The Sounds of Spacetime

Craig J Hogan. American Scientist. Volume 94, Issue 6. Nov/Dec 2006.

Of all the habits shared by ancient and modern people, stargazing may be the most serene. When we look up at a clear night sky, or view the fabulously beautiful pictures of stars and galaxies coming from the Hubble Space Telescope, we enter awestruck and humble into a magical realm that has the sacred hush of an ancient cathedral or a great art museum. We almost feel we should keep our voices down and turn off our cell phones out of respect.

So how would you feel if suddenly, as you quietly admired a dark and starry sky, you heard the stars making all kinds of crazy noises?

After the initial shock of being jolted out of your poetic reverie, I think you would find that the universe felt much more immediate, present, real and alive. It is one thing to see flashes of lightning in the distance, quite another to be shaken by the sound of rolling thunder. Hearing the universe is more like touching than looking. Happily, astronomers are finding ways to do that-to feel as well as see the active universe around us.

Einstein’s theory of spacetime tells us that the real universe is not silent, but is actually alive with vibrating energy. Space and time carry a cacophony of vibrations with textures and timbres as rich and varied as the din of sounds in a tropical rain forest or the finale of a Wagner opera. It’s just that we haven’t heard those sounds yet. The universe is a musical that we’ve been watching all this time as a silent movie.

Vibrations of Spacetime

The sounds of the cosmos are not the familiar sounds our ears sense, carried by vibrations in air. Space is a near-perfect vacuum, and ordinary sound carries only where there is matter to vibrate. That’s one reason why our immediate knowledge of the universe far away from the solar system, from pre-scientific astronomy up to now, comes almost entirely from studying one form of energy: light. As James Clerk Maxwell showed in the 19th century, light is another name for vibrations in electrical and magnetic fields that travel through space-at the speed of light.

(To be fair, we should not forget here other messengers from afar-cosmic rays, neutrinos, cosmic dust, meteorites and other matter falling to Earth from outer space-and most of all, we should not forget the cosmic origin of all the atoms which make up Earth and ourselves! But those are other stories.)

In contrast to the swift-traveling vibrations in electrical and magnetic fields that we call light, the sounds of the universe are carried by vibrations in spacetime called gravitational waves. Albert Einstein’s general theory of relativity tells us that all forms of matter create warps in spacetime and that motions of matter create vibrations that travel throughout space at the speed of light. The vibrations stretch the fabric of space itself back and forth in a way that can be detected far away. The fastest accelerations of the densest objects, with the strongest gravity, presumed to be black holes (which are themselves nothing but dense knots of spacetime curvature), create the loudest vibrations. When we can hear them, those vibrations will let us listen to huge and often invisible cataclysms throughout the observable universe.

Gravitational waves are emitted when big masses accelerate; light is emitted when tiny electrical charges accelerate. That means that gravitational waves have much lower frequencies than light, and come from totally different kinds of happenings in the universe. For example, normal stars sitting on their own emit lots of light, from jiggling electrons in their hot atmospheres, but almost no gravitational radiation. At the opposite extreme, the most powerful energy transformations in the universe, where two black holes merge with each other and form a larger black hole, emit almost all of their energy as gravitational waves and almost none of it as light. Indeed, for the brief time of the merger, up to an hour or so for the largest holes we know about, just one such merging pair emits a thousand times more power in gravitational waves than all the stars in all the galaxies in the visible universe, everything combined, emit as light. So the loudest things in the universe are not the brightest things, and vice versa; the two kinds of energy really are like entirely different senses of what is happening out there.

As Peter S. Shawhan explained in these pages (“Gravitational Waves and the Effort to Detect Them,” July-August 2004), Einstein’s theory allows us to calculate many properties of gravitational waves. It tells us that gravitational waves pass through anything; they traverse the farthest reaches of spacetime, the earliest moments of the Big Bang, to reach us. The theory tells us that ordinary pairs of stars orbiting each other, including binaries we know about already, should be emitting gravitational waves, and exactly how much energy they emit. It tells us the exact mathematical shape of the warped spacetime in black holes, which is encoded in precisely predictable gravitational waves emitted by any object falling in.

In short, we have a definite mathematical model for the ways space and time around us should vibrate. By eavesdropping on gravitational waves, we can explore the whole universe in an entirely new way, and at the same time test our fundamental ideas about how space and time behave.

There is precise indirect evidence that gravitational waves exist. Russell Hulse and Joseph Taylor were awarded the Nobel Prize in 1993 in part for measuring the effects of gravitational-wave energy loss on a binary pulsar system. But up to now, nobody has detected a gravitational wave directly. As I write this, the first major detector is a few months into its first sustained period of listening.

Superbly Sensitive Microphones

Astronomers would love to tune in to the many-voiced soundtrack of the cosmos and listen to what is going on everywhere. The problem is, these vibrations, although they carry a lot of energy, are very hard to detect. (This is related to the fact that they penetrate anything!) Close to black holes, spacetime is highly warped, so much so that escape is impossible if you get too close. However, the gravitational waves that reach us from great distances away distort space by only a tiny amount, causing a fractional stretching less than the ratio of the black hole size to the distance away. Another way of saying the same thing is that spacetime is the stiffest medium there is, so even a huge amount of energy creates only tiny vibrations. How then can we listen to them?

When a gravitational wave passes, it stretches space back and forth. That means the distance between objects changes. For a given amount of fractional stretching, the change in distance is bigger the farther apart the objects are, so we want to measure tiny variations in the distance between objects that are far apart. One exquisitely sensitive way to detect the minuscule stretching over big distances is with laser interferometry, the technology at the heart of the most sensitive gravitational-wave detectors.

Laser light is a “pure color,” made of waves of just one wavelength. In an interferometer, some light from a laser is bounced off a mirror. Any stretch in the distance to the mirror changes the wavelength of the light. (Since it is a stretching of spacetime, it is also okay to think of this change as due to the Doppler shift from the motion of the mirror.) The reflected light is then combined with some unreflected original laser light so that the two sets of waves can interfere with each other. The light changes brightness depending on exactly where the two sets of laser waves are in their relative vibrations. By measuring variations in the intensity of the light, tiny motions of the mirror can be measured to very high accuracy, even if it is very far away. The interferometric gravitational-wave detectors now deployed on Earth (described in detail in Shawhan’s article) can measure motions much smaller than an atomic nucleus, over a distance of several kilometers; the future detector planned for space, the Laser Interferometer Space Antenna (LISA), will measure motions much smaller than an atom, over a distance of 5 million kilometers-about 13 times the distance to the Moon.

Twenty Octaves of Spacetime Sound

The reason to build interferometers both on the ground (LIGO, the Laser Interferometer Gravitational-Wave Observatory, and others around the globe) and in space (LISA) is that they observe very different frequencies of gravitational waves, in the same way that optical and radio telescopes observe different frequencies of electromagnetic radiation. The frequencies span the same range as a piano keyboard with 20 octaves of sound. That means that they will detect very different kinds of things bumping around the universe.

Ground-based detectors listen to spacetime wiggles at audible frequencies, in a broad band around 100 cycles per second, or hertz-a bit over three octaves, or about the range of a versa tile soprano. These frequencies come screaming from neutron stars and black holes with around the mass of single stars; that’s how fast they spin and orbit each other when they are at their loudest, just before their catastrophic-mergers. LIGO will hear these death rattles of stars.

In space, detectors can listen to frequencies a million times lower. Those deep rumbling noises, in a broad band around a millihertz, come from catastrophic mergers of black holes much bigger than those LIGO hears-millions of times the mass of a single star. They can also come from binary stars that are not so massive and that are more slowly and distantly orbiting each other. Indeed, binary stars are so common that their gravitational waves pile together and are the main source of “noise” for LISA at some frequencies. For LISA, the universe is a bustling, noisy place. As soon as it rums on, there will be a cacophony of sounds; the science challenge will be to distinguish them from one another, like trying to understand conversations at a cocktail party where everyone is talking at once.

The LIGO and LISA styles of observing are quite different. LIGO is a bit more like bird-watching. It lies in wait for the rare songs of merger events which tend to be brief, high intensity flurries of activity from the final coalescence of stars. These events are happening all the time in the universe, but we don’t know exactly how often, or when exactly one will happen nearby enough for LIGO to hear it. Depending on the rate of events, and on our luck, LIGO-which began its first extended data run at full sensitivity earlier this year-may detect gravitational waves sometime in the next year or the next decade. When LISA flies, perhaps a decade from now, it will detect gravitational waves from some known sources immediately. From then on astrophysicists and cosmologists will be occupied with sorting out a wide variety of known and unknown cosmic noises from one another.

What will we learn from gravitational radiation when it is detected? We know we will learn many new things about what is happening in the universe, ushering in a new way of doing astronomy. We also know we will study the physics of gravity and spacetime in a completely new way; the results might either confirm what we think we know-that is, Einstein’s theory of spacetime-or they might tell us something new about how spacetime behaves. We may also find something radically new, such as entirely new states of mass and energy that we have only guessed at until now. Such a discovery could illuminate some of the deepest mysteries of physics, such as the unification of ideas about space and time with ideas of energy and quanta, perhaps in the form of a string theory.

Chirps, Rings, Black Holes, and Binaries

The most spectacular LISA events will be huge, roaring events when two very big black holes, somewhere in the universe, spiral together and merge into a single bigger black hole. The final hole weighs a lot less than did the original two, and the difference in mass is radiated as gravitational waves. As I mentioned above, in terms of radiated power, just one of these mergers far outshines everything else in the universe combined.

These events will be fun to listen to. They sing a song called a “chirp.” For a long while the orbiting black holes emit a nearly constant set of tones, like a single note on a violin that gets higher only very slowly. Then, just before the holes merge, the note quickly gets higher and louder at the same time, like a virtuoso’s flourish. Finally, after the merger, there is a “ringdown” when the sound rapidly goes away, like the reverberations in a vast concert hall.

We think mergers happen pretty frequently somewhere in the universe. Most galaxies have a massive black hole right in the middle, and every galaxy has swallowed or merged with another galaxy more than once in the past; that is how galaxies grow. When two galaxies merge, their two massive black holes sink to the middle of the new galaxy because they lose energy to stars and gas by gravitational interactions. Finally the holes find each other and merge together. There are roughly ten billion galaxies to listen to, and if each of them does this just once during the ten billion years of active galaxy assembly, that’s about one event every year, on average.

But most massive black holes don’t have to wait so long to swallow something; they are snacking all the time on the smaller occupants of the galaxies around them. The big holes live in dense swarms of stars in the centers of galaxies, and every now and then one of the stars gets too close to its neighbor for its own good.

Sometimes a very compact stellar remnant-a neutron star or a stellarmass black hole-finds itself in a death dance, where it whirls in and out and around a massive black hole many times until it finally plunges into the oblivion of the event horizon and disappears from view. All the time it is doing that dance, it emits gravitational radiation. The gravitational radiation records a history of the orbit and makes a detailed map of the spacetime around the massive black hole. Remember that the black hole is made of gravity alone, and Einstein’s theory tells us what the structure of black holes ought to be. This kind of event will tell us a lot about the structure of black holes themselves-how spacetime ties itself into the stable spinning knots we call black holes.

LISA also has some sure targets. Our galaxy is full of stars. Stars have a life cycle-they only last as normal stars until their hydrogen fuel runs out-and many of them have burned out and died. Most of the time the remnant is a very small and dense ember such as a white dwarf or a neutron star, and much of the time, because stars tend to form in binaries, the remnant is in a binary system with a similar companion. Those remnants that orbit each other once every few minutes to an hour radiate at frequencies that LISA can hear.

In fact we already know of a few nearby binaries, discovered by astronomers using normal telescopes, that LISA will be able to hear. We call these “calibration binaries” because we already have a pretty good idea of many of their properties, such as their frequency and distance. After LISA, we will know a lot more-the gravitational waveform will tell us their inclination and much about their detailed masses and other properties. The nearby binaries will also reassure us that LISA is actually working and detecting gravitational waves. Thousands of more distant binaries blend into a noisy backup chorus that will also be heard as soon as LISA turns on.

Mapping the Distant Universe

Using the known physics of gravitational-wave emission, LISA will let us use gravitational waves as a tool to map distances to galaxies in the distant universe. By measuring the chirp of a distant binary black-hole merger-how long it lasts until its tone changes-we can tell how massive the merging black holes are. By measuring the loudness, we can then tell how far away the holes are. This is a completely new way to map the cosmic expansion that can be more precise and direct than cither techniques we have, insofar as the physics of black-hole mergers is completel) understood.

A tricky aspect of this project is that astronomers need to actually identify the host galaxy with visible light (because we need an independent measure of the redshift, the amount by which wavelengths have been stretched by the expanding universe). We don’t know for sure that this will be possible. For loud binaries, LISA will sometimes let us measure the direction the sound is coming from, by combining the data from different times of year to act as a stereo microphone. The best precision is about one degree of arc, narrowing it down to a patch of sky which includes tens of thousands of galaxy images. It is reasonable to hope that the very special galaxy among these with a merging pair of black holes will look different enough for us to identify it-perhaps by time-varying nuclear activity in optical light, perhaps by changes in shape in response to the disturbance created by a recent galaxy merger.

Accurate distance mapping with supernovae led to the discovery of the cosmic dark energy that is accelerating the expansion of the universe; measuring distances better with gravitational waves will be a way to learn more details about that new force of nature.

The String Section

Although they sound exotic, all of the sources just discussed, even the huge binary black-hole mergers, are actually expected to happen in the normal course of events according to our current understanding of the universe. But what about really weird stuff? What new, unexpected things might really knock our socks off?

Physics now extends its reach back to the early moments of the Big Bang, to incredibly high temperatures, even to the inflation epoch when the cosmic expansion got the kick that made it as big as it is today. If you go back far enough, even space and time were not like they are today. A still-untested quantum version of Einstein’s theory, string theory, suggests that space has 10 dimensions, many of which are highly curved or compact, and that all the particles of matter, and maybe even spacetime and gravitational waves, are ultimately composed of tiny quantum strings. The problem with string theory is that despite its seemingly miraculous ability to tie ideas from different parts of physics and mathematics together, nobody has yet found any realworld evidence for it. Might LISA hear any whispers from that new physics?

There is at least one kind of new, truly “stringy” object that, if it exists at all, fills the universe with gravitational radiation that LISA might hear. The tiny quantum strings might also form into cosmic superstrings, which are microscopically thin but astronomically long.

In the very early universe, a dense network of them forms by rapid quenching as the universe expands. This formation process resembles the cracking of cold ice cubes when you drop them suddenly into water, the mottled patterning of alloy domains in a finely forged Samurai sword or the trapped vortex lines that sometimes form in sudden cooling of superconductors, superfluids or liquid crystals. As the universe expands further, the strings unravel and rush around at almost the speed of light; when they cross they can exchange partners, spawning closed loops of string. A large population of these loops accumulates and doesn’t easily disappear. The loops thrash around but are almost stable and remain around for a long time, shrinking only slowly. Indeed the main way the loops lose energy is by gravitational waves! If we estimate the strength of gravitational waves, they rum out to be easily detectable by LISA for some scenarios suggested by string-theory inflation.

The most interesting stringy events from these loops are rather rare occasions when an unusually nearby loop beams gravitational waves in our direction by a sort of whipping action, or cusp catastrophe. The motion of the string for an instant, in one place, formally approaches the speed of light, and as this moment approaches, the gravitational waves are beamed and amplified. Such bursts, if detected, would be a rich source of data and a completely new window on how string theory works in the real world.

It’s also possible that we might see gravitational waves directly from the early universe, possibly from the end of inflation when the fields driving the Big Bang converted their energy into normal light, matter and antimatter, or at a later phase transition when light and matter spawned the excess of matter over antimatter that became our atoms. Gravitational waves are so penetrating that they reach us from the entire history of the universe, right back to the start of the Big Bang.

Picometers over Gigameters

When will LISA fly; when can we don our earbuds and listen to what’s happening out there? The instrument is challenging to build, but a team of scientists and engineers from the United States and Europe think they can do it.

The basic LISA concept is simple. The heart of the system, a gold/platinum cube, floats freely within each spacecraft, not touching anything. The cube is protected from all forces except gravity; the spacecraft very gently senses its position and maneuvers with tiny thrusters to avoid running into it. Laser light reflects off the cubes and is sent by telescopes, over the 5 million kilometers between the multiple L IS A spacecraft, to measure the tiny changes in distance between the cubes caused by gravitational waves. The measured changes in distance are given by the fractional stretch in spacetime, 10 :1 times smaller than the distance between them, or around 0.05 picometers. That distance is much smaller than an atom-it is almost as small as the nucleus of an atom.

It seems incredible to contemplate building an instrument that will measure distances far larger than the distance to the Moon, to an accuracy far smaller than a single atom. Among the many technical challenges in making this work, a major one is to create an environment for the cubes that is free of all but gravitational forces. The spacecraft surrounding the mass must somehow sense its position, without disturbing it, and follow it around as it follows the wiggles of spacetime alone. The most sensitive accelerometers on the planet-torsion balances that have also been used to search for tiny forces from extra dimensions and new shapes to gravity-are helping to find ways of minimizing forces.

Of course, one reason LISA goes into space is because of all the gravitational noise on Rarth. To test technology to the exquisite precision required, especially after undergoing the rigors of rocket launch, we must send machines into space. A satellite called LISA Pathfinder will launch in a few years, to check the most sensitive LISA technologies that can’t be tested on Earth. It is just one satellite, so it won’t be able to detect gravi tational waves, but the proof masses and sensors on board, and the tiny micronewton thrusters that allow the spacecraft to maneuver delicately, will have the same design as LISA. Engineering prototypes of these systems already exist. As far as we know, no fundamental technology hurdles exist to building LISA.

The actual launch of LISA itself is still many years away and will take substantial and sustained commitments from the science and engineering communities and from the agencies and taxpayers that fund them from both sides of the Atlantic. At over a billion dollars, it is a major undertaking, although it is not unprecedented for an important science project: For example, this budget is still much smaller than that of the largest particle accelerators, such as the new Large Hadron Collider at the European particle-physics laboratory CERN, or space telescopes, such as the Hubble Space Telescope. It is unusual for the first step in such a new area to be such a big one, but then it’s also unusual for a science project to probe the universe in such an entirely new way.