Date: May 26, 2011
Title: Gravitational Waves
Podcaster: Rob Knop
Organization: Quest University Canada
Links: My home page : http://www.questu.ca/academics/faculty/rob_knop.php
Description: Did you know that there are waves of gravity? It’s a hard concept to wrap your mind about; so what are they?
Bio: Rob Knop obtained a PhD in Physics from Caltech in 1997. He then worked with the Supernova Cosmology Project and was part of the discovery that the expansion of the Universe is accelerating. After six years as an assistant professor at Vanderbilt University, he worked in the computer industry for two years. He now teaches physics the new college Quest Unviersity in British Columbia. He gives regular astronomy talks in Second Life in association with the Meta-Institute of Computational Astronomy.
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Transcript:
Hello! Thank you for listening to 365 Days of Astronomy. This is professor Rob Knop, tutor of physical science at Quest University Canada.
Did you know that there are waves of gravity? It’s a hard concept to wrap your mind about; what would a gravitational wave be? Gravity is a force; it’s the force that pulls us towards the Earth, and it’s the force that keeps the Earth in orbit around the Sun. This is very different from what we think about when we think about waves. Probably the most common sort of wave that people are familiar with are waves on the surface of water.
Even if you don’t live anywhere near the shore where ocean waves wash up on the beach, you’re familiar with surface water waves. The surface of the water defines a medium; if there are no waves on it, we would describe the medium as undisturbed. If you have a glass of water sitting on the counter, the undisturbed medium is the smooth surface at the top of the glass. Or, if you look at a perfectly reflecting pool or pond on a very still, windless day, you see the undisturbed surface of that pool or pond. However, if you flick your finger against the side of the glass, blow some wind across the surface of the pond, or drop a stone into the pool, you will see ripples on the surface. The disturbance creates waves which move out away from the source of the disturbance.
In this case, the thing being waved is the height of the water surface. The wave is a series of crests and troughs that propagate at a speed characteristic of the medium. Here, the crests are where the water is highest, and the troughs are where the water is lowest.
Another type of wave you may be familiar with is sound waves. In this case, it’s not the surface of anything being disturbed. Rather, sound waves are pressure waves, waves of density through the air. If you make a noise, you are creating a disturbance in the air. Waves will propagate away from the source of the noise. The crests, in this case, are where the air molecules get compressed together; at the crests, the air has higher density. At the troughs, the air has lower density. Each crest or trough moves along at the speed of sound, which in room-temperature air at around sea level is approximately three hundred meters per second. It seems like quite a different thing than waves on the surface of water, and indeed it’s different physics that drives the waves. However, it’s a very similar phenomenon. The same mathematical equations can describe the propagation of both kinds of waves.
And, of course, there are light waves. If something, say a lamp, is emitting light, light waves are moving away from that lamp at the speed of light, which is a million times faster than the speed of sound. With ocean waves, it is the surface of the ocean that is being waved. With sound waves, it is the density of the medium through which the sound is moving that is being waved. What is being waved in the case of light waves? In this case, it’s a little more abstract. We say that the electromagnetic field is what is being waved. Light, it turns out is composed of electric and magnetic fields interacting with each other. A changing electric field can induce a changing magnetic field, and vice versa. So, if you create an oscillating electric field, that will induce magnetic fields, which in turn will induce electric fields, and the whole thing will keep moving along as an electromagnetic wave. So, light is an electromagnetic wave.
You are probably also familiar with the idea that there are electric and magnetic forces. While physicists talk about this as “the electromagnetic force”, in our everyday life, we usually experience the two aspects of the force separately. If you rub a balloon against your hair, or against a cat, and then stick that balloon to the wall, it is the electric force that holds the balloon against the wall. And, of course, when you stick a magnet on the fridge, it is the magnetic force that holds it there. However, at a fundamental level, these forces are exactly the same things that compose electromagnetic waves, that is, light waves.
So, back to gravity. We usually think of gravity as a force; indeed, the classical equation for gravity, as developed a few centuries ago by Isaac Newton, looks very similar to the equation for the electric force. But, there’s no force to go along with gravity the way the magnetic force goes along with the electric force. So, how then could we have waves of gravity? To answer that, we have to go to a more modern conception of gravity, as described by Einstein’s General Relativity.
Relativity describes gravity as part of the structure of “spacetime”. The first observation of Relativity, which comes out of Special Relativity where no gravity is involved, is that space and time can mix into each other when two things are moving at different speeds. As such, rather than talking about the three-dimensional space in which all the objects in our Universe reside, to be fully relativistic we have to talk about a four-dimensional spacetime. In General Relativity, gravity is not a force at all. Objects will move in as straight of lines as possible through spacetime. If you’re at rest, then that straight line is pointing forward in time. The direction of motion will only change if a force moves the object around; so, electromagnetic forces could cause an object’s path to change. If you change the path of an object from straight in the time direction to partly in the space and partly in the time direction, you would observe that as the object starting at rest but accelerating.
Gravity, then, comes in as a curvature of spacetime. If there are massive objects about, spacetime becomes intrinsically curved. This means that the paths of objects through space time are no longer lines, but things called “geodesics”, which at each point are as straight as they can be. On a flat plane, if you have two parallel lines, they stay parallel forever. However, imagine the surface of a sphere. A geodesic on the surface of this sphere is a “great circle”, a circle that when it closes back on itself has a circumference that is the same as the circumference of the sphere. Imagine two great circles that start parallel: one right at the equator, and one just north of it, both moving due east. These two paths do in fact cross, a quarter of the way around the sphere. This is an analogy to two objects falling next to each other towards a massive object; for example, consider two asteroids at rest in space on either side of a star. Initially, their paths through spacetime are parallel, as they are both moving entirely in the time direction. However, thereafter the rocks both fall towards the star, and both eventually hit it. They are getting closer and closer together in space. Their paths in spacetime are no longer parallel. Both followed geodesics, but because of the curvature of spacetime near the star, those two geodesics converged.
Gravitational waves, then, are ripples in spacetime. You’ve seen a mesh to represent the structure of space before; just imagine a diagram of a town or a house on graph paper. The lines of the graph paper give you a two dimensional mesh that lets you measure distances in two of the spacial dimensions. You can similarly imagine a four-dimensional mesh representing separations in spacetime. Now, I can’t imagine four dimensions all at once; if you can, I’m quite impressed with you! However, hopefully you can understand that this could be done, by analogy to the graph paper. In empty space, with no massive objects, that mesh is regular, just like graph paper. If there are massive objects about, then spacetime is curved. That curvature is represented by a warping of the mesh around the massive object.
With this picture, you can now imagine gravitational waves. Imagine an oscillating disturbance at one point in the mesh. That will disturb the mesh lines near it, which in turn will disturb the mesh lines farther out, and so forth. You get ripples in the mesh which propagate through space at… you guessed it, the speed of light. But why, if gravity is a different force, would the speed of electromagnetic waves be the speed at which ripples in spacetime propagate? It turns out that this speed is actually a property of spacetime itself. The thing we call the speed of light would better be called the speed of spacetime. Anything massless, including light waves and gravitational waves, moves at that speed.
If you’re an experimentalist, and you want to measure one of these gravitational waves, the ripple in spacetime could be seen as objects moving closer together, then farther apart, then closer together, over time. Have we seen this happen as the result of a passing gravitational wave? Alas, no. It turns out that the strongest gravitational waves that we expect to see here on Earth represent a very, very tiny change in distances. LIGO, the Laser Interferometric Gravitational Observatory, is one of a few projects designed to measure gravitational waves from astronomical sources. They bounce laser light back and forth between mirrors separated by kilometers in order to measure changes in the separation of the mirrors that are a fraction of the wavelength of green light. That is, they’re looking for changes of something like a nanometer between objects that are kilometers apart. That’s tiny! LIGO is currently undergoing some upgrades to improve its sensitivity. After these upgrades are complete, we do expect to observe directly some gravitational waves.
How do you make gravitational waves? Because massive objects curve space time, and gravitational waves are ripples in this curvature of spacetime, any time something massive is moving about it’s creating gravitational waves. The more massive it is, and the faster it moves, the stronger those waves will be. The best gravitational wave sources, then, are very massive objects moving very quickly. That is, black holes or neutron stars orbiting very close around each other, or, even better, running into each other and merging. When galaxies run into each other– and they do, but that’s a topic for another day– eventually the supermassive black holes at the cores of the galaxies will themselves merge. The gravitational waves emitted by these mergers in the distant Universe is something that we will be able to observe hopefully in the next decade.
Because we haven’t seen them, can we be sure that gravitational waves really exist? The answer is yes! First, they’re a strong prediction of General Relativity, a theory of gravity that is working with every other test we’ve thrown at it. However, we do have an observation that is in detail consistent with what we’d expect as a result of gravitational waves. Just as light waves carry off energy, so do gravitational waves. Therefore, if you have a small enough orbit of massive enough objects, you should be able to observe the decay of that orbit due to the loss of energy to gravitational radiation. And, indeed, we have observed this in binary pulsar systems, where the orbits of two neutrons stars about each other decay at exactly the rate you’d expect as a result of their gravitational radiation.
Right now, almost everything we know about the Universe outside our Solar System comes from having observed the light that comes to us from objects in the Universe. Although budget woes have cast the future of a gravitational wave space mission into doubt, sometime in the 21st century humanity will be able to start using gravitational waves to open up a completely new window on the Universe.
End of podcast:
365 Days of Astronomy
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