## Gravitational Waves

### Ripples in the Fabric of Space Time

No amount of experimentation can ever prove me right; a single experiment can prove me wrong.

Albert Einstein

In the section on Relativity, we've seen how space and time can curve. Near the Earth, this curvature is fairly constant. The "pull of gravity" we experience is basically the same at any two points in time. There is a gentle variation in the pull, however. This fact is made clear in the existence of ocean tides — changing gravity from the pull of the Sun and the Moon changes the level of water in different parts of the oceans. But we know that the gravitational "pull" is really just curvature of spacetime (Spacetime: A concept in physics which merges our usual notion of space with our usual notion of time.), so the curvature is changing slightly in time. One of the most interesting predictions of the General Theory of Relativity (General Theory of Relativity: Einstein's version of the laws of physics, when there is gravity. Building on the Special Theory of Relativity (Special Theory of Relativity: Einstein's version of the laws of physics, when there is no gravity. The two fundamental concepts in the foundation of this theory are equality of observers, and the constancy of the speed of light. The first of these means that the laws of physics must be the same, no matter how quickly an observer is moving. The second means that everyone measures the exact same speed of light. This theory is useful whenever the effects of gravity can be ignored, but objects are moving at nearly the speed of light. It has been successfully tested many times in particle accelerators, and orbiting spacecraft. For objects moving much more slowly than light, Special Relativity (Special Theory of Relativity: Einstein's version of the laws of physics, when there is no gravity. The two fundamental concepts in the foundation of this theory are equality of observers, and the constancy of the speed of light. The first of these means that the laws of physics must be the same, no matter how quickly an observer is moving. The second means that everyone measures the exact same speed of light. This theory is useful whenever the effects of gravity can be ignored, but objects are moving at nearly the speed of light. It has been successfully tested many times in particle accelerators, and orbiting spacecraft. For objects moving much more slowly than light, Special Relativity becomes very nearly the same as Newton's theory, which is much easier to use. ) becomes very nearly the same as Newton's theory, which is much easier to use. ), this theory generalizes Einstein's work so that the laws of physics must be the same for all observers (Observer: A person or piece of equipment that measures something in physics. Frequently, we speak of an observer measuring time or a distance in a particular place. ), even in gravity. Einstein showed that gravity is best understood as a warping of the geometry of spacetime, rather than as a pulling of objects on each other. The crucial idea is that objects move along geodesics — which are determined by the warping of spacetime — while spacetime is warped by massive objects according to the formula \(G = 8 π T\). )}) is that this changing curvature can travel through space, much like a wave across water. If we rotate a paddle in water, waves travel out across the surface of the water. The Earth orbiting the Sun is just like a paddle spinning and stirring up spacetime so that gravitational waves (Gravitational Wave: A gravitational disturbance that travels through space like a wave. This type of wave is analogous to an Electromagnetic Wave. Gravitational waves are given off by most movements of anything with mass. Usually, however, they are quite difficult to detect. Physicists are currently working hard to directly detect gravitational waves. Experiments like LIGO and LISA are designed for this purpose. ) travel out across spacetime.

#### Reshaping Space  We can better understand what a gravitational wave (Gravitational Wave: A gravitational disturbance that travels through space like a wave. This type of wave is analogous to an Electromagnetic Wave. Gravitational waves are given off by most movements of anything with mass. Usually, however, they are quite difficult to detect. Physicists are currently working hard to directly detect gravitational waves. Experiments like LIGO and LISA are designed for this purpose. ) is by looking at how it affects anything it passes through. Imagine a ship on water. As a water wave passes from right to left, the ship will rock up and down. If a gravitational wave passes in the same direction, on the other hand, the ship grows taller, then shorter — it waves.

These waves have some important features. We are familiar with the idea of the speed (Speed: For a wave, the speed of a particular point (such as its crest).) of a wave on water—this is just how far the crest of a wave moves per unit time (miles per hour, or meters per second, for example). The same idea applies to a gravitational wave. Here, the crest is the point where the ship is most stretched out. In the picture above, you can watch as this point moves along the ship from right to left. For a real gravitational wave, this speed is always equal to the speed of light (Speed of Light: A constant of Nature. This speed is precisely 299,792,458 meters per second, or roughly 670,616,629 miles per hour. One of the most unusual discoveries of science has been the fact that all Observers measure light as moving at exactly this speed, even if those observers are moving relative to each other. This fact is one of the basic ingredients in Einstein's Special Theory of Relativity.). (The gravitational wave is slowed down in these pictures, because it would be very hard to see otherwise.) Another important aspect of these waves is their wavelength (Wavelength: The distance between two neighboring peaks or troughs of a wave. )}). This is just the distance between wave crests.  We can turn our boat a little to see the waves from a second perspective. Imagine the waves broadsiding the boat. For a water wave, this will just raise and lower the boat, as it rides on the crest and then in the trough of the wave. For a gravitational wave, the ship will be pulled and then pinched, as we see in the pictures.

These pictures show one more interesting feature of the waves — their amplitude (Amplitude: The height of the peak of a wave, measured relative to its center. Equivalently, the depth of the trough of a wave.), or size. For the water wave, this is the distance the ship moves up or down from its center position. For the gravitational wave, this is the percentage of squeeze or stretch by which the wave distorts the ship.

#### The Sound of a Gravitational Wave

Watch the flag at the top of the ship's bow in the first gravitational wave picture above. As it moves back and forth, it is following a geodesic (Geodesic: Essentially the "straightest path" in a curved space or curved spacetime. This is the path followed by an object with no forces acting on it. In the curved spacetime of General Relativity, these paths may seem to be very curved — even appearing as circles or ellipses, for example. A geodesic is easily understood by looking at a very small region around the object. Even in highly curved spacetime, a small enough region will seem flat, so there is a natural idea of a "straight path". By following short segments, the whole geodesic is built up into one long path. )}). Nothing is pushing it back and forth; spacetime is simply warped in such a way that the path it follows is a "straight" line. Notice especially that the distance between the flag and the center of the ship is changing. If that gravitational wave were passing through your head, the same thing would be happening. In particular, the distances between parts of your ears would change. The eardrum would be moving back and forth, for example. But this is just what causes you to experience sound. Could you hear a gravitational wave?

In principle, yes! If the gravitational wave were strong enough, and the sound it made were a pitch humans could hear, then you would hear it passing through you. To be at the right pitch, the wave would have to move the ship's flag up and down at least twenty times per second. Of course, if it were strong enough to be heard, you would probably have other problems. Nonetheless, you could amplify the sounds if you had a microphone that was sensitive enough.

One question is whether anything in Nature makes these sounds at the right pitch, and loud enough, for humans to hear. Astrophysicists have found many sources for sounds that we actually could hear, with a good enough microphone. The next sections will take us through a set of possible sources of gravitational waves which may be heard in coming years. This will provide the strongest test yet for Einstein's ideas about spacetime.