LIGO: The set of arms that feels space-time waves

( A follow-up to my last story about what makes things fall, composed using the Up-Goer Five text editor)

What sort of thing can we build to see the waves? It has to be able to feel those tiny pulls and pushes. So we make a thing with two long arms. Imagine putting one arm up over your head, and one arm straight out to your side, and then lie down on the ground. That's how the arms need to be. When a wave coming from the sky pulls you taller, the arm above your head would become longer than the one out to your side. Then, as the wave makes you wider, the arm out to your side gets longer than the one over your head. We need to know about how the arms get longer or shorter than each other.

The longer the arms are, the bigger the change the waves make by pushing or pulling on them. So we make very long arms, arms that would go across half a hundred city blocks. And still the arm gets longer or shorter by a very tiny bit: a bit that is as much smaller than a human hair is wide as the human hair is smaller than  sun is wide. That is crazy small!

This is why we don't feel any of these waves going through us.

So how do we know if the arms got longer or shorter?

We use the fact that light is also made of waves, and light waves will go up and down many many times as they go along the arms. We start the waves going down the arms with their ups and downs matched. Then they hit a mirror at the end of the arm and come back. We line the mirrors up so, when there are no space-time waves, the ups and downs in the light from one arm come back in such a way that they end up going down and up instead when they reach the middle. In the middle we add the light from the two arms together. We add down with up and up with down, and end up with nothing: no light gets out.

But if a wave goes through, one of the waves has farther to go because one arm is longer. That means it gets through a little bit more of its up and down on the way. So now not-quite-down-anymore adds with up and not-quite-up-anymore adds with down and a little bit of light can escape the middle. This little light tells us a wave is going past.

There are a lot more parts to our set of arms to make it feel space-time waves better.  Like, the light gets turned around to go through the arms lots of times before it comes back to the middle, and we carefully make sure all the parts are very still, and we're also starting to use some other weird things that light can do. But adding the light from two arms is the biggest idea.

It's still very hard to do this, so we make more than one of these sets of arms. Then we can check the light from the two sets against each other. In case something that's not a space-time wave lets light through one of them, the other one will say "No! That's not a real wave. If it was, I would have felt it too." We also have friends around the world with their own sets of arms and we share what we know about the waves going past.

We also think a lot about what kind of waves will come from the sky. If we know what kind of wave we expect to see, we can look more carefully for exactly that type of wave and ignore some of the other things going on.

We haven't seen any space-time waves yet, but people are hard at work making our sets of arms even better. If we're right about what's going on in space, we should be able to notice some of the space-time waves before five more years have passed!

Gravity and gravitational waves in the most common words

This is a story about what makes things fall down.

(Written using the Up-Goer Five text editor)

1. The world and the sun

On our world, when you drop something, it falls down to ground. This is because the whole world - and by that I mean everything under the ground - is pulling on it. It turns out that all the things we know about pull on each other in this way.

All the things around us wants to fall toward other things. The closer to each other and the heavier they are, the more they want to fall together. In our day-to-day lives we only notice stuff falling towards the ground, because the world is by far the heaviest thing that's close to us.

But this same falling also explains how our world goes around the sun every year. Our world is much bigger than we are, so it doesn't really notice the pull from things we do. Instead, our world falls toward the biggest, heaviest thing it sees: the sun.

(We're actually falling toward the sun too, but since the world and everything on it is falling together, we don't really notice.)

Our world is moving through space, and with nothing in space to slow it down, it will keep moving for all time. Alone in space it would keep moving in a straight line, but there are other things around it. Since the sun is the heaviest thing around, the world starts to fall toward the sun.

If our world started out still, then it would fall toward the sun the same way a rock falls toward the ground. Instead, since it's moving pretty fast, it doesn't fall enough to hit the sun. It just makes a bit of a turn toward the sun. This keeps happening as it goes along and the turns add up along the way. The world ends up going around and around the sun, always falling and always missing, always as fast and always as far away.

(Well, actually, it gets a little bit closer and faster and then a little bit farther and slower as each year passes, but that's just a small change from how far away it usually is.)

2. Falling and falling

Things only stop falling if something gets in the way. Like when you drop a rock, it stops falling when it hits the ground. So why isn't the ground falling? Under the ground are more things, like rocks, and the ground can't fall past those rocks. When stuff falling onto them presses the rocks together, they push back. The stuff of the world pushes back against the falling, all the way down to the middle, deep under our feet.

Some other worlds are made of other things, like air, but even air pushes back if you try and make it small, like if you force a lot of it into a small bag. For big stars, like the sun, the middle part gets really hot and sends out a lot of light, which pushes on the outside bits and stops them from falling in further.


Most of the things we see in the sky, the sun and stars and other worlds going around the sun, are as big as they are because that's where the stuff getting pressed together pushes back and stops things from falling in any further.

3. Pulling from far away

So this explains most of the falling and not-falling we see. But there's still one weird thing: The sun doesn't touch our world, so how does it pull on it?

It turns out that heavy things actually change the space and time around them.  The changes are stronger near the heavy thing and then settle down far away. When the world tries to move straight ahead, it's doesn't exactly feel the pull of a far-away sun, it just goes through the space that the sun has changed a bit. The change in the space makes the world move a little bit toward the sun when it's trying to go straight ahead.

It's kind of like if you drove over a big dog and your car got pushed a little to one side. Imagine that space near the sun is full of dogs that push you toward the sun as you drive, bigger dogs close to the sun and smaller dogs far away. And if you try and stay still the dogs push you toward the sun anyway. It's only really far away from the sun you can drive straight ahead again.

(There aren't actually any dogs, I'm just trying to explain how the space makes you move and I don't have a lot of words for things that push you as you go).

Everything that moves through the space around the sun, even light, gets pushed a little as it passes. Light moves really fast, so it makes a very small turn, but it makes stars look like they're in different places than where they are when when the sun doesn't get in the way. People were first able to see this about a hundred years ago, during one of the times the sun got covered and went dark during the day.

For any round thing, like the sun or the world, the changes in space and time look a lot alike when you're outside it. They're the same kind of changes, they just get bigger and reach further out as the thing gets heavier. Even things much bigger than the sun have the same sort of change in space and time outside of them. We can sometimes see bright far-away things looking really weird in space because their light has come past some really heavy thing, like a huge group of stars. It can look like there are four of the same bright spot if the bright spot's light went around the heavy thing  to our eyes in four different ways. Or sometimes the light gets pushed around so that the bright spot looks long, kind of like an eyebrow, instead of small and round.

4. Falling toward nothing

If you have a round thing that is heavy and really small, the changes in space and time get really strong close to it. Even light, which moves as fast as anything can move, can get pushed around a lot as it passes. If the heavy thing is small enough, any light that passes too close will fall in toward the middle.  A heavy thing can even get so small that there is a place, quite close to the middle of the heavy thing, where if light tried to go away from it, moving straight out and as fast as anything can go, it would still end up falling back toward the middle, never to be seen again.

Now, as soon as something gets small enough that we could find that place, it doesn't look like any other kind of world or sun or star. If light can't stop from falling in, we know that nothing else can stop from falling either: not hard rocks, not air pushing back, no matter how hot it gets or how fast it moves. Nothing can escape. All the stuff that made the heavy thing will keep falling toward the middle, getting pushed closer and closer together with no way to stop. And we can't see what happens then, because none of the light can get out to tell us. We don't see any stuff, we just see a dark place in space that things fall toward, like they are falling toward nothing.

We know these dark places are out in space, because we can see other stars move around them, getting pulled enough that we know they are going around something really heavy. And sometimes things like air and tiny rocks falling into a dark place rub against each other, and they get really hot and bright and we see light from that. So we're pretty sure the dark heavy places are really out there. Let's call them dark stars.

5. Waves in space and time

Remember how the sun didn't just pull on the world, but changed the space and time outside so the world moved in a different way? This means that if the sun suddenly moved, the world doesn't know right away. It takes some time for the new changes to go from near the sun to where the world is.

If heavy things move the right way, the changes in space and time become like waves. Waves go out from the moving things, kind of like if you throw a rock into the water and waves go out from it in all directions. The waves can go along for a long time, but they get smaller as they go.

If you were in the way of a strong space-time wave and you were looking at the moving thing that it's coming from, you might feel something pull on your head and feet and push your sides in, then push you shorter and pull you wider. You'd feel a pull and push, pull and push, as the wave is going past you.


Everything we know about that makes these waves is far enough away that we only see very small waves on our world, so small that we'll never notice them. We have to carefully build a thing with lots of parts that can see the waves.

(Read more about how we see the waves here: LIGO: A set of arms that can feel space-time waves)

Science in the most common words

My friend Dave linked me to this text editor which restricts you to the 1000 most commonly used words in the English language, as inspired by Randall Munroe's Up Goer Five. I wrote up a summary of my research:

There are some tiny but heavy stars that are left over after normal stars die. Imagine our whole sun---hundreds of hundreds of our worlds---forced down to fit inside a city. We don't know exactly what's inside the tiny stars because the stuff there is pretty weird, but we have some ideas. 

Sometimes two of these tiny stars go around each other, like our world goes around the sun. When they go around really fast and close together they make waves in space and time that we try to see from our world. As the waves go out the stars move closer and closer together until they hit each other. 

The stuff inside the stars gets moved around when they're close together, so different kinds of stuff make different waves. Also, when they hit each other, sometimes they make a new star and sometimes they fall in to nothing (falling into nothing is another cool story). If we see these waves, the way they look at the end will tell us something about the weird stuff inside these tiny stars.

Gravitational-wave emission and shifts in time

There's some recent buzz about a new indirect measurement of gravitational waves in Rapid Orbital Decay in the 12.75-minute WD+WD Binary J0651+2844. It presents a measurement the period decrease in a binary system of two white dwarfs which orbit each other every 13 minutes:

Summary figure from phys.org: on the top is the accumulated shift in eclipse time, and on the bottom are some light curves of eclipse measurements.

The shifting eclipse time agrees with the general-relativistic prediction, where gravitational waves carry away some of the energy and the two stars slowly fall together as they orbit.

In the comments on the associated Phys.org news post there was some confusion on how exactly the six second time shift over 380 days translated into the two objects merging in two million years. And I have seen (and experienced) similar confusions when looking at the canonical Hulse-Taylor plots for example the one on the Cardiff Gravitational Physics Tutorial on the Hulse-Taylor pulsar , which show cumulative shift in the periastron time of the orbits:

Figure (from Weisberg and Taylor (2004) via the Cardiff site) showing the accumulating shift in periastron time over years of measurements. 

This plot is often presented as showing "decrease in the period due to gravitational-wave emission." But the period decrease is approximately constant over the times considered in both these systems, and then seeing plots of the quadratic accumulation of time shifts can be confusing. So here's how that works (also worked out in Kepler et all 1991 as cited in the WD+WD paper):

If we want to estimate the time taken by some number of orbits $n$, if the time per orbit is a slowly varying function, we can approximate by Taylor expanding:

$$ t_n = t_0 + \frac{dt}{dn} (n- n_0) + \frac{1}{2} \frac{d^2t}{dn^2} (n - n_0)^2 +... $$

The period $P$ of the orbit is then $\frac{dt}{dn}$ in this notation, and

$$ \begin{aligned}
\frac{d^2t}{dn^2} &= \frac{d}{dn}\left( \frac{dt}{dn} \right) \\
&= \frac{dt}{dn} \frac{d}{dt} \left(\frac{dt}{dn}\right) \\
&= P \dot{P}
\end{aligned} $$

where $\dot{P} = dP/dt$ and we throw infinitesimals around like physicists. This means that we have after $n$ orbits:

$$ t_n = t_0 + P (n- n_0) + \frac{1}{2} P \dot{P} (n - n_0)^2 $$

compared to the constant period estimate,

$$ t_n^{\text{no-GW}} = t_0 + P (n- n_0) $$

so the accumulated time shift $T$ over $N$ orbits is quadratic in $N$:
$$ T = \frac{1}{2} P \dot{P} N^2 $$

In the case of the WD-WD system, we have $T \simeq - 6$ seconds, $ P \simeq 13$ minutes, and

$$ N  \simeq \frac{380 \text{ days}}{13 \text{ minutes} / \text{ orbit}} = 42000 \text{ orbits} $$

therefore

$$\begin{aligned}
\dot{P} &= \frac{2 T}{P} \frac{1}{N^2} = \frac{ 2 T} { (P N) N }\\
&\simeq 2 (- 6 \text{ seconds}) / (380 \text{ days}) / (42000 \text{ orbits}) \\
&= - 8.7 \times 10^{-12} \text{ s / s} = - 0.27 \text{ ms / year} \\
\end{aligned}$$

with some Google unit conversions, which is almost the same as the result in the paper abstract. If we just keep extrapolating this with a constant $\dot{P}$, we will have a period of $0$ minutes in

$$\frac{0 - 13 \text{ minutes} }{- 0.27 \text{ ms / year}} = 3 \text{ million years} $$

which is pretty soon, astronomically speaking.

This white dwarf system would be a powerful "verification binary," detectable in a future space-based gravitational-wave telescope like LISA or eLISA; Antoine Petiteau on the LISA Facebook group estimated signal-to-noise ratios of 40-70 in LISA and 20 in eLISA based on their current designs. The frequency is too low for the ground-based detectors to see, since Earth's seismic noise and gravity-gradient noise get in the way.

New Blogger: Starting Teaching

So, I've recently started a new faculty position and I'd like to get back into some sort of blogging. Enter the New Math Blogger Initiative! Now, I'm not exactly a math blogger, but I think teaching physics will have similar features - especially after my conversation with some of the new math faculty at my institution.

I'm going to shortly answer two of the blog prompts this week:

Where does the name of your blog originate? Why did you choose that? (Bonus follow up: Why did you decide to blog?)

My blog address I addressed in one of my first posts: Making Science, along with some thoughts about why I originally started blogging. The title of my blog, "I will do science to it," was inspired by the webcomic Dresden Codak - specifically the one that inspired this shirt - so I should credit that! The webcomic is full of neat science fiction, a bit of philosophy, and other such delights, and I occasionally identify with the protagonist despite a much more normal and stable upbringing.

If you are a new teacher, what are two specific things you plan on doing this year?

The course I will teach this year is Introduction to Astronomy, and I am incredibly lucky in being able to build off and alongside an experienced faculty member who is teaching the course again this semester and sharing notes. This means I get to incorporate all sorts of things like pre/post conceptual tests to measure the course impact on student learning, lecture tutorials, paper clickers, without the overhead of developing the material for the course myself. My goal, though, is to make it my own. To make this specific for myself, I'll break it in to two goals. 

First, I want to be able to clearly justify each form of class activity and explain to students how we know it will help them learn, especially for the activities that will take extra effort on their part.  I'm reading a great book on Learner-Centered Astronomy Teaching, Strategies for Astro 101, which has tons of explanations of this sort of thing.

Second, I want to actually walk the walk about learning goals that are required by the university policies. Also spurred by the book mentioned above, this is a general pattern I'm trying to implement: In both reasearch and teaching, I'm trying to take things that might be considered "overhead" (e.g. grant-writing in research) seriously as an opportunity to improve my understanding of the work and build long-term effective project management. So I want to link activities to learning goals, with serious reflection rather than a vague "close enough" (which, I have already found, is tempting). This may be over-ambitious for my first semester teaching. So let me consider this successful if I make a link for at least one thing each class.

It works! IT WORKS!!

Here is a pdf of an eighth

import processing.pdf.*;

int segments = 8;
int radii = 20;
float radiispacing = 20;

float horizon = 80;

float horizondistance(float rf) {
return sqrt(rf*(rf - horizon)) 
    + 0.5* horizon * log(rf) - 0.5 * horizon * log(horizon) 
    + horizon * log(1 + sqrt(1 - horizon/rf));
}
float sqrt_grr(float rf){
  return 1.0 / sqrt(1 - horizon/rf);
}



void setup()
{ 
  size(400,600,PDF, "filename.pdf");
//  size(400,600);
  background(255);
  
}
  
void draw(){
  translate(width/2,height-radiispacing);
  noFill();  
  line(-PI/segments*horizon,0,PI/segments*horizon,0);
  for(float radius = horizon + radiispacing;
            radius < horizon + radii*radiispacing; 
            radius += radiispacing) {
    println(radius + " " + horizondistance(radius) + " " + radius*sqrt_grr(radius));
    ellipseMode(RADIUS);
    //ellipse(0,radius*sqrt_grr(radius)-horizondistance(radius),2,2);
    //ellipse(0,
    //    radius*sqrt_grr(radius)-horizondistance(radius),
    //    radius*sqrt_grr(radius),
    //    radius*sqrt_grr(radius));
    arc(0,
        radius*sqrt_grr(radius)-horizondistance(radius),
        radius*sqrt_grr(radius),
        radius*sqrt_grr(radius),
        -PI/2.0-PI/segments/sqrt_grr(radius),
        -PI/2.0+PI/segments/sqrt_grr(radius)
        );
   }
  exit();
}

Making better science

Three quotes from an article html-titled "The Decline Effect and the Scientific Method": The Truth Wears Off in the New Yorker. In light of my musings last night, a few quotes stood out particularly:

1.

The situation is even worse when a subject is fashionable. In recent years, for instance, there have been hundreds of studies on the various genes that control the differences in disease risk between men and women. [...] But the most troubling fact emerged when he looked at the test of replication: out of four hundred and thirty-two claims, only a single one was consistently replicable.

2.

He notes that nobody even tries to replicate most science papers—there are simply too many. (According to Nature, a third of all studies never even get cited, let alone repeated.)

3.

In a forthcoming paper, Schooler recommends the establishment of an open-source database, in which researchers are required to outline their planned investigations and document all their results. “I think this would provide a huge increase in access to scientific work and give us a much better way to judge the quality of an experiment,” Schooler says. “It would help us finally deal with all these issues that the decline effect is exposing.”

4.

The disturbing implication of the Crabbe study is that a lot of extraordinary scientific data are nothing but noise. [...] The problem, of course, is that such dramatic findings are also the most likely to get published in prestigious journals, since the data are both statistically significant and entirely unexpected. Grants get written, follow-up studies are conducted. The end result is a scientific accident that can take years to unravel.