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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 , 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.

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The Poetry of LIGO’s Gravitational Waves

Yesterday the LIGO scientific collaboration announced that they had detected the gravitational waves from the in-spiral and merger of two black holes, shown in figure 1. It would not be an overstatement to say that this result has changed science forever. As a gravitational physicist, it is hard for me to put into words how scientifically important and emotionally powerful this moment is for me and for everyone in my field. But I’m going to try. This is my attempt to capture some of the science—and the poetry—of LIGO’s gravitational wave announcement.

To read this post in blog form, see here:

The Source

About 1.3 billion years ago and as many light years away, two spinning black holes, each about thirty times the mass of the sun (one a bit bigger, one a bit smaller) ended their lives as separate entities. These two monsters had probably lived out many separate lives together: first as a binary system of two massive stars and most recently as two black holes orbiting each other. Somewhere in between, each one probably briefly outshone the entire galaxy as a core-collapse supernova.

But nothing lasts forever. Einstein tells us that mass distorts spacetime, warping distance and duration. And an accelerating mass (like a black hole in an orbit) releases some of its energy in ripples of this distortion. And so, over the billions of years of their shared lives, our black holes lost energy to these gravitational waves and their orbit decayed. They slowly, inevitably, spiralled towards each other.

As the partners approached, their orbit sped up and their slow, stately waltz gradually transitioned into a frantic tarantella toward coalescence. Eventually the partners came within about 500 kilometres of each other (about the distance from Paris to Frankfurt!). By this time, they were orbiting each other about thirty-five times per second!

The black holes spiralled towards each other at roughly the same rate about five more times before they suddenly plunged together, spinning around their shared centre of mass 250 times per second. But this stage didn’t last that long. Before even one second had passed, the black holes’ event horizons overlapped, and they merged into a single rapidly rotating object. This new single black hole oscillated wildly as it settled down into its final configuration, emitting gravitational waves all the while.

In-spiral. Merger. Ringdown. After (possibly) millions of years in a slowly decaying orbit, the final plunge took less than a fifth of a second. In those last moments, gravitational waves carried away 1.8x10^(47) Joules. That’s three times the energy contained in our Sun. Three suns, released as ripples in spacetime.

This is a computer simulation of the in-spiral and merger of two black holes much like the ones I described, produced by my friends and collaborators in the Simulating Extreme Spacetimes collaboration:

(Note my calculations of distances are based on extremely rough Newtonian approximations. They are not very accurate. Maybe not even by an order of magnitude. But at these scales, it's not super important.)

Gravitational Waves

But what of the gravitational waves emitted by our ill-fated dance partners? These ripples in distance, in the very fabric of space and time, travel outwards from their source at the speed of light. Space is large and empty and it is mostly a lonely journey. Perhaps they pass through a cloud of gas and dust. Perhaps they don’t. If they do, the distortions of distance move the gas. Some gas particles move apart, some together. The gravitational waves might move a ring of gas particles, as shown in figure 2.

The effect is small; if the gas cloud were a few kilometres in width, the gas particles would move a distance less than one one-thousandth of the width of a proton. But they would move. And if they moved enough (they don’t) they would make a sound—the sound of the merging black holes:


Eventually, after about 1.3 billion years, on September 14th, 2015, the gravitational waves reached Earth. They were too weak to make a sound, but we could detect them. A gravitational wave is a distortion in distance, one that travels. So we can measure this distortion with a very precise ruler. And light is one of the best possible rulers.

Actually, we used two gigantic, perpendicular light-rulers, each several kilometres long. As a gravitational wave passed the rulers, it shrank distance in one direction and grew it in the other. The scientists who use these light-rulers call this discrepancy a “strain.” The paired light-rulers themselves are called “interferometers.”

We’ve built several interferometers to detect gravitational waves. There’s one in Livingston, Louisiana (, which is shown in figure 3, and one in Hanford, Washington ( There’s another in Sarstedt, Germany ( and another in Cascina, Italy ( One, destined for India, is in storage ( And another is under construction underground in Kamioka, Japan (

On that fateful day, only the detectors in Livingston and Hanford were active. (Some of the others aren’t even sensitive enough for their intended purpose. When people first started building gravity-wave detectors, it wasn’t clear how far away the sources would be.) The waves hit Livingston first, at exactly 3:50:45 AM local time. About seven-thousandths of a second later, they reached Hanford and distorted the light-ruler there, too. And a fifth of a second after that, they were gone. The sound of the black holes had passed us by and continued its journey into the void.

But they did not pass without a trace. No, the Livingston and Hanford detectors recorded their passage, shown beautifully in figure 4. The 1.3 billion-year-old waveform passed through our world and changed us forever.

Learning from the Waves

We already knew gravitational waves exist. That measurement took 30 years and won the Nobel prize ( And we had a pretty good idea of what they should look like. But the only way to confirm that they looked like we expected was to observe them. So the first thing the LIGO team did was to use sophisticated statistical techniques, without any assumption about the final waveform, to extract the true wave from the noisy signal shown in figure 4.

They then compared that waveform to the wave predicted by general relativity. The two agree spectacularly. Score one for Einstein! Of course, there are possible modifications of general relativity such that a black hole in-spiral wouldn’t look any different. So only time, and more gravitational waves, will tell if those modifications are wrong. But for now, this result is a triumph of relativity.

Independently, the LIGO team matched the raw data to a “template bank” of possible gravitational waves, each generated for a different configuration of the black holes—different masses, different rotation rates, different orientations, et cetera. Eventually, they found a match. (Actually they found several, all of which were very similar.) And, fantastically, this match agreed perfectly with the wave extracted using the statistical technique. The extracted waveforms from the two detectors, calculated in both ways, are shown in figure 5.

As a huge bonus, matching the waveform in this way told the LIGO team the masses and rotation rates of the initial black holes and the final black hole that they became.

From the ripples in spacetime, they had extracted astrophysics!

Two Detections

I want to emphasize that one reason we can be so confident in the LIGO detection is that it happened twice, once for each detector. Both detectors are extremely sensitive—they could easily see an earthquake or a car driving down the highway and misinterpret it as a gravitational wave. But the gravitational wave was seen at both detectors, and the odds of them both getting exactly the same false positive are extremely low.

What We’ve Learned

In this one detection, we’ve learned a tremendous amount…some of it very definitive, some of it not. But at the very least, we now know the following:

1. Gravitational waves look very much like we expected.

2. Black holes definitively exist. No other two objects in the universe could have been so close before colliding. Of course, we had pretty good evidence that black holes existed before now (see:

3. Binary black hole systems definitely exist. A few years ago, it was not obvious that these systems formed. To get a pair of black holes orbiting each other, you need a pair of supernovae. And that could easily destroy the orbit.

What We Stand to Learn

For most of the history of astronomy, humans relied on their unaided eyes to look at the stars. In the early 1600s, telescopes were invented and the universe opened up. Suddenly the twinkle of stars and planets resolved into gas giants and moons, clusters and nebulae and galaxies. In the 1930s, we discovered a new kind of telescope: the radio telescope. Once again, we saw space in literally a whole new light. Suddenly objects we thought we understood looked very different. And wild new things appeared, like radio pulsars. Every advance in telescope technology sparked a huge leap in our understanding of the universe. We could, essentially, see a whole new side of the universe.

This is just as big. Now we can hear the universe. We’re going to learn so, so much.

Related Reading

If you enjoyed this post and want to learn more about general relativity and gravitational waves, you may be interested in my series on #howgrworks :

1. In Galileo Almost Discovered General Relativity, I explain the motivating idea behind general relativity and how Galileo almost figured it out.

2. In General Relativity Is the Dynamics of Distance, I explain how simple arguments can tell us that gravity stretches or shrinks space and time.

3. In General Relativity Is the Curvature of Spacetime, I describe how the distortion of distance and duration from gravity translates into curvature, and how this bends the path of light (and other stuff).

4. In Distance Ripples, I explain how gravitational waves work.

5. In Our Local Spacetime, I present a visualization of the curvature of spacetime near Earth.

6. In Classical Tests of General Relativity, I explain a little history.

7. In the Geodetic Effect, I talk about how we can use gyroscopes to directly measure the curvature of spacetime.

Further Reading

Here are some nice lay resources on the recent LIGO discovery. (Thanks to +Johnathan Chung  for finding some of these.)

1. This is LIGO’s online press release. It contains, for example, a number of fantastic videos.

2. In this video, Brian Green explains the take-home message.

3. This is a great explanation of gravitational waves by quantum gravity physicist +Sabine Hossenfelder

4. This is the lay article about the discovery by the American Physical Society:

5. +Yonatan Zunger wrote up this nice explanation:

6. This is a nice article by +Brian Koberlein  on the existence of black holes.

7. This is the press release for the Nobel prize awarded for the indirect discovery of gravitational waves:

8. This Nature article talks about several questions we can answer with gravitational waves:

Scholarly Reading

For the very brave, here are my academic sources.

1. This is the LIGO detection paper. Already peer reviewed. Kudos to the LIGO collaboration for going through peer-review before announcing their result!

2. This is the LIGO paper describing how they extracted the mass and spin of the black holes.

3. This paper describes the LIGO team’s investigation of whether or not the December detection could have been a mistake. (Obviously, they concluded it was real, or I wouldn’t be writing this blog post…)

4. This paper describes the LIGO team’s model-agnostic approach to measuring the wave. This is how they know they’re not falling victim to wishful thinking.

5. This technical paper describes how the LIGO team estimated their noise and error

6. This paper discusses how we’ve tested general relativity with this observation.

7. This is an assessment of the rates of black hole binary mergers in the universe based on the measurements LIGO has made so far.

8. This is a related paper on what that means for detectors.

9. This paper is a search for neutrinos from the black hole merger that LIGO observed. (None were found.)

10. This is the population model for binary black holes which may be wrong.

#howgrworks #physics #science #ScienceEveryDay #gravitationalwaves #astronomy #astrophysics
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LIGO Detected Gravitational Waves!

Here is the real waveform, generated by two merging black holes, each about 30 times more massive than the sun.

The figure came from this paper, which I am still trying to read, because the journal's server has been hugged to death by eager scientists:

Stay tuned. I'll be live-tweeting the panel at the +Perimeter Institute for Theoretical Physics (streamed here: in about an hour. And I'll write up a blog post tonight.

My twitter handle is @thephysicsmill and I'll use the hashtags #PILIGO   and #gravitationalwaves  

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