In 1915, Albert Einstein first proposed the general theory of relativity. In general relativity, the gravitational pull between matter is interpreted as a geometric effect of the curvature of space-time. In the early summer of 1916, Albert Einstein obtained the gravitational field wave equation for the first time in a four-dimensional space-time under the condition of a weak gravitational field and a linearly approximate vacuum: [1-3]. This equation shows that the perturbation of space-time will propagate outward at the speed of light, and this wave that causes the curvature of space-time to change is called gravitational wave. Therefore, in 1916, Albert Einstein boldly predicted the existence of gravitational waves, and he published the first research results on gravitational waves in the Proceedings of the Prussian Academy of Sciences. Since then, the prelude to human research and detection of gravitational waves has officially begun.
In daily life, we are more familiar with electromagnetic waves, which are widely used, which are formed by electromagnetic fields that are disturbed in space. Whereas, gravitational waves are perturbations of the curvature of space-time propagating in space-time in the form of waves, i.e., gravitational waves are ripples in space-time. However, there are some similarities and differences between gravitational waves and electromagnetic waves in some physical characteristics. Although in the direction of propagation they are both transverse waves, in a vacuum they both propagate at the speed of light. Transverse waves have polarization modes, however the polarization of gravitational waves and electromagnetic waves is very different in nature. The two polarization modes of electromagnetic waves are perpendicular to each other, and their polarization is defined by the direction of the electric field. However, the two polarization modes of gravitational waves are angled, and the two polarization modes are described by the geodesic deviation equation [4].
Figure 1: The polarization mode of the gravitational wave causes the space-time to stretch and compress in the two axes of the plane, and the polarization mode of the gravitational wave causes the space-time to stretch and compress in the direction of the axis of the plane
Figure 2: The two polarization modes of the gravitational wave cause the deformation of the test particle ring at different phases
Modern astronomical observations and theories suggest that there may be two types of gravitational waves in the universe. The first is the possible primordial gravitational waves (PGWs), which are generated by the gravitational pull in the early universe ( ) and quantum fluctuations between matter. Based on current astronomical observations, cosmologists speculate that there was a physical process of "inflation" in the very early universe at that time, a mechanism that caused the universe to expand violently within its birth by nearly twice its original volume. During the inflationary phase, the energy scale of particles in the universe is so high that the gravitational field, like other material fields, has some quantum perturbations. The quantum perturbation of this gravitational field will be elongated with the expansion process of the universe, so that its wavelength will be much larger than the scale of the cosmic horizon at that time, and eventually become the primordial gravitational wave that has been classicized. If primordial gravitational waves are detected, then they could serve as a key evidence of the very early cosmic inflation process. The second is the strong gravitational waves generated by the orbit and merger of dense binary star systems (binary black holes, binary neutron stars, binary white dwarfs, black holes and neutron stars, etc.), and their rotation and merger will cause the system to lose a large amount of energy, and the energy lost by the system will propagate into space in the form of gravitational radiation (gravitational waves). For the orbiting Sun-Earth system, calculations show that the radiation power of the gravitational wave emitted by the orbiting system is very low, and the gravitational wave signal is so weak that it is difficult to detect. However, for a near-range, supermassive neutron star or black hole binary system, the gravitational radiation power is even greater than the combined power of all the stars in the observed universe, and the strong gravitational wave signal emitted by such a gravitational wave source is more easily detectable.
Of the four fundamental forces in nature, gravity is the weakest interaction, so the accuracy of the instrument must be on the order of magnitude to detect gravitational waves. To put it more figuratively, when gravitational waves pass near the Earth, the length between the Sun and the Earth changes by only one atomic diameter. In 1957, physicists Feynman and Bondi made a bold prediction based on relevant theoretical calculations: if gravitational waves existed, they could theoretically be detected.
In modern physics, the detection of gravitational waves by human beings has a difficult and tortuous history. The timeline of the story goes back to 1918, when Weber first claimed to have successfully detected gravitational waves with his resonant mass detector (Weber's rod), which was also the world's first gravitational wave detector. However, the sensitivity of his instrument was only , and the results were wrong, but he also accumulated experience for subsequent laser interferometer detectors. Between 1974 and 1978, two United States physicists, Taylor and Hulse, discovered a pair of rare binary star systems, with extremely significant relativistic effects and a clean space environment that provided valuable conditions for testing binary orbital changes caused by radiating gravitational waves. Taylor and Hulse were awarded the Nobel Prize in Physics in 1993 for their discovery. The scientific exploration of the universe is never-ending, and the discoveries of Taylor and Hulse have further promoted the experimental detection and research of gravitational waves by subsequent scientists.
图三: Taylor和Hulse
In 1984, United States physicists Weiss, Drever and Thorne led their research team to set up a laser interferometer detector called "LIGO" (Laser Interferometer Gravitational-Wave Observatory) to detect extraterrestrial gravitational wave signals, and its detection principle is the Michael Erson laser interferometer. The next seven years were not smooth for LIGO because many scientists, including Albert Einstein, had previously failed to believe that gravitational waves could be detected, and Weber's reputation was discredited by erroneous gravitational wave detections. Thorne et al. have always insisted that gravitational wave detection is a supplement to traditional electromagnetic wave astronomy, and after his lobbying and scientific efforts, the LIGO team finally received funding support from the United States National Science Foundation in 1991.
After years of construction and improvement and the relay of generations of researchers, the LIGO detector finally succeeded in detecting a brief gravitational wave signal on September 14, 2015 after upgrading to Advanced LIGO. The gravitational wave signal is sourced from two large black holes with masses of 36 and 29 solar masses swirling around each other, and this gravitational wave case was named GW150914 in honor of the extremely unusual day when the gravitational wave signal was discovered for the first time in the history of human science. In 2017, three physicists, Weiss, Barish and Thorne, were awarded the Nobel Prize in Physics for their important contributions to the logo.
图四：Rainer Weiss 、Barry C. Barish和Kip S. Thorne
A hundred years ago, Albert Einstein thought that gravitational waves could not be detected by humans. But 100 years later, in 2015, LIGO did it! Now that the existence of gravitational waves has been confirmed, can the quantum gravitational problem that has plagued the contemporary theoretical physics community for many years be solved, and will humans be able to detect traces of gravitons in gravitational waves? Theoretically, it is very difficult to detect gravitons from gravitational waves, and it is like looking for a needle in a haystack.
Recently, three physicists, such as Parikh, Wilczek, and Zahariade, have suggested that it is theoretically feasible [5], and that humans may be able to detect the presence of gravitons indirectly by finding the noise of gravitons in more sophisticated gravitational wave detectors in the future. When gravitational waves pass through two gravitational wave detectors, the spatial distance between the two detectors is elongated or compressed. When the graviton in the gravitational wave collides with the detector, the graviton carrying the mass will cause the mass of the detector to fluctuate randomly, which is the noise of the graviton. If the noise of gravitons were detected one day, the graviton predicted by the Standard Model of particle physics would also be confirmed, which would be a big breakthrough in physics.
Figure 5: LIGO detector based on the detection principle of Michael Ersun laser interferometer
The development of scientific and technological civilization is finally to serve human society, just like the electromagnetic wave technology widely used in today's society, it is believed that in the near future, human beings can also use gravitational waves as interstellar communication, although this is a big technical problem at present. In the science fiction movie "Interstellar", the male protagonist Cooper enters a five-dimensional space constructed by future people, in which Cooper transmits information to the past four-dimensional space-time through gravitational waves. The M theory of quantum gravity states that the space-time that makes up the universe is 11 dimensions, but we humans live in a four-dimensional space-time composed of three-dimensional space and one-dimensional time. So whether gravitational waves can detect additional high-dimensional space-time with more than four dimensions [6] is believed to be possible in the future development of gravitational wave technology.
图六：LIGO Livingston和LIGO Hanford
This approximation means that the Riemannian space-time gauge describing the curved can be approximated by a flat Min-style space-time gauge plus a perturbation term , where the determinant value of the gauge tensor satisfies and .
where is the d'Alembert operator: , c is the speed of light propagating by gravitational waves in a vacuum.
A mechanical wave in which the direction of vibration and the direction of propagation are perpendicular to each other is called a transverse wave, and a transverse wave has a polarization phenomenon.
Geodesic refers to the shortest path between two points in a Riemannian surface that describes a four-dimensional curved space-time. In general relativity, free particles in a gravitational field move along a geodesic line.
Quantum electrodynamics and particle physics can explain the nature of electromagnetic interactions, strong and weak interactions: it is photons that transmit electromagnetic interactions, gluons that transmit strong interactions, and intermediate bosons, and and weak interactions. However, the quantization of gravitational interaction is a major unsolved physical problem, and superstring theory is a set of quantum gravitational theories generally accepted in the physics community, which believes that gravitational interactions are transmitted by gravitons generated by closed-string excitation.
About the Author
Siyi Zhou, graduated from the University of Science and Technology of China with a bachelor's degree in 2014, entered the Wang Yi research group of the Hong Kong University of Science and Technology for a Ph.D. in the same year, joined the Bo Sundborg research group at Stockholm University in 2019 as a Ph.D., and joined the Toshifumi Noumi research group of Kobe University in 2021 as a special researcher for foreigners.
Guo Changzhong, graduated from Nanchang University in 2023 with a master's degree, is a high school physics teacher at Bailuzhou Middle School in Ji'an. His research interests include general relativity and quantum field theory. His current research interests mainly focus on the problem of black hole information in high-dimensional space-time and the entangled entropy in two-dimensional conformal field theory.
References (swipe to view)
[1] Michele Maggiore, Gravitational Waves Volume1: Theory And Experiments [M]. Oxford University Press, 2008.
[2] Wang Yunjiu, Gravitational wave detection [M], Science Press, 2020.4.
[3] S. M. Carroll, Spacetime and Geometry [M]. Cambridge University Press, 2019
[4] Shu Fuwen, Feng Jiaqian, Gravitational Waves: The "Sound" of the Universe[J]. SCIENCE, VOL. 74, NO. 6
[5] M. Parikh, F. Wilczek, and G. Zahariade, “The noise of gravitons”, Int. J. Mod. Phys. D 29 (2020) 2042001.
[6] Hao Yu (喻豪), Zi-ChaoLin (林子超) and Yu-Xiao Liu (刘玉孝), Gravitational Waves and Extra Dimensions：A Short Review [J]. Commun. Thror. Phys. 71 (2019) 991
Source: Institute of Theoretical Physics, Chinese Academy of Sciences
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