Great explanation

Great explanation

Originally shared by Yonatan Zunger

We have observed gravitational waves!

This morning, the LIGO observatory announced a historic event: for the very first time in history, we have observed a pair of black holes colliding, not by light (which they don't emit), but by the waves in spacetime itself that they form. This is a tremendously big deal, so let me try to explain why.

What's a gravitational wave?

The easiest way to understand General Relativity is to imagine that the universe is a big trampoline. Imagine a star as a bowling ball, sitting in the middle of it, and a spaceship as a small marble that you're shooting along the trampoline. As the marble approaches the bowling ball, it starts to fall along the stretched surface of the trampoline, and curve towards the ball; depending on how close it passes to the ball and how fast, it might fall and hit it. 

If you looked at this from above, you wouldn't see the stretching of the trampoline; it would just look black, and like the marble was "attracted" towards the bowling ball.

This is basically how gravity works: mass (or energy) stretches out space (and time), and as objects just move in what looks like a straight path to them, they curve towards heavy things, because spacetime itself is bent. That's Einstein's theory of Relativity, first published in 1916, and (prior to today) almost every aspect of it had been verified by experiment.

Now imagine that you pick up a bowling ball and drop it, or do something else similarly violent on the trampoline. Not only is the trampoline going to be stretched, but it's going to bounce -- and if you look at it in slow-motion, you'll see ripples flowing along the surface of the trampoline, just like you would if you dropped a bowling ball into a lake. Relativity predicts ripples like that as well, and these are gravitational waves. Until today, they had only been predicted, never seen.

(The real math of relativity is a bit more complicated than that of trampolines, and for example gravitational waves stretch space and time in very distinctive patterns: if you held a T-square up and a gravitational wave hit it head-on,  you would see first one leg compress and the other stretch, then the other way round)

The challenge with seeing gravitational waves is that gravity is very weak (after all, it takes the entire mass of the Earth to hold you down!) and so you need a really large event to emit enough gravity waves to see it. Say, two black holes colliding off-center with each other.

So how do we see them?

We use a trick called laser interferometry, which is basically a fancy T-square. What you do is you take a laser beam, split it in two, and let each beam fly down the length of a large L. At the end of the leg, it hits a mirror and bounces back, and you recombine the two beams.

The trick is this: lasers (unlike other forms of light) form very neat wave patterns, where the light is just a single, perfectly regular, wave. When the two beams recombine, you therefore have two overlapping waves -- and if you've ever watched two ripples collide, you'll notice that when waves overlap, they cancel in spots and reinforce each other in spots. As a result, if the relative length of the legs of the L changes, the amount of cancellation will change -- and so, by monitoring the brightness of the re-merged light, you can see if something changed the length of one leg and not the other.

LIGO (the Laser Interferometer Gravitational-Wave Observatory) consists of a pair of these, one in Livingston, Louisiana, and one in Hartford, Washington, three thousand kilometers apart. Each leg of each L is four kilometers long, and they are isolated from ambient ground motion and vibration by a truly impressive set of systems.

If a gravitational wave were to strike LIGO, it would create a very characteristic compression and expansion pattern first in one L, then the other. By comparing the difference between the two, and looking for that very distinctive pattern, you could spot gravity waves.

How sensitive is this? If you change the relative length of the legs of an L by a fraction of the wavelength of the light, you change the brightness of the merged light by a predictable amount. Since measuring the brightness of light is something we're really good at (think high-quality photo-sensors), we can spot very small fractions of a wavelength. In fact, the LIGO detector can currently spot changes of one attometer (10⁻¹⁸ of a meter), or about one-thousandth the size of an atomic nucleus. (Or one hundred-millionth the size of an atom!) It's expected that we'll be able to improve that by a factor of three in the next few years.

With a four-kilometer leg, this means that LIGO can spot changes in length of about one-quarter of a part in 10²¹. That's the resolution you need to spot events like this: despite the tremendous violence of the collision (as I'll explain in a second), it was so far away -- really, on the other end of the universe -- that it only created vibrations of about five parts in 10²¹ on Earth.

So what did LIGO see?

About 1.5 billion light years away, two black holes -- one weighing about 29 times as much as the Sun, the other 36 -- collided with  each other. As they drew closer, their gravity caused them to start to spiral inwards towards each other, so that in the final moments before the collision they started spinning around each other more and more quickly, up to a peak speed of 250 orbits per second. This started to fling gravity waves in all directions with great vigor, and when they finally collided, they formed a single black hole, 62 times the mass of the Sun. The difference -- three solar masses -- was all released in the form of pure energy.

Within those final few milliseconds, the collision was 50 times brighter than the entire rest of the universe combined. All of that energy was emitted in the form of gravitational waves: something to which we were completely blind until today.

Are we sure about that?

High-energy physics has become known for extreme paranoia about the quality of its data. The confidence level required to declare a "discovery" in this field is technically known as 5σ, translating to a confidence level of 99.99994%. That takes into account statistical anomalies and so on, but you should take much more care when dealing with big-deal discoveries; LIGO does all sorts of things for that. For example, their computers are set up to routinely inject false signals into the data, and they don't "open up the box" to reveal whether a signal was real or faked until after the entire team has finished analyzing the data. (This lets you know that your system would detect a real signal, and it has the added benefit that the people doing the data analysis never know if it's the real thing or not when they're doing the analysis -- helping to counter any unconscious tendency to bias the data towards "yes, it's really real!")

There are all sorts of other tricks like that, and generally LIGO is known for the best practices of data analysis basically anywhere. From the analysis, they found a confidence level of 5.1σ -- enough to count as a confirmed discovery of a new physical phenomenon.

(That's equal to a p-value of 3.4*10⁻⁷, for those of you from fields that use those)

So why is this important?

Well, first of all, we just observed a new physical phenomenon for the first time, and confirmed the last major part of Einstein's theory. Which is pretty cool in its own right.

But as of today, LIGO is no longer just a physics experiment: it is now an astronomical observatory. This is the first gravity-wave telescope, and it's going to let us answer questions that we could only dream about before.

Consider that the collision we saw emitted a tremendous amount of energy, brighter than everything else in the sky combined, and yet we were blind to it. How many more such collisions are happening? How does the flow of energy via gravitational wave shape the structure of galaxies, of galactic clusters, of the universe as a whole? How often do black holes collide, and how do they do it? Are there ultramassive black holes which shape the movement of entire galactic clusters, the way that supermassive ones shape the movement of galaxies, but which we can't see using ordinary light at all, because they aren't closely surrounded by stars?

Today's discovery is more than just a milestone in physics: it's the opening act of a much bigger step forward.

What's next?

LIGO is going to keep observing! We may also revisit an old plan (scrapped when the politics broke down) for another observatory called LISA, which instead of using two four-kilometer L's on the Earth, consists of a big triangle of lasers, with their vertices on three satellites orbiting the Sun. The LISA observatory (and yes, this is actually possible with modern technology) would be able to observe motions of roughly the same size as LIGO -- one attometer -- but as a fraction of a leg five million kilometers long. That gives us, shall we say, one hell of a lot better resolution. And because it doesn't have to be shielded from things like the vibrations of passing trucks, in many ways it's actually simpler than LIGO.

(The LISA Pathfinder mission, a test satellite to debug many of these things, was launched on December 3rd)

The next twenty years are likely to lead to a steady stream of discoveries from these observatories: it's the first time we've had a fundamentally new kind of telescope in quite a while. (The last major shift in this was probably Hubble, our first optical telescope in space, above all the problems of the atmosphere)

The one catch is that LIGO and LISA don't produce pretty pictures; you can think of LIGO as a gravity-wave camera that has exactly two pixels. If the wave hits Louisiana first, it came from the south; if it hits Washington first, it came from the north. (This one came from the south, incidentally; it hit Louisiana seven milliseconds before Washington) It's the shift in the pixels over time that lets us see things, but it's not going to look very visually dramatic. We'll have to wait quite some time until we can figure out how to build a gravitational wave telescope that can show us a clear image of the sky in these waves; but even before that, we'll be able to tease out the details of distant events of a scale hard to imagine.

You can read the full paper at http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.061102 , including all of the technical details. Many congratulations to the entire LIGO team: you've really done it. Amazing.

Incidentally, Physical Review Letters normally has a strict four-page max; the fact that they were willing to give this article sixteen pages shows just how big a deal this is.