## Feb 19, 2016

### waves

There was a lot of news last week regarding the detection of gravitational waves. And as usual most of it wasn't particularly straightforward or clear. Nor did it really focus on what was a big deal and what wasn't. Here's the short version that remedies that.

Gravitational Waves
Gravitational waves are frankly not that amazing. Einstein predicted gravitational waves in some sense with his theory of relativity. But frankly gravitational waves in some ways exist even under Newton's gravitational theory. Under both theories if a mass is moving around we 'feel' that gravity change. If the Sun moved closer and farther in relation to the Earth repeatedly we would feel this oscillation of gravitational intensity; even under Newton's incorrect (but useful) theory.

What makes Einstein's gravitation waves different Newton's is two additional items.

First, the time it takes for the effect mentioned above is instantaneous in Newton's world. With Einstein this effect travels at the speed of light (i.e., ~300,000 km/s). If the sun disappeared we'd feel the effect immediately under Newton's incorrect theory. In reality it would take the effect 8 minutes to reach us and cause Earth to take a trajectory out of our solar system (sans Sun) in a linear path along with all the other objects in it.

Second, under Einstein's theory we know that gravity is a distortion of space-time rather than a discrete force. I rarely come across a decent explanation of this. It's confusing to explain the theory using only words. The equations are relatively clear but translating these into words creates all sorts of problems. The usual approaches (e.g., stretched sheets with ball bearings distorting them) all have inherent problems. In particular this explanation is tautological because the 'experiment' still involves and relies on gravity. See the video below. It doesn't work without gravity.

Let me try to explain this is a slightly different way. We talk about space-time as a single thing because in Einstein's theory they are linked. One way to think about this is that everything travels through space-time and everything travels at the speed of light. We don't inherently sense this but it is true. The reason we don't sense this is because speed to us is something that is accomplished in space. We don't think of ourselves as traveling through time the same way we travel through space. As I sit here typing this I don't seem to be traveling at the speed of light. But I am. I'm traveling through the dimension of time at the speed of light. If I'm sitting perfectly still then I am traveling through time at the speed of light. If I start moving in space then part of my speed is now traveling through space. Which means that some of my speed through time has been reduced. If I travel through space at the speed of light then all of my speed through time has been eliminated. What does this mean exactly? It means that if I travel through space at the speed of light there is no speed left to travel through time and my clock stops. We (meaning objects with mass) can't actually do this. For photons (massless) this is the situation they are stuck in. They travel through space at the speed of light (clearly) and so their clock doesn't tick. They are as old as when they were born.

Next, objects that exist in space-time influence space-time. Namely things with mass. What mass does is distort this space-time. This is where people invoke the "fabric" in the video above. But what do we mean by distort? For one, spatial dimensions become distorted like the video. What was straight in the absence of the mass seems bent now. Space with mass has straight lines that are actually bent to an external observer. This is why light can be "bent" by black holes or any mass really. Light has no mass and thus isn't attracted to other objects with mass. Rather, it's still traveling in a straight line, but that line is bent to an external observer. Space is not rectilinear in the presence of mass. By using the word "distortion" we are implying that lengths get stretched and shrunk and bent. A ruler in this region of space will get longer or shorter (and bent) depending on the location of the mass and orientation of the ruler.

But it also has another effect, one that affects space-time. The presence of mass forces objects with mass to shift some of their speed in the time dimension to the space dimensions. In other words the presence of mass or gravity forces things to move. The bigger the mass the more it forces objects to travel through space by forcing it from moving through time at the speed of light. Still confusing I know. :) But more accurate.

So what are gravitational waves? The movement of any object that contains mass creates gravitational waves. These objects, at all times, create distortions in space and space-time. All masses do this. Not just black holes. The reason we're talking about black holes is they make big distortions. You and I don't make big distortions. So if you want to detect those distortions you are better off detecting something that makes a big effect. Gravity is inherently a weak force (I won't get into this but it's clear that a giant planet like Earth doesn't pull us down that strongly since we can stand and walk). If we move the masses back and forth (jiggle them or have two objects spinning around each other in an orbit) we get an oscillation of their positions and therefore an oscillation in the distortions the objects make. The "WAVE" in "gravitational wave" implies something's position is changing over time. And in this case it's the location of the objects by being jiggled or spinning around.

So the situation that was measured last week was the orbit of 2 black holes around each other. One about 29 times the size of the Sun and one 36 times the size of the Sun. The orbit over time decayed such that the objects became closer and closer. As they did they spun around each other faster and faster until eventually they coalesced into a single black hole. As this happened a great amount of energy was released. The energy that was released was from some of the matter that made up the previous 2 black holes. Upon coalescence this matter was converted to energy (E=MC^2). Specifically, 3 Sun's worth of matter was converted. So the resulting black hole was 29 Suns black hole + 36 Suns black hole - 3 Suns of expelled energy = 62 Suns black hole.

So where did that energy go? Normally we see matter converting to energy in the electromagnetic realm (e.g., light, x-rays, gamma rays, etc.). There was certainly some of this kind of conversion. But in this case most of the energy was released in the form of a gravitational wave; an intense distortion of space-time. Note I said wave not waves. That final whoosh from the collisions created one big space-time distortion. But there were also smaller less energetic waves emanating as the black holes spiraled towards each other. As they got closer they create more gravitational distortion and spiraled more quickly. Here's what the theory says this will look like.

Note the gravitational waves are always there. Even before time = 0 in this graph. These black holes were making gravitational waves since their existence. Just as we ourselves make gravitational distortions and waves as we move about. But as they get closer the distortion becomes greater (noted by the amplitude of the graph) and the inspiraling orbit gets shorter (note how the frequency of the graph gets shorter and shorter as it approaches time of 0.1)

This waveform if converted into a sound wave is why scientists referred to it as a "chirp" - rising frequency and rising amplitude. In order to really hear it you need to slow it down.

Go here to listen to what this waveform sounds like - Link

For some god damn unexplainable reason every online version of the actual chirp has 4 chirps. There's no explanation as to what these are. I think these are just four instances of the same chirp under different processing or from each of the 4 legs of the LIGO. But I don't know. It's one chirp that occurred.

So let me end with this. Nothing about gravitational waves is surprising. We expected to see / hear them. It would have been a much bigger deal if they didn't exist. There isn't much new about all this in some sense.

So what's the big deal then?

Detecting Gravitational Waves
This is the big deal. Detecting them. When the original scientists started planning to measure them I'm sure most people thought they were insane. I'm still bewildered about the details of how they did it frankly.

Let's start with the first problem. How do you measure gravitational waves? Well since they distort space we should be able to measure that space distortion some how. But how? Can we use a ruler? No. Because the ruler distorts as much as space distorts. What they hell? Are we stuck then? No. There's one available option to us. And that is that light travels at a constant speed. If we use light by measuring how long it takes to travel a distance then we eliminate this problem. We can't use matter to measure the change in distance. Light on the other hand travels at all times at the same speed so if the distance grows it is going to take longer for light to travel that distance.

The second problem we have - and in some ways I have now idea how they overcame this - is that we are talking minute changes in distance. This is not a big effect. Near the black holes it was but as those waves and spatial distortions traveled 1.5 billion light years they thinned out. How thinned out? We're talking 1 part in 10^21. In other words over a distance of 5 kilometers we're talking about the change in distance of one one-thousandths of an atomic nuclei. Yowza. Considering this observation was done on Earth, this is amazing. Any rumble from movement around the detector, extremely tiny tectonic movements for example, are going to screw up the readings. I really don't know how they got around this. But they did.

The detector was called LIGO. Or rather Advanced LIGO after it got a substantial upgrade in equipment. And the way it worked was as follows. The detector has an L-shaped configuration. Two channels about 4 km in distance spanned out across the ground in perpendicular directions. A laser was split into two beams and then directed down both channels. At the end were mirrors that reflected the beams back and a detector was placed where they intersected. The lasers and photodetector were set up so that the two incoming beams cancelled each other out at the photodetector. Meaning the detector 'saw' no light. If one channel experienced a gravitational distortion and the other didn't then the distances would be different and the two beams wouldn't cancel each other out any more. The detector would detect something. It would detect light at the photodetector. The resulting sinusoidal wave we see in the press articles is that increase and decrease in light at the photodetector.

As gravitational waves pass through Earth, and assuming that the direction of the waves wasn't such that it stretched the channels equally (highly unlikely but possible) then the detector would detect gravitational waves when  it detected some light returning from the combination of beams in the channel.

What this means
There are a few important points to be made about this experiment that I haven't heard elsewhere.

First, LIGO detected gravitational waves a few days after it was turned on. This was either highly fortunate or, more likely, gravitational waves are ubiquitous. There are black holes colliding all the time. I mean we could have waited years or centuries before something showed up. Gravitational waves must be common. And I'm curious to see how many events LIGO picks up over the next year to verify this.

Second, This is a new way to detect and observe astronomical events. Historically we have used electromagnetic radiation for all observances. Whether that is light or X-rays or what have you. This is a fundamentally new way to observe the universe. And it has the ability to detect things we can't with radiation. For example no one simultaneously observed on any telescope the coalescence of these black holes. Telescopes couldn't see this event. As a result we can make new measurements of black hole phenomena. But also what happens inside supernovas where the mechanics of these explosions are largely unknown because of radiation shielding around the core. Also the big bang. That explosion is shielded by the cosmic background microwave radiation. But perhaps more importantly what's out in the universe that we don't know about? What things will this detect that we just don't even know exists? This is the really exciting part.

Third, we are building a much bigger and better LIGO. It's called ELISA. It will be a LIGO in outer space. And it will have "channels" that are 1 million km apart compared to LIGO's 4 km. ELISA will be able to detect much lower frequencies as a result and be free of any terrestrial disturbances. It will consist of 3 satellites using the same laser interferometry technique as LIGO. This hasn't launched yet. But a preliminary satellite (the LISA Pathfinder) has been launched Dec. 2015 to test out some of the technologies. The full system won't be up for decades. But when it is it will expand our capabilities significantly.