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Gravitational waves are a significant development in astrophysics, opening up new avenues of cosmic ...
2021-10-06 09:00:00

Space on the Wave
The Astronomy of Gravitational Waves

Illustration by Joanna Grochocka
Space on the Wave
Space on the Wave

In 1915, Einstein predicted the existence of gravitational waves, or the vibration of space-time. 100 years later, scientists were finally able to observe them, opening a new chapter in the history of astrophysics and enabling us to peek into new areas in space.

Read in 12 minutes

It was 14th September 2015, 11:50 CET, when a message arrived on the mail account of Marc Drago at the Max Planck Institute in Hannover. This may seem like nothing out of the ordinary; after all, many people receive loads of automatically-generated messages, especially scientists. This time, however, it was one of the most important e-mails in the history of physics.

GW150914

The e-mail contained graphs of two signals: one detected at the observatory in Livingston on the Gulf of Mexico, and the other 3000 kilometres away in Hanford on the American West Coast. The signals were almost identical; moreover, they were registered nearly simultaneously, just 0.0067 seconds apart. It looked as if something had gone straight through Earth at tremendous speed. It was not a measuring error or a local interference in either laboratory (the two centres were established precisely to exclude this possibility). Further, it was neither a test signal sent by engineers to test procedures, nor a message from an alien civilization, as in the books of Sagan and Lem. So what was it?

The graphs showed a gravitational wave. Thus, the LIGO programme (Laser Interferometer Gravitational-Wave Observatory) could announce its first huge success. Some even claimed that it has been the greatest scientific discovery of the 21st century so far. Not only was Einstein’s theory of relativity confirmed yet another time, but also brand new vistas opened, inaugurating an entirely novel way of studying the universe.

The first gravitational wave observed by humanity was given a romantic name worthy of its import: GW150914. Its origin was the merger of two black holes, 1.3 billion light years away from Earth, one of them 36 times the mass of the sun, and the other – 29 times. After travelling for 1.3 billion years, the wave passed through Earth, and was first recorded in Louisiana, before being picked up again 6.7 milliseconds later in the state of Washington. Interestingly, based on these two observations it was impossible to establish where the wave came from. Most probably it arrived from the direction of the Magellanic Clouds in the southern hemisphere of the sky, though its source was likely located much further away – 10,000 times the distance from Earth to the Clouds. The fundamental question of how these waves were actually detected is something that we will return to later. First, however, we need to address an even more basic concern and explain what gravitational waves are.

It is often difficult to clarify the latest ideas and achievements in contemporary science, especially when it comes to physics. Gravitational waves are both an exception to this and no exception at all. Their nature can be summarized in two words: they are ‘space-time vibrations’. As simple as that. Still, explaining these two words is a bottomless pit. Let us peer into it together!

What’s waving?

Let’s start at the beginning: what is a wave? It is a distortion moving through space. A distortion of what exactly? The surface of water is an obvious example. Throwing a stone causes water particles to move, in turn setting others in motion, and so on and so forth. This is how waves travel. To put it in philosophical terms, a wave is something different than its source. It cannot be reduced to the movement of any specific particles, but involves transmitting the distortion from some to others: A moving B, B moving C, etc. Further movement of a wave can be described using an appropriate mathematical equation.

Everyone has seen waves on water. The substance that vibrates in this case is none other than the good old tangible H2O. Electromagnetic waves are a little bit more tricky, but the basic idea stays the same. Waves of this type – for example, light, infrared, radio waves, etc. – are a distortion of the electromagnetic field that moves through space. According to Maxwell’s equations, vibrations in one place initiate vibrations in another, and so on.

Importantly, in the case of gravitational waves, the vibrating medium is space-time itself. What is this about? Let’s drop the ‘time’ bit and briefly consider gravitational waves as vibrations of space. Crucially, it is space itself that is moving – and not any matter contained in it. It is neither air (as in the case of sound waves), nor water (as in the case of ocean waves), but just space. This might seem counter-intuitive. How can space – an abstract entity – vibrate? This reaction is not only rooted in common sense, but also affected by the long shadow of Cartesianism, cast by the French philosopher over all of us. We have been taught that space is a purely mathematical concept without any properties, a bare, descriptive tool that is independent of any observers: just three dimensions, the coordinates x, y, z – that’s all. This, naturally, works well in everyday life or in computer graphics, but not so much in physics (for at least more than a century).

In fact, space has properties. Just like the expansion of the universe is best grasped as the enlargement of space (‘extending the pool of available space’), gravitational waves can be conceived of as its vibration at the speed of light. One only needs to recall that, in accordance with the theory of relativity, space is not just space but space-time. That’s the basic idea, or at least its early intimation.

Vibrating space

If we agree that space-time can vibrate, it needs to be explained how this works. In the case of waves on water, matter is moving up and down, similarly to waves formed on ropes or strings. However, how can space vibrate if its ‘directions’ are actually inside it?

The answer is that space does not vibrate in any direction, but cyclically expands and contracts, thus creating vibrations. Let us imagine a perfectly round sphere in laboratory conditions. If a gravitational wave from a distant galaxy passed through it, the orb would be deformed for a split second and then return to its former shape. Nothing would pressure it in the mechanical sense – it would be just space itself changing shape along with everything inside it (i.e., all material objects). This naturally occurs at an immensely small scale, which makes gravitational waves extremely difficult to detect. We shall return to this, but in the meantime let us pose one more question that many readers are probably already asking themselves. Why are these waves called gravitational at all? So far, we have not touched upon the subject of gravity.

The answer is provided by the general theory of relativity. It is, in fact, not true that we have not addressed gravity. The present discussion concerns properties of space-time; further, thanks to Einstein we know that gravity is about bending it. The theory of relativity predicted the existence of gravitational waves. Still, their amplitude is so low that we can only detect ones formed, to put it in poetic terms, during gravitational events of the highest rank, ones involving huge masses and astonishing acceleration. Such conditions occur in tight neutron star systems or when black holes merge – this is the scale we need to imagine. In this context, it is also possible to add that gravitational waves are, as it were, parts of a gravitational field that have detached from their source and travel through space. Hence their name.

A radio pulsar

Gravitational waves are a remarkable confirmation that, after many decades, observations can really confirm theoretical predictions. Their existence was postulated by Einstein already in 1915, but they were also mentioned by Henri Poincaré 10 years earlier in the article “On the Dynamics of the Electron”. This is worth mentioning, not only because Poincaré was first, but also due to Einstein’s equations being too complicated to discuss here. Poincaré’s argumentation should be more approachable to those who paid at least some attention during physics classes in high school. In a nutshell, accelerated electrical charges generate electromagnetic waves. Analogously, accelerated masses create gravitational waves – l’onde gravifique, as Poincaré put it in French.

Illustration by Joanna Grochocka
Illustration by Joanna Grochocka

The devil is, of course, in the numbers. A tennis ball hit by Novak Djoković (accelerated mass) or a rocket carrying Elon Musk’s Starlink satellites into orbit (also accelerated mass) create gravitational waves only in theory, because in practice they are undetectable. Mass and acceleration need to have a truly cosmic scale, involving celestial bodies like neutron stars and black holes. Even then, gravitational waves have an amplitude so low that their detection long seemed impossible. Einstein himself doubted their existence so much that at one point he even questioned his own theory.

As is often the case in science, the first observations confirming the existence of gravitational waves were indirect. How were they made? Since gravitational waves carry energy, objects that emit them continuously should be losing it. If we could use the theory of relativity to precisely calculate this energy loss, observing and gauging it to verify if the measurements match the theory, we would develop a sure way to prove the existence of gravitational waves.

A good example is provided by the tight binary system of neutron stars PSR B1913+16, the first such system known to astronomy, discovered in 1974. On Earth, we can observe regular radio emissions from one of these stars (meaning that it is a pulsar). On this basis, we can precisely describe the behaviour of the system. The mass and gravitational field strength are so great in this case that these stars should theoretically emit high quantities of energy in gravitational waves (specifically seven trillion terawatts, which is 1021 times more than the entire solar system is emitting). This is enough to visibly change the orbit of these two stars circling each other. If the system is losing energy, their orbit should be tightening, reducing the period of revolution. This can be precisely calculated: according to the theory of relativity, each year this period should decrease by 77 microseconds. This may not be much, but such changes ought to be easily detectable given the availability of radio waves coming from the pulsar. Indeed, an alteration was detected. Observations and theory aligned to three decimal places. It was 1979 and humanity obtained the first evidence that gravitational waves do exist. However, their direct observation became possible only in the 21st century.

Measuring up to measurement

Such observations are immensely difficult because gravitational waves are very small. What scale are we talking about? The waves that passed through Earth in September 2015 had a peak amplitude of 10-21. What does this mean? As already stated, gravitational waves are the vibration of space-time, its cyclical contraction and expansion. For a split second, every metre – kilometre, mile, fathom, furlong – shortens by 10-21 of its length. In human terms, the distance between Warsaw and Glasgow would shorten by the diameter of a single proton. How can this be measured at all?

In physics, it is often the case that changes in certain values can be calculated more accurately than the value itself. In fact, as it sometimes happens, only change can be meaningful. Speed is a good example. The measurements of a speed camera may seem absolute and unquestionable, but the velocity of space probes is much more relative. What would be the point of reference? Earth? The sun? Mars? In space, everything is in motion. This is why astronautics concerns itself not with speed itself but its change: delta-v. There is even a special term, ‘delta-v budget’, which is used in planning space flights.

Measuring length is similar. Rulers and steel tape have accustomed us to the comfort of being able to easily measure everything. This certainly makes a lot of sense in the case of metres and millimetres. It is reasonable to say that a stick is two-metres long, but not so much to claim that it is 2.0171246239441712312-metres long. The most precise measurements are not absolute, but indicate change.

Note that rulers and steel tape can help us measure tables, bridges and sticks, but how do we measure changes of space itself when the ruler’s length is altered as well? If everything changes length, nothing does, in a relative sense. This is a serious concern! Out of this quandary, the idea of an interferometer was born – the device used to search for gravitational waves.

In the LIGO project, interferometers were constructed using two perpendicular pipes, each four-kilometres long. Why two? Precisely because of the above reason. Gravitational waves cause space to contract and expand, but not exactly the same in all dimensions. This is why we can detect them! One arm will always change its length a little bit differently than the other. We can observe this relative change, even if it is of the order of 10-21.

How is this done? Interferometry is one of the miracles of physics. As we know, light is also a wave going up and down like an infinite sinusoid. If we set up two light beams of exactly the same wavelength, using a laser, we can detect even the slightest phase shift. This is possible thanks to the phenomenon of interference. Two identical waves that are misaligned by half a phase period cancel each other out (with the ‘ups’ coinciding with the ‘downs’). When they shift even minimally, the cancellation will not be perfect, which can be observed. Moreover, laser light does not travel just once through the four-kilometre arms, but bounces back and forth. A system of mirrors causes the waves to cover the distance hundreds of times, accordingly extending the basis for measurements. Made with the precision of 10-21, these estimates are the most precise ones made in human history.

Further details, including mirror optics, signal enhancing and filtering (not to mention mathematical elaboration), lie beyond the scope of this article. Still, it is worth discussing certain technical aspects, because the LIGO observatories in Hanford and Livingston are true wonders of engineering. Each of them is L-shaped, the laboratory located at the intersection. Their arms are four-kilometres long and need to take into account the Earth’s curvature, because they need to be perfectly straight. At this distance, the planet’s surface drops by 1.25 metres, which means that the arms must point straight ahead and slightly upwards in order to compensate for curvature. Inside, there are laser beams of tremendous power. As one employee succinctly put it, they would not tear off one’s head, but simply evaporate it. Laser light must travel in a perfect vacuum so as not to diffuse in contact with air particles or dust. For this reason, LIGO is the second biggest vacuum device in the world. 10,000 m3 of air was pumped out from each observatory, which lasted 40 days and created pressure amounting to one trillionth of that in the Earth’s atmosphere, the same as in the vacuum on the planet’s orbit. This is indeed a miracle of science.

The future is today

These ingenious observatory-laboratories are our new window onto the world. This worn out phrase in fact fits perfectly here. Having made the above pioneering observations, we are only beginning our journey, but it already seems that we are standing at the threshold of an entirely new discipline: the astronomy of gravitational waves. It preoccupies itself with studying the universe through observations of gravitational waves. Entirely new possibilities have thus opened before astronomy. Gravitational waves cannot be ‘blocked’, just like one can prevent light or radio waves from spreading, because they penetrate into locations that cannot be studied using electromagnetic waves – places where black holes merge or other remarkable events take place, ones that we may find difficult to imagine just yet.

The astronomy of gravitational waves can also aid us in the study of the young universe, when it was still opaque to electromagnetic waves. The possibilities are dazzling, while the concept itself is indeed quite metaphysical. The future is today; both Lem and Sagan would be delighted with it. 411 years have passed since the January night when Galileo pointed his telescope towards Jupiter and became the first man to observe its moons. Today, not only astronomy but also humanity is in a much different place. We are truly discovering more things in the skies than are dreamt of in philosophy.

 

Translated from the Polish by Grzegorz Czemiel

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