Story of gravitational waves — how it is propagated


Artist's impression of merging neutron stars by ESO/L. Calçada/M. Kornmesser (CC BY 4.0)
By ESO/L. Calçada/M. Kornmesser -, CC BY 4.0,

The last two years have presented one of the most significant events in physics in my lifetime, that is, direct detections of gravitational waves and solid observational proof of the source in the most recent event. They are, as far as I am concerned, rather unexpected, and are very exciting to any one. Immediately before the most recent discovery, it seemed a strict embargo was in place for one of my friends, an astronomer. An institution-wide embargo is rather unusual [Afternote 1], and it implies how exciting the news would be, and it was, as it turned shortly afterwards.

Here is my bold attempt to make a summary of the story of gravitational waves — what is significant and what is the implication? [Note(2017-11-01): I have tried to keep the description in this article plain so any one with interest in science would easily understand. I hope you get the significance of this great discovery!]


  1. What is the gravitational wave?
  2. Road to the first direct detection of the gravitational wave
    1. A bit of historical background
    2. Early attempts
    3. Direct detection
  3. Tables turned
    1. First detection of gravitational waves
  4. Birth of gravitational-wave astronomy
    1. What have we learnt?
    2. Short γ-ray burst
    3. Origin of heavy elements, like gold
    4. Intermediate-mass black holes
  5. History repeats

What is the gravitational wave?

In a word, the gravitational wave is a propagation of a fluctuation of the gravitational field from a source event (in some conditions), where some enormous change in the gravitational field occurs. The wave travels at the speed of light. An observer is affected (moved) by a passing gravitational wave. Mind you, everything else surrounding the observer is equally affected, and so the detection is not straightforward.

Road to the first direct detection of the gravitational wave

A bit of historical background

We all know electromagnetic waves. No life would exist without them. Classically, even the old Bible recognizes it in the first page, Let there be light. Light is a form of electromagnetic waves. Or more accurately, a bandwidth (in the wavelength) of electromagnetic waves is called (visible) light. Also, the modern society is critically dependent on radio-wave, which is another bandwidth of electromagnetic waves, for the communication from radio/TV broadcast to mobile phone network. Microwave, infrared, ultraviolet, X-ray and γ-rays too are all electromagnetic waves in different bands.

Physicists solved how the electromagnetic dynamics work over a century ago. Maxwell's equations and Einstein's special relativity are the two pinnacles. The theory shows electromagnetic waves are produced when charged particles are accelerated (or decelerated, which is just the negative form of acceleration) in the electromagnetic field, which is omnipresent in the universe.

The other omnipresent field in the universe is the gravitational field. Isaac Newton successfully formulated the theory of gravitation in the 17th century, and two centuries later Albert Einstein amended and completed it, called the theory of general relativity. Because both the electromagnetic entity and gravitation are essentially fields, it might not require a great deal of imagination to think of a potential existence of gravitational waves, as an analogy to electromagnetic waves.

A trouble is, the theory of general relativity is, although it looks beautifully simple in the core equations, awfully difficult in practice to extract what it actually means from. It took some months even for Einstein himself to derive the suggestion of potential existence of gravitational waves.

Unsurprisingly, the theory of gravitational waves met serious scruitinisation and even some criticism from the top physicists at the time. Then, in 1936, 21 years after publishing the theory of general relativity, Einstein concluded gravitational waves would not exist, and submitted a paper about it to Physical Review, the most prestigious journal in physics in the world. The anonymous reviewer (known as Howard Robertson later) pointed out a flaw in logic in the paper. Receiving the unfavourable referee report, Einstein got angry and withdrew the paper (see a vivid description by Cervantes-Cota et al. (2016) for detail). However, Einstein's new colleague Leopold Infeld managed to convince him that his logic was wrong, and they submitted a paper with the completely opposite conclusion, that is, gravitational waves should exist, to another journal in the same year!

Early attempts

Unlike Newton's theory of classical dynamics, which was almost immediately proved to be correct experimentally, the theory of general relativity was more hypothetical when it was first published, in the sense it was extremely hard to prove or disprove experimentally. By now, however, it has been proved at utmost precision, whereas no observations or experiments present a reliable counter-proof. A culmination in the modern world is the GPS technology used by Sat-Nav and smart phones and alike. Its supreme accuracy is achieved only with a use of the theory of general relativity to the full extent.

Nevertheless, detection of gravitational waves has been the missing key proof of the theory of general relativity. Physicists calculate to show the effect would be extremely subtle and hence would be very hard to detect. So, non-detection was not a disproof of the theory by any means, but it would be reassuring to get another important proof of the elusive theory.

In 1974, Russell Hulse and Joseph Taylor found the first indirect evidence of gravitational waves. They found the orbital period of roughly 7.75 hours in the binary pulsar system PSR B1913+16 decayed at a rate of 76.5 μs (or 0.0000765 seconds) per year. As far as physicists can tell, there are no other factors which could cause this decay, and hence it was regarded as the firm, though indirect, proof of gravitational waves. They were later (1993) awarded Nobel Prize in Physics for their discovery.

Direct detection

By the late 1990s, groups of astrophysicists in several countries were gradually gearing up for the first direct detection of the gravitational wave. I remember how it was like in the Japanese community of astronomers. Whereas virtually no astronomers doubted the existence of gravitational waves, it seemed many were doubtful if humans could detect it in the foreseeable future. Not many astronomers in Japan were overly supportive for them.

Why? Direct detection of gravitational waves was a great technical challenge. The LIGO project, with which the first detection was finally made in late 2015, achieved the precision of one part in 5×1022 (in length). To fathom the extent, here is an example: the LIGO can detect the difference in length of half a circumference of the earth (20,000km, like London to Sydney) by roughly one-quarter-trillionth of 1 milli-meter. I have no doubt it is the most precise measurement of any kinds humans have ever made. [Addendum: In the original version, I wrote "billion". It is corrected to the correct "trillion" now]

In the late 1990s, the TAMA project was starting in Japan. The LIGO project had been already in the planning phase, and TAMA was much inferior to it. Some astronomers in Japan wondered What's the point (to build such an inferior observatory)? The answer was If there is a massive event like a supernova explosion nearby like in our Galaxy, we can detect it (before other gravitational observatories in the world start operation). That made some sense, thought I, though they did not have a luck in the end.

The problem was of course the resources. To build and run such a facility is expensive both in money and human resources. And there is no guarantee the gravitational-wave observatories, even at the size of LIGO, could detect anything. In fact, the astronomers surrounding me were rather pessimistic. Considering most astronomers were struggling to get funding for their own projects, as well as seeking for immediate and selling results (to get a funding and stable positions in academia), it might be understandable they were not overly supportive for the project of gravitational-wave observatory, which is costly, yet might end in complete vain. Looking back at it now, I think it was not an ideal attitude for scientists, but was a reality in the competitive field.

Tables turned

First detection of gravitational waves

I wasn't following the development of the gravitational-wave astronomy in recent years, except none of them started as originally advertised, perhaps due to difficulty in securing the funding.

It was out of blue when I heard of the LIGO team's announcement in early 2016 of the first direct detection of gravitational waves. The fact those pioneers were awarded Nobel Prize in Physics in the following year 2017 shows how extraordinary their achievement is, considering it usually takes decades before an achievement is appreciated by the Nobel Prize Committee, such as almost 20 years delay for Hulse and Taylor.

As exciting as the first detection of gravitational waves is, the emitting source was, and still is, a speculation. Gravitational-wave observatories monitor the entire sky, and they manage to detect the strongest events only, but that means the constraint on the source position is very limited. Another intrinsic difficulty in gravitational-wave astronomy is that many of such "significant events" would be unlikely to emit any other normal electromagnetic waves, notably light (or radio-wave or X-rays). Indeed, the sources of the first five detected gravitational-wave events [corrected from "four" in the original manuscript on 2017-10-23] are considered to be merger events of two black-holes. As violent as it sounds, it would not emit light or else simultaneously, because nothing escapes from black holes. Only the sign in the outside world would be gravitational waves, which are the tracer of sudden change in the gravitational field in the system.

It is wonderful humans now get another probe to explore the universe to find previously undetected events. However, it is frustrating we have no independent evidence or information of what has been observed.

Birth of gravitational-wave astronomy

Since the first detection of gravitational waves, four more detections have been reported [corrected from "three" in the original manuscript on 2017-10-23]. Then came the revolution: the gravitational-wave detection with the solid counterpart in electromagnetic-wave on 2017-08-17, named GW170817 (in gravitational-wave), GRB 170817A (in γ-rays), and AT 2017gfo (in optical light), near the galaxy NGC 4993 [Note2]. It was also detected in the entire range of wavelengths from radio, infrared, ultraviolet, to X-rays. No detection was reported from neutrino observatories.

We now know what it is!!

In short, it turned out to be an event of merger of two neutron stars. Neutron stars, unlike black holes, do have a solid surface made by matter — predominantly neutrons (surprise?). So, when something extreme happens, those matter emits a signal in a more conventional way.

Humans had a luck at the occasion. Multiple gravitational observatories were operating by that time, and with the combined result the position was fairly precisely determined (Note in the case of gravitational-wave observations, detections in observatories located far-apart are crucial to improve the positional accuracy; an animated GIF by @NASAFermi nicely demonstrates how the position was constrained). The source was only 130 million light-years away, which is 10 times closer than the previously detected gravitational-wave sources and hence the observed signal would be 100 times stronger (for the same source-intensity). The two γ-ray observatories of Fermi and INTEGRAL were operating, ready to detect a potential γ-ray signal, which lasted for only a few seconds. It is known γ-ray bursts usually show an after-glow in visible light, and so optical astronomers more or less knew what to expect before their observations. Also, the source was located in an open field, and not in or behind a molecular or dust cloud in the host or our own galaxy, in which case the optical detection would have been impossible.

Obviously, it was not just a sheer luck. Humans had been prepared to observe such a rare event, and that made an immediate, intensive and extensive follow-up observation campaign possible. The location of the source was pretty close to the sun, and for that reason the observation opportunity for any ground-based telescopes was limited to only an hour after twilight for any given telescope. The collaboration by multiple observatories in different locations was a key.

What have we learnt?

In a word, we now get the (arguably?) final crucial piece to confirm the theory of general relativity is correct to the extreme precision and also our current understanding of the universe is about right.

Science is all about constant and never-ending evaluation of the existing theories. If a single observational fact was discovered that disproves the theory, then the theory must be immediately discarded or modified, no matter how many pieces of supporting evidence have been presented before. All the established theories in science have gone through countless serious scruitinisation, and are still going through it. The fact those theories are established means it is extremely unlikely to find any counter-evidence. So, when one claims to have counter-evidence (as so-called "pseudo-scientists" often do), usually it is the claimed "evidence" that is erroneous and wrong. However, the possibility of disproving can never be entirely excluded. If a scientist succeeded in disproving the established theory, it would be an extremely honourable prize s/he could ever hope for.

Following the recent multiple detection of gravitational-wave events, the theory of general relativity is now established more than ever, marking a century after Einstein's formulation. Like or not, some fantasies presented in fictions, cartoons, or films, are proved to be impossible, such as teleportation, anti-gravity floating, and time-travelling.

Short γ-ray burst

A more positive note is a celebration of the efforts by the physicists and astronomers in various fields. The gravitational-wave source GW170817 was associated with a short γ-ray burst. That is a phenomenal discovery.

The γ-ray burst is a fairly short bursting event in γ-rays, and one of the most energetic events in the universe. It was first discovered as early as in 1967 (during nuclear-weapon-testing monitoring). But no one had had a clue to what they are before 1997, when the epoch-making discovery was made. With the intensive observation campaign since then, we now have a fairly good understanding of what they are, as far as the population of long γ-ray bursts is concerned, which consists 70% of all the γ-ray bursts and in which the burst lasts over 2 seconds. By contrast, the origin of the other population, short γ-ray bursts, is not yet well understood, majorly because to identify the counterpart in other wavelengths is extremely difficult. At least it seems likely they have a different origin from long γ-ray bursts.

The discovery of the association of a short γ-ray burst to the gravitational-wave source GW170817 gives a rather definitive answer to it, albeit for a single case. It is a merger event of two neutron-stars. The neutron-star merger has been arguably the most promising model to explain the origin of short γ-ray bursts, but has been lacking, like other models, definitive observational evidence. Reportedly the observed nature of GW170817 from the gravitation wave to the entire wavelengths of electromagnetic waves is fully consistent with the theory.

That is, I would say, a celebration of human intelligence. The scientists in the field have collectively put many pieces together and have reached the best guess, and now the guess by intelligence is supported by the observational evidence from an entirely new and different field.

I note that this discovery obviously does not mean the origin of all the short γ-ray bursts is neutron-star mergers. However, at least we now understand some, potentially many, of them should be. Our understanding of the universe was a little bit advanced now.

Origin of heavy elements, like gold

On the earth, and I suppose in the universe in general, there are 94 natural atoms. Only 3 of them, hydrogen (75% in mass abundance), helium (25%), and a tiny bit of Lithium, are primordial, that is, exist since (pretty much) the beginning of the universe. Elements up to the atomic number of 26 (iron) have been created via nuclear fusion inside stars, and emitted outside mainly via supernova explosion at the end of life of stars. Stars are everywhere in the universe, and the lives of massive stars, which undergo supernovae, are relatively short. That is why these lighter elements were already in the interstellar space when the earth was formed out of the interstellar matter 4.5 billion years ago.

A big problem is nuclear fusion can not generate the elements heavier than iron. Yet, plenty of them exist, though not as abundant as iron, on and in the earth, including zinc, lead, uranium, and ever loved gold.

The widely-believed theory explains those heavy elements must be created at the time of supernova explosions. However, there is hardly any observational evidence, or certainly there is no quantitative confirmation of the theory. Allegedly, even compelling theories have been proposed to claim the amount of heavy elements created supernova explosions is limited.

We do not know any other phenomena in the universe that are energetic enough to produce heavy elements, than supernova explosions, and that is why the theory is generally accepted.

The discovery of GW170817 brings another potential candidate: the neutron-star merger. It is extremely energetic and apparently should produce plenty of heavy elements, including gold. We still do not know how many of them exist in the universe, and so it is too early to make a quantitative argument. But we have a fairly good idea how frequently short γ-ray bursts occur in the universe. Once the relation between gravitational-wave events and short γ-ray bursts has been estabilished, I wildly guess it would be possible to make an intelligent estimate about the contribution of neutron-mergers to production of heavy elements in the universe.

I should note the hypothesis neutron-star mergers are responsible to a certain extent to heavy-element production is not entirely new. The potential of neutron-star mergers have been discussed for some time, especially with regard to the origin of gamma-ray bursts like GRB 130603B. The discovery of GW170817 is a nice encouragenment for the hypothesis.

Intermediate-mass black holes

Astronomers have detected a large number of black holes. They are categorised into the two populations depending on their mass: those of a few to 20 times mass of the sun and those of a million times or more. A big problem is the population of black holes with a mass in between, called intermediate-mass black holes, has been somehow missing. Do they not exist intrinsically in the universe, perhaps related to how black holes are formed, or is it more an observational bias that they are for some reason difficult to detect, even though they do exist?

The theory of the formation of both the known populations of black holes is more or less established. Basically, those in the former population is created after the end of the life of massive stars, and those in the latter reside in the cores of galaxies, including our own Milky Way Galaxy, and have grown over the lifetime of the universe. As for the former, because there is a fairly well-defined upper limit for a mass of stars according to the established theory of stars, there must be an upper limit for the mass of black holes born from them.

Now, the past gravitational-wave detections suggest all the events so far but GW170817 were originated from the merger of intermediate-mass black-holes; so they have revealed the population of intermediate-mass black holes do exist in the universe. How were they formed? Maybe through mergers, or else? Are they rare, compared with the known populations of black holes? Or, are there any reasons they are difficult to detect with conventional observations? It would be interesting to see how this new observational fact would affect the theory of black holes and beyond. After all those years, black holes are still the most exotic entity in the universe!

History repeats

The discovery of gravitational-wave sources and even a counterpart of one of them reminds me of the early history of X-ray astronomy.

X-rays are emitted (mainly) from extremely hot objects at a temperature over 1 million kelvin (or degrees in centigrade). Apparently, almost no one imagined there would be such sources in the universe that are hot enough to emit strong X-rays in the pre-1962, before the first detection of cosmic X-ray sources by Bruno Rossi, Giacconi, et al. We now know countless objects in the universe emit strong X-rays, and so there are countless hot spots and regions, some of which are extended for the inter-galactic scale, in the universe. One of the primary pioneers, Riccardo Giacconi, deservedly received the Nobel Prize in Physics in 2002 (a half century after the first discovery).

Allegedly, when Giacconi and co tried the first X-ray observation, they did not expect too much. They just wanted to see, and somehow managed to get the funding for their adventurous attempt. They might be more surprised at the results than any one else?

I just guess the scientists who have devoted their life in the ambitious projects of gravitational-wave observations are also surprised and in a very joyful manner. Admittedly, unlike the birth of X-ray astronomy, almost every one believed the gravitational wave should exist in the universe. However, we did not know how frequent the detectable events would be, apart from a kind of wild (and maybe optimistic?) guess. After all, we didn't known much about the population of intermediate-mass black holes! Worse, when the gravitational-wave observatories were first planned in the 1990s, humans' knowledge about the high-energy universe was far more immature than now. They were truly ambitious projects back then.

I marvel their vision over 2 decades ago, and congratulate the teams in the world! Thank you for giving us an excitement and showing what humans can achieve with a vision, tenacity, and taking a risk.

(Masa Sakano, 2017-10-20)

Afternote 1
[Added on 2017-10-23] In the case of LIGO, the embargo is written in the contract between LIGO and collaborating observatories, which would receive the early (informal) notification after gravitational-wave events, and so this event was no exception (according to Dr. Tatehiro Mihara, thanks!). However, in this particular case of GW170817, it seems to have been impossible to suppress the information completely (see a good summary post in the blog "In the Dark")。In fact, the rumour appeared even in Nature a mere week after the detection, while the official press release was made 2 months later. It was maybe a half open secret.
Afternote 2
[Added on 2017-10-23] The main paper. It lists over 3,500 co-authors from 70 or so institutes. For the review for astronomers, see, for example, "Welcome to the Multi-Messenger Era! Lessons from a Neutron Star Merger and the Landscape Ahead by Brian D. Metzger" (B. D. Metzger 2017).



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