Seeing ripples in spacetime

One hundred years after Albert Einstein shared it with the world, the general relativity is waiting for its last confirmation: direct observation of gravitational waves. These ripples in the curvature of spacetime are created when a massive object accelerates. Typical examples of such systems are binary neutron stars or black holes; as the two stars (or black holes) orbit each other, they gradually lose energy which gets emitted in the form of gravitational waves until, eventually, they collide.¹

How large are these waves? That depends on how far their sources are but scientists generally assume that the relative size of waves we can expect to see can be about 10^-20. This means that, due to a passing gravitational wave, a one-metre long rod will expand and shrink by 0.000 000 000 000 000 000 01 metre, which is a hundred thousand times smaller than a proton. In other words, if a proton were the size of a football field, a gravitational wave would be as small as a grain of sand. Said proton is, at the same time, just a grain of sand compared to a football-field sized atom; if atoms where as large as grains of sand, a single human hair would have one kilometre in diameter.

Scheme of a Michelson interferometer. Light from a laser (left) is split on a beam splitter (middle) and travels through two arms of the interferometer (top and right); after reflection, the light recombines on the beam splitter. If both arms are equally long (top scheme), all light is reflected back to the laser. If the lengths of the two arms differ (bottom scheme), part of the light will escape through the bottom port where it can be detected.

To detect something that small, scientists build large interferometers. If both arms of such an interferometer are exactly the same length, all light that we send in will come out through the same port it came in. But if the length of the arms differs slightly (for example, because of a gravitational wave), part of the light will leak through the other port where it can be detected.

The interferometers have to be large because it is then easier to detect small changes in the arm length. With metre-long arms, the small change in length that has to be detected is 10^-20 m. The interferometers of the LIGO detector are each four kilometres long so their length changes by about 10^-17 m. For the eLISA interferometer (which will be sent to space to detect gravitational waves from there), arms long one million kilometres are planned; their length will change by 10^-11 m which is just ten times smaller than the size of atoms.

The precision needed in LIGO still cannot be achieved with a simple interferometer. The solution is to place a set of mirrors into the arms so the light bounces back and forth many times. If light travels million times between the mirrors, it is as if the arms where 4 million km long and the required measurement precision is similar to eLISA. Further improvement can be achieved by adding another mirror into the input of the interferometer. Light leaving through this port then returns back into the interferometer and the intensity in the interferometer grows. And the more light is circulating through the interferometer, the more will leak through the output port where it can be detected. Final improvement is achieved by placing another mirror into the output that we are trying to measure.

The effective length of the arms can be extended by letting the light travel many times through them (top). The sensitivity can be further improved by adding mirrors into the input and output ports (bottom).

Unfortunately, gravitational waves are not the only thing that can cause such small shifts in arm length. Any sort of vibrations can distort the measurement. Therefore, gravitational-wave detectors are built in remote locations where there is little or no human activity. Still, the occasional lorry driving by or even a person stomping near one of the mirrors will disturb the measurement. Other noise comes from various technical imperfections in the interferometer, such as fluctuations in laser frequency and intensity, presence of residual gas in the arms (which are supposed to be in vacuum), or heating of the mirrors due to light absorption. Finally, there is the quantum noise which ultimately limits the precision when all other imperfections are eliminated.

The hunt for gravitational waves will not be over once they are detected and Einstein’s theory confirmed. Once we are able to detect them with sufficient precision in a large frequency window (ranging from fractions of hertz to tens of kilohertz), we can use them to learn more about the universe. They can, for instance, tell us more about black holes than electromagnetic radiation can. Cosmic inflation is another source of gravitational waves which could tell us more about the universe shortly after the Big Bang. With a successful detection of gravitational waves, we will open a new window into the universe.

¹ The loss of energy by such objects, in perfect agreement with Einstein’s predictions, has already been observed and was awarded the Nobel Prize in physics 1993. Scientists are therefore confident that such waves do exist.