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THE FABRIC of the COSMOS, Brian Greene, 2004
```(annotated and with added bold highlights by Epsilon=One)
```(annotated and with added bold highlights by Epsilon=One)
Chapter 14 – Up in the Heavens and Down in the Earth
Catching the Wave
An essential lesson of general relativity is that mass and energy cause the fabric of spacetime to warp; we illustrated this in Figure 3.10 by showing the curved environment surrounding the sun. One limitation of a still figure, though, is that it fails to illustrate how the warps and curves in space evolve when mass and energy move or in some way change their configuration. 3 General relativity predicts that, just as a trampoline assumes a fixed, warped shape if you stand perfectly still, but heaves when you jump up and down, space can assume a fixed, warped shape if matter is perfectly still, as assumed in Figure 3.10, but ripples undulate through its fabric when matter moves to and fro. Einstein came to this realization between 1916 and 1918, when he used the newly fashioned equations of general relativity to show that — much as electric charges racing up and down a broadcast antenna produce electromagnetic waves (this is how radio and television waves are produced) — matter racing this way and that (as in a supernova explosion) produces gravitational waves. And since gravity is curvature, a gravitational wave is a wave of curvature. Just as tossing a pebble into a pond generates outward-spreading water ripples, gyrating matter generates outward-spreading spatial ripples; according to general relativity, a distant supernova explosion is like a cosmic pebble that's been tossed into a spacetime pond, as illustrated in Figure 14.2. The figure highlights an important distinguishing feature of gravitational waves: unlike electromagnetic, sound, and water waves — waves that travel through space — gravitational waves travel within space. They are traveling distortions in the geometry of space itself.
Figure 14.2 Gravitational waves are ripples in the fabric of spacetime.
While gravitational waves are now an accepted prediction of general relativity, for many years the subject was mired in confusion and controversy, at least in part because of overadherence to Machian philosophy. If general relativity fully incorporated Mach's ideas, then the "geometry of space" would merely be a convenient language for expressing the location and motion of one massive object with respect to another. Empty space, and motion of one massive object with respect to another. Empty space, in this way of thinking, would be an empty concept, so how could it be sensible to speak of empty space wiggling? Many physicists tried to prove that the supposed waves in space amounted to a misinterpretation of the mathematics of general relativity. But in due course, the theoretical analyses converged on the correct conclusion: gravitational waves are real, and space [I]can[I] ripple.
Figure 14.3 A passing gravitational wave stretches an object one way and then the other. (In this image, the scale of distortion for a typical gravitational wave is hugely exaggerated.)
With every passing peak and trough, a gravitational wave's distorted geometry would stretch space — and everything in it — in one direction, and then compress space — and everything in it — in a perpendicular direction, as in the highly exaggerated depiction in Figure 14.3. In principle, you could detect a gravitational wave's passing by repeatedly measuring distances between a variety of locations and finding that the ratios between these distances had momentarily changed.
In practice, no one has been able to do this, so no one has directly detected a gravitational wave. (However, there is compelling, indirect evidence for gravitational waves. 4) The difficulty is that the distorting influence of a passing gravitational wave is typically minute. The atomic bomb tested at Trinity on July 16, 1945, packed a punch equivalent to 20,000 tons of TNT and was so bright that witnesses miles away had to wear eye protection to avoid serious damage from the electromagnetic waves it generated. Yet, even if you were standing right under the hundred-foot steel tower on which the bomb was hoisted, the gravitational waves its explosion produced would have stretched your body one way or another only by a minuscule fraction of an atomic diameter. That's how comparatively feeble gravitational disturbances are, and it gives an inkling of the technological challenges involved in detecting them. (Since a gravitational wave can also be thought of as a huge number of gravitons traveling in a coordinated manner — just as an electromagnetic wave is composed of a huge number of coordinated photons — this also gives an inkling of how difficult it is to detect a single graviton.)
Of course, we're not particularly interested in detecting gravitational waves produced by nuclear weapons, but the situation with astrophysical sources is not much easier. The closer and more massive the astrophysical source and the more energetic and violent the motion involved, the stronger the gravitational waves we would receive. But even if a star at a distance of 10,000 light-years were to go supernova, as the resulting gravitational wave passed by earth it would stretch a one-meter-long rod by only a millionth of a billionth of a centimeter, barely a hundredth the size of an atomic nucleus. So, unless some highly unexpected astrophysical event of truly cataclysmic proportions were to happen relatively nearby, detecting a gravitational wave will require an apparatus capable of responding to fantastically small length changes.
The scientists who designed and built the Laser Interferometer Gravitational Wave Observatory (LIGO) (being run jointly by the California Institute of Technology and the Massachusetts Institute of Technology and funded by the National Science Foundation) have risen to the challenge. LIGO is impressive and the expected sensitivity is astounding. It consists of two hollow tubes, each four kilometers long and a bit over a meter wide, which are arranged in a giant L. Laser light simultaneously shot down vacuum tunnels inside each tube, and reflected back by highly polished mirrors, is used to measure the relative length of each to fantastic accuracy. The idea is that should a gravitational wave roll by, it will stretch one tube relative to the other, and if the stretching is big enough, scientists will be able to detect it.
The tubes are long because the stretching and compressing accomplished by a gravitational wave is cumulative. If a gravitational wave were to stretch something four meters long by, say, 10^-20 meters, it would stretch something four kilometers long by a thousand times as much, 10^-17 meters. So, the longer the span being monitored, the easier it is to detect a change in its length. To capitalize on this, the LIGO experimenters actually direct the laser beams to bounce back and forth between mirrors at opposite ends of each tube more than a hundred times on each run, increasing the roundtrip distance being monitored to about 800 kilometers per beam. With such clever tricks and engineering feats, LIGO should be able to detect any change in the tube lengths that exceeds a trillionth of the thickness of a human hair — a hundred millionth the size of an atom.
Oh, and there are actually two of these L-shaped devices. One is in Livingston, Louisiana, and the other is about 2,000 miles away in Hanford, Washington. If a gravity wave from some distant astrophysical hullabaloo rolls by earth, it should affect each detector identically, so any wave caught by one experiment had better also show up in the other. This is an important consistency check, since for all the precautions that have been taken to shield the detectors, the disturbances of everyday life (the rumble of a passing truck, the grinding of a chainsaw, the impact of a falling tree, and so on) could masquerade as gravitational waves. Requiring coincidence between distant detectors serves to rule out these false positives.
Researchers have also carefully calculated the gravitational wave frequencies — the number of peaks and troughs that should pass by their detector each second — that they expect to be produced by a range of astrophysical phenomena including supernova explosions, the rotational motion of nonspherical neutron stars, and collisions between black holes. Without this information the experimenters would be looking for a needle in a haystack; with it, they can focus the detectors on a sharply defined frequency band of physical interest. Curiously, the calculations reveal that some gravitational wave frequencies should be in the range of a few thousand cycles per second; if these were sound waves, they'd be right in the range of human audibility. Coalescing neutron stars would sound like a chirp with a rapidly rising pitch, while a pair of colliding black holes would mimic the trill of a sparrow that's received a sharp blow to the chest. There's a junglelike cacophony of gravitational waves oscillating through the spacetime fabric, and if all goes according to plan, LIGO will be the first instrument to tune in. 5
What makes this all so exciting is that gravitational waves maximize the utility of gravity's two main features: its weakness and its ubiquity. Of all four forces, gravity interacts with matter most feebly. This implies that gravitational waves can pass through material that's opaque to light, giving access to astrophysical realms previously hidden. What's more, because everything is subject to gravity (whereas, for example, the electromagnetic force only affects objects carrying an electric charge), everything has the capacity to generate gravitational waves and hence produce an observable signature. LIGO thereby marks a significant turning point in the way we examine the cosmos.
There was a time when all we could do was raise our eyes and gaze skyward in the seventeenth century, Hans Lippershey and Galileo Galilei changed that; with the aid of the telescope, the grand vista of the cosmos came within humanity's purview. But in time, we realized that visible light represented a narrow band of electromagnetic waves. In the twentieth century, with the aid of infrared, radio, X-ray, and gamma ray telescopes, the cosmos opened up to us anew, revealing wonders invisible in the wavelengths of light that our eyes have evolved to see. Now, in the twenty-first century, we are opening up the heavens once again. With LIGO and its subsequent improvements,* we will view the cosmos in a completely new way. Rather than using electromagnetic waves, we will use gravitational waves; rather than using the electromagnetic force, we will use the gravitational force.
To appreciate how revolutionary this new technology may be, imagine a world on which alien scientists were just now discovering how to detect electromagnetic waves — light — and think about how their view of the universe would, in short order, profoundly change. We are on the cusp of our first detection of gravitational waves and so may well be in a similar position. For millennia we have looked into the cosmos; now it's as if, for the first time in human history, we will listen to it.
Figure 14.2 Gravitational waves are ripples in the fabric of spacetime.
While gravitational waves are now an accepted prediction of general relativity, for many years the subject was mired in confusion and controversy, at least in part because of overadherence to Machian philosophy. If general relativity fully incorporated Mach's ideas, then the "geometry of space" would merely be a convenient language for expressing the location and motion of one massive object with respect to another. Empty space, and motion of one massive object with respect to another. Empty space, in this way of thinking, would be an empty concept, so how could it be sensible to speak of empty space wiggling? Many physicists tried to prove that the supposed waves in space amounted to a misinterpretation of the mathematics of general relativity. But in due course, the theoretical analyses converged on the correct conclusion: gravitational waves are real, and space [I]can[I] ripple.
Figure 14.3 A passing gravitational wave stretches an object one way and then the other. (In this image, the scale of distortion for a typical gravitational wave is hugely exaggerated.)
With every passing peak and trough, a gravitational wave's distorted geometry would stretch space — and everything in it — in one direction, and then compress space — and everything in it — in a perpendicular direction, as in the highly exaggerated depiction in Figure 14.3. In principle, you could detect a gravitational wave's passing by repeatedly measuring distances between a variety of locations and finding that the ratios between these distances had momentarily changed.
In practice, no one has been able to do this, so no one has directly detected a gravitational wave. (However, there is compelling, indirect evidence for gravitational waves. 4) The difficulty is that the distorting influence of a passing gravitational wave is typically minute. The atomic bomb tested at Trinity on July 16, 1945, packed a punch equivalent to 20,000 tons of TNT and was so bright that witnesses miles away had to wear eye protection to avoid serious damage from the electromagnetic waves it generated. Yet, even if you were standing right under the hundred-foot steel tower on which the bomb was hoisted, the gravitational waves its explosion produced would have stretched your body one way or another only by a minuscule fraction of an atomic diameter. That's how comparatively feeble gravitational disturbances are, and it gives an inkling of the technological challenges involved in detecting them. (Since a gravitational wave can also be thought of as a huge number of gravitons traveling in a coordinated manner — just as an electromagnetic wave is composed of a huge number of coordinated photons — this also gives an inkling of how difficult it is to detect a single graviton.)
Of course, we're not particularly interested in detecting gravitational waves produced by nuclear weapons, but the situation with astrophysical sources is not much easier. The closer and more massive the astrophysical source and the more energetic and violent the motion involved, the stronger the gravitational waves we would receive. But even if a star at a distance of 10,000 light-years were to go supernova, as the resulting gravitational wave passed by earth it would stretch a one-meter-long rod by only a millionth of a billionth of a centimeter, barely a hundredth the size of an atomic nucleus. So, unless some highly unexpected astrophysical event of truly cataclysmic proportions were to happen relatively nearby, detecting a gravitational wave will require an apparatus capable of responding to fantastically small length changes.
The scientists who designed and built the Laser Interferometer Gravitational Wave Observatory (LIGO) (being run jointly by the California Institute of Technology and the Massachusetts Institute of Technology and funded by the National Science Foundation) have risen to the challenge. LIGO is impressive and the expected sensitivity is astounding. It consists of two hollow tubes, each four kilometers long and a bit over a meter wide, which are arranged in a giant L. Laser light simultaneously shot down vacuum tunnels inside each tube, and reflected back by highly polished mirrors, is used to measure the relative length of each to fantastic accuracy. The idea is that should a gravitational wave roll by, it will stretch one tube relative to the other, and if the stretching is big enough, scientists will be able to detect it.
The tubes are long because the stretching and compressing accomplished by a gravitational wave is cumulative. If a gravitational wave were to stretch something four meters long by, say, 10^-20 meters, it would stretch something four kilometers long by a thousand times as much, 10^-17 meters. So, the longer the span being monitored, the easier it is to detect a change in its length. To capitalize on this, the LIGO experimenters actually direct the laser beams to bounce back and forth between mirrors at opposite ends of each tube more than a hundred times on each run, increasing the roundtrip distance being monitored to about 800 kilometers per beam. With such clever tricks and engineering feats, LIGO should be able to detect any change in the tube lengths that exceeds a trillionth of the thickness of a human hair — a hundred millionth the size of an atom.
Oh, and there are actually two of these L-shaped devices. One is in Livingston, Louisiana, and the other is about 2,000 miles away in Hanford, Washington. If a gravity wave from some distant astrophysical hullabaloo rolls by earth, it should affect each detector identically, so any wave caught by one experiment had better also show up in the other. This is an important consistency check, since for all the precautions that have been taken to shield the detectors, the disturbances of everyday life (the rumble of a passing truck, the grinding of a chainsaw, the impact of a falling tree, and so on) could masquerade as gravitational waves. Requiring coincidence between distant detectors serves to rule out these false positives.
Researchers have also carefully calculated the gravitational wave frequencies — the number of peaks and troughs that should pass by their detector each second — that they expect to be produced by a range of astrophysical phenomena including supernova explosions, the rotational motion of nonspherical neutron stars, and collisions between black holes. Without this information the experimenters would be looking for a needle in a haystack; with it, they can focus the detectors on a sharply defined frequency band of physical interest. Curiously, the calculations reveal that some gravitational wave frequencies should be in the range of a few thousand cycles per second; if these were sound waves, they'd be right in the range of human audibility. Coalescing neutron stars would sound like a chirp with a rapidly rising pitch, while a pair of colliding black holes would mimic the trill of a sparrow that's received a sharp blow to the chest. There's a junglelike cacophony of gravitational waves oscillating through the spacetime fabric, and if all goes according to plan, LIGO will be the first instrument to tune in. 5
What makes this all so exciting is that gravitational waves maximize the utility of gravity's two main features: its weakness and its ubiquity. Of all four forces, gravity interacts with matter most feebly. This implies that gravitational waves can pass through material that's opaque to light, giving access to astrophysical realms previously hidden. What's more, because everything is subject to gravity (whereas, for example, the electromagnetic force only affects objects carrying an electric charge), everything has the capacity to generate gravitational waves and hence produce an observable signature. LIGO thereby marks a significant turning point in the way we examine the cosmos.
There was a time when all we could do was raise our eyes and gaze skyward in the seventeenth century, Hans Lippershey and Galileo Galilei changed that; with the aid of the telescope, the grand vista of the cosmos came within humanity's purview. But in time, we realized that visible light represented a narrow band of electromagnetic waves. In the twentieth century, with the aid of infrared, radio, X-ray, and gamma ray telescopes, the cosmos opened up to us anew, revealing wonders invisible in the wavelengths of light that our eyes have evolved to see. Now, in the twenty-first century, we are opening up the heavens once again. With LIGO and its subsequent improvements,* we will view the cosmos in a completely new way. Rather than using electromagnetic waves, we will use gravitational waves; rather than using the electromagnetic force, we will use the gravitational force.
To appreciate how revolutionary this new technology may be, imagine a world on which alien scientists were just now discovering how to detect electromagnetic waves — light — and think about how their view of the universe would, in short order, profoundly change. We are on the cusp of our first detection of gravitational waves and so may well be in a similar position. For millennia we have looked into the cosmos; now it's as if, for the first time in human history, we will listen to it.
* One of these is the planned Laser Interferometer Space Antenna (LISA), a space-based version of LIGO comprising multiple spacecraft, separated by millions of kilometers, playing the role of LIGO's four-kilometer tubes. There are also other detectors that are playing a critical role in the search for gravitational waves, including the German-British GEO600, the French-Italian detector VIRGO, and the Japanese detector TAMA300.