When Einstein predicted the existence of gravitational waves 100 years ago, he never thought that one day humans would actually be able to observe gravitational waves: the effect is so weak that it is undetectable...

Today, February 11, 2016, at 23:30 Beijing time, Caltech, MIT, the LIGO Scientific Alliance, and the U.S. National Science Foundation announced to the world: We have really detected gravitational waves!

The related paper, titled Observation of Gravitaiton Waves from a Binary Black Hole Merger, was published in Physical Review Letters. The authors of the paper include the LSC gravitational wave research team of Tsinghua University.

Zhishe Academic Circle specially invited one of the authors of the paper, core member of the LIGO Scientific Alliance, Professor Chen Yanbei of the California Institute of Technology, and Chinese gravitational wave expert, Dr. Fan Xilong of Hubei Second Normal University, to write an article to introduce the long, tortuous and exciting experience of gravitational wave detection, and some little-known anecdotes, from gravity 300 years ago, relativity 100 years ago, to today's gravitational waves.

At the end of the article, there is an exclusive interview with Professors Chen Yanbei and Fan Xilong by Zhishe Academic Circle.

Here is the text:

In 1915, Einstein published a paper on general relativity, which revolutionized the concept of gravity and space-time since Newton, and creatively demonstrated that the essence of gravity is the curvature of space-time geometry under the influence of matter. In 1916, within the framework of general relativity, Einstein published another paper demonstrating that the effect of gravity is transmitted in the form of waves.

Because the effect of gravitational waves is extremely weak, Einstein 100 years ago believed that gravitational waves could be ignored under any conceivable circumstances. 50 years ago, experimental physicist Joe Weber bravely pioneered the detection of gravitational waves. 40 years ago, astronomers Hulse and Taylor discovered binary pulsars and indirectly confirmed the existence of gravitational waves. 25 years ago, physicists Drever, Thorne and Weiss began to build the Laser Interferometer Gravitational-wave Observatory (LIGO) with funding from the National Science Foundation of the United States. Today, the LIGO gravitational wave detectors in the United States and the VIRGO gravitational wave detectors in Europe jointly announced that they have detected gravitational waves emitted by the collision of two black holes with a mass of about 30 solar masses, about 1.3 billion light-years from the Earth.

In this event (GW150914) that lasted less than a second and that physicists have been looking forward to for 50 years , four pairs of 40-kilogram glass mirrors, 4 kilometers apart in a vacuum, vibrated more than a dozen times with an amplitude one thousandth the size of an atomic nucleus. Such tiny vibrations were read out by a 100-kilowatt laser hitting these mirrors, allowing humans to "closely contact" a black hole for the first time. Black holes are no longer magical objects in science fiction works, no longer hiding behind high-temperature magnetized plasma, and no longer sitting steadily in the center of a galaxy. This time, we actually observed the high distortion and pulsation of time and space near a black hole. The success of gravitational wave detection provides humans with a brand new window to observe the universe.

｜ Gravity

Gravity is everywhere. It dominates the sky, allowing the universe, galaxies, stars, and planets to form and evolve in an orderly manner; it dominates the earth, dividing the earth we live on into various spheres, allowing apples to fall to the ground, making humans envy birds flying, and making the sun rise and set, and the mountains and rivers beautiful. However, although gravity is everywhere, it is low-key and outstanding, so that we often ignore it: the colorful, sweet, bitter, and spicy in our lives are all produced by electromagnetic interactions. And so far, at the microscopic level, gravity still cannot be integrated with other basic interactions!

Gravity is the earliest interaction that humans have quantitatively understood, and it has led humans from ignorance to science. In the 17th century, Galileo's Leaning Tower experiment proved through kinematics that gravity is equal to all beings, that is, the equivalence principle - objects of different materials fall with the same acceleration. In 1687, Newton created the law of universal gravitation and invented the mathematical method of calculus to accurately describe the movement of planets. Later generations used Newton's theory to discover Neptune and Pluto. Although the precession of Mercury's perihelion has always been in very small contradiction with Newton's prediction, it seems that the ultimate theory of gravity has been completed.

In the hundreds of years after Newton discovered gravity, the progress of physics was more focused on the study of electricity and magnetism. In 1865, Maxwell finally established a grand unified theory of electric and magnetic fields. In 1905, Einstein proposed the special theory of relativity, which insightfully demonstrated that the unity of the electromagnetic field implies the unity of time and space: physical theory must consider time and space together, and time and space themselves have lost their absolute meaning. A new concept, "spacetime", was born.

｜ General Relativity

Although Newton's law of universal gravitation has almost perfect experimental verification, it conceptually considers time and space separately, and Newton's gravity propagates instantaneously . Therefore, Newton's gravity and the theory of special relativity are conceptually contradictory. After proposing the special theory of relativity, Einstein further studied the relationship between gravity and "space-time geometry", rethinking the phenomenon observed by Galileo that the acceleration of falling objects is consistent, and realized that gravity is a very special interaction. If we enter a freely falling reference frame, then gravity disappears! This is why astronauts near the earth feel weightless: not because they are too far away from the earth, but because they are in free fall!

If we enter a freely falling reference frame, gravity seems to disappear. Does this mean that gravity is just a product of the reference frame transformation, not a real physical existence? No, because the freely falling reference frames at different positions are different on a macroscopic scale! If we consider a large enough space station, we will find that objects at different positions on the space station will have a relative acceleration phenomenon, which is the so-called tidal acceleration. And this acceleration is applicable to all objects. Einstein attributed this to the curvature of space-time geometry .

The spacetime geometry in general relativity is what makes freely falling objects that are originally parallel to each other move closer or farther away from each other. Just like the falling apple in Newton's gravity, the curved geometry in general relativity can also be explained by apples. On the surface of the apple, if you draw some initially parallel curves and start from these parallel curves with the same initial velocity, then depending on the position and direction of these parallel curves, some of them will move closer to each other (positive curvature) and some will move away from each other (negative curvature).

Einstein's equations relating the geometry of spacetime to the distribution of matter can be expressed in a very concise tensor form:

This is the very beautiful Einstein equation. Before explaining why general relativity can solve the instantaneous propagation of gravity, let's take a look at its difficult and wonderful side.

Solving Einstein's Equations

The equations of general relativity are beautiful in form, but the mathematical structure is much more complex than the geometry of the surface of an apple. For quite a long time, mathematicians and physicists could only watch from a distance and could not get close to them. They only obtained solutions to Einstein's equations in a few cases, but did not understand the meaning of these equations. It was not until the early 1970s that mathematical physicists proved that Einstein's equations can be systematically solved by the method of initial conditions plus time evolution in principle. In 1979, Professor Shing-Tung Yau and his student Richard Schoen proved the "Positive Mass Theorem" using the method of geometric analysis, laying the mathematical foundation for the concept of mass in general relativity. The charm of a true goddess is lasting. The global properties of the solutions to Einstein's equations and the convergence of the numerical solutions used by physicists are still cutting-edge issues in mathematical research.

Black Hole

Since Einstein established his gravitational equation, scientists have discovered some analytical solutions, Schwarzschild solutions under spherical symmetry and Kerr solutions under axial symmetry. These solutions correspond to spacetime without any mass, seemingly a curvature of pure spacetime geometry.

Later, through the research of Oppenheimer, Wheeler and others, people gradually realized that this was a state reached by a massive star after its nuclear fuel was burned out through "collapse". Wheeler named these space-time structures "black holes" .

Mathematically, the space-time of a black hole has many wonderful structures. For example, a black hole has a structure called the "event horizon". On the "space-time diagram", the event horizon divides space-time into two parts, one part that can be connected to distant places, and the other part that cannot be connected to distant places. When a star collapses into a black hole, an observer sitting on the surface of the star will pass through the event horizon of the black hole, while an observer standing outside will not see the observer on the surface of the star passing through the event horizon, but will only see his movement becoming slower and slower, as if he is "frozen" on the surface of the event horizon.

For another example, not far outside the event horizon, there is a "light ball". Under the influence of gravity, light can revolve around the black hole on the light ball, neither escaping to infinity nor falling into the black hole.

In the 1970s, scientists deduced some other properties of black holes from mathematics. On the one hand, mathematicians proved a series of "black hole uniqueness" theorems, showing that spacetime with "horizon" and no matter can only be the spacetime structure of a finite number of black holes. On the other hand, the creation of "Black Hole Microcirculation Theory" allowed physicists to intuitively prove the process of the geometric structure of black holes in the process of stars collapsing into black holes. When physicists such as Hawking applied quantum mechanics to black holes, they were surprised to find that black holes would also evaporate through the so-called "Hawking radiation".

｜ Black holes in astronomy

The mathematically fascinating properties of black holes have aroused people's endless imagination and have become an important subject of science fiction. However, do they really exist physically? In science, to prove the existence of an object, at least its effect on other objects must be observed.

You can’t create a black hole behind closed doors, you have to look up at the sky!

In astronomical observations, scientists have discovered some objects that are suspected to be black holes. Due to their trust and favor for Einstein's theory, astronomers unanimously believe that these objects are black holes.

The first type of objects has a mass of several to dozens of times that of the sun. They exist in X-ray binaries and are smaller than tens of kilometers in size. According to the calculations of general relativity, such objects must be black holes . The X-rays emitted by these objects are emitted by the gas emitted by the black hole's companion star, which squeezes, rubs, and heats each other as it falls into the black hole.

The second type of object is the supermassive black holes that exist at the center of galaxies. They can have masses that are tens or millions of times greater than the mass of our sun, and they are also very small, leading people to assume that they must also be black holes. For example, at the center of the Milky Way, there is a black hole with a mass of four million suns. In other galaxies, gas is constantly falling into the black hole, forming an "accretion disk" that rotates around the black hole and emitting "jets" near the black hole's axis of rotation. Such a system is called an active galactic nucleus, and it emits strong electromagnetic radiation, making it an important target for astronomical observations.

Another type of object is the intermediate-mass black hole. They may be produced by the merger of small-mass black holes, or by the small black holes eating many stars, or by the collapse of massive stars in the early universe. There are some traces of them in some low-luminosity active galactic nuclei, ultra-bright X-ray sources and globular clusters.

These astronomical observations prove the existence of black holes from one aspect, but it is currently impossible to accurately determine the geometric structure near black holes. These black holes are also stable black holes that remain unchanged over time, and the space-time structure around them remains unchanged during the period of time we observe.

Gravitational waves

Einstein predicted the existence of gravitational waves in 1916: He found that his equations had a set of solutions that were similar to electromagnetic waves and propagated at the speed of light. But he also said in his article (the last sentence in the picture below) that because the energy of this gravitational wave radiation is very small, the radiation of gravitational waves can be ignored in all conceivable cases.

（Albert Einstein, Approximate Integration of the Field Equations of Gravitation, Proceedings of the Royal Prussian Academy of Sciences (Berlin), 1916.）

For a long time, physicists could not figure out the physical meaning of this solution, and they did not expect that this wave could have any observational value. Around 1960, the physical meaning of gravitational waves began to become clear, and physicists believed that gravitational waves could be regarded as the propagation of gravitational interactions and could be regarded as carrying gravitational energy. This means that gravitational interactions propagate at the speed of light.

To understand the spacetime geometry corresponding to gravitational waves, we need to turn the smooth apple into a rough orange: there are two curved geometric structures on the surface of the orange. The large-scale spacetime geometry (the radius of the orange) represents the gravity in the universe, while the small-scale geometry (the rough dots) represents the gravitational waves.

In the reference frame of a freely falling object, gravitational waves can be regarded as a "tidal gravitational field". That is, the farther away an object is from the object, the greater the gravitational field it feels. Between free objects, the tidal gravitational field will cause a proportional change in their relative displacement (that is, "strain"). The amplitude h of the gravitational wave is usually represented by this strain.

If it is not a separate object in free fall, but a whole elastic body, then the effect of the gravitational field depends on the response of the elastic body itself to external forces.

｜ The history of gravitational wave detection

Einstein said that gravitational waves are very weak, but how weak are they? Let's take an example. Even if it is the largest hydrogen bomb explosion in human history, we can roughly estimate the amplitude of the gravitational waves within one meter of the explosion, that is, the strain between the free-falling objects caused by it. This strain is only on the order of 10^-27.

Although gravitational waves are so weak, they did not scare the brave experimental physicist Joe Weber. He firmly believed that although the gravitational waves generated on the earth were very weak, there might be astronomical phenomena in the universe that could cause strong enough gravitational waves. In the late 1960s, Weber began to measure gravitational waves using the resonance method. Specifically, a large metal object was used to take advantage of the characteristic that gravitational waves cause resonance at the resonant frequency of the object, hoping to extract the gravitational wave signal from the vibration of the object. Weber published some experimental results and believed that gravitational waves had been discovered. But unfortunately, no one could repeat his experiment, and it was difficult to prove in theory what kind of process sent out such a strong gravitational wave signal. However, Weber's work inspired a group of scientists to devote themselves to the cause of gravitational waves. Since the 1970s, a group of theoretical and experimental physicists have joined the ranks of theoretical research and experimental detection of gravitational waves.

Weiss, an experimental physicist at MIT, noticed that the change in the distance between objects caused by gravitational waves is proportional to the original distance between the objects. In this case, if the distance between the objects is pulled very far, and they are made into mirrors, and then the distance between the mirrors is measured using laser ranging methods, the accuracy of gravitational wave measurements can be increased exponentially.

At the same time, Drever of Glasgow University in the UK and Forward of Hughes Aircraft Company also began laser interferometry gravitational wave measurement experiments.

In 1975, just as the gravitational wave experiment was gradually developing, astronomers Hulse and Taylor discovered a pair of binary pulsars. In 1982, Taylor and Weisberg inferred that the binary was losing energy through the evolution of its orbital frequency, and the energy loss rate was consistent with that caused by gravitational waves. This provided a strong indirect evidence for the existence of gravitational waves: gravitational waves finally came out of paper! Hulse and Taylor won the Nobel Prize for this in 1993, and binary pulsars became an important system for studying general relativity and neutron stars.

Kip Thorne

To talk about the history of LIGO, we have to mention Kip Thorne, the "unknown movie actor" in "Interstellar". He was a student of John Wheeler, the physicist who named the black hole, and was also a junior of Richard Feynman. When Thorne was a graduate student at Princeton in his early years, he studied the process of gravitational collapse with Wheeler and made important contributions to the theory of black holes as the final state of stellar evolution. From then on, Thorne had an indissoluble bond with black holes. Don't be surprised, the T and W in the "Gravity Bible MTW" are Kip Thorne and John Wheeler. Since Weber "discovered" gravitational waves, Thorne has been committed to the study of black holes and gravitational waves, a new type of radiation.

Thorne retired from Caltech in 2009. He met Spielberg and Nolan through his old lover Lynda Obst, and participated in the writing and filming of the black hole-themed movie "Interstellar", and entered Hollywood. Every time someone asked him to do something, if he wanted to refuse, he would say that he had started a new film career and was too busy. However, he still made a comeback at the press conference in Washington DC this time, and his style was definitely no less brilliant than his brilliance in Hollywood!

In the late 1970s, Thorne persuaded Caltech to support gravitational wave research, and Drever established a gravitational wave detection laboratory at Caltech. In 1979, the National Science Foundation began to fund Drever and Thorne at Caltech, and Weiss at MIT for laser interferometer gravitational wave measurement preliminary research.

LIGO's gravitational wave sources and theoretical research

Initially, the academic community was generally skeptical about the possibility of detecting gravitational waves. In the early days, people had very little knowledge about the source of gravitational waves, and once believed that supernova explosions were the main source of gravitational wave detection. Later, through detailed calculations of supernova explosions, people inferred that the gravitational waves they emitted were far less than previously imagined.

In the early 1990s, Thorne and his collaborators realized that the gravitational waves emitted by the collision of binary black holes and binary neutron stars could have sufficient amplitude to be detected. He began to systematically promote and carry out research on astrophysics, relativistic dynamics and data analysis methods of gravitational wave sources. Although most people believe that binary neutron stars are the most reliable wave source, Thorne has always believed that binary black holes have a relatively large mass and LIGO can see at a relatively long distance, so there will be more possibilities in the corresponding volume. Therefore, although the formation process of binary black holes is not very clear, it is still possible that they will be detected first. To study the gravitational waves of binary black holes, it is necessary to first calculate the predictions of general relativity for the collision of binary black holes. Physicists use large computers to solve Einstein's equations through the method of "numerical relativity."

｜ Implementation of the LIGO Project

In the early 1990s, the LIGO project led by Drever, Thorne and Weiss received funding from the National Science Foundation of the United States to build an interferometer with an arm length of four kilometers in Washington State and Louisiana, respectively. In the earliest LIGO plan, the collision process of binary black holes and binary neutron stars was the main goal. They mentioned a three-step plan: the first step of initial LIGO can see the collision of binary black holes 500 million light-years away at the design sensitivity, and the second step of Advacned LIGO can see the collision of binary black holes 7 billion light-years away at the design sensitivity. This extra 14 times the distance is equivalent to covering nearly 3,000 times the volume of the universe. Today's Advanced LIGO has not yet reached the design sensitivity, but has already seen the collision of binary black holes 1.4 billion light-years away.

So, how many billions of light years of coverage is enough? Astronomical observations have a certain degree of randomness, but random processes can also be controlled statistically. In order not to repeat Joe Weber's mistakes, LIGO scientists must calculate the incidence of black hole and neutron star collisions within a certain volume in advance. To estimate the incidence, astronomers must comprehensively consider a series of information such as the distribution of galaxies in the universe, the formation and evolution of binary stars in galaxies, etc. In the absence of gravitational wave detection as a basis, there are large errors in the inference of these incidences. According to the best estimates at the time, initial LIGO should have only a small hope of seeing the collision of binary black holes, and almost no hope of seeing the collision of binary neutron stars. Advanced LIGO is likely to be able to easily see the collision of binary black holes, and should be able to guarantee the detection of at least a few binary neutron star collisions. From this perspective, today's success, although lucky, is not unexpected. And since we have detected an event at this sensitivity, it means that if we continue to detect at this sensitivity, more events will inevitably be detected.

LIGO's sensitivity and operation

The LIGO detector was first built in 1999, and it took five years to reach its design sensitivity in 2005. It can measure gravitational waves above 60Hz and below 10kHz, and the displacement sensitivity reaches 10^-21. What does this mean? If such a strain is used for the distance from the earth to the sun, the distance change caused is no more than one hundred thousandth of a hair. Converted to an arm length of kilometers, its sensitivity to the displacement of the test mass can reach 10-18 ^meters , which is 1/1000 of the size of an atomic nucleus!

Why can LIGO achieve a sensitivity smaller than the size of an atomic nucleus?

From the perspective of optical positioning, this is because LIGO uses very strong lasers and uses the method of optical resonance amplification. Each photon can measure the position of about one wavelength of light. When the photon propagates repeatedly in the resonant cavity 100 times, it can measure the distance change of one percent of the wavelength of light, that is, 10^-8 meters. If multiple photons are used, the sensitivity will increase by the square root of the number of photons. Therefore, 10^20 photons can achieve a sensitivity of 10^-18 meters.

From the atomic scale, it is because LIGO's beam hits many atoms, and this averaging effect allows us to measure displacements smaller than the size of a single atom. From 2003 to 2009, LIGO-1 collected some data and made an analysis. However, no gravitational waves were found in this data. From 2009 to 2015, LIGO underwent a six-year upgrade from LIGO-1 to LIGO-2, also known as Advanced LIGO.

Large gravitational wave detectors around the world

After the LIGO project in the United States began, Europe also began to carry out gravitational wave detection projects. Currently, the larger detectors are the GEO 600 detector built by the United Kingdom and Germany near Hannover, Germany, and the VIRGO detector built by France and Italy near Pisa, Italy. The wall length of the GEO 600 detector is 600 meters, while the arm length of VIRGO is 3,000 meters. In comparison, the cost and performance of VIRGO are much higher than GEO 600, but comparable to LIGO.

You may ask, why can't the economically stronger countries of Britain and Germany compare favorably with France and Italy in terms of the scale of their gravitational wave detectors? It is said that the former West Germany was also going to build a detector with a 4-kilometer arm length. However, due to the reunification of East and West Germany, West Germany supported East Germany, so the funding was cut and they had to build a 600-meter detector.

Recently, Japan has also started to build a large KaGRA gravitational wave detector. In the early years, there was a TAMA300 detector in Japan, located in Mitaka City near Tokyo, at the National Astronomical Observatory of Japan, with an arm length of 300 meters. Japanese scientists have been committed to promoting large-scale gravitational wave detection for many years, and the KaGRA project was finally approved in 2008. At present, the construction of this detector has been basically completed and has entered the debugging stage.

A few years ago, India also began to join the ranks of gravitational wave detection. The LIGO Laboratory and the Indian gravitational wave physics community have reached an agreement to ship some of LIGO's experimental equipment to India and open a LIGO-India gravitational wave observatory in India.

｜ GW150914

As the saying goes, “Man proposes, God disposes.” Looking back at 150914, its discovery was an accident, just like many great discoveries in human history.

Discover

In the official operation of LIGO, a blind injection operation is performed: a few collaborators secretly add some simulated gravitational wave signals to the data, and keep the parameters of these signals confidential. In this way, even if other people processing the data discover something, they cannot know whether it is true or false. It was not until the last moment that the host opened the envelope and announced the parameters of the secretly added signal that everyone suddenly realized it. Blind injection not only improves morale, but also prevents leaks. This method is quite effective in the operation of LIGO-1.

In September 2015, LIGO started an engineering run. Because it was just a debugging run, the blind injection mechanism was not organized, so there was no blind injection at all. Unexpectedly, some things cannot be tried casually. A gravitational wave signal with a very high confidence was discovered within a few days of the start. How big is this signal? It can be found in the waveform of the data with the naked eye after only some simple filtering. Look at the data yourself:

The collision process

Apart from reaffirming Einstein's magic, what can we learn from this detected gravitational wave event?

Judging from the frequency evolution of the wave, it starts in the low-frequency part.

Phase 1. The gravitational wave frequency of the two black holes starts at 30Hz. This is a relatively low frequency band in gravitational wave astronomy, but it means that the black holes have an orbital frequency of 15Hz. More specifically, the two black holes are 36 and 30 solar masses, each with a radius of about 100 kilometers, and the distance is 1,000 kilometers. They rotate around each other 15 times per second.

The second stage: When the two black holes are about to merge, the frequency of gravitational waves reaches 100Hz, and the orbital frequency reaches 50Hz, which means 50 revolutions per second. At this time, the two black holes are almost integrated, and the distance between their "centers" is about 200 kilometers.

The third stage. Then, the distorted black hole that merged into one continued to oscillate, gradually becoming a new, rotating black hole (the Kerr black hole). The mass of this black hole is 63 solar masses, and its radius is about 160 kilometers. During this oscillation process, the black hole mainly emits gravitational waves with a frequency of about 240Hz, indicating that it is rotating at about 120Hz, that is, 120 times per second. This process can also be seen as gravitational waves circling around the "light ball" of the black hole and gradually escaping to a distance.

Why is the final mass less than the sum of the two merging black holes? Didn't we say that gravitational waves carry energy? A portion of the mass was released in the form of gravitational waves. The energy carried by these gravitational waves is equal to 3 solar masses, which is equivalent to 5% of the "mass" converted into "energy." By the way, the gamma-ray burst, which is known as the brightest celestial body in the universe, generally releases energy equivalent to a few thousandths of the mass of the sun. The peak power of this gravitational wave reached 50 times the luminous power of the entire visible universe.

The distance of the black hole from the Earth is inferred from the absolute amplitude of the gravitational waves. Based on this inference, we know that the collision process occurred 1.4 billion light years away. Corresponding to the "redshift" in standard cosmology, the redshift of this event is 0.09. When this event occurred, the "size" of our universe was 91% of the current size.

significance

The above three processes allow us to "see with our own eyes" the existence of black holes for the first time . Since gravitational waves can be seen as directly driving the mechanical vibration of the mirror, we can also say that we heard the existence of black holes with our own ears !

Why do we know that two black holes become one black hole? Here is a rough explanation. The mass of a single object can be measured by the amplitude and frequency of the waveform evolving over time. The conversion in the first and second stages above allows us to infer the size of each object and thus determine that they are all black holes. In the third stage, the frequency and decay rate of the waveform allow us to infer the existence of the "light ball" that finally forms the black hole and the geometric structure near the light ball.

LIGO scientists also tested the predictions of relativity based on the waveform of the gravitational wave, and found no difference from relativity within the statistical error range. Roughly speaking, the waveform is consistent with the predictions of relativity at different times and frequencies, and no systematic differences were found.

One of the more distinctive tests is the test of the propagation speed of gravitational waves. Without other methods for comparison, how can we prove that gravitational waves propagate at the speed of light? The simple answer is that for this event, since there is no other method for comparison, we can only indirectly test the propagation of gravitational waves. Since the waveforms in different frequency bands are consistent with the predictions of general relativity, we can infer that the propagation speed of gravitational waves at different frequencies is consistent. Waves with the same propagation speed at different frequencies should generally propagate at the speed of light according to the requirements of "covariance of special relativity". So, in this sense, this is also a partial and indirect verification of the property that gravitational waves propagate at the speed of light.

｜ Gravitational wave astronomy

Directly detecting the collision of two black holes is only the beginning of gravitational wave astronomy. Even if you guess the beginning, you can never guess the end! Because there is no end!

GW150914 is just the beginning of the study of gravitational waves from binary black holes. More binary black hole events will allow us to understand in more detail the geometry of spacetime near black holes, as well as the geometric dynamic properties of spacetime when black holes collide. In the next step, using LIGO, we are also looking forward to the discovery of binary neutron stars and black hole neutron star collisions. These will also allow us to understand the internal structure of neutron stars. Furthermore, LIGO also hopes to detect continuous gravitational wave radiation emitted from a single neutron star, or even background gravitational wave radiation. LIGO has opened a new window to explore the universe, and what is even more exciting is that gravitational wave bursts from some unknown sources may also be detected.

Most gravitational wave sources also emit traditional astronomical "messengers" when emitting gravitational waves: electromagnetic waves, neutrinos and cosmic rays. Combined with the messengers of traditional astronomy, further joint observations of the gravitational wave-multi-messenger counterparts-host galaxies system will not only help improve the accuracy of gravitational wave positioning and parameter estimation, but also provide more understanding of the nature of gravitational wave multi-messenger counterparts.

After Advanced LIGO, we hope to improve the accuracy of ground-based gravitational wave detectors, so as to detect more binary black holes, binary neutron stars , neutron star-black hole binaries, etc. This will provide more accurate data on the formation and evolution of black holes, and will enable us to directly infer more interesting problems in physics, astronomy, and cosmology, such as the equation of state of neutron stars and the equation of state of dark energy. Adding more events and detecting signals with higher signal-to-noise ratios will also help to accurately study the properties of black holes and make more detailed comparisons with general relativity.

Furthermore, we want to build gravitational wave detectors in space. In space, the distances between objects are longer, and there is no vibration disturbance on the ground, so we can observe low-frequency gravitational waves and explore interesting phenomena such as the rotation of supermassive black holes and the rotation of small black holes around large black holes, so as to understand the process of galaxy formation and further understand the space-time structure around black holes.

The following is an exclusive interview with Professors Chen and Fan by Zhishe Academic Circle

Yanbei Chen is a professor of physics at the California Institute of Technology and a fellow of the American Physical Society. He received his Ph.D. from the California Institute of Technology in 2003 under the guidance of Kip Thorne. He returned to Caltech as an assistant professor in 2007 and was promoted to full professor in 2013.

Fan Xilong is an associate professor of physics at Hubei Second Normal University and a member of the Chinese Society of Gravitational and Relativistic Astrophysics. He visited the Max Planck Institute for Gravitational Physics in Germany for one year from 2006 to 2007, studying with Chen Yanbei, Wen Linqing and others. In 2008, he obtained a master's degree from Beijing Normal University under the guidance of Professor Zhu Zonghong. In 2012, he obtained a doctorate from the University of Trieste, Italy. He has received funding from the Royal Society's "Newton International Fellowships" and the National Natural Science Foundation of China.

Chen Yanbei (right) and Fan Xilong (left) in their office at Caltech

Zhishe: Can you introduce your work in the LIGO Scientific Alliance and your contribution to gravitational wave detection?

Chen Yanbei: When I entered Caltech in 1999, I didn’t have much purpose. But after listening to Kip Thorne’s lectures, I felt that he was an interesting professor: he not only had a wide range of interests, but he could often solve very complex problems with very simple methods. At that time, I felt that my mathematical foundation was not very good, and I didn’t dare to study particularly abstract high-energy physics theories. I was also clumsy and couldn’t do experiments, so I decided to follow Kip Thorne.

Starting in 1980, Kip Thorne and his student Carlton Caves, and collaborators Vladimir Braginsky and Farid Khalili of Moscow State University, were working on the sensitivity of LIGO, which involved the theory of continuous measurements of single quantum objects, an issue that I was particularly interested in when I first enrolled.

I started by doing some quantum optical calculations with a postdoc, Alessandra Buonanno. Now Alessandra is one of the directors of the Max Planck Institute for Gravitational Physics in Germany, and played a decisive leading role in the analysis of this gravitational wave event. Later, these calculations could be used to calculate the noise caused by the quantum fluctuations of light in the optical structure of Advanced LIGO. In fact, our formula has not been used yet because Advanced LIGO does not use enough laser light intensity. I have continued to calculate quantum noise and study the optical design of the next generation of LIGO. My second work during my doctoral studies was also with Alessandra and two other graduate students, Michele Vallisneri and Pan Yi, to study how to optimally extract the signal of binary black holes in the first generation of LIGO. At that time, numerical relativity simulation was not yet mature, so we were all considering how to use the results of perturbation theory in LIGO data analysis.

After graduating from my PhD, I went to the Max Planck Institute for Gravitational Physics in Germany and continued to participate in LIGO research. During the last few years of my PhD at Caltech and in Germany, initial LIGO was extracting data but had not detected gravitational waves. However, since everyone thought that LIGO might also discover gravitational waves, the Humboldt Foundation in Germany gave me a Sofja Kovalevskaya Award and let me lead a research team. During those years, I mainly studied the quantum measurement of macroscopic objects and how to use LIGO as a tool to test quantum mechanics. I also collaborated with Professor Kawamura of the National Astronomical Observatory of Japan on the design of some space gravitational wave detectors, and with Linqing Wen, a postdoctoral fellow at the Max Planck Institute (now at the University of Western Australia), on the study of multi-detector gravitational wave data analysis strategies. I also did some space gravitational wave detector design and gravitational wave data analysis strategies. The Phenominological Template Bank, which I invented with P. Ajith, a graduate student at the Max Planck Institute at the time, and Martin Hewitson, a postdoctoral fellow, is now an important method in LIGO binary black hole data processing .

After returning to Caltech, I continued to do research on quantum measurement and LIGO optical design. I also worked with Professor Rana Adhikari of Caltech to do some research on thermal noise of optical devices in LIGO. In general relativity, I began to study black hole perturbation theory and some characteristics of geometric dynamics when black holes merge. In data analysis, I worked with Professor Linqing Wen of the University of Western Australia to develop a data processing solution for quickly extracting neutron star merger waveforms. This solution is being implemented by Professor Wen in LIGO.

Zhishe: Did you have confidence in detecting such weak gravitational waves at the beginning? Did you have any doubts in the middle? What was your feeling when you saw the data?

Chen Yanbei: For me personally, LIGO has given me a great opportunity to study a variety of physical problems. Even if LIGO has not detected gravitational waves, there are still many interesting problems to study. For example, quantum optics, general relativity and black hole physics, data analysis methods, and some knowledge of non-equilibrium thermodynamics. In the first ten years of my scientific research career, I feel that I have tried and learned a lot. For me, the success of the binary black hole detection may be a turning point. I may have to focus more on studying problems related to black holes in the future.

Fan Xilong: The first time I noticed this event was at Beijing Normal University. At that time, my colleagues and I were planning to hold a gravitational wave astronomy seminar. In addition, we had blind injections before, so we didn't pay much attention to it. Around September 16, 2015 , I discussed this signal with LVC members from the University of Glasgow in the Normal University cafeteria during breakfast time. My point of view was that if it was true, it would be too lucky. I didn't believe it . Interestingly, due to the principle of confidentiality, we could not mention anything about gravitational waves. If people nearby listened carefully, they would hear the English version of the conversation: "Is that event true?" "Is it possible? No way!" "That thing is too obvious!" During our conversation, Professor Zhu Zonghong from the Department of Astronomy came over. He is a gravitational wave expert who is not a member of the LVC. The situation was that we suddenly stopped talking and everyone looked at each other. It was very interesting.

My level of skepticism about the signal did not change until an LVC conference call, where the blind injection team said there was no known signal injection behavior, and then the instrument team said the data was clean. I had a glimmer of faith that we might have really done it. At 1:36 a.m. on January 22, 2016, after a short wait with trembling all over my body, I burst into tears because the LVC conference call announced: LVC collectively voted to submit the 10th edition of the "Detection Article". I knew we had done it.

Even now, my heart still beats faster when I think of this discovery.

Zhishe: What is the probability of such an astronomical event? Are you lucky to detect such a strong signal during the debugging and operation? Will it be detected frequently in the future?

Chen Yanbei: Astronomical observations cannot be left entirely to chance. For LIGO, we inferred the probability of detecting an event per unit time at a certain sensitivity based on some knowledge in astronomy. Although this probability itself has a large uncertainty, LIGO also took this issue into consideration when designing it. So, to a certain extent, it is not surprising that Advanced LIGO was able to detect this event. And it was also expected that initial LIGO could not see anything. Since we have detected an event at this sensitivity, it means that more events are bound to be detected.

Zhishe: What impact does LIGO's detection of gravitational waves have on China's Tianqin project?

Chen Yanbei: Academician Luo Jun of Sun Yat-sen University is a leading figure in China's gravitational physics community. His research on the measurement of the gravitational constant and the verification of the law of gravity are at the forefront of the world. Academician Luo's team recently proposed the "Tianqin Project", which is to measure gravitational waves in space. In space, we can measure gravitational waves with lower frequencies. On the one hand, it can verify the LIGO gravitational wave source and the nature of gravitational wave propagation from the side, and on the other hand, it may also detect massive or even supermassive black holes. I hope that this time LIGO's detection of gravitational waves will be a boost to the Tianqin Project.

Zhishe: The speed of gravitational waves is consistent with the speed of light. Is there any intrinsic connection here, or is it just a coincidence? Is it possible to provide a direction for the grand unified theory?

Chen Yanbei: This is a very profound question. In general relativity, when the wavelength of gravitational waves and light waves is much smaller than the radius of space-time curvature, their propagation can be regarded as propagating along the so-called "light-like geodesics". The so-called light-like geodesics can be said to be the fastest path to escape from a point in space-time geometry. When the wavelength can be compared with the radius of space-time curvature, the propagation of gravitational waves and light waves is different. The wavelength of the gravitational waves detected this time is much smaller than the radius of space-time curvature in the universe, so the propagation speed should be the same as that of light. The existence of gravitational waves and the propagation of gravitational waves at the speed of light are already a very recognized phenomenon in theoretical physics. Therefore, the detection of gravitational waves itself should not contribute to the grand unified theory.

Zhishe: Finally, let me ask a question on behalf of science fiction fans: Can we use gravitational waves to achieve interstellar travel and time travel?

Chen Yanbei: A few years ago, when I was in Germany, I had a postdoctoral fellow from Japan named Kentaro Somiya. Professor Somiya is an experimental physicist and now an associate professor at Tokyo Institute of Technology. He is an important participant in Japan's gravitational wave detector KaGRA. Professor Somiya and I are both fans of Doraemon . When we were in Germany, we often drove from Potsdam to Hannover and chatted on the way. I remember he told me that the reason he participated in gravitational waves was because he felt that discovering gravitational waves and black holes was the first step to building the "time machine" in Doraemon.

Professor Zong Gong may have been naive at the time, but we should not forget that Joe Weber's "naivety" led to the discovery of binary black holes 50 years later. If we detect any clues that are inconsistent with the current general relativity through gravitational wave observations, it may lead to a breakthrough in basic theory.

[Author introduction] Zhishe Academic Circle is a public welfare academic exchange platform initiated by overseas returnees, aiming to share academic information, integrate academic resources, strengthen academic exchanges, and promote academic progress. Note: This article is an exclusive interview with Zhishe. If you need to reprint it, please contact Zhishe.