, we gave the baffles deep saw teeth with random heights (Figure 15, bottom), and to minimize the noise further we chose the teeth pattern optimally and optimized the locations of the baffles in the beam tube.31 A segment of one of our random-saw-toothed baffles is my contribution to the Nobel Museum in Stockholm. Humans working near a LIGO mirror create oscillating gravitational forces that might move the mirror more than does a gravitational wave. My wife, Carolee Winstein, is a biokinesiologist (expert on human motion). Using experimental data on human motion from her colleagues, we computed the size of this noise and concluded that, if humans are kept more than 10 meters from a LIGO mirror, the noise is acceptably small.32 This was used as a specification for the layout of the buildings that house the LIGO mirrors. Theory students scoped out noise produced by the gravitational forces of seismic waves in the Earth,33 and of airborne objects such as tumbleweeds.34 Thermal vibrations (vibrations caused by finite temperature) make LIGO's mirrors jiggle. These vibrations can arise in many different ways. Theory student Yuri Levin devised a new method to compute this thermal noise and to identify its many different origins.35 Most importantly he used his method to discover that thermal vibrations in the coatings of LIGO's mirrors (which previously had been overlooked) might be especially serious. This has turned out to be true: In the Advanced LIGO interferometers, and likely in the next generation of gravitational interferometers, coating thermal noise is one of the two most serious noise sources; the other is quantum noise. Quantum noise is noise due to the randomness of the photon distribution in an interferometer's light beams. In each initial LIGO interferometer (Parts I and II of this lecture), the quantum noise had two parts: phot