The size of modern day interferometers, especially those which are used for detecting gravitational waves, is much larger than the table of Michelson and Morley. Let us sort of summarise the type of detectors that we have nowadays. We have seen that the wavelength of the gravitational wave is directly related to the size of the site where the mass of the explosion, for example, the mass has been moving. Now, we have two different types of sites in the cosmos. One which are stellar mass objects on the order of the mass of the sun.
In this case the site– because remember we are talking about very complact stars– the site is a few thousand kilometres, and in this case you expect that the wavelength is a few thousand kilometres, and so the detector is also a few thousand kilometres. And we have seen that there is a relation between the wavelength and the frequency. The wavelength is the velocity divided by the frequency. And so you can easily identify a frequency which is on the order of 1 to 10 or 100 Hertz. So gravitational waves with frequencies between, say, 1 and 100 Hertz are detected with interferometers of basically a few thousand kilometres.
Now, we also have much larger sites which are, for example, as we will see later, black holes at the center of galaxies, and those are the size of a few million kilometres, so that means in that case, we need detectors– interferometers– of a few million kilometre wide. Of course, we cannot find them on the ground. We find them in space, as we will see, and the frequency range in that case, again, is computed by the same formula, and we find a frequency between 10 to the minus 4 Hertz and, say, 10 to the minus 1 Hertz. And again, this type of interferometers have to be built in space.
Let me start with the smaller interferometer, the one that can be on Earth– what we call a ground interferometer– and I will choose the interferometer Virgo, which is near Pisa in Italy. And I can use the set up that we described for the Michelson-Morley experiment– Michelson interferometer, which is slightly changed, because, remember, we would like a size of a few thousand kilometres. Of course, it is difficult to find such a site on Earth, so physicists have been using a trick. You remember these beam splitters, which is transmitting some light and reflecting another part of it, so physicists put two beam splitters on each of the arms of the interferometer.
And because the role of these beam splitters is to transmit and reflect part of the light, so it means that the light which goes through– which is transmitted through this beam splitter– goes to the mirror, is reflected. Some of it goes through, but another part is reflected, and so some of the light will go back and forth for quite a while, and similarly on the other side. And so the average length that the light is travelling is hugely increased, and so such an interferometer with this improvement is equivalent to an interferometer with a length of arm which should be a few thousand kilometres.
So this is the way– the trick– that physicists have played in order to put in a region not too large. In the case of the Virgo interferometer, it’s a few kilometres to put an instrument that is sensitive to the kind of gravitational waves that one is looking for. Now I said that the frequency range of this type of instrument is between a few Hertz and something like 100 Hertz. In the lower range, there is a difficulty which is associated with seismic waves. Seismic waves have a frequency on the order of a few Hertz or below, and so they might change the geometry of interferometer, and so you might confuse seismic waves for gravitational waves.
And so one has to try to avoid this at all cost. And so one is suspending the mirrors– I give here an example of suspension– one is suspending the mirrors and, in fact, suspending the whole set up, in order precisely to avoid any effect coming from a seismic wave, the suspension are precisely there to decouple the interferometer from any seismic wave in the environment. There are basically two advantages of going into space. The first one is that obviously there are no seismic waves, and the second one is that one can build interferometers of very large size, as you will see a few million kilometre size.
The concept for building such a gravitational wave detector in space was conceived in the late ’70s, early ’80s, but we still have to build the final gravitational wave observatory in space, but let me describe the concept. The idea is to have three satellites which make a triangle, and which exchange laser light, so we have laser beams between two pairs of satellites. And so you recognise here a Michelson interferometer so I can make and interferences in this satellite, so this amounts to one Michelson interferometer. And of course, you can choose the size.
If you take, for example, these two satellites, one million kilometres apart, you have built– and one million on the other side– you have built an interferometer of a size of one million kilometre. And of course, what you want to do if you have a gravitational wave passing in this direction, this is going to slightly change these distances, and you monitor these changes of distances by checking the interference pattern in this satellite. And the goal to reach for a million kilometre side detector is to have a precision of measurement of a few picometers, 10 to minus 12 metres.
Now, in the original concept, which is called the LISA concept, the last two satellites were also exchanging laser beams, and so you see that instead of having a single interferometer, we can consider these two links as another Michelson interferometer and these last two pairs of links as a third Michelson interferometer. And so you see that with this triangular shaped constellation– we call constellation this group of satellites– we have three Michelson interferometers. Now, this constellation is travelling– orbiting around the sun, following– trailling– the Earth, as can be seen on this simulation.
It is often believed that the difficulty of the experiment in this case is the fact of measuring variation of distances of 10 to the minus 12 metres across a distance line of a million kilometre. Well, interference can do that for you, so this is not the real difficulty. The difficulty is to make sure that the distance is between two bodies that are only submitted to a gravitational force. And of course, a satellite like this one is submitted to many other forces. For example, the constellation is orbiting around the sun, the solar wind is pushing the satellites. You could have micrometeorites and all that.
So the real difficulty of the mission is to precisely avoid this and to be comparing the distance of two objects which are following gravitational trajectories. So the idea is to put inside the satellites– each of the three satellelites– what we call test masses, which are protected from any perturbation from the satellite, which means that, for example, let me take one satellite here with its test mass, and there’s a perturbation on this side which pushes the satellite to this side, well the satellite monitors its position with respect to the mass, which will be completely unperturbed and will be repositioning itself by having some microthrusters which take the satellite back to the original position around the test mass.
And so in this way, it is really the test mass that is following a gravitational trajectory, and the role of the satellite is really to protect the test mass from any such perturbation. And it is this principle of measurement, which is sometimes called drag free, which will be tested in a technological mission called LISAPathfinder this very fall by the European Space Agency. And if that mission is a success, this will pave the way for the full mission, the space observatory of gravitational waves, eLISA, to be launched in the 2030s. To summarise, the direct detection of gravitational waves requires large detectors either on ground or in space, and the principle of measurement is interferometry.
On the ground the detectors, which have now reached a sensitivity which should allow a discovery in the coming years, are looking at rather compact sources which are in the vicinity of our own galaxy. On the other hand, in space, the gravitational wave observatory eLISA, which will be launched by the European Space Agency in the 2030s, will observe sources of gravitational waves in the whole universe, and this mission is prepared by a technological mission LISAPathfinder launched this fall by the European Space Agency.