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This article is from the official account of Wechat: back to Park (ID:fanpu2019), by Chen Xuelei (researcher of the National Astronomical Observatory of the Chinese Academy of Sciences)

Dark matter has always been one of the big problems to be solved in physics. Astronomers have found that the actual observed velocity of galaxies can not be explained by conventional dynamics, and more sources of gravity are needed, so they propose to introduce "invisible" dark matter, which is the current mainstream theory. But there is not only one explanation for dark matter phenomena. There is a competing scientific theory, modified Gravity Theory (MOND)-to explain dark matter phenomena by modifying Newtonian dynamics without introducing dark matter. Is it an excellent theory? Where are its successes and challenges? This paper will briefly introduce this theory and compare it with the dark matter model theory.

In popular science lectures or friend gatherings, I often need to explain the concept of "dark matter" to amateur listeners. I will tell them that today's astronomers have found that ordinary matter as we are familiar with accounts for only about 4.7% of the total density of the universe, while more than 95% of the density comes from two unknown components: dark matter (about 25%) and dark energy (about 70%). People often ask a powerful question: "you say that the evidence of dark matter comes from its gravity. Is it possible that you astronomers have got gravity wrong?" Some of the more skeptical friends said, "maybe one day, there will be no dark matter at all, just like there is no ether." I think these questions are very good and reflect a healthy scientific skepticism. In fact, although limited time may not be mentioned in popular science reports or articles, trying to explain the "dark matter phenomenon" with a new gravitational theory without introducing dark matter is also a school in astrophysics research, that is, the so-called modified gravitational theory school.

The problem of dark matter what is now called the problem of dark matter was first discovered in the 1930s. At the time, astronomer Fritz Zwicky (figure 1), who works at the California Institute of Technology, measured the speed of galaxies in a cluster. Based on these velocities, we can calculate how strong gravity is needed to bind them; on the other hand, we can also measure the total brightness of galaxies in the cluster, and then estimate how many stars are there based on the average brightness of stars, and then calculate the mass of stars from the ratio of mass to luminosity (mass-to-light ratio for short). As a result, Zwicki found that the gravity produced by the mass of stars in the cluster is not enough to bind these galaxies, and it is necessary to assume that there is a lot of non-luminous material in the cluster, which may be many times the number of stars. Zwicki calls these non-luminous matter dark matter.

For nearly 40 years, Zwicki's dark matter hypothesis, although widely known, has not attracted much attention. Galaxy clusters are places with high galaxy density in the universe, only a small number of galaxies in the universe are in galaxy clusters, and most galaxies are not in galaxy clusters, so this phenomenon is not a common phenomenon. Astronomers see so many strange and inexplicable phenomena that it is an isolated phenomenon in the absence of a complete and reliable physical image or model of celestial bodies.

Figure 1. Fritz Zwicky (left) and the Coma cluster he studied, but in the 1970s, people observed the rotation curves of our Milky way and many other galaxies-that is, the rotation speeds of stars or gas at different distances to the center of the galaxy. The rotation speed of stars or gas should be related to their gravitational force. Stars in the center of a galaxy are denser, while the density of stars at the edge is lower, and the distance from the center is farther away, so the farther away from the center, the lower the gravity should be. Then its rotation speed should be slower. However, the actual observation is not the case, most of the galaxy rotation curve tends to be a constant, which is the so-called "flat rotation curve" (figure 2). Even, people can use radio telescopes to look at the rotating gas of neutral hydrogen gas in galaxies, which is much larger than the disk formed by stars, so it can be seen that there are almost no stars at the edge of these gases, and the amount of these gases themselves is small, so the gravity here should have dropped, but the rotational speed of these gases has not decreased.

Figure 2. The rotation curve of the galaxy. If only the gravity caused by the distribution of stars (dots) or gas (dots) visible in the galaxy is taken into account, the rotation speed will be smaller than the observed value and will decrease with the increase of the distance to the center. The combination of dark halos, star disks and gas can explain the observed rotation curves. One possible explanation for this phenomenon is "dark matter", a kind of matter that does not emit light and therefore cannot be seen by us, assuming that it is spherical in a larger range than the disk formed by luminous stars and the gas disk. Form the so-called dark matter halo (figure 3). When we are farther away from the center of the galaxy, a large part of the gravity there actually comes from this dark matter halo, so that the rotation speed caused by this gravity will not decrease to a certain extent. In order to provide such a strong gravity, the total amount of matter in these halos is much larger than that of the visible disk of galaxies. Just like any complex scientific issue, there are many technical details in the observational evidence and theoretical explanation of dark matter, which have caused a lot of controversy. But in the early 1980s, with the improvement of observation methods and the accumulation of data, the evidence became more and more persuasive, and most astronomers accepted the idea that there was a large amount of dark matter in the universe (far more than visible matter). The dark matter model has become the mainstream research paradigm.

Figure 3. Dark matter halo around galaxies 02, modify Newtonian dynamics, of course, there are people who don't want to follow the crowd. In 1980, Mordehai Milgrom (figure 4), a 34-year-old Israeli physicist, took an academic vacation to visit the Advanced Research Institute in Princeton, the mecca of theoretical physics, during which he proposed a new explanation. Perhaps, Milgrom points out, there is no dark matter halo, but the laws of gravitation or motion that we are used to need to be modified [1, 2].

Figure 4. Before Mordehai Milgrom, an Israeli physicist, Newton's law of universal gravitation was generally accepted. Although Einstein's general theory of relativity is a revolution to Newton's theory, the difference between it and Newton's theory is mainly obvious when the speed of motion is close to the speed of light, or the scale involved is close to the radius of curvature of space-time. For the rotation curves of galaxies, there is little difference between the predictions given by Newton and Einstein's theory. However, whether it is Newton's theory or Einstein's theory, the direct test is on the solar system scale, while there is no direct experimental verification on the galactic scale. Therefore, we cannot rule out the possibility that gravity does not conform to Newton or Einstein's theory on this scale.

The model proposed by Milgrom is a theory based on the law of experience. He assumes that when the strength of gravitation (the magnitude of gravitational acceleration) is relatively large, the gravitation on an object can be described by the formula of Newtonian gravitation, but when it weakens to a certain extent, it deviates from the standard Newtonian dynamics. Specifically, the law of motion that we are familiar with is Newton's second law of motion F=ma, that is, the acceleration of a body times mass equals force. He changed this law to

(1)

Here a0 is a new constant in theory, and the correction factor μ (a / a0) is a function of a / a0, which satisfies μ (x > > 1) ≈ 1, μ (x)

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