in which gravitational waves carry to Earth
encoded symphonies of black holes colliding,
and physicists devise instruments
to monitor the waves
and decipher their symphonies
Symphonies
In the core of a far-off galaxy, a billion light-years from Earth and a billion years ago, there accumulated a dense agglomerate of gas and hundreds of millions of stars. The agglomerate gradually shrank, as one star after another was flung out and the remaining 100 million stars sank closer to the center. After 100 million years, the agglomerate had shrunk to several light-years in size, and small stars began, occasionally, to collide and coalesce, forming larger stars. The larger stars consumed their fuel and then imploded to form black holes, and pairs of holes, flying close to each other, occasionally were captured into orbit around each other.
Figure 10.1 shows an embedding diagram for one such black-hole binary. Each hole creates a deep pit (strong spacetime curvature) in the embedded surface, and as the holes encircle each other, the orbiting pits produce ripples of curvature that propagate outward with the speed of light. The ripples form a spiral in the fabric of spacetime around the binary, much like the spiraling pattern of water from a rapidly rotating lawn sprinkler. Just as each drop of water from the sprinkler flies nearly radially outward, so each bit of curvature flies nearly radially outward; and just as the outward flying drops together form a spiraling stream of water, so all the bits of curvature together form spiraling ridges and valleys in the fabric of spacetime.
10.1 An embedding diagram depicting the curvature of space in the orbital “plane” of a binary system made of two black holes. At the center are two pits that represent the strong spacetime curvature around the two holes. These pits are the same as encountered in previous black-hole embedding diagrams, for example, Figure 7.6. As the holes orbit each other, they create outward propagating ripples of curvature called gravitational waves. [Courtesy LIGO Project, California Institute of Technology.]
Since spacetime curvature is the same thing as gravity, these ripples of curvature are actually waves of gravity, or gravitational waves. Einstein’s general theory of relativity predicts, unequivocally, that such gravitational waves must be produced whenever two black holes orbit each other—and also whenever two stars orbit each other.
As they depart for outer space, the gravitational waves push back on the holes in much the same way as a bullet kicks back on the gun that fires it. The waves’ push drives the holes closer together and up to higher speeds; that is, it makes them slowly spiral inward toward each other. The inspiral gradually releases gravitational energy, with half of the released energy going into the waves and the other half into increasing the holes’ orbital speeds.
The holes’ inspiral is slow at first, but the closer the holes draw to each other, the faster they move, the more strongly they radiate their ripples of curvature, and the more rapidly they lose energy and spiral inward (Figures 10.2a,b). Ultimately, when each hole is moving at nearly the speed of light, their horizons touch and merge. Where once there were two holes, now there is one—a rapidly spinning, dumbbell-shaped hole (Figure 10.2c). As the horizon spins, its dumbbell shape radiates ripples of curvature, and those ripples push back on the hole, gradually reducing its dumbbell protrusions until they are gone (Figure 10.2d). The spinning hole’s horizon is left perfectly smooth and circular in equatorial cross section, with precisely the shape described by Kerr’s solution to the Einstein field equation (Chapter 7).
By examining the final, smooth black hole, one cannot in any way discover its past history. One cannot discern whether it was created by the coalescence of two smaller holes, or by the direct implosion of a star made of matter, or by the direct implosion of a star made of antimatter. The black hole has no “hair” from which to decipher its history (Chapter 7).
10.2 Embedding diagrams depicting the curvature of space around a binary system made of two black holes. The diagrams have been embellished by the artist to give a sense of motion. Each successive diagram is at a later moment of time, when the two holes have spiraled closer together. In diagrams (a) and (b), the holes’ horizons are the circles at the bottoms of the pits. The horizons merge just before diagram (c), to form a single, dumbbell-shaped horizon. The rotating dumbbell emits gravitational waves, which carry away its deformation, leaving behind a smooth, spinning, Kerr black hole in diagram (d). [Courtesy LIGO Project, California Institute of Technology.]
However, the history is not entirely lost. A record has been kept: It has been encoded in the ripples of spacetime curvature that the coalescing holes emitted. Those curvature ripples are much like the sound waves from a symphony. Just as the symphony is encoded in the sound waves’ modulations (larger amplitude here, smaller there; higher frequency wiggles here, lower there), so the coalescence history is encoded in modulations of the curvature ripples. And just as the sound waves carry their encoded symphony from the orchestra that produces it to the audience, so the curvature ripples carry their encoded history from the coalescing holes to the distant Universe.
The curvature ripples travel outward in the fabric of spacetime, through the agglomerate of stars and gas where the two holes were born. The agglomerate absorbs none of the ripples and distorts them not at all; the ripples’ encoded history remains perfectly unchanged. On outward the ripples propagate, through the agglomerate’s parent galaxy and into intergalactic space, through the cluster of galaxies in which the parent galaxy resides, then onward through one cluster of galaxies after another and into our own cluster, into our own Milky Way galaxy, and into our solar system, through the Earth, and on out toward other, distant galaxies.
If we humans are clever enough, we should be able to monitor the ripples of spacetime curvature as they pass. Our computers can translate them from ripples of curvature to ripples of sound, and we then will hear the holes’ symphony: a symphony that gradually rises in pitch and intensity as the holes spiral together, then gyrates in a wild way as they coalesce into one, deformed hole, then slowly fades with steady pitch as the hole’s protrusions gradually shrink and disappear.
If we can decipher it, the ripples’ symphony will contain a wealth of information:
1.The symphony will contain a signature that says, “I come from a pair of black holes that are spiraling together and coalescing.” This will be the kind of absolutely unequivocal black-hole signature that astronomers thus far have searched for in vain using light and X-rays (Chapter 8) and radio waves (Chapter 9). Because the light, X-rays, and radio waves are produced far outside a hole’s horizon, and because they are emitted by a type of material (hot, high-speed electrons) that is completely different from that of which the hole is made (pure spacetime curvature), and because they can be strongly distorted by propagating through intervening matter, they can bring us but little information about the hole, and no definitive signature. The ripples of curvature (gravitational waves), by contrast, are produced very near the coalescing holes’ horizons, they are made of the same material (a warpage of the fabric of spacetime) as the holes, they are not distorted at all by propagating through intervening matter—and, as a consequence, they can bring us detailed information about the holes and an unequivocal black-hole signature.
2.The ripples’ symphony can tell us just how heavy each of the holes was, how fast they were spinning, the shape of their orbit (circular? elongated?), where the holes are on our sky, and how far they are from Earth.
3.The symphony will contain a partial map of the inspiraling holes’ spacetime curvature. For the first time we will be able to test definitively general relativity’s black-hole predictions: Does the symphony’s map agree with Kerr’s solution of the Einstein field equation (Chapter 7)? Does the map show space swirling near the spinning hole, as Kerr’s solution demands? Does the amount of swirl agree with Kerr’s solution? Does the way the swirl changes as one approaches the horizon agree with Kerr’s solution?
4.The symphony will describe the merging of the two holes’ horizons and the wild vibrations of the newly merged holes—merging and vibrations of which, today, we have only the vaguest understanding. We understand them only vaguely because they are governed by a feature of Einstein’s general relativity laws that we comprehend only poorly: the laws’ nonlinearity (Box 10.1). By “nonlinearity” is meant the propensity of strong curvature itself to produce more curvature, which in turn produces still more curvature—much like the growth of an avalanche, where a trickle of sliding snow pulls new snow into the flow, which in turn grabs more snow until an entire mountainside of snow is in motion. We understand this nonlinearity in a quiescent black hole; there it is responsible for holding the hole together; it is the hole’s “glue.” But we do not understand what the nonlinearity does, how it behaves, what its effects are, when the strong curvature is violently dynamical. The merger and vibration of two holes is a promising “laboratory” in which to seek such understanding. The understanding can come through hand-in-hand cooperation between experimental physicists who monitor the symphonic ripples from coalescing holes in the distant Universe and theoretical physicists who simulate the coalescence on supercomputers.
Nonlinearity and Its Consequences
A quantity is called linear if its total size is the sum of its parts; otherwise it is nonlinear.
My family income is linear: It is the sum of my wife’s salary and my own. The amount of money I have in my retirement fund is nonlinear: It is not the sum of all the contributions I have invested in the past; rather, it is far greater than that sum, because each contribution started earning interest when it was invested, and each bit of interest in turn earned interest of its own.
The volume of water flowing in a sewer pipe is linear: It is the sum of the contributions from all the homes that feed into the pipe. The volume of snow flowing in an avalanche is nonlinear: A tiny trickle of snow can trigger a whole mountainside of snow to start sliding.
Linear phenomena are simple, easy to analyze, easy to predict. Nonlinear phenomena are complex and hard to predict. Linear phenomena exhibit only a few types of behaviors; they are easy to categorize. Nonlinear phenomena exhibit great richness—a richness that scientists and engineers have only appreciated in recent years, as they have begun to confront a type of nonlinear behavior called chaos. (For a beautiful introduction to the concept of chaos see Gleick, 1987.)
When spacetime curvature is weak (as in the solar system), it is very nearly linear; for example, the tides on the Earth’s oceans are the sum of the tides produced by the Moon’s spacetime curvature (tidal gravity) and the tides produced by the Sun. By contrast, when spacetime curvature is strong (as in the big bang and near a black hole), Einstein’s general relativistic laws of gravity predict that the curvature should be extremely nonlinear—among the most nonlinear phenomena in the Universe. However, as yet we possess almost no experimental or observational data to show us the effects of gravitational nonlinearity, and we are so inept at solving Einstein’s equation that our solutions have taught us about the nonlinearity only in simple situations—for example, around a quiescent, spinning black hole.
A quiescent black hole owes its existence to gravitational nonlinearity; without the gravitational nonlinearity, the hole could not hold itself together, just as without gaseous nonlinearities, the great red spot on the planet Jupiter could not hold itself together. When the imploding star that creates a black hole disappears through the hole’s horizon, the star loses its ability to influence the hole in any way; most important, the star’s gravity can no longer hold the hole together. The hole then continues to exist solely because of gravitational nonlinearity: The hole’s spacetime curvature continuously regenerates itself nonlinearly, without the aid of the star; and the self-generated curvature acts as a nonlinear “glue” to bind itself together.
The quiescent black hole whets our appetites to learn more. What other phenomena can gravitational nonlinearity produce? Some answers may come from monitoring and decoding the ripples of spacetime curvature produced by coalescing black holes. We there might see chaotic, bizarre behaviors that we never anticipated.
To achieve this understanding will require monitoring the holes’ symphonic ripples of curvature. How can they be monitored? The key is the physical nature of the curvature: Spacetime curvature is the same thing as tidal gravity. The spacetime curvature produced by the Moon raises tides in the Earth’s oceans (Figure 10.3a), and the ripples of spacetime curvature in a gravitational wave should similarly raise ocean tides (Figure 10.3b).
General relativity insists, however, that the ocean tides raised by the Moon and those raised by a gravitational wave differ in three major ways. The first difference is propagation. The gravitational wave’s tidal forces (curvature ripples) are analogous to light waves or radio waves: They travel from their source to the Earth at the speed of light, oscillating as they travel. The Moon’s tidal forces, by contrast, are like the electric field of a charged body. Just as the electric field is attached firmly to the charged body and the body carries it around, always sticking out of itself like quills out of a hedgehog, so also the tidal forces are attached firmly to the Moon, and the Moon carries them around, sticking out of itself in a never-changing way, ready always to grab hold of and squeeze and stretch anything that comes into the Moon’s vicinity. The Moon’s tidal forces squeeze and stretch the Earth’s oceans in a way that seems to change every few hours only because the Earth rotates through them. If the Earth did not rotate, the squeeze and stretch would be constant, unchanging.
The second difference is the direction of the tides (Figures 10.3a,b): The Moon produces tidal forces in all spatial directions. It stretches the oceans in the longitudinal direction (toward and away from the Moon), and it squeezes the oceans in transverse directions (perpendicular to the Moon’s direction). By contrast, a gravitational wave produces no tidal forces at all in the longitudinal direction (along the direction of the wave’s propagation). However, in the transverse plane, the wave stretches the oceans in one direction (the up–down direction in Figure 10.3b) and squeezes along the other direction (the front–back direction in Figure 10.3b). This stretch and squeeze is oscillatory. As a crest of the wave passes, the stretch is up-down, the squeeze is front–back; as a trough of the wave passes, there is a reversal to up–down squeeze and front–back stretch; as the next crest arrives, there is a reversal again to up–down stretch and front–back squeeze.
10.3 The tidal forces produced by the Moon and by a gravitational wave. (a) The Moon’s tidal forces stretch and squeeze the Earth’s oceans; the stretch is longitudinal, the squeeze is transverse. (b) A gravitational wave’s tidal forces stretch and squeeze the Earth’s oceans; the forces are entirely transverse, with a stretch along one transverse direction and a squeeze along the other.
The third difference between the Moon’s tides and those of a gravitational wave is their size. The Moon produces tides roughly 1 meter in size, so the difference between high tide and low tide is about 2 meters. By contrast, the gravitational waves from coalescing black holes should produce tides in the Earth’s oceans no larger than about 10−14 meter, which is 10−21 of the size of the Earth (and 1/10,000 the size of a single atom, and just 10 times larger than an atom’s nucleus). Since tidal forces are proportional to the size of the object on which they act (Chapter 2), the waves will tidally distort any object by about 10−21 of its size. In this sense, 10−21 is the strength of the waves when they arrive at Earth.
Why are the waves so weak? Because the coalescing holes are so far away. The strength of a gravitational wave, like the strength of a light wave, dies out inversely with the distance traveled. When the waves are still close to the holes, their strength is roughly 1; that is, they squeeze and stretch an object by about as much as the object’s size; humans would be killed by so strong a stretch and squeeze. However, when the waves have reached Earth, their strength is reduced to roughly (1/30 of the holes’ circumference) / (the distance the waves have traveled).1 For holes that weigh about 10 times as much as the Sun and are a billion light-years away, this wave strength is (
) × (180 kilometers for the horizon circumference)/(a billion lightyears for the distance to Earth) 
10−21. Therefore, the waves distort the Earth’s oceans by 10−21 × (107 meters for the Earth’s size) = 10−14 meter, or 10 times the diameter of an atomic nucleus.
It is utterly hopeless to think of measuring such a tiny tide on the Earth’s turbulent ocean. Not quite so hopeless, however, are the prospects for measuring the gravitational wave’s tidal forces on a carefully designed laboratory instrument—a gravitational-wave detector.
Bars
Joseph Weber was the first person with sufficient insight to realize that it is not utterly hopeless to try to detect gravitational waves. A graduate of the D.S. Naval Academy in 1940 with a bachelor’s degree in engineering, Weber served in World War II on the aircraft carrier Lexington, until it was sunk in the Battle of the Coral Sea, and then became commanding officer of Submarine Chaser No. 690; and he led Brigadier General Theodore Roosevelt, Jr., and 1900 Rangers onto the beach in the 1943 invasion of Italy. After the war he became head of the electronic countermeasures section of the Bureau of Ships for the D.S. Navy. His reputation for mastery of radio and radar technology was so great that in 1948 he was offered and accepted the position of full professor of electrical engineering at the University of Maryland—full professor at age twenty-nine, and with no more college education than a bachelor’s degree.
While teaching electrical engineering at Maryland, Weber prepared for a career change: He worked toward, and completed, a Ph.D. in physics at Catholic University, in part under the same person as had been John Wheeler’s Ph.D. adviser, Karl Herzfeld. From Herzfeld, Weber learned enough about the physics of atoms, molecules, and radiation to invent, in 1951, one version of the mechanism by which lasers work, but he did not have the resources to demonstrate his concept experimentally. While Weber was publishing his concept, two other research groups, one at Columbia University led by Charles Townes and the other in Moscow led by Nikolai Gennadievich Basov and Aleksandr Michailovich Prokharov, independently invented alternative versions of the mechanism, and then went on to construct working lasers.2 Though Weber’s paper had been the first publication on the mechanism, he received hardly any credit; the Nobel Prize and patents went to the Columbia and Moscow scientists. Disappointed, but maintaining close friendships with Townes and Basov, Weber sought a new research direction.
As part of his search, Weber spent a year in John Wheeler’s group, became an expert on general relativity, and with Wheeler did theoretical research on general relativity’s predictions of the properties of gravitational waves. By 1957, he had found his new direction. He would embark on the world’s first effort to build apparatus for detecting and monitoring gravitational waves.
Through late 1957, all of 1958, and early 1959, Weber struggled to invent every scheme he could for detecting gravitational waves. This was a pen, paper, and brainpower exercise, not experimental. He filled four 300-page notebooks with ideas, possible detector designs, and calculations of the expected performance of each design. One idea after another he cast aside as not promising. One design after another failed to give high sensitivity. But a few held promise; and of them, Weber ultimately chose a cylindrical aluminum bar about 2 meters long, a half meter in diameter, and a ton in weight, oriented broadside to the incoming waves (Figure 10.4 below).
As the waves’ tidal force oscillates, it should first compress, then stretch, then compress such a bar’s ends. The bar has a natural mode of vibration which can respond resonantly to this oscillating tidal force, a mode in which its ends vibrate in and out relative to its center. That natural mode, like the ringing of a bell or tuning fork or wine glass, has a well-defined frequency. Just as a bell or tuning fork or wine glass can be made to ring sympathetically by sound waves that match its natural frequency, so the bar can be made to vibrate sympathetically by oscillating tidal forces that match its natural frequency. To use such a bar as a gravitational-wave detector, then, one should adjust its size so its natural frequency will match that of the incoming gravitational waves.
What frequency will that be? In 1959, when Weber embarked on this project, few people believed in black holes (Chapter 6), and the believers understood only very little about a hole’s properties. Nobody then imagined that holes could collide and coalesce and eject ripples of spacetime curvature with encoded histories of their collisions. Nor could anyone give much hopeful guidance about other sources of gravitational waves.
So Weber embarked on his effort nearly blind. His sole guide was a crude (but correct) argument that the gravitational waves probably would have frequencies below about 10,000 Hertz (10,000 cycles per second)—that being the orbital frequency of an object which moves at the speed of light (the fastest possible) around the most compact conceivable star: one with size near the critical circumference. So Weber designed the best detectors he could, letting their resonant frequencies fall wherever they might below 10,000 Hertz, and hoped that the Universe would provide waves at his chosen frequencies. He was lucky. The resonant frequencies of his bars were about 1000 Hertz (1000 cycles of oscillation per second), and it turns out that some of the waves from coalescing black holes should oscillate at just such frequencies, as should some of the waves from supernova explosions and from coalescing pairs of neutron stars.
The most challenging aspect of Weber’s project was to invent a sensor for monitoring his bars’ vibrations. Those wave-induced vibrations, he expected, would be tiny: smaller than the diameter of the nucleus of an atom [but he did not know, in the 1960s, how very tiny: just 10−21 × (the 2-meter length of his bars) 10−21 meter or one-millionth the diameter of the nucleus of an atom, according to more recent estimates]. To most physicists of the late 1950s and the 1960s, even one-tenth of the diameter of an atomic nucleus looked impossibly difficult to measure. Not so to Weber. He invented a sensor that was up to the task.
10.4 Joseph Weber, demonstrating the piezoelectric crystals glued around the middle of his aluminum bar; ca. 1973. Gravitational waves should drive the bar’s end-to-end vibrations, and those vibrations should squeeze the crystals in and out so they produce oscillating voltages that are detected electronically. [Photo by James P. Blair, courtesy the National Geographic Society.]
Weber’s sensor was based on the piezoelectric effect, in which certain kinds of materials (certain crystals and ceramics), when squeezed slightly, develop electric voltages from one end to the other. Weber would have liked to make his bar from such a material, but these materials were far too expensive, so he did the next best thing: He made his bar from aluminum, and he then glued piezoelectric crystals around the bar’s middle (Figure 10.4). As the bar vibrated, its surface squeezed and stretched the crystals, each crystal developed an oscillating voltage, and Weber strung the crystals together one after another in an electric circuit so their tiny oscillating voltages would add up to a large enough voltage for electronic detection, even when the bar’s vibrations were only one-tenth the diameter of the nucleus of an atom.
In the early 1960s, Weber was a lonely figure, the only experimental physicist in the world seeking gravitational waves. With his bitter aftertaste of laser competition, he enjoyed the loneliness. However, in the early 1970s, his impressive sensitivities and evidence that he might actually be detecting waves (which, in retrospect, I am convinced he was not) attracted dozens of other experimenters, and by the 1980s more than a hundred talented experimenters were engaged in a competition with him to make gravitational-wave astronomy a reality.
I first met Weber on a hillside opposite Mont Blanc in the French Alps, in the summer of 1963, four years after he embarked on his project to detect gravitational waves. I was a graduate student, just beginning research in relativity, and along with thirty-five other students from around the world I had come to the Alps for an intensive two-month summer school focusing solely on Einstein’s general relativistic laws of gravity. Our teachers were the world’s greatest relativity experts—John Wheeler, Roger Penrose, Charles Misner, Bryce DeWitt, Joseph Weber, and others—and we learned from them in lectures and private conversations, with the glistening snows of the Aguille de Midi and Mont Blanc towering high in the sky above us, belled cows grazing in brilliant green pastures around us, and the picturesque village of Les Houches several hundred meters below us, at the foot of our school’s hillside.
In this glorious setting, Weber lectured about gravitational waves and his project to detect them, and I listened, fascinated. Between lectures Weber and I conversed about physics, life, and mountain climbing, and I came to regard him as a kindred soul. We were both loners; neither of us enjoyed intense competition or vigorous intellectual give-and-take. We both preferred to wrestle with a problem on our own, seeking advice and ideas occasionally from friends, but not being buffeted by others who were trying to beat us to a new insight or discovery.
Over the next decade, as research on black holes heated up and entered its golden age (Chapter 7), I began to find black-hole research distasteful—too much intensity, too much competition, too much rough-and-tumble. So I cast about for another area of research, one with more elbow room, into which I could put most of my effort while still working on black holes and other things part time. Inspired by Weber, I chose gravitational waves.
Like Weber, I saw gravitational waves as an infant research field with a bright future. By entering the field in its infancy, I could have the fun of helping mold it, I could lay foundations on which others later would build, and I could do so without others breathing down my neck, since most other relativity theorists were then focusing on black holes.
For Weber, the foundations to be laid were experimental: the invention, construction, and continual improvement of detectors. For me, they were theoretical: try to understand what Einstein’s gravitational laws have to say about how gravitational waves are produced, how they push back on their sources as they depart, and how they propagate; try to figure out which kinds of astronomical objects will produce the Universe’s strongest waves, how strong their waves will be, and with what frequencies they will oscillate; invent mathematical tools for computing the details of the encoded symphonies produced by these objects, so when Weber and others ultimately detect the waves, theory and experiment can be compared.
In 1969 I spent six weeks in Moscow, at Zel’dovich’s invitation. One day Zel’dovich took time out from bombarding me and others with new ideas (Chapters 7 and 12), and drove me over to Moscow University to introduce me to a young experimental physicist, Vladimir Braginsky. Braginsky, stimulated by Weber, had been working for several years to develop techniques for gravitational-wave detection; he was the first experimenter after Weber to enter the field. He was also in the midst of other- fascinating experiments: a search for quarks (a fundamental building block of protons and neutrons), and an experiment to test Einstein’s assertion that all objects, no matter what their composition, fall with the same acceleration in a gravitational field (an assertion that underlies Einstein’s description of gravity as spacetime curvature).
I was impressed. Braginsky was clever, deep, and had excellent taste in physics; and he was warm and forthright, as easy to talk to about politics as about science. We quickly became close friends and learned to respect each other’s world views. For me, a liberal Democrat in the American spectrum, the freedom of the individual was paramount over all other considerations. No government should have the right to dictate how one lives one’s life. For Braginsky, a nondoctrinaire Communist, the responsibility of the individual to society was paramount. We are our brothers’ keepers, and well we should be in a world where evil people like Joseph Stalin can gain control if we are not vigilant.
Joseph Weber, Kip Thorne, and Tony Tyson at a conference on gravitational radiation in Warsaw, Poland, September 1973. [photo by Marek Holzman, courtesy Andrzej Trautman;]
Vladimir Braginsky and Kip Thorne, in Pasadena, California, October 1984. [courtesy Valentin N. Rudenko.]
Braginsky had foresight that nobody else possessed. During our 1969 meeting, and then again in 1971 and 1972, he warned me that the bars being used to search for gravitational waves have a fundamental, ultimate limitation. That limitation, he told me, comes from the laws of quantum mechanics. Although we normally think of quantum mechanics as governing tiny objects such as electrons, atoms, and molecules, if we make sufficiently precise measurements on the vibrations of a one-ton bar, we should see those vibrations also behave quantum mechanically, and their quantum mechanical behavior will ultimately cause problems for gravitational-wave detection. Braginsky had convinced himself of this by calculating the ultimate performance of Weber’s piezoelectric crystals and of several other kinds of sensors that one might use to measure a bar’s vibrations.
I didn’t understand what Braginsky was talking about; I didn’t understand his reasoning, I didn’t understand his conclusion, I didn’t understand its importance, and I didn’t pay much attention. Other things he was teaching me seemed much more important: From him I was learning how to think about experiments, how to design experimental apparatus, how to predict the noise that will plague the apparatus, and how to suppress the noise so the apparatus will succeed in its task—and from me, Braginsky was learning how to think about Einstein’s laws of gravity, how to identify their predictions. We were rapidly becoming a team, each bringing to our joint enterprise his own expertise; and over the next two decades, together we would have great fun and make a few discoveries.
Each year in the early and mid-1970s, when we saw each other in Moscow or Pasadena or Copenhagen or Rome or wherever, Braginsky repeated his warning about quantum mechanical trouble for gravitational- wave detectors, and each year I again did not understand. His warning was somewhat muddled because he himself did not understand fully what was going on. However, in 1976, after Braginsky, and independently Robin Giffard at Stanford University, managed to make the warning more clear, I suddenly understood. The warning was serious, I finally realized; the ultimate sensitivity of a bar detector is severely limited by the uncertainty principle.
The uncertainty principle is a fundamental feature of the laws of quantum mechanics. It says that, if you make a highly accurate measurement of the position of an object, then in the process of your measurement you will necessarily kick the object, thereby perturbing the object’s velocity in a random, unpredictable way. The more accurate your position measurement is, the more strongly and unpredictably you must perturb the object’s velocity. No matter how clever you are in designing your measurement, you cannot circumvent this innate uncertainty. (See Box 10.2.)
The Uncertainty Principle and Wave/Particle Duality
The uncertainty principle is intimately related to wave/particle duality (Box 4.1)—that is, to the propensity of particles to act sometimes like waves and sometimes like particles.
If you measure the position of a particle (or any other object, for example, the end of a bar) and learn that it is somewhere inside some error box, then regardless of what the particle’s wave might have looked like before the measurement, during the measurement the measuring apparatus will “kick” the wave and thereby confine it inside the error box’s interior. The wave, thereby, will acquire a confined form something like the following:
Such a confined wave contains many different wavelengths, ranging from the size of the box itself (marked max above) to the tiny size of the corners at which the wave begins and ends (marked min). More specifically, the confined wave can be constructed by adding together, that is, superimposing, the following oscillatory waves, which have wavelengths ranging from max down to min:
Now, recall that the shorter the wavelength of the wave’s oscillations, the larger the energy of the particle, and thus also the larger the particle’s velocity. Since the measurement has given the wave a range of wavelengths, the particle’s energy and velocity might now be anywhere in the corresponding ranges; in other words, its energy and velocity are uncertain.
To recapitulate, the measurement confined the particle’s wave to the error box (first diagram above); this made the wave consist of a range of wavelengths (second diagram); that range of wavelengths corresponds to a range of energy and velocity; and the velocity is therefore uncertain. No matter how hard you try, you cannot avoid producing this velocity uncertainty when you measure the particle’s position. Moreover, when this chain of reasoning is examined in greater depth, it predicts that the more accurate your measurement, that is, the smaller your error box, the larger the ranges of wavelengths and velocity, and thus the larger the uncertainty in the particle’s velocity.
The uncertainty principle governs not only measurements of microscopic objects such as electrons, atoms, and molecules; it also governs measurements of large objects. However, because a large object has large inertia, a measurement’s kick will perturb its velocity only slightly. (The velocity perturbation will be inversely proportional to the object’s mass.)
The uncertainty principle, when applied to a gravitational-wave detector, says that the more accurately a sensor measures the position of the end or side of a vibrating bar, the more strongly and randomly the measurement must kick the bar.
For an inaccurate sensor, the kick can be tiny and unimportant, but because the sensor was inaccurate, you do not know very well the amplitude of the bar’s vibrations and thus cannot monitor weak gravitational waves.
For an extremely accurate sensor, the kick is so enormous that it strongly changes the bar’s vibrations. These large, unknowable changes thus mask the effects of any gravitational wave you might try to detect.
Somewhere between these two extremes there is an optimal accuracy for the sensor: an accuracy neither so poor that you learn little nor so great that the unknowable kick is strong. At that optimal accuracy, which is now called Braginsky’s standard quantum limit, the effect of the kick is just barely as debilitating as the errors made by the sensor. No sensor can monitor the bar’s vibrations more accurately than this standard quantum limit. How small is this limit? For a 2-meter-long, 1-ton bar, it is about 100,000 times smaller than the nucleus of an atom.
In the 1960s, nobody seriously contemplated the need for such accurate measurements, because nobody understood very clearly just how weak should be the gravitational waves from black holes and other astronomical bodies. But by the mid-1970s, spurred on by Weber’s experimental project, I and other theorists had begun to figure out how strong the strongest waves were likely to be. Roughly 10−21 was the answer, and this meant the waves would make a 2-meter bar vibrate with an amplitude of only 10−21 × (2 meters), or about a millionth the diameter of the nucleus of an atom. If these estimates were correct (and we knew they were highly uncertain), then the gravitational-wave signal would be ten times smaller than Braginsky’s standard quantum limit, and therefore could not possibly be detected using a bar and any known kind of sensor.
Though this was extremely worrisome, all was not lost. Braginsky’s deep intuition told him that, if experimenters were especially clever, they ought to be able to circumvent his standard quantum limit. There ought to be a new way to design a sensor, he argued, so that its unknowable and unavoidable kick does not hide the influence of the gravitational waves on the bar. To such a sensor Braginsky gave the name quantum nondemolition3; “quantum” because the sensor’s kick is demanded by the laws of quantum mechanics, “nondemolition” because the sensor would be so configured that the kick would not demolish the thing you are trying to measure, the influence of the waves on the bar. Braginsky did not have a workable design for a quantum nondemolition sensor, but his intuition told him that such a sensor should be possible.
This time I listened, carefully; and over the next two years I and my group at Caltech and Braginsky and his group in Moscow both struggled, on and off, to devise a quantum nondemolition sensor.
We both found the answer simultaneously in the autumn of 1977—but by very different routes. I remember vividly my excitement when the idea occurred to Carlton Caves and me4 in an intense discussion over lunch at the Greasy (Caltech’s student cafeteria). And I recall the bittersweet taste of learning that Braginsky, Yuri Vorontsov, and Farhid Khalili had had a significant piece of the same idea in Moscow at essentially the same time—bitter because I get great satisfaction from being the first to discover something new; sweet because I am so fond of Braginsky and thus get pleasure from sharing discoveries with him.
Our full quantum nondemolition idea is rather abstract and permits a wide variety of sensor designs for circumventing Braginsky’s standard quantum limit. The idea’s abstractness, however, makes it difficult to explain, so here I shall describe just one (not very practical) example of a quantum nondemolition sensor.5 This example has been called, by Braginsky, a stroboscopic sensor.
A stroboscopic sensor relies on a special property of a bar’s vibrations: If the bar is given a very sharp, unknown kick, its amplitude of vibration will change, but no matter what that amplitude change is, precisely one period of oscillation after the kick the bar’s vibrating end will return to the same position as it had at the moment of the kick (black dots in Figure 10.5). At least this is true if a gravitational wave (or some other force) has not squeezed or stretched the bar in the meantime. If a wave (or other force) has squeezed the bar in the meantime, then the bar’s position one period later will be changed.
To detect the wave, then, one should build a sensor that makes stroboscopic measurements of the bar’s vibrating ends, a sensor that measures the position of the bar’s ends quickly once each period of vibration. Such a sensor will kick the bar in each measurement, but the kicks will not change the position of the bar’s ends at the times of subsequent measurements. If the position is found to have changed, then a gravitational wave (or some other force) must have squeezed the bar.
Although quantum nondemolition sensors solved the problem of Braginsky’s standard quantum limit, by the mid-1980s I had become rather pessimistic about the prospects for bar detectors to bring gravitational- wave astronomy to fruition. My pessimism had two causes.
10.5 The principle underlying a stroboscopic quantum nondemolition measurement. Plotted vertically is the position of the end of a vibrating bar; plotted horizontally is time. If a quick, highly precise measurement of the position is made at the time marked KICK, the sensor that makes the measurement will give the bar a sudden, unknowable kick, thereby changing the bar’s amplitude of vibration in an unknown way. However, there will be no change of the position of the bar’s end precisely one period after the kick, or two periods, or three periods. Those positions will be the same as at the time of the kick and will be completely independent of the kick.
First, although the bars built by Weber, by Braginsky, and by others had achieved far better sensitivities than anyone had dreamed possible in the 1950s, they were still only able to detect with confidence waves of strength 10−17 or larger. This was 10,000 times too poor for success, if I and others had correctly estimated the strengths of the waves arriving at Earth. This by itself was not serious, since the march of technology has often produced 10,000-fold improvements in instruments over times of twenty years or less. [One example was the angular resolution of the best radio telescopes, which improved from tens of degrees in the mid-1940s to a few arc seconds in the mid-1960s (Chapter 9). Another was the sensitivity of astronomical X-ray detectors, which improved by a factor of 1010 between 1958 and 1978, that is, at an average rate of 10,000 every eight years (Chapter 8).] However, the rate of improvement of the bars was so slow, and projections of the future technology and techniques were so modest, that there seemed no reasonable way for a 10,000-fold improvement to be made in the foreseeable future. Success, thus, would likely hinge on the waves being stronger than the 10−21 estimates—a real possibility, but not one that anybody was happy to rely on.
Second, even if the bars did succeed in detecting gravitational waves, they would have enormous difficulty in decoding the waves’ symphonic signals, and in fact would probably fail. The reason was simple: Just as a tuning fork or wine glass responds sympathetically only to a sound whose frequency is close to its natural frequency, so a bar would respond only to gravitational waves whose frequency is near the bar’s natural frequency; in technical language, the bar detector has a narrow bandwidth (the bandwidth being the band of frequencies to which it responds). But the waves’ symphonic information should typically be encoded in a very wide band of frequencies. To extract the waves’ information, then, would require a “xylophone” of many bars, each covering a different, tiny portion of the signal’s frequencies. How many bars in the xylophone? For the types of bars then being planned and constructed, several thousand—far too many to be practical. In principle it would be possible to widen the bars’ bandwidths and thereby manage with, say, a dozen bars, but to do so would require major technical advances beyond those for reaching a sensitivity of 10−21.
Although I did not say much in public in the 1980s about my pessimistic outlook, in private I regarded it as tragic because of the great effort that Weber, Braginsky, and my other friends and colleagues had put into bars, and also because I had become convinced that gravitational radiation has the potential to produce a revolution in our knowledge of the Universe.
LIGO
To understand the revolution that the detection and deciphering of gravitational waves might bring, let us recall the details of a previous revolution: the one created by the development of X-ray and radio telescopes (Chapters 8 and 9).
In the 1930s, before the advent of radio astronomy and X-ray astronomy, our knowledge of the Universe came almost entirely from light. Light showed it to be a serene and quiescent Universe, a Universe dominated by stars and planets that wheel smoothly in their orbits, shining steadily and requiring millions or billions of years to change in discernible ways.
This tranquil view of the Universe was shattered, in the 1950s, 1960s, and 1970s, when radio-wave and X-ray observations showed us our Universe’s violent side: jets ejected from galactic nuclei, quasars with fluctuating luminosities far brighter than our galaxy, pulsars with intense beams shining off their surfaces and rotating at high speeds. The brightest objects seen by optical telescopes were the Sun, the planets, and a few nearby, quiescent stars. The brightest objects seen by radio telescopes were violent explosions in the cores of distant galaxies, powered (presumably) by gigantic black holes. The brightest objects seen by X-ray telescopes were small black holes and neutron stars accreting hot gas from binary companions.
What was it about radio waves and X-rays that enabled them to create such a spectacular revolution? The key was the fact that they brought us very different kinds of information than is brought by light: Light, with its wavelength of a half micron, was emitted primarily by hot atoms residing in the atmospheres of stars and planets, and it thus taught us about those atmospheres. The radio waves, with their 10million- fold greater wavelengths, were emitted primarily by near-light-speed electrons spiraling in magnetic fields, and they thus taught us about the magnetized jets shooting out of galactic nuclei, about the gigantic, magnetized intergalactic lobes that the jets feed, and about the magnetized beams of pulsars. The X-rays, with their thousand-fold shorter wavelengths than light, were produced mostly by high-speed electrons in ultra-hot gas accreting onto black holes and neutron stars, and they thus taught us directly about the accreting gas and indirectly about the holes and neutron stars.
The differences between light, on the one hand, and radio waves and X-rays, on the other, are pale compared to the differences between the electromagnetic waves (light, radio, infrared, ultraviolet, X-ray, and gamma ray) of modern astronomy and gravitational waves. Correspondingly, gravitational waves might revolutionize our understanding of the Universe even more than did radio waves and X-rays. Among the differences between electromagnetic waves and gravitational waves, and their consequences, are these6:
•The gravitational waves should be emitted most strongly by large-scale, coherent vibrations of spacetime curvature (for example, the collision and coalescence of two black holes) and by large-scale, coherent motions of huge amounts of matter (for example, the implosion of the core of a star that triggers a supernova, or the inspiral and merger of two neutron stars that are orbiting each other). Therefore, gravitational waves should show us the motions of huge curvatures and huge masses. By contrast, cosmic electromagnetic waves are usually emitted individually and separately by enormous numbers of individual and separate atoms or electrons; and these individual electromagnetic waves, each oscillating in a slightly different manner, then superimpose on each other to produce the total wave that an astronomer measures. As a result, from electromagnetic waves we learn primarily about the temperature, density, and magnetic fields experienced by the emitting atoms and electrons.
•Gravitational waves are emitted most strongly in regions of space where gravity is so intense that Newton’s description fails and must be replaced by Einstein’s, and where huge amounts of matter or spacetime curvature move or vibrate or swirl at near the speed of light. Examples are the big bang origin of the Universe, the collisions of black holes, and the pulsations of newborn neutron stars at the centers of supernova explosions. Since these strong-gravity regions are typically surrounded by thick layers of matter that absorb electromagnetic waves (but do not absorb gravitational waves), the strong-gravity regions cannot send us electromagnetic waves. The electromagnetic waves seen by astronomers come, by contrast, almost entirely from weak-gravity, low-velocity regions; for example, the surfaces of stars and supernovae.
These differences suggest that the objects whose symphonies we might study with gravitational-wave detectors will be largely invisible in light, radio waves, and X-rays; and the objects that astronomers now study in light, radio waves, and X-rays will be largely invisible in gravitational waves. The gravitational Universe should thus look extremely different from the electromagnetic Universe; from gravitational waves we should learn things that we will never learn electromagnetically. This is why gravitational waves are likely to revolutionize our understanding of the Universe.
It might be argued that our present electromagnetically based understanding of the Universe is so complete compared with the optically based understanding of the 1930s that a gravitational-wave revolution will be far less spectacular than was the radio-wave/X-ray revolution. This seems to me unlikely. I am painfully aware of our lack of understanding when I contemplate the sorry state of present estimates of the gravitational waves bathing the Earth. For each type of gravitational-wave source that has been thought about, with the exception of binary stars and their coalescences, either the strength of the source’s waves for a given distance from Earth is uncertain by several factors of 10, or the rate of occurrence of that type of source (and thus also the distance to the nearest one) is uncertain by several factors of 10, or the very existence of the source is uncertain.
These uncertainties cause great frustration in the planning and design of gravitational-wave detectors. That is the downside. The upside is the fact that, if and when gravitational waves are ultimately detected and studied, we may be rewarded with major surprises.
In 1976 I had not yet become pessimistic about bar detectors. On the contrary, I was highly optimistic. The first generation of bar detectors had recently reached fruition and had operated with a sensitivity that was remarkable compared to what one might have expected; Braginsky and others had invented a number of clever and promising ideas for huge future improvements; and I and others were just beginning to realize that gravitational waves might revolutionize our understanding of the Universe.
My enthusiasm and optimism drove me, one evening in November 1976, to wander the streets of Pasadena until late into the night, struggling with myself over whether to propose that Caltech create a project to detect gravitational waves. The arguments in favor were obvious: for science in general, the enormous intellectual payoff if the project succeeded; for Caltech, the opportunity to get in on the ground floor of an exciting new field; for me, the possibility to have a team of experimenters at my home institution with whom to interact, instead of relying primarily on Braginsky and his team on the other side of the world, and the possibility to play a more central role than I could commuting to Moscow (and thereby have more fun). The argument against was also obvious: The project would be risky; to succeed, it would require large resources from Caltech and the D.S. National Science Foundation and enormous time and energy from me and others; and after all that investment, it might fail. It was much more risky than Caltech’s entry into radio astronomy twenty-three years earlier (Chapter 9).
After many hours of introspection, the lure of the payoffs won me over. And after several months studying the risks and payoffs, Caltech’s physics and astronomy faculty and administration unanimously approved my proposal—subject to two conditions. We would have to find an outstanding experimental physicist to lead the project, and the project would have to be large enough and strong enough to have a good chance of success. This meant, we believed, much larger and stronger than Weber’s effort at the University of Maryland or Braginsky’s effort in Moscow or any of the other gravitational-wave efforts then under way.
The first step was finding a leader. I flew to Moscow to ask Braginsky’s advice and feel him out about taking the post. My feeler tore him every which way. He was torn between the far better technology he would have in America and the greater craftsmanship of the technicians in Moscow (for example, intricate glassblowing was almost a lost art in America, but not in Moscow). He was torn between the need to build a project from scratch in America and the crazy impediments that the inefficient, bureaucracy-bound Soviet system kept putting in the way of his project in Moscow. He was torn between loyalty to his native land and disgust with his native land, and between his feelings that life in America is barbaric because of the way we treat our poor and our lack of medical care for everyone and his feelings that life in Moscow is miserable because of the power of incompetent officials. He was torn between the freedom and wealth of America and fear of KGB retribution against family and friends and perhaps even himself if he “defected.” In the end he said no, and recommended instead Ronald Drever of Glasgow University.
Others I consulted were also enthusiastic about Drever. Like Braginsky, he was highly creative, inventive, and tenacious—traits that would be essential for success of the project. The Caltech faculty and administration gathered all the information they could about Drever and other possible leaders, selected Drever, and invited him to join the Caltech faculty and initiate the project. Drever, like Braginsky, was torn, but in the end he said yes. We were off and running.
I had presumed, when proposing the project, that like Weber and Braginsky, Caltech would focus on building bar detectors. Fortunately (in retrospect) Drever insisted on a radically different direction. In Glasgow he had worked with bar detectors for five years, and he could see their limitations. Much more promising, he thought, were interferometric gravitational-wave detectors (interferometers for short—though they are radically different from the radio interferometers of Chapter 9).
Interferometers for gravitational-wave detection had first been conceived of in primitive form in 1962 by two Russian friends of Braginsky’s, Mikhail Gertsenshtein and V.I. Pustovoit, and independently in 1964 by Joseph Weber. Unaware of these early ideas, Rainer Weiss devised a more mature variant of an interferometric detector in 1969, and then he and his MIT group went on to design and build one in the early 1970s, as did Robert Forward and colleagues at Hughes Research Laboratories in Malibu, California. Forward’s detector was the first to operate successfully. By the late 1970s, these interferometric detectors had become a serious alternative to bars, and Drever had added his own clever twists to their design.
Figure 10.6 shows the basic idea behind an interferometric gravitational-wave detector. Three masses hang by wires from overhead supports at the corner and ends of an “L” (Figure 10.6a). When the first crest of a gravitational wave enters the laboratory from overhead or underfoot, its tidal forces should stretch the masses apart along one arm of the “L” while squeezing them together along the other arm. The result will be an increase in the length L1 of the first arm (that is, in the distance between the arm’s two masses) and a decrease in the length L2 of the second arm, When the wave’s first crest has passed and its first trough arrives, the directions of stretch and squeeze will be changed: L1 will decrease and L2 will increase. By monitoring the arm-length difference, L1 – L2, one can seek gravitational waves.
10.6 A laser interferometric gravitational-wave detector. This instrument is very similar to the one used by Michelson and Morley in 1887 to search for motion of the Earth through the aether (Chapter 1). See the text for a detailed explanation.
The difference L1 – L2 is monitored using interferometry (Figure 10.6b and Box 10.3). A laser beam shines onto a beam splitter that rides on the corner mass. The beam splitter reflects half of the beam and transmits half, and thereby splits the beam in two. The two beams go down the two arms of the interferometer and bounce off mirrors that ride on the arms’ end masses, and then return to the beam splitter. The splitter half-transmits and half-reflects each of the beams, so part of each beam’s light is combined with part from the other and goes back toward the laser, and the other parts of the two beams are combined and go toward the photodetector. When no gravitational wave is present, the contributions from the two arms interfere in such a way (Box 10.3) that all the net light goes back toward the laser and none toward the photodetector. If a gravitational wave slightly changes L1 - L2, the two beams will then travel slightly different distances in their two arms and will interfere slightly differently—a tiny amount of their combined light will now go into the photodetector. By monitoring the amount of light reaching the photodetector, one can monitor the arm-length difference L1 - L2, and thereby monitor gravitational waves.
Box 10.3
Interference and Interferometry
Whenever two or more waves propagate through the same region of space, they superimpose on each other “linearly” (Box 10.1); that is, they add. For example, the following dotted wave and dashed wave superimpose to produce the heavy solid wave:
Notice that at locations such as A where a trough of one wave (dotted) superimposes on a crest of the other (dashed), the waves cancel, at least in part, to produce a vanishing or weak total wave (solid); and at locations such as B where two troughs superimpose or two crests superimpose, the waves reinforce each other. One says that the waves are interfering with each other, destructively in the first case and constructively in the second. Such superimposing and interference occurs in all types of waves—ocean waves, radio waves, light waves, gravitational waves—and such interference is central to the operation of radio interferometers (Chapter 9) and interferometric detectors for gravitational waves.
In the interferometric detector of Figure 10.6b, the beam splitter superimposes half the light wave from one arm on half from the other and sends them toward the laser, and it superimposes the other halves and sends them toward the photodetector. When no gravitational wave or other force has moved the masses and their mirrors, the superimposed light waves have the following forms, where the dashed curve shows the wave from arm 1, the dotted curve the wave from arm 2, and the solid curve the superimposed, total wave:
Toward the photodetector, the waves interfere perfectly destructively, so the total, superimposed wave vanishes, which means that the photodetector sees no light at all. When a gravitational wave or other force has lengthened op.e arm slightly and shortened the other, then the beam from the one arm arrives at the beam splitter with a slight delay relative to the other, and the superimposed waves therefore look like this:
The destructive interference in the photodetector’s direction is no longer perfect; the photodetector receives some light. The amount it receives is proportional to the arm length difference, L1 – L2 which in turn is proportional to the gravitational-wave signal.
It is interesting to compare a bar detector with an interferometer. The bar detector uses the vibrations of a single, solid cylinder to monitor the tidal forces of a gravitational wave. The interferometric detector uses the relative motions of masses hung from wires to monitor the tidal forces.
The bar detector uses an electrical sensor (for example, piezoelectric crystals squeezed by the bar) to monitor the bar’s wave-induced vibrations. The interferometric detector uses interfering light beams to monitor its masses’ wave-induced motions.
The bar responds sympathetically only to gravitational waves over a narrow frequency band, and therefore, decoding the waves’ symphony would require a xylophone of many bars. The interferometer’s masses wiggle back and forth in response to waves of all frequencies higher than about one cycle per second,7 and tllerefore the interferometer has a wide bandwidth; three or four interferometers are sufficient to fully decode the symphony.
By making the interferometer’s arms a thousand times longer than the bar (a few kilometers rather than a few meters), one can make the waves’ tidal forces a thousand times bigger and thus improve the sensitivity of the instrument a thousand-fold.8 The bar, by contrast, cannot be lengthened much. A kilometer-Iong bar would have a natural frequency less than one cycle per second and thus would not operate at the frequencies where we think the most interesting sources lie. Moreover, at such a low frequency, one must launch the bar into space to isolate it from vibrations of the ground and from the fluctuating gravity of the Earth’s atmosphere. Putting such a bar in space would be ridiculously expensIve.
Because it is a thousand times longer than the bar, the interferometer is a thousand times more immune to the “kick” produced by the measurement process. This immunity means that the interferometer does not need to circumvent the kick with the aid of a (difficult to construct) quantum nondemolition sensor. The bar, by contrast, can detect the expected waves only if it employs quantum nondemolition.
If the interferometer has such great advantages over the bar (far larger bandwidth and far larger potential sensitivity), then why didn’t Braginsky, Weber, and others build interferometers instead of bars? When I asked Braginsky in the mid-1970s, he replied that bar detectors are simple, while interferometers are horrendously complex. A small, intimate team like his in Moscow had a reasonable chance of making bar detectors work well enough to discover gravitational waves. However, to construct, debug, and operate interferometric detectors success fully would require a huge team and large amounts of money—and Braginsky doubted whether, even with such a team and such money, so complex a detector could succeed.
Ten years later, as the painful evidence mounted that bars would have great difficulty reaching 10−21 sensitivity, Braginsky visited Caltech and was impressed with the progress that Drever’s team had achieved with interferometers. Interferometers, he concluded, will probably succeed after all. But the huge team and large money required for success were not to his taste; so upon returning to Moscow, he redirected most of his own team’s efforts away from gravitational-wave detection. (Elsewhere in the world bars have continued to be developed, which is fortunate; they are cheap compared to interferometers, for now they are more sensitive, and in the long run they might play special roles at high gravity-wave frequencies.)
Wherein lies the complexity of interferometric detectors? After all, the basic idea, as described in Figure 10.6, looks reasonably simple.
In fact, Figure 10.6 is a gross oversimplification because it ignores an enormous number of pitfalls. The tricks required to avoid these pitfalls make an interferometer into a very complex instrument. For example, the laser beam must point in precisely the right direction and have precisely the right shape and wavelength to fit into the interferometer perfectly; and its wavelength and intensity must not fluctuate. After the beam is split in half, the two beams must bounce back and forth in the two arms not just once as in Figure 10.6, but many times, so as to increase their sensitivity to the wiggling masses’ motions, and after these many bounces, they must meet each other perfectly back at the beam splitter. Each mass must be continually controlled so its mirrors point in precisely the right directions and do not swing as a result of vibrations of the floor, and this must be done without masking the mass’s gravitational-wave-induced wiggles. To achieve perfection in all these ways, and in many many more, requires continuously monitoring many different pieces of the interferometer and its light beams, and continuously applying feedback forces to keep them perfect.
One gets some impression of these complications from a photograph (Figure 10.7) of a 40-meter-Iong prototype interferometric detector that Drever’s team has built at Caltech—a prototype which itself is far simpler than the full-scale, several-kilometer-Iong interferometers that are required for success.
10.7 The Caltech 40-meter interferometric prototype gravitational-wave detector, ca. 1989. The table in front and the front caged vacuum chamber hold lasers and devices to prepare the laser light for entry into the interferometer. The central mass resides in the second caged vacuum chamber—the chamber above which a dangling rope can be seen faintly. The end masses are 40 meters away, down the two corridors. The two arms’ laser beams shine down the larger of the two vacuum pipes that extend the lengths of the corridors. [Courtesy LIGO Project, California Institute of Technology.]
During the early 1980s four teams of experimental physicists struggled to develop tools and techniques for interferometric detectors: Drever’s Caltech team, the team he had founded at Glasgow (now led by James Hough), Rainer Weiss’s team at MIT, and a team founded by Hans Billing at the Max Planck Institut in Munich, Germany. The teams were small and intimate, and they worked more or less independently,9 pursuing their own approaches to the design of interferometric detectors. Within each team the individual scientists had free rein to invent new ideas and pursue them as they wished and for as long as they wished; coordination was very loose. This is just the kind of culture that inventive scientists love and thrive on, the culture that Braginsky craves, a culture in which loners like me are happiest. But it is not a culture capable of designing, constructing, debugging, and operating large, complex scientific instruments like the several-kilometer-long interferometers required for success.
To design in detail the many complex pieces of such interferometers, to make them all fit together and work together properly, and to keep costs under control and bring the interferometers to completion within a reasonable time require a different culture: a culture of tight coordination, with subgroups of each team focusing on well-defined tasks and a single director making decisions about what tasks will be done when and by whom.
The road from freewheeling independence to tight coordination is a painful one. The world’s biology community is traveling that road, with cries of anguish along the way, as it moves toward sequencing the human genome. And we gravitational-wave physicists have been traveling that road since 1984, with no less pain and anguish. I am confident, however, that the excitement, pleasure, and scientific payoff of detecting the waves and deciphering their symphonies will one day make the pain and anguish fade in our memories.
The first sharp turn on our painful road was a 1984 shotgun marriage between the Caltech and MIT teams—each of which by then had about eight members. Richard Isaacson of the D.S. National Science Foundation (NSF) held the shotgun and demanded, as the price of the taxpayers’ financial support, a tight marriage in which Caltech and MIT scientists jointly developed the interferometers. Drever (resisting like mad) and Weiss (willingly accepting the inevitable) said their vows, and I became the marriage counselor, the man with the task of forging consensus when Drever pulled in one direction and Weiss in another. It was a rocky marriage, emotionally draining for all; but gradually we began to work together.
The second sharp turn came in November 1986. A committee of eminent physicists—experts in all the technologies we need and experts in the organization and management of large scientific projects—spent an entire week with us, scrutinizing our progress and plans, and then reported to NSF. Our progress got high marks, our plans got high marks, and our prospects for success—for detecting waves and deciphering their symphonies—were rated as high. But our culture was rated as awful; we were still immersed in the loosely knit, freewheeling culture of our birth, and we could never succeed that way, NSF was told. Replace the Drever—Weiss—Thorne troika by a single director, the committee insisted—a director who can mold talented individualists into a tightly knit and effective team and can organize the project and make firm, wise decisions at every major juncture.
Out came the shotgun again. If you want your project to continue, NSF’s Isaacson told us, you must find that director and learn to work with him like a football team works with a great coach or an orchestra with a great conductor.
We were lucky. In the midst of our search, Robbie Vogt got fired.
Vogt, a brilliant, strong-willed experimental physicist, had directed projects to construct and operate scientific instruments on spacecraft, had directed the construction of a huge millimeter-wavelength astronomical interferometer, and had reorganized the scientific research environment of NASA’s Jet Propulsion Laboratory (which carries out most of the American planetary exploration program)—and he then had become Caltech’s provost. As provost, though remarkably effective, Vogt battled vigorously with Caltech’s president, Marvin Goldberger, over how to run Caltech—and after several years of battle, Goldberger fired him. Vogt was not temperamentally suited to working under others when he disagreed profoundly with their judgments; but on top, he was superb. He was just the director, the conductor, the coach that we needed. If anybody could mold us into a tightly knit team, he could.
A portion of the Caltech/MIT team of LIGO scientists in late 1991. Left: Some Caltech members of the team, counterclockwise from upper left: Aaron Gillespie, Fred Raab, Maggie Taylor, Seiji Kawamura, Robbie Vogt, Ronald Drever, Lisa Sievers, Alex Abramovici, Bob Spero, Mike Zucker. Right: Some MIT members of the team,. counterclockwise from upper left: Joe Kovalik, Yaron Hefetz, Nergis Mavalvala, Rainer Weiss, David Schumaker, Joe Giaime. [Left: courtesy Ken Rogers/ Black Star; right: courtesy Erik L. Simmons.
“It will be painful working with Robbie,” a former member of his millimeter team told us. “You will emerge bruised and scarred, but it will be worth it. Your project will succeed.”
For several months Drever, Weiss, I, and others pleaded with Vogt to take the directorship. He finally accepted; and, as promised, six years later our Caltech/MIT team is bruised and scarred, but effective, powerful, tightly knit, and growing rapidly toward the critical size (about fifty scientists and engineers) required for success. Success, however, will not depend on us alone. Under Vogt’s plan important inputs to our core effort will come from other scientists10 who, by being only loosely associated with us, can maintain the individualistic, free-wheeling style that we have left behind.
A key to success in our endeavor will be the construction and operation of a national scientific facility called the Laser Interferometer Gravitational-Wave Observatory, or LIGO. The LIGO will consist of two L-shaped vacuum systems, one near Hanford, Washington, and the other near Livingston, Louisiana, in which physicists will develop and operate many successive generations of ever-improving interferometers; see Figure 10.8.
Why two facilities instead of one? Because Earth-bound gravitational-wave detectors always have ill-understood noise that simulates gravitational-wave bursts; for example, the wire that suspends a mass can creak slightly for no apparent reason, thereby shaking the mass and simulating the tidal force of a wave. However, such noise almost never happens simultaneously in two independent detectors, far apart. Thus, to be sure that an apparent signal is due to gravitational waves rather than noise, one must verify that it occurs in two such detectors. With only one detector, gravitational waves cannot be detected and monitored.
10.8 Artist’s conception of LIGO’s L-shaped vacuum system and the experimental facilities at the corner of the L, near Hanford, Washington. [Courtesy LIGO Project, California Institute of Technology.]
Although two facilities are sufficient to detect a gravitational wave, at least three and preferably four are required, at widely separated sites, to fully decode the wave’s symphony, that is, to extract all the information the wave carries. A joint French/Italian team will build the third facility, named VIRGO,11 near Pisa, Italy. VIRGO and LIGO together will form an international network for extracting the full information. Teams in Britain, Germany, Japan, and Australia are seeking funds to build additional facilities for the network.
It might seem audacious to construct such an ambitious network for a type of wave that nobody has ever seen. Actually, it is not audacious at all. Gravitational waves have already been proved to exist by astronomical observations for which Joseph Taylor and Russell Hulse of Princeton University won the 1993 Nobel Prize. Taylor and Hulse, using a radio telescope, found two neutron stars, one of them a pulsar, which orbit each other once each 8 hours; and by exquisitely accurate radio measurements, they verified that the stars are spiraling together at precisely the rate (2.7 parts in a billion per year) that Einstein’s laws predict they should, due to being continually kicked by gravitational waves that they emit into the Universe. Nothing else, only tiny gravitational-wave kicks, can explain the stars’ inspiral.
What will gravitational-wave astronomy be like in the early 2000s? The following scenario is plausible:
By 2007, eight interferometers, each several kilometers long, are in full-time operation, scanning the skies for incoming bursts of gravitational waves. Two are operating in the vacuum facility in Pisa, Italy, two in Livingston, Louisiana, in the southeastern United States, two in Hanford, Washington, in the northwestern United States, and two in Japan. Of the two interferometers at each site, one is a “workhorse” instrument that monitors a wave’s oscillations between about 10 cycles per second and 1000; the other, only recently developed and installed, is an advanced, “specialty” interferometer that zeroes in on oscillations between 1000 and 3000 cycles per second.
A train of gravitational waves sweeps into the solar system from a distant, cosmic source. Each wave crest hits the Japanese detectors first, then sweeps through the Earth to the Washington detectors, then Louisiana, and finally Italy. For roughly a minute, crest is followed by trough is followed by crest. The masses in each detector wiggle ever so slightly, perturbing their laser beams and hence perturbing the light that enters the detector’s photodiode. The eight photodiode outputs are transmitted by satellite links to a central computer, which alerts a team of scientists that another minute-long gravitational-wave burst has arrived at Earth, the third one this week. The computer combines the eight detectors’ outputs to produce four things: a best-guess location for the burst’s source on the sky; an error box for that best-guess location; and two waveforms—two oscillating curves, analogous to the oscillating curve that you obtain if you examine the sounds of a symphony on an oscilloscope. The history of the source is encoded in these waveforms (Figure 10.9).
There are two waveforms because a gravitational wave has two polarizations. If the wave travels vertically through an interferometer, one polarization describes tidal forces that oscillate along the east—west and north-south directions; the other describes tidal forces oscillating along the northeast—southwest and northwest—southeast directions. Each detector, with its own orientation, feels some combination of these two polarizations; and from the eight detector outputs, the computer reconstructs the two waveforms.
The computer then compares the waveforms with those in a large catalog, much as a bird watcher identifies a bird by comparing it with pictures in a book. The catalog has been produced by simulations of sources on computers, and by five years of previous experience monitoring gravitational waves from colliding and coalescing black holes, colliding and coalescing neutron stars, spinning neutron stars (pulsars), and supernova explosions. The identification of this burst is easy (some others, for example, from supernovae, are far harder). The waveforms show the unmistakable, unique signature of two black holes coalescing.
10.9 One of the two waveforms produced by the coalescence of two black holes. The wave is plotted upward in units of 10−21 time is plotted horizontally in units of seconds. The first graph shows only the last 0.1 second of the inspiral part of the waveform; the preceding minute of the waveform is similar, with gradually Increasing amplitude and frequency. The second graph shows the last 0.01 second, on a stretched-out scale. The Inspiral and Ringdown segments of the waveform are well understood, in 1993, from solutions of the Einstein field equation. The coalescence segment is not at all understood (the curve shown is my own fantasy); future supercomputer simulations will attempt to compute it. In the text these simulations are presumed to have been successful in the early twenty-first century.
The waveforms have three segments:
•The minute-long first segment (of which only the last 0.1 second is shown in Figure 10.9) has oscillating strains that gradually grow in amplitude and frequency; these are precisely the waveforms expected from the inspiral of two objects in a binary orbit. The fact that alternate waves are smaller and larger indicates that the orbit is somewhat elliptical rather than circular.
•The O.Ol-second-long middle segment matches almost perfectly the waveforms predicted by recent (early twenty-first century) supercomputer simulations of the coalescence of two black holes to form one; according to the simulations, the humps marked “H” signal the touching and merging of the holes’ horizons. The double wiggles marked “D,” however, are a new discovery, the first one made by the new specialty interferometers. The older, workhorse interferometers had never been able to detect these wiggles because of their high frequency, and they had never yet been seen in any supercomputer simulations. They are a new challenge for theorists to explain. They might be the first hints of some previously unsuspected quirk in the nonlinear vibrations of the colliding holes’ spacetime curvature. Theorists, intrigued by this prospect, will go back to their simulations and search for signs of such doublet wiggles.
•The 0.03-second-long third segment (of which only the beginning is shown in Figure 10.9) consists of oscillations with fixed frequency and gradually dying amplitude. This is precisely the wave form expected when a deformed black hole pulsates to shake off its deformations, that is, as it rings down like a struck bell. The pulsations consist of two dumbbell-type protrusions that circulate around and around the hole’s equator and gradually die out as ripples of curvature carry away their energy (Figure 10.2 above).
From the details of the waveforms, the computer extracts not only the history of the inspiral, coalescence, and ringdown; it also extracts the masses and spin rates of the initial holes and the final hole. The initial holes each weighed 25 times what the Sun weighs, and were slowly spinning. The final hole weighs 46 times what the Sun weighs and is spinning at 78 percent of the maximum allowed rate. Four solar masses’ worth of energy (2 × 25 - 46 = 4) were converted into ripples of curvature and carried away by the waves. The total surface area of the initial holes was 136,000 square kilometers. The total surface area of the final hole is larger, as demanded by the second law of black-hole mechanics (Chapter 12): 144,000 square kilometers. The waveforms also reveal the distance of the hole from Earth: 1 billion light-years, a result accurate to about 20 percent. The waveforms tell us that we on Earth were looking down nearly perpendicularly onto the plane of the orbit, and are now looking down the north pole of the spinning hole; and they show that the holes’ orbit had an eccentricity (elongation) of 30 percent.
The computer determines the holes’ location on the sky from the wave crests’ times of arrival in Japan, Washington, Louisiana, and Italy. Since Japan was hit first, the holes were more or less overhead in Japan, and underfoot in America and Europe. A detailed analysis of the arrival times gives a best-guess location for the source, and an error box around that location of 1 degree in size. Had the holes been smaller, their waveforms would have oscillated more rapidly and the error box would have been tighter, but for these big holes 1 degree is the best the network can do. In another ten years, when an interferometric detector is operating on the Moon, the error boxes will be reduced in size along one side by a factor of 100.
Because the holes’ orbit was elongated, the computer concludes that the two holes were captured into orbit around each other only a few hours before they coalesced and emitted the burst. (If they had been orbiting each other for longer than a few hours, the push of gravitational waves departing from the binary would have made their orbit circular.) Recent capture means the holes were probably in a dense cluster of black holes and massive stars at the center of some galaxy.
The computer therefore examines catalogs of optical galaxies, radio galaxies, and X-ray galaxies, searching for any that reside in the 1 -degree error box, are between 0.8 and 1.2 billion light-years from Earth, and have peculiar cores. Forty candidates are found and turned over to astronomers. For the next few years these forty candidates will be studied in detail, with radio, millimeter, infrared, optical, ultraviolet, X-ray, and gamma-ray telescopes. Gradually it will become clear that one of the candidate galaxies has a core in which a massive agglomerate of gas and stars was beginning, when the light we now see left the galaxy, a million-year-Iong phase of violent evolution—an evolution that will trigger the birth of a gigantic black hole, and then a quasar. Thanks to the burst of gravitational waves which identified this specific galaxy as interesting, astronomers can now begin to unravel the details of how gigantic black holes are born.
1. The factor comes from detailed calculations with the Einstein field equation. It includes a factor 1/(2π), which is approximately 
to convert the hole’s circumference into a radius, and an additional factor 
that arises from details of the Einstein field equation.
2. Their lasers actually produced microwaves (short-wavelength radio waves) rather than light, and thus were called masers rather than “lasers.” “Real” lasers, the kind that produce light, were not successfully constructed until several years later.
3. Braginsky has a remarkable mastery of the nuances of the English language; he can construct an eloquent English phrase to describe a new idea far more readily than most Americans or Britons.
4. A key foundation for our idea came from a colleague, William Unruh, at the University of British Columbia. The development of the idea and its consequences was carried out jointly by Caves, me, and three others who were gathered around the lunch table with us when we discovered it: Ronald Drever, Vernon Sandberg, and Mark Zimmermann.
5. The full idea is described by Caves et al. (1980) and by Braginsky, Vorontsov, and Thorne (1980).
6. These differences, their consequences, and the details of the waves to be expected from various astrophysical sources have been elucidated by a number of theorists including, among others, Thibault Damour in Paris, Leonid Grishchuk in Moscow, Takashi Nakamura in Kyoto, Bernard Schutz in Wales, Stuart Shapiro in Ithaca, New York, Clifford Will in St. Louis, and me.
7. Below about one cycle per second, the wires that suspend the masses prevent them from wiggling in response to the waves.
8. Actually, the details of the improvement are far more complicated than this, and the resulting sensitivity enhancement is far more difficult to achieve than these words suggest; however, this description is roughly correct.
9. Though with a close link, through Drever, between the Glasgow and Caltech teams.
10. These, as of 1993, include Braginsky’s group in Moscow, a group led by Bob Byers at Stanford University, a group led by Jim Faller at the University of Colorado, a group led by Peter Saulson at Syracuse University, and a group led by Sam Finn at Northwestern University.
11. It is named for the Virgo cluster of galaxies, from which waves might be detected.