The cosmos quakes

How researchers succeed in tracking down gravitational waves

September 14, 2015 will go down in history. This is the day when researchers first detected gravitational waves – 100 years after Albert Einstein put forward his General Theory of Relativity which predicts such distortions of space-time. They pulled off this sensation with the Advanced LIGO installation, whose sensitivity to the gentle trembling from space is based substantially on technologies and methods thought up by scientists at the Max Planck Institute for Gravitational Physics in Hanover and Golm.

Text: Helmut Hornung

The discovery on 14 September – it was 11.51 CEST as the waves swept through two detectors at the Livingston and Hanford observatories in the USA – was the most recent climax in the history of gravitational research. The General Theory of Relativity has now passed its ultimate test with flying colours. It also finally offers researchers the opportunity to investigate massive cosmic monsters in detail: models predict that the gravitational waves observed originate from two fusing black holes with a mass of 29 and 36 solar masses each, around 1.3 billion light years away (Fig. A).

But why all the fuss about waves from outer space? To understand this we need to make our way back to the roots of modern gravitational research – to Switzerland in the year 1907. An “Expert II Class” at  Berne Patent Office is giving some intensive thought to gravity. Two years earlier, he had submitted five articles to the journal Annalen der Physik, one of which was titled “On the Electrodynamics of Moving Bodies”. In the article, the hobby researcher shook the foundations of physics just as he did with the three-page addendum “Does the Inertia of a Body Depend upon its Energy Content?”

The author is called Albert Einstein. The two publications are later called the Special Theory of Relativity. With this theory, Einstein breaks with Isaac Newton’s dogma of absolute time, among other things, and refutes the claim that velocities would always add together directly. In addition, the change in the gravitational effect of a body should be detectable immediately throughout the whole of space according to Newtonian theory. This means: gravity acts everywhere immediately. This is not compatible with Einstein’s statement, which stated that there was a natural speed limit for the propagation of the effects of any kind of force – the speed of light (c = 300,000 km/s).

Einstein thus sets about putting the laws of gravitation onto a new footing. He later recalled: “It was 1907 when I had the happiest thought of my life (...) … the gravitational field has ... only a relative existence. For if one considers an observer in free fall, for instance from the roof of a house, there exists for him during his fall no gravitational field – at least in his immediate vicinity. All objects dropped by this observer actually remain in a state of rest or uniform motion, regardless of their chemical or physical nature.”

Einstein’s trick can be explained in very simple terms: he simulates gravity using acceleration, since acceleration generates forces as well, as occur in a rapidly accelerating lift, for instance. If the lift car was soundproof and lightproof, people could think that terrestrial gravity had suddenly increased.

The realization that gravitation is at least partially a question of the reference system leads Albert Einstein to the revolutionary ideas which he presents in autumn 1915 after eight years of work in his General Theory of Relativity. It results in tiny deviations from the Newtonian model for the motions of the planets. They occur most clearly for the rapidly orbiting Mercury close to the Sun. Its so-called perihelion precession can be explained and calculated exactly: “For some days I was beside myself with merry excitement,” writes Einstein after he has solved this mystery.

The General Theory of Relativity is ultimately a field theory. It states that the accelerated motion of masses in a gravitational field leads to perturbations that move through space at the speed of light. These perturbations are called gravitational waves. They are by no means hypothetical. If you jump up and down on a trampoline, for instance, you lose energy (not only in the form of calories) and generate such waves in space-time. A person has a low mass and jumps relatively slowly, however. The gravitational waves emitted by the person are therefore immeasurably small.

Space is home to large masses, however – and even a trampoline: space-time. Everything is in motion here, because not a single celestial body remains at rest in one location. Earth bends space as it orbits the Sun, radiating gravitational waves with a power of 200 watts. But even these gravitational waves are still too weak to be tracked down with a detector.

Fortunately, much more violent tremors of space-time occur in the universe: when two neutron stars or black holes orbit each other extremely rapidly or even collide with each other. Or when a massive star explodes as a supernova. Such cosmic events generate gravitational waves with an energy of around 10⁴⁵ watts – energy which is lost by moved bodies.

The two American astronomers Russell Hulse and Joseph Taylor actually showed that the orbital period of the two neutron stars PSR 1913+16 decreases because the binary system orbiting around its common centre sheds energy – and emits it as gravitational waves. The researchers were awarded the Nobel Prize for Physics for this in 1993. But how can these waves in space-time be measured? How do they make themselves felt?

For this purpose, imagine a virtual rubber sheet, which two experimenters – let’s call them Albert and Isaac – each hold at two opposite corners. Albert and Isaac now pull simultaneously at the sheet by taking two or three steps backwards. As they move away from each other, their arms remain close to their body. The rubber sheet becomes longer and narrower at the same time.

Next, Albert and Isaac move towards each other again, extending their arms away from their body as they do so: the rubber sheet becomes shorter and wider at the same time. Finally, the two experimenters return to their original position. During the experiment, a portrait of Albert Einstein painted on the rubber sheet would expand and compress as if a gravitational wave spreading from the bottom to the top through the plane of the rubber sheet had distorted space.

In a second experiment, we paint two circles onto the rubber sheet as far away from each other as possible. We call one start/finish, the other turning point. We then organize an army of well-trained ants. We put all of them in the circle start/finish and let one after the other run to the turning point and back again at regular time intervals. Since the ants are moving with constant speed, they all arrive back at the finish circle at the same time intervals and separation as they left it at the start.

Now Albert and Isaac stretch the rubber sheet to double its size. This also causes the marching formation of the ant army to be stretched out, the distances between the ants increase: the ants arrive back at the finish separated by twice their original separation time. This time delay is only a temporary occurrence, however, because it applies only to those ants which are just en route. If the sheet remains stretched by a factor of two, the ants starting out also return at the same time intervals again. The (simulated) gravitational wave has the effect that the ants follow each other at times faster, at times slower than expected.

As described above, a gravitational wave changes the separation between the objects contained in space at right angles to the direction of propagation. It is extremely difficult to measure this. Let’s imagine a worst-case scenario in our galaxy: the explosion of a massive star. The gravitational waves emitted by this collapse would – when they arrive at our solar system after a propagation time of a few thousand years – change the distance between Sun and Earth (1.5 x 10¹¹ metres) by only the diameter of a hydrogen atom (10^-10 metres) in a few ten thousandths of a second.

Albert Einstein therefore thought it was impossible to detect gravitational waves. And yet a number of scientists nevertheless conjured up instruments that have succeeded in doing this. The first generation of instruments in the 1960s consisted of aluminium cylinders, weighing several tons, equipped with sensors. Pulses of gravitational waves should cause them to oscillate like the clapper of a church bell. However, these resonance detectors produced no results despite their having highly sensitive amplifiers.

The researchers therefore designed receivers which were even much more sensitive. Their principle is based on the thought experiment with the rubber sheet. For this purpose, we replace the start/finish circle with a laser, the turning point with a mirror, and imagine the ants to be the wave crests of a light signal. In order to detect the tiny delays in the arrival time, a second beam path must be arranged perpendicular to the first one so that the light waves of these two arms superpose. The signal being measured finally impinges onto a photodiode and can now be evaluated (Fig. B).

Such a Michelson interferometer has been around in principle since 1882; it was originally built to test the constancy of the speed of light. Equipped with state of the art technology, it is nowadays perfect for detecting gravitational waves. The Advanced LIGO installation (Fig. C), with which they have now been discovered, also operates according to the principle of the Michelson interferometer.

In the 1970s, Max Planck researchers began to develop the technology of the interferometer further and adapt it to the requirements of research. Decades of work resulted in the construction of GEO600. This detector stands in a field in Ruthe near Hanover and is one of several terrestrial listening posts which listen in on the concert of the stars. At their heart are several diode lasers, similar to those found in a CD player. A small crystal converts the light into an infrared laser beam, whose power amounts to only ten watts after high-precision preparation and filtering – much more than a laser pointer, but also much too weak for useful measurements.

Detectors such as GEO600 or Advanced LIGO in Livingston (US state of Louisiana) and Hanford (Washington) therefore operate with “power recycling”: a mirror sends some of the light back towards the laser, which directs it again towards the interferometer. This cycle is repeated several times and amplifies the circulating light power considerably.

The LIGO lasers developed in Hanover thus initially achieve a base power of 200 watts, which feel like almost one megawatt (10⁶ watts) thanks to the recycling trick in the interferometer. This increases the sensitivity of the detector significantly. Moreover, the lasers are extremely stable: the light they produce always maintains the same amplitude and frequency over months and years.

The two arms of Advanced LIGO are each made up of tubes four kilometres long; those at GEO600 are 600 metres long. The laser beams therein must travel between the mirrors without being disturbed by external influences. In practice, vibrations caused by traffic or natural seismic movement must be eliminated. Seismometers thus measure the oscillations, which are then compensated by piezoelectric actuators.

In addition to this active system, all optical components are equipped with a passive system: the mirrors, for example, are suspended as multi-stage pendulums and also equipped with dampers made of rubber and stainless steel and leaf springs. In order to keep the thermal fluctuations in the air density within the installation as low as possible, the interferometers are housed in evacuated stainless steel tubes. GEO600, for example, has turbomolecular pumps to generate an ultra-high vacuum better than 10^-11 bar.

To discover the miniscule gravitational wave signals in the jumble of data, the scientists have to know what they have to look for in the first place. A department at the Max Planck Institute for Gravitational Physics is therefore calculating what the signals look like for all possible sources of gravitational waves – fusing black holes or neutron stars. The researchers then use these templates to analyze the measurement data of the detectors on high-performance supercomputers.

Once the signals have been found, further questions raise their head: where exactly is the source? What is behind it? Black holes or neutron stars? What is their mass? This is when the experts who calculate theoretical models and compare them with the observed data come into their own (Fig. A). This close interplay of experiment, simulations, analytical calculations and data analysis ultimately allows the scientists to bring light into the dark universe.

Whereas Advanced LIGO and GEO600 are already in operation, the VIRGO detector near the Italian city of Pisa is currently being expanded with measuring arms three kilometres in length, and Japanese scientists are currently building the subterranean detector KAGRA of the same size. The plan is also to have an observatory in India. And in 2034, the eLISA interferometer is to listen from space for low-frequency gravitational waves from the whole visible universe and thus supplement the ground-based detectors. The hunt for gravitational waves is going full steam ahead all over the world.

The Key Statements

Special Theory of Relativity

• There is no ether to carry light and radio waves.
• All physical laws have the same form in all systems moving uniformly with respect to each other.
• Space and time are inseparably linked to each other.
• There is no absolute simultaneousness.
• The speed of light is a universal constant and independent of the motion relative to the light source.
• Energy and mass are equivalent, mass is a direct measure of the energy contained in a body. And: light transmits mass.

General Theory of Relativity

• Gravity is not a force in the conventional sense, but a property of the geometry of space-time.
• Matter bends space-time, the extent of the curvature increasing with the mass of a body and decreasing with increasing separation from it. Space and time are dynamic quantities and determine in turn the motion of matter.
• Time plays an important role in the General Theory of Relativity. A clock ticks more slowly near a massive celestial body than further away from it in regions which are affected less by its gravity.