Gravitational waves

"Ladies and gentlemen, we have detected gravitational waves. We did it." Dave Reitze (Executive director of LIGO)

Well that's awesome. What a day, what a moment to be alive. Today it was officially reported that the LIGO collaboration has detected gravitational waves. You've probably seen scientists everywhere shouting with joy. And we have every reason to be happy. 

A few weeks ago, rumours started circulating about a potential discovery of gravitational waves. I really think rumours should be kept out of science, but the good side of those rumours is that they got people talking. I've discussed this topic quite a few times one Periscope, you can watch the most recent one here.

Just to get you started, this video was released a few days before the announcement of detection, and I think it's great. It provides a quick three-minute summary of gravitational waves. This video is like a trailer to my post - you can get an overview, but do stay for all the juicy details.

Now that we've seen an overview, let's try to understand everything going on here.

Massive objects curve spacetime.
Simulation made by C. Joana.

What are gravitational waves?

Einstein's theory of general relativity tells us that space and time are not two separate concepts: they are intrinsically linked - spacetime. You can't have one without the other, they are two sides of the same coin. Furthermore, Einstein's theory says that gravity is just a curvature of this spacetime. Imagine you have a big sheet and you put a ball in the middle: this will curve the sheet (or spacetime), causing other objects to move towards it, following the curvature of spacetime. This means that objects will travel in a straight line on a curved surface. While this might seem strange, it's a phenomenon that we encounter daily: if you take a flight from Los Angeles to Berlin, the plane will pass over Greenland, even though if you look at a flat map this seems like a longer, curved route. If you look at a globe, however, you will see that this is the shortest path (and therefore the straightest) on a curved surface.
Einstein summarised his theory as 'massive objects tell spacetime how to curve; spacetime tells objects how to move'.

This brings us to the idea of gravitational waves.

Gravitational waves are ripples in the fabric of spacetime. Imagine you are in a pool with a friend, and you start dancing in circles around each other. You would notice ripples forming around you and moving outwards. The same thing happens in spacetime. Like all waves, these waves have an amplitude (height of wave), a frequency (how often the crests pass us by), a wavelength (distance between the crests), and a certain speed. The first three are determined by the source of the wave. Therefore, if we are able to measure these characteristics, we could get information about the source. The speed, however, is fixed: gravitational waves move at the speed of light. This should not be surprising as the speed of light is the speed at which 'spacetime talks to itself'.

When Einstein came up with his theory in 1915, he made many predictions: the perihelion precession of Mercury's orbit (the closest point between the Sun and Mercury changes every year), the deflection of light by massive objects (light travels in a straight line on a curved surface), the gravitational redshift of light (light waves are stretched or compressed by gravitational fields), and gravitational waves. The latter was the only prediction from general relativity we hadn't been able to observe. The final proof of Einstein's theory had eluded us. Until now.

What could cause them?
The mathematical formulas from Einstein's general relativity tell us that any massive accelerating object would disrupt spacetime, sending ripples through the universe. So what type of objects accelerate?

• Two objects orbiting each other, like two neutron stars or black holes, will emit gravitational waves.
• Any non-spherical planet or moon; like a planet with a big bump. If it looks more like an American football than a 'rest-of-the-world' football, it would emit gravitational waves.
• A supernova will probably create gravitational waves, unless it explodes in a perfect sphere, symmetrical in every direction.

Just to be clear, we can see some examples of objects that would not create gravitational waves:

• A lonely, non-spinning, solid object, moving at a constant speed and not interacting with the world around it will not generate gravitational waves. This is what we like to call 'conservation of linear momentum'.
• Flat objects, like disks (think galaxies) will not radiate gravitational waves. If you spin a pizza base on your finger (a skill I am yet to master), the pizza will not emit gravitational waves. This is because of something we like to call 'conservation of angular momentum'.

Simulations have existed for years to show us what the merging of two black holes would look like, as well as the gravitational waves they would produce. Like this one, from NASA's Scientific Visualization Studio:

What effects do these waves have? What would they look like?
These small, circular, ripples in spacetime would present themselves as small changes in the distance between two objects. The waves would stretch and compress spacetime; first in one direction, then in the other. If we had particles arranged in a cylinder, this is what we would see:

Here the wave is moving through the cylinder, from back-right to front-left. (A more detailed explanation of this image can be found here.)
How noticeable is this effect? It's really small. Ridiculously small. Even the most powerful gravitational waves (like those that would form in the merging of two black holes) would only change a length by a factor of $10^{-21}$ (zero point twenty zeros and a 1). That's a difference of one thousandth billionth billionth. If this wave went through you, it would change your height by one millionth billionth the width of a single hair.

From a physical point of view, one of the main effects of gravitational wave is that they carry energy away from the source. This means that the waves carry a lot of information about the source objects. In the case of two bodies orbiting around each other, this causes their orbits to decrease: the two objects get closer.

You might be wondering at this point if the Sun-Earth system emits gravitational waves. The answer is yes, it does. This means that the Earth and the Sun are gradually getting closer. Fortunately, gravitational waves become more significant as you increase the mass of the objects, and decrease the distance between them. The Earth and the Sun are really small (on cosmic scales), and quite far apart. The effect of the waves produced in the Earth-Sun system is the Earth gets $10^{-12}$ meters closer to the Sun every year. That means in $10^{12}$ years (a trillion years), we would be one metre closer to the Sun. Considering that is more than the current age of the universe, it's not something we should worry about.

This decrease in orbit has led us to see indirect evidence for gravitational waves before. There is a system of two orbiting stars, known as the Hulse-Taylor system, that we have been able to observe for more than thirty years. Physicists R. Hulse and J. Taylor measured the decay in their orbit: the gradual decrease in the distance between the two stars. This decrease is directly related to the energy carried away by gravitational waves. They were able to show that the decay in the orbit and the decay predicted by Einstein's general relativity were in agreement with less than a 0.2% error. They were awarded the 1993 Nobel Prize in Physics for this indirect detection.

How can we directly detect them?
We can infer their existence from decaying orbits, but we would like to see them directly. So how do we detect something so small and unnoticeable? With lasers!

Recently, Julia Majors PhD (@Feynwoman), everyone's favourite laser physicist, wrote a great article explaining the LIGO set-up and how they used lasers to find these tiny waves. You should definitely read it.

The ideal way to detect gravitational waves would be to measure the small changes in distance between two points. But this presents a problem: a gravitational wave would also make our ruler longer or shorter. We need something that would not change with the gravitational wave. And so we go back to Einstein. His theory of relativity shows us that the speed of light is constant, it would not be affected by gravitational waves. Speed is defined as distance travelled over the time of travel. If the speed of light is constant, changes in the distance of travel would change the time it takes light to cover this distance. All we need to do is use light as a stopwatch.

Enter LIGO, the Laser Interferometer Gravitational-Wave Observatory. LIGO is an experiment currently running in the USA, designed to find gravitational waves using lasers. Like any interferometer (device that measures the interference of light), it relies on constructive and destructive interference.

The red wave is the result of adding the two blue ones together

When two waves overlap, different things can happen. Let's assume the waves have the same frequency and amplitude, as seen in the picture on the right. If the waves meet with the crests overlapping, we have constructive interference, and a bigger wave is created. If, on the other hand, the waves meet with the crests of one wave overlapping with the valleys of the of the other wave, we have destructive interference, and the waves annihilate.

LIGO starts by sending a laser beam to a 'beam splitter', where the light is split in two and sent down LIGO's two arms, each 4 km long. This light is then bounced off of mirrors and sent back to the start, where it is recombined. It is set up so that the beams coming back should produce destructive interference: the light waves cancel out and no signal is produced. However, if a gravitational wave passes through LIGO, it would stretch or contract one of the arms, causing a difference in distance. A difference in distance implies a difference in time: the returning light waves would no longer by synchronised, creating interference that can be measured. If this sounds confusing, don't worry; LIGO made a nice video showing this effect:

Wow, what an incredible system. We use lasers, bounced off of mirrors, to detect minuscule differences in distances, caused by a wave created thousands of miles away. Human ingenuity has no limits.

You might be thinking that such a small difference could be caused by any number of things. What if a train goes past and vibrates the laser? What if there is an earthquake? Wouldn't that create background noise? LIGO has you covered: they made two detectors; one in Louisiana and one in Washington. They are separated by 3000 km, and they serve as a check. A real wave would be detected in both places, with a difference of ten milliseconds (the time it takes the wave to travel that distance), so we can discriminate between real waves and noise. Take that, background noise!

What has LIGO found? 
LIGO had its first run between 2002-2010. They didn't detect anything in that time (not surprising, due to the low sensitivity), so they shut the machine down for five years. In that time, they upgraded everything; better lasers, smoother mirrors, better measuring devices. They switched the Advanced LIGO (we are really not imaginative when it comes to naming our experiments) on in September 2015, with high expectations. In February 2016, they called a press conference, and everyone got excited. Had they finally found the elusive gravitational waves predicted by Einstein a hundred years ago?

Not ones to beat around the bush, LIGO representatives opened their press conference with a dramatic 'We did it.' They found the waves. They had really seen them. This is the official plot they released:

Now we've had a hundred years to prepare for this moment. Physicists have made lists of what interference pattern gravitational waves from different sources would create. And now we have something to compare it to. LIGO compared their signal with all of the predictions (notice the white line in the plots listed as 'prediction'), and found that their signal (received in both detectors, as expected) was compatible with the merging of two black holes. Two black holes, with masses 36 and 29 times the solar mass, merged to create a black hole of 62 times the solar mass. The three missing solar masses were radiated away in the form of gravitational waves. They released a nice simulation showing what they think happened:

Let's just think about this for a moment. 1,3 billion years ago, 12 thousand million million kilometres away, two black holes started a deathly dance, resulting in them merging and sending waves throughout the universe. In September last year, these waves were detected by humans using lasers and mirrors. A hundred years ago, Einstein came up with a way of understanding the universe. He made lots of predictions, and every single one of them has come true. General relativity has stood up to every test we could think of.
That is truly amazing.

For many years mankind has studied the universe. The universe talks to us in different ways, but until now we only listened to one main form of communication: the electromagnetic spectrum. We now have a new way to listen, to uncover the secrets of the universe: gravitational waves. We are the first humans to ever be able to say this. This is a great moment for us.