### Space Tells Matter How to Move

John Archibald Wheeler (American theoretical physicist, 1911-2008) said: “Space tells matter how to move. Matter tells space how to curve.” What does that mean?

Since Spock isn't here to explain, allow me to try...

Any mass exerts gravity on any other mass, so the strength of the gravitational force is proportional to the two masses interacting, as well as inversely proportional to the distance between them. Therefore, if you have a bigger mass, you have a greater gravitational force. But if the masses are further apart from each other, the force gets weaker. This property is exactly like the electric and the magnetic force (except that gravity does not repel). That’s one aspect of this story. Another aspect, also predicted by Albert Einstein, and we're sure Spock would concur, is that mass and gravity influence space itself. That means that if you have a mass sitting in space, this mass will curve space such that it makes a dimple. The larger the mass the larger (and deeper) the dimple will be. In this sense matter tells space how to curve. If another mass comes along, this second mass can not travel past the first mass in a straight line but has to follow the curvature of space created by the first mass. In this sense space tells matter how to move.

Figure 1: One mass (Earth) makes a dimple in space, another smaller mass (satellite) moves along the outlines of the dimple. And if, like the satellite, it does not have enough velocity to escape the dimple it will stay within and keep orbiting. Credit: LIGO/Caltech

In 1915, Einstein said that if electromagnetic radiation (i.e. light) is generated by moving charges or changing magnetic fields, then gravitational radiation should be generated by moving masses. Sounds pretty logical, right? It took us a hundred years to prove him right.

Let’s imagine we have two masses, for example two neutron stars in a binary system orbiting each other as mentioned in the previous blog. They are both massive objects, making big dimples (properly called gravitational wells) in space. As they move, their dimples move with them, and that is what creates the waves.

Figure 2: Two massive bodies orbiting each other creating gravitational waves (see the URL for an animation of this at the bottom). Credit: R. Hurt/Caltech-JPL/EPA

As these two objects orbit each other (or more properly their common center of mass), they spiral in, and in doing so they lose energy, which is carried away from the system in form of gravitational waves. But as the objects come closer to each other the gravitational force between them becomes stronger, increasing the amplitude of the wave. As the objects finally merge, there is a final large wave, and then… nothing. Because once the objects have merged, there is only one resulting object remaining, which is not moving, so there are no more waves. These three stages of this process are called “inspiral,” “merger,’ and “ringdown.” The merger is often referred to as the “chirp” because if you hook up a speaker to the detector you can hear the final wave.

Figure 3: The process of two massive objects spiraling in and merging into one resulting object. The strain measures the amplitude of the resulting gravitational wave. Credit: LIGO/Caltech.

As the gravitational waves travel through space, they lose energy along the way, which is why they are very small by the time they arrive here. And that is a good thing, because Earth would otherwise be squeezed a lot, which would be rather unfortunate for us. However, this is inconvenient for the researchers, as it is very difficult to measure a wave with a really small amplitude. The book *Ripples in Spacetime* by my colleague Govert Schilling tells the compelling story of the trials and tribulations of the research teams in coming up with a way to detect these gravitational waves. In 2015 they detected the first gravitational waves, for which they received the Nobel Prize in physics in 2016.

Figure 4: Detection of the first gravitational waves in 2015. Credit: LIGO/Caltech

So, how do you detect these gravitational waves? You use an interferometer with very long arms.

Light travels in waves much like water. When you have two waves, they can interfere with each other constructively (the two waves add resulting in a bigger wave), or destructively (the two waves cancel each other out resulting in no wave), or something in between. The important bit for our purposes is the fact that the only way you get no wave is when they interfere perfectly destructively. An interferometer is a device that splits a beam of light into two beams, and then lets these two beams interfere with each other. If the lengths of the two light paths are precisely the same, the two light waves will interfere destructively and the detector will see no light. The research team set up two light paths 4 kilometers long at right angles to each other, bouncing the light beams off mirrors to increase the length of the path even further to increase precision. The idea here is this: If a gravitational wave comes along and squeezes Earth just a tiny little bit, the two arms will no longer have the exact same length, and the detector will see some light, since the two waves no longer interfere perfectly destructively. You might argue that a heavy truck going past the research facility might do the same thing. That is very true, which is why they built two facilities far away from each other, one in Hanford (Washington State) and one in Livingston (Louisiana). If they both detect the same event at the same time, it’s real! Several other facilities are already under construction or planned (Belgium, Italy, India, Japan).

Figure 5: Schematic of an interferometer. Credit: LIGO/Caltech.

Figure 6a: Picture of an American facility in Washington. Credit: LIGO/Caltech.

Figure 6b: Picture of an American facility in Louisiana. Credit: LIGO/Caltech.

Figure 7: Current and planned gravitational wave detection facilities. Credit: LIGO/Caltech.

The first detection of gravitational wave in 2015 came from a merger of two black holes (see the URL for an animation of this at the bottom). Since they have a lot of mass, the waves were stronger and more easily detected. If we look at the GW “baseball card” in Figure 8, we see that the resulting black hole has less mass than the sum of the two original black holes. The difference is the energy carried off by the gravitational waves, so we can see that these waves carry a lot of energy indeed.

Figure 8: The first gravitational wave detection in numbers. Credit: LIGO/Caltech.

Since 2015 several other gravitational waves have been detected. This research will continue. And as always, Einstein was right.

Here are a few links if you’d like to know more about this topic.

An animation of binary bodies emitting gravitational waves:

https://www.ligo.caltech.edu/video/gravitational-waves

Animations of merging binary black holes:

https://www.ligo.caltech.edu/LA/video/ligo20160211v10

https://www.ligo.caltech.edu/video/ligo20160211v3

A very understandable book (no math) on the subject of gravitational waves:

*Ripples in Spacetime*, by Govert Schilling

https://www.amazon.com/Ripples-Spacetime-Einstein-Gravitational-Astronomy/dp/0674971663/

Inge Heyer