Gravitational Wave Detectors: How They Work

Simplified gravitational wave detectors

It’s official: this Thursday, February 11, at 10:30 EST, there will be parallel press conferences at the National Press Club in Washington, D.C., in Hannover, Germany, and near Pisa in Italy. Not officially confirmed, but highly probable, is that people running the LIGO gravitational wave detectors will announce the first direct detection of a gravitational wave. The first direct detection of minute distortions of spacetime, travelling at the speed of light, first postulated by Albert Einstein almost exactly 100 years ago. Nobel prize time.

Time to brush up on your gravitational wave basics, if you haven’t done so! In Gravitational waves and how they distort space, I had a look at what gravitational waves do. Now, on to the next step: How can we measure what they do? How do gravitational wave detectors such as LIGO work?

Recall that this is how a gravitational wave will change the distances between particles, floating freely in a circular formation in empty space: How distances change when a simple gravitational wave passes through a ring of particles. This is what gravitational wave detectors need to measure.The wave is moving at right angles to the screen, towards you. I’ve greatly exaggerated the distance changes. For a realistic wave, even the giant distance between the Earth and the Sun would only change by a fraction of the diameter of a hydrogen atom. Tiny changes indeed.

How to detect something like this?

The first unsuccessful attempts to detect gravitational waves in the 1960s tried to measure how they make aluminum cylinders ring like a very soft bell. (Tragic story; Joe Weber [1919-2000], the pioneering physicist behind this, was sure he had detected gravitational waves in this way; after thorough analysis and replication attempts, community consensus emerged that he hadn’t.)

Afterwards, physicists came up with alternative scheme. Imagine that you are replacing the black point in the center of the previous animation with a detector, and the rightmost red particle with a laser light source. Now you send light pulses (represented here by fast red dots) from the light source to the detector; let’s first look at this with the gravitational wave switched off:Simplified gravitational wave detector without gravitational wave

Every time a light pulse reaches the detector, an indicator light flashes yellow. The pulses are sent out regularly, they all travel at the same speed, hence they also reach the detector in regular intervals.

If a gravitational wave passes through this system, again from the back and coming towards you, distances will change. Let us keep our camera trained on the detector, so the detector remains where it is. The changing distance to the light source, and also the changing distances between the light pulses, and some of the changes in distance between light pulses and detector or source, are due to the gravitational wave. Here is what that would look like (again, hugely exaggerated): The same simplified gravitational wave detector, but now with a gravitational wave passing through.

Keep your eye on the blinking light, and you will see that its blinking is not so regular any more. Sometimes, the light blinks faster, sometimes slower. This is an effect of the gravitational wave. An effect by which we can hope to detect the gravitational wave.

“We” in this case are the radio astronomers working on what are known as Pulsar Timing Arrays. The sender of regular pulses are pulsars, rotating neutron stars sweeping a radio beam across our antennas like a cosmic lighthouse. The detectors are radio telescopes here on Earth. Detection is anything but easy. With a single pulsar, you’d need to track pulse arrival times with an accuracy of a few billionths of a second over half a year, and make sure you are not being fooled by various other sources of timing variations. So far, no gravitational waves have been detected in this way, although the radio astronomers are keeping at it.

To see how gravitational wave detectors like LIGO work, we need to make things a little more complex.

Interferometric gravitational wave detectors: the set-up

Here is the basic set-up: Two mirrors, a receiver (or “light detector”), a light source and what is known as a beamsplitter: Basic setup for an interferometric gravitational wave detector

Light is sent into the detector from the (laser) light source LS to the beamsplitter B which, true to its name, sends half of the light on to the mirror M1 and lets the other half through to the mirror M2. At M1 and M2, respectively, the light is reflected back to the beam splitter. There, the light arriving from M1 (or M2) is split again, with half going towards the light detector LD, the other half back in the direction of the light source LS. We will ignore the latter half and pretend, for the sake of our simplified explanation, that all the light reaching B from M1 or M2 goes on to the light detector LD.

(To avoid confusion, I will always refer to LD as the “light detector” and take the unqualified word “detector” to mean the whole setup.)

This setup, by the way, is called a Michelson Interferometer. We’ll see below why it is a good setup for gravitational wave detectors.

In what follows, we will assume that the mirrors and the beam splitter, shown as being suspended, react to the gravitational wave in the same way freely floating particles would react. The key effects are between the mirrors and the beam splitter in what are called the two arms of the detector. Arm length is huge in today’s detectors, running to a few kilometers. In comparison, light source and light detector are very close to the beamsplitter; changes of the distances between these three do not signify.

Light pulses in a gravitational wave detector

Next, let us see how light pulses run through this detector. Here is the same setup, seen from above: Simple interferometric gravitational wave detector, seen from aboveLight source LS, the two mirrors M1 and M2, the beamsplitter B and the light detector LD: all present and accounted for.

Next, we let the light source emit light pulses. For greater clarity, I will make two artificial and unrealistic changes. I will send red and green pulses into the detector, representing the light that goes into the horizontal and the vertical arm, respectively. In reality, there is no distinction, just light apportioned at the beamsplitter. Light running towards M1 will be offset a little to the left, light coming back from M1 to the right, for better clarity. Same goes for M2. This, too, is different in a real detector. That said, here come the light pulses: Simplified interferometric gravitational wave detector with light running through both armsLight starts at the light source to the left. Light that has left the source together, travels together (so green and red pulses are side by side) until the beam splitter. The beam splitter then sends the green pulses on their upward journey and lets the red pulses pass on their way towards the mirror on the right. All the particles that arrive back at the beamsplitter after reflection at M1 or M2. At the beamsplitter, they are directed towards the light detector at the bottom.

In this setup, the horizontal arm is slightly longer than the vertical arm. Red particles have to cover some extra distance. That is why they arrive at the detector a bit later, and we get an alternating rhythm: green, red, green, red, with equal distances in between. This will become important later on.

Here is a diagram, a kind of registration strip, which shows the arrival times for red and green pulses at the light detector (time is measured in “animation frames”): Arrival times at the light detector of a simplified gravitational wave detectorThe pattern is clear: red and green pulses arrive evenly spaced, one after the other.

Bring on the gravitational wave!

Next, let’s switch on our standard gravitational wave (exaggerated, passing through the screen towards you, and so on). Here is the result: Simple interferometric gravitational wave detector with a gravitational wave passing throughWe have trained our camera on the beamsplitter (so in our image, the beamsplitter doesn’t move). We ignore any slight changes in distance between beamsplitter and light source/light detector. Instead, we focus on the mirrors M1 and M2, which change their distance from the beamsplitter just as we would expect from the earlier animations.

Look at the way the pulses arrive at our light detector: sometimes red and green are almost evenly spaced, sometimes they close together. That is caused by the gravitational wave. Without the wave, we had strict regularity.

Here is the corresponding “registration strip” diagram. You can see that at some times, the light pulses of each color are closer together, at others, farther apart: Arrival times for light pulses in a gravitational wave detector

At the time I have marked with a hand-drawn arrow, red and green pulses arrive almost in unison!

The pattern is markedly different from the scenario without a gravitational wave. Detect this change in the pattern, and you have detected the gravitational wave.

Running interference

If you’ve wondered why detectors like LIGO are called interferometric gravitational wave detectors, we will need to think about waves a bit more. If not, let me just state that detectors like LIGO use the wave properties of light to measure the changes in pulse arrival rate you have seen in the last animation. To skip the details, feel free to jump ahead to the last section, “…and now for something a thousand times more complicated.”

Light is a wave, with crests and troughs corresponding to maxima and minima of the electric and of the magnetic field. While the animations I have shown you track the propagation of light pulses, they can also be used to understand what happens to a light wave in the interferometer. Just assume that each of the moving red and green dots in the detector marks the position of a wave crest.

Particles just add up. Take 2 particle and add 2 particles, and you will end up with 4 particles. But if you add up (combine, superimpose) waves, it depends. Sometimes, one wave plus another wave is indeed a bigger wave. Sometimes, it’s a smaller wave, or no wave at all. And sometimes it’s complicated.

When two waves are in perfect sync, the crests of the one aligning with the crests of the other, and the troughs aligning, too, you indeed get a bigger wave. The following diagram shows at which times the different parts of two light waves arrive at the light detector, and how they add up. (I’ve placed a dot on top of each crest; that is what the dots where meant to signify, after all.) Constructive interference of light wavesOn top, the green wave, perfectly aligned with the red wave (which, for clarity, is shown directly below the green wave). Add the two waves up, and you will get the (markedly stronger) blue wave in the bottom panel.

Not so if the two waves are maximally misaligned, the crests of each aligned with the troughs of the other. A crest and a trough cancel each other out. The sum of a wave and a maximally misaligned wave of equal strength is: no wave at all. Here is the corresponding diagram: Destructive interference of light wavesRecall that this was exactly the setup for our gravitational wave detector in the absence of gravitational waves: Red and green pulses with equal spacing; troughs of the one wave perfectly aligned with the crests of the other. The result: No light at the light detector. (For realistic gravitational wave detectors, that is almost true.)

When a gravitational wave passes through the detector, the situation changes. Here is the corresponding pattern of pulse/wave crest arrival times for the animation above: Interference pattern for a gravitational wave passing through the simplified gravitational wave detectorThe blue pattern, which is the sum of the red and the green, is complex. But it is not a flat line. There is light at the light detector where there was no light before, and the cause of the change is the gravitational wave passing through.

All in all, this makes a (highly simplified) version of how gravitational wave detectors such as LIGO work. Whatever the scientists will report this Thursday, it is based on light signals at the exit of such an interferometric detector.

And now for something a thousand times more complicated

Real gravitational wave detectors are, of course, much more complicated than that. I haven’t even started talking about the many disturbances scientists need to take into account – and to suppress as far as possible. How do you suspend the mirrors so that (at least for certain gravitational waves) they will indeed be influenced as if they were freely floating particles? How do you prevent seismic noise, cars or trains in the wider neighborhood and so on from moving your mirrors a tiny little bit (either by vibrations or by their own gravity)? What about fluctuations of the laser light?

Gravitational wave hunting is largely a hunt for noise, and for ways of suppressing that noise. The LIGO gravitational wave detectors and their kin are highly complex machines, with hundreds of control circuits, highly elaborate mirror suspensions, the most stable lasers known to physics (and some of the most high-powered). The technology has been contributed by numerous group from all over the world.

But all this is taking us too far, and I refer you to the pages of the detectors and collaborations for additional information:

LIGO pages at Caltech

Pages of the LIGO Scientific Collaboration

GEO 600 pages

VIRGO / EGO pages

You can find some further information about gravitational waves on the Einstein Online website:

Einstein Online: Spotlights on gravitational waves

Update: Gravitational Waves Discovered

Gravitational Waves and How They Distort Space

Gravitational waves distort space in a rhythmic fashion. These simple animations show how.

It’s official: on February 11, 10:30 EST, there will be a big press conference about gravitational waves by the people running the gravitational wave detector LIGO. It’s a fair bet that they will announce the first direct detection of gravitational waves, predicted by Albert Einstein 100 years ago. If all goes as the scientists hope, this will be the kick-off for an era of gravitational wave astronomy: for learning about some of the most extreme and violent events in the cosmos by measuring the tiny ripples of space distortions that emanate from them.

Time to brush up on your gravitational wave knowledge, if you haven’t already done so! Here’s a visualization to help you – and we’ll go step by step to see what it means: Visualization of a simple gravitational wave. Gravitational waves distort space in a rhythmic fashion.

Einstein’s distorted spacetime

In the words of the eminent relativist John Wheeler, Einstein’s theory of general relativity can be summarized in two statements: Matter tells space and time how to curve. And (curved) space and time tell matter how to move. (Here is a slightly longer version on Einstein Online.)

Einstein published the final form of his theory in November 1915. By spring 1916, he had realized another consequence of distorting space and time: general relativity allows for gravitational waves, rhythmic distortions which propagate through space at the speed of light.

For quite some time, physicists weren’t sure whether these gravitational waves were real or a mathematical artifact within Einstein’s theory. (For more about this controversy, see Daniel Kennefick’s book “Traveling at the Speed of Thought and  this article.) But since the 1980s, there has been indirect evidence for these waves (which earned its discoverers a Nobel prize, no less, in 1993).

Gravitational waves are emitted by orbiting bodies and certain other accelerated masses. Right now, major international efforts are underway to detect gravitational waves directly. Once detection is possible, the scientists hope to use gravitational waves to “listen” to some of the most violent processes in the universe: merging black holes and/or neutron stars, or the core region of supernova explosions.

Just as regular astronomy uses light and other forms of electromagnetic radiation to learn about distant objects, gravitational wave astronomy will decipher the information contained within gravitational waves. And if you go by recent rumors, gravitational wave astronomy might already have kicked off in mid-September 2015.

What do gravitational waves do?

But what do gravitational waves do? For that, let us look at a simplified, entirely hypothetical situation. (The following are variations on images and animations originally published here on Einstein Online.) Consider particles drifting in space, far from any sources of gravity. Imagine that the particles (red) are arranged in a circle around a center (marked in black): A ring of particles floating in space in a circle

If a simple gravitational wave were to pass through this image, coming directly at the reader, distances between these particles would change rhythmically as follows: How distances change when a simple gravitational wave passes through a ring of particles

Note the distinctive pattern: When the circle is stretched in the vertical direction, it is compressed in the horizontal direction, and vice versa. That’s typical for gravitational waves (“quadrupole distortion”).

It’s important to keep in mind that this animation, and the ones that will follow, exaggerate the gravitational wave’s effect quite considerably. The gravitational waves detectors such as aLIGO hope to measure are much, much weaker. If our hypothetical circle of particles were as large as the Earth’s orbit around the Sun, a realistic gravitational wave would distort it by less than the diameter of a hydrogen atom.

Gravitational waves moving through space

The animation above shows what could be called a “gravitational oscillation.” To see the whole wave, we need to consider the third dimension.

We talk about a wave when oscillations propagate through space. Consider a water wave: At each point of the surface, we have an oscillation, with the surface rising and falling rhythmically. But it’s only the fact that this oscillation propagates, and that we can see a crest moving over the surface, that makes this into a wave.

It’s the same with gravitational waves. To see that, we will look not at a single circle of freely floating particles, but at many such circles, stacked one behind the other, forming the surface of a cylinder: Circles of particles, stacked so as to form a cylinder

In this image, it’s hard to see which points are in front and which in the back. Let us join each particle to its nearest neighbors with a blue line, and let us also fill out the area between those lines. That way, the geometry is much more obvious:  The previous cylinder, with neighboring particles joined with lines.

Just remember that neither the lines nor the whitish surface is physical. On the contrary, if we want the particles to be maximally susceptible to the effect of the gravitational wave, we should make sure they are truly floating freely, and certainly they shouldn’t be linked in any way!

Now, let us see what the same gravitational wave we saw before does to this assembly of particles. From this perspective, the wave is passing from the right-hand side in the back towards the left-hand side on the front: A gravitational wave passing through a 3d cylinder of particlesAs you can see, the wave is propagating through space. For instance, the point where the vertical distances within the circle of particles is maximal is moving towards the observer. The wave nature can be seen even more clearly if we look at this cylinder directly from the side: The action of a gravitational wave on an assembly of particles, seen directly from the side

What the animations show is just one kind of simple gravitational wave (“linearly polarized”). Here is another kind (“circularly polarized”): Action of a circularly polarized gravitational wave

This, then, is what the gravitational wave hunters are looking for. Except that they do not have particles floating in free space. Instead, their detectors contain test masses (notably large mirrors) elaborately suspended here on Earth, with laser light to detect the minute distance changes caused by gravitational waves.

More realistic gravitational wave signals, which contain information about merging black holes or the bulk motion of matter inside a supernova explosion, are more complicated still. They combine many simple waves of different frequencies, and the strength of such waves (their amplitude) will change over time in a characteristic fashion.

In these animations, gravitational waves look a bit like wriggling space worms. But these space worms could become the astronomers’ best friends, carrying information about the cosmos that is hard or even impossible to obtain in any other way.

[Don’t miss the sequel: Gravitational wave detectors: how they work]

Update: Gravitational Waves Detected