Gravitational waves are “ripples in space time” that propagate through it like waves on water. That’s the common story and, for the most part, it’s right. But what does that mean? This is part four in my many-part series on general relativity. The first three parts introduce general relativity from the ground up. You can find them here:
- Galileo almost discovered general relativity
- General relativity is the dynamics of distance
- General relativity is the curvature of spacetime
Okay. Without further ado, gravitational waves!
Spooky Action at a Distance
First, I want to help you get an intuition for why gravitational waves should exist. So before we dive into the relativity, let’s step back for a moment and imagine boring old Newtonian gravity. Suppose we have a bowling ball (blue) and a marble (red), as shown in figure 2. We take the bowling ball and we move it periodically towards and away from the marble. As we do, we measure the strength of the gravitational pull the bowling ball exerts on the marble. It gets stronger as the bowling ball gets near and weaker as it moves further away. This is plotted in the bottom of figure 2.
Notice how wavy the gravitational strength looks? At this point, you might be tempted to call it a gravitational wave. But that temptation is leading you astray. See, an important property of waves is that they travel at finite speed. Information can’t travel instantly. But in Newtonian physics, the marble feels the change in the gravitational pull of the bowling ball instantly.
So what needs to change? Well, all we need to do is sprinkle a little bit of special relativity into the mix, since special relativity says that information can travel no faster than light. Then the wiggles plotted in figure 2 would be delayed. So the marble would only feel a gravitational force a bit after we move the bowling ball.
That would be a gravitational wave.
Since special relativity is basically true, and we feel gravitational forces, this should convince you that gravitational waves should exist. And it should also give you a sense on what a gravitational wave should be like. We should feel a temporary change in the “pull” from the gravity a distant object, which is an echo of its motion.
Gravitational Waves in General Relativity
But of course, gravitational waves don’t actually work the way I just described. Gravity is not a force, it’s a distortion in the way we measure distance. So how do gravitational waves work in this context? Well, in some sense, I already told you. Gravity is a distortion of how we measure distance. So a gravitational wave is a distortion in how we measure distance that travels.
Of course, there are some caveats, most of which I won’t get into. The most important caveat is how the distance distorts. Distances don’t just grow and shrink evenly in every direction. They grow in one direction and shrink in another. For example, if you took a circular ring of particles, I’m a fan of marbles, floating in outer space, and a gravitational wave passed by, you’d observe them distort into one ellipse and then another, as shown in figure 3. And this happens because the distances between the particles are changing. (For experts: I’m showing the + polarization. If you rotate by 45 degrees, you get the x polarization.)
Detecting Gravitational Waves, Part 1
So how would you detect a gravitational wave? Should we arrange a bunch of marbles in space and wait for them to distort? Well, in principle we could do that. But spacetime is very stiff and the distortion in distance from a gravitational wave is quite small, which is why we haven’t detected any gravitational waves yet. To see a distortion large enough that we could see, we’d need a very big ring of marbles.
Fortunately, we have one. An artist’s impression is shown in figure 4. Except our marbles are all neutron stars and our ring is millions of lightyears wide. Basically, each marble is a type of star called a millisecond pulsar, which is a neutron star that’s rotating very fast. For reasons I won’t get into, this makes it emit light (though usually not visible light) in a beam. And as it rotates, we see a pulse as the beam points towards us, like a lighthouse. To measure a distortion in spacetime due to a gravitational wave, we measure how long a pulse takes to reach us over many many pulses. If a pulse comes before or later than it should, that might be a gravitational wave! To see if it is, we need to check with all the pulsars in the “ring” to see if they distorted in the right way and do some fancy math.
This whole scheme is called pulsar timing, which is done with pulsar timing arrays. A pulsar timing array is a collaboration of people who use telescopes, like the one at Arecibo shown in figure 5, that keep track of millisecond pulsars and do statistics to see if they’ve detected a gravitational wave.
Detecting Gravitational Waves, Part 2
Pulsar timing is great and all… but is there a more… direct way we can find gravitational waves? Maybe something we can build on Earth? I’m glad you asked! We don’t really need a ring of particles, right? All we actually need are two very very precise rulers… set up so that we can measure distance growing in one direction and shrinking in another.
Fortunately, light makes an incredibly good ruler. So we can make our rulers out of laser light and compare them to detect a gravitational wave. That’s how the two LIGO detectors and detectors like them work. One of the detectors is shown in figure 6.
Each LIGO detector has two 4km long, vacuum-sealed, seismically isolated, supercooled laser arms that measure distance incredibly accurately. If you compare the distances measured in the two arms (which is actually all you can do because LIGO is a laser interferometer), the measurement in the difference is accurate to better than one part in . This means they can measure a change in distance one one-thousandth of the width of a proton.
The LIGO systems were recently upgraded and they’re coming online this year. So stay tuned in the following years for news of a gravitational wave detection!
I should mention that moving a mass in a straight line back and forth, as in figure 2, is not enough to excite a gravitational wave in general relativity. The motion of the mass needs to have a so-called quadrupole moment. Most motions in the real world, such as orbiting a star, do have a quadrupole moment. But I wanted to mention this so that you’re not under the impression that all motion produces gravitational waves. Just most motion.
I have a lot more to say about gravitational waves. But I think this is enough for now. In future posts, look forward to learning about the astrophysical systems that produce gravitational waves and listening to the sound of two black holes colliding.
I didn’t pull my description from a single source, this time. I used a bunch of textbooks, such as Spacetime and Geometry by Sean Carroll and Introduction to 3+1 Numerical Relativity by Miguel Alcubierre. But here’s some more accessible resources:
- My collaborators, the Simulating Extreme Spacetimes Collaboration, have a great article on gravitational waves.
- NANOGrav’s science page isn’t bad either.
- And here’s a nice blog post on gravitational waves and pulsar timing.
If you liked this post (and my other general relativity posts) you may be interested in some of my posts on relativistic astrophysics: