What is General Relativity?

General Relativity A theory that describes the gravitational interaction between matter. The foundation was completed by A. Einstein in 1915 and officially published in 1916. For the first time, this theory explained the gravitational field as a curvature of time and space. ^[1]

Simply put, the two basic principles of general relativity are:

Equivalent principle : divided into

Equivalent principle

Einstein proposed the "equivalent principle", that is, gravity and inertial force are equivalent. This principle is based on the equivalence of gravitational mass and inertial mass. According to the principle of equivalence, Einstein extended the principle of special relativity to the principle of general relativity, that is, the form of the laws of physics is constant in all reference frames. The equation of motion of the object is the

Mercury precession

In 1859, astronomers

Einstein's fourth hypothesis is a generalization of his first hypothesis. It can be expressed as follows: the laws of nature are the same in all departments.

Admittedly, it sounds more "natural" to claim that the laws of nature are the same in all departments than to claim that the laws of nature are the same in the Galileo system. But we don't know if (external) a Galileo system exists.

This principle is called "Principle of General Relativity"

Causal structure and global geometry

An infinite static Minkowski universe

If general relativity is one of the two pillars of modern physics, then quantum theory, as the basic theory we use to understand basic particle and condensed matter physics, is another pillar of modern physics. However, how to apply the concepts in quantum theory to the framework of general relativity is still an unsolved problem. ^[11]

In gravity and

The principle of general relativity and the principle of equivalent special relativity hold that all physical laws are the same in different inertial reference systems. On this basis, Einstein has taken a big step forward and believes that the physical laws are the same in any reference frame (including non-inertial frames). This is the principle of general relativity.

The following introduces another basic principle of general relativity-the principle of equivalence.

Equivalent principle

Assuming that the spacecraft is completely closed, the astronaut has no connection with the outside world, then he has no way to judge whether the force that causes the object to fall at a certain acceleration is gravitational or inertial. In fact, not only the free-fall experiments, any physical process inside the spacecraft cannot tell us whether the spacecraft is accelerating or mooring on the surface of a planet. The scenarios mentioned here are very similar to those in the Galileo ship described in the first section of this chapter. This fact reminds us that a uniform gravitational field is equivalent to a frame of reference that performs uniform acceleration. Einstein regarded it as the second basic principle of general relativity, which is the famous equivalent principle.

From these two basic principles, some unexpected conclusions can be directly drawn. Suppose there is a spaceship in a space where the gravity can be ignored, and it performs a uniformly accelerating linear motion, and a beam of light enters the spacecraft perpendicular to the direction of motion. Observers who are stationary outside the ship will of course see that this beam of light propagates in a straight line, but observers in the spacecraft seeing the spacecraft as a reference frame are another scene. In order to record the track of the light beam in the spacecraft, he placed some translucent screens (as shown in the figure) at a medium distance from the ship. Light can pass through these screens while leaving spots on the screen. Because the spacecraft is advancing, the position of the light reaching the next screen is always closer to the stern than the position of the previous show. If the spacecraft moves in a straight line at a uniform speed, when the light flies between any two adjacent screens, the distance the spacecraft advances is equal, and the observer on the spacecraft sees the light trail as a straight line (as the dotted line in the figure), The direction of the straight line is different from that seen by a stationary observer outside the ship. If the spacecraft moves in a straight line with uniform acceleration, the speed of the spacecraft will continue to increase while the light propagates to the right, so the track of the light recorded by the observer on the ship is a parabola (as shown by the solid line in the figure).

According to the principle of equivalence, observers in the spacecraft can completely think that the spacecraft does not accelerate, but there is a huge object in the direction of the stern, and its gravitational field affects the physical process in the spacecraft. Therefore we conclude that the gravitational force of an object can bend light.

Generally, the gravitational field of an object is too weak, and only the bending of light caused by the gravitational field of the sun can be observed in the early 20th century. Due to the gravitational field of the sun, we may see stars behind the sun (pictured). However, the usual bright sky prevents us from stargazing, so the best time is when a total solar eclipse occurs. On May 29, 1919, there was a total solar eclipse, and the two British expeditions went to the Gulf of Guinea and Brazil for observation. The results fully confirmed Einstein's prediction. This is the earliest verification of general relativity.

The time interval is related to the gravitational field. The existence of the gravitational field makes the time course different in different positions in space.

General relativity (2 photos)

We examine a large rotating disc (pictured). Seen from the ground, all points on the disc are accelerating except the position of the rotation axis. The closer to the edge, the greater the acceleration, and the direction points to the center of the disc. It can also be seen from the ground that the closer to the edge point, the greater the speed. According to the special theory of relativity, the more the same process takes place near the edge, the longer this process lasts. In other words, the time process near the edge is relatively slow.

This phenomenon is studied with the disc itself as the reference frame. People on the disc believe that there is a gravitational field on the disc, the direction of which is from the center of the disc to the edge. Since the time process near the edge is relatively slow, the person on the disk can conclude that the time process is slower at the position with lower gravitational potential.

There is a class of stars in the universe. They are small but not small. They are called dwarfs. The gravitational force on the surface of dwarf stars is very strong, and the gravitational potential is much lower than the surface of the earth. The time course of the dwarf star is relatively slow, and the atoms there emit light at a lower frequency than the same kind of atoms on the earth, which looks reddish. This phenomenon is called gravitational redshift and has been confirmed in astronomical observations. Modern technology can also verify the gravitational redshift on the earth.

The length of the rod is related to the gravitational field. The rotating disc is still under investigation. The same rods are placed at different positions on the disk, and their speed with the disk is different. According to the special theory of relativity, their lengths are different. The closer they are to the edges, the shorter the rods are. People on the disc also observed this difference, but he used the disc as a frame of reference, and thought that the disc was stationary. At the same time, he also thought that there was gravity at each point on the disc, which pointed to the edge of the disc, so he concluded: gravity The lower the position, the shorter the length of the rod.

The length of the rod is related to the distribution of the gravitational field. This phenomenon reflects the fact that the actual space is not uniform due to the existence of matter, which is very different from our previous ideas. For example, the grid on a piece of cloth is neat (see Figure A). If you press down with your hands, the grid will bend (see Figure B). Physics borrows the word "curvy", and it is generally said that the actual space is curved due to the existence of matter.

Planets move around the sun in elliptical orbits, sometimes closer to the sun and sometimes further away. The huge mass of the sun bends the space around it. As a result, the long axis of its orbit is deflected by an angle from the previous cycle every revolution of the planet. This phenomenon is called the precession of planetary orbits. Theoretical analysis shows that only the precession of Mercury's orbit is significant, reaching about 0.01 ° per century. This phenomenon was discovered long before the emergence of general relativity, but it could not be explained, so it is actually the earliest proof of general relativity.

General Relativity and Geometry Finally, we return to the rotating disc. The special theory of relativity tells us that only the length along the direction of movement changes, and the length perpendicular to the direction of movement does not change; if the disk is used as the reference frame, it can be said that the spatial scale along the direction of gravity has not changed, only the perpendicular to The spatial scale of the direction of gravity has changed. This is of profound significance, because at this time the circumference and diameter of the disc are measured, their ratio is no longer 3.141 59 ... but other values, and the sum of the internal angles of the triangle will not be 180 ° ... In short, because the actual space is curved, the geometry we have learned is no longer applicable.

Geometry reflects people's understanding of spatial relationships. Historically, people only encountered weak gravitational fields on a relatively small spatial scale. In this case, the curvature of space can be ignored. On this basis, humans have developed Euclidean geometry, which reflects the reality of flat space. General relativity tells us that real space is curved, so the description of real space should be more general non-Euclidean geometry. However, as a special case of non-Euclidean geometry, Euclidean geometry is still correct within its scope of application and will continue to play a role.

After Einstein published the special theory of relativity in 1905, he began to think about how to incorporate gravity into the special relativity framework. Starting from the ideal experiment of an observer in a free-fall state, he began an exploration of the theory of relativity of gravity for eight years from 1907. After many detours and mistakes, he spoke at the Prussian Academy of Sciences in November 1915, and its content was exactly the famous Einstein's gravitational field equation. This equation describes how matter in space and time affects the space-time geometry around it and becomes the core of Einstein's general theory of relativity [1].

Einstein's gravitational field equation is a system of second-order nonlinear partial differential equations. Mathematically, it is very difficult to ask for a solution to the equation. Einstein used a number of approximations to derive many initial predictions from the gravitational field equations. However, as soon as genius astrophysicist Carl Schwarzschild obtained the first non-mediocre exact solution of the gravitational field equation in 1916, the Schwarzschild metric, this solution is the final stage of studying the gravitational collapse of a star The theoretical basis of black holes. In the same year, research work to extend Schwarzschild geometry to charged masses also began, and the final result was the Ressler-Nostrom metric, which corresponds to a charged static black hole [2 ]. In 1917, Einstein applied the theory of general relativity to the entire universe and opened up the research field of relativity cosmology. Considering that the theory of the static universe was still widely accepted in the same period of cosmological research, Einstein added a new constant to his gravitational field equation, which is called the cosmological constant term. "Observation" corresponds to [3]. By 1929, however, observations by Hubble et al. Showed that our universe was in an expanded state, and the corresponding expanded universe solution had been solved by Alexander Friedman from his Friedman equation (also by Einstein's field equation was introduced), and this expanded cosmic solution does not require any additional cosmological constant terms. Belgian priest Lemet applied these solutions to construct the earliest model of the Big Bang. The model predicted that the universe evolved from a high temperature and dense state [4]. Einstein later acknowledged that adding the cosmological constant term was the biggest mistake he made in his life [5].

In that era, general relativity still maintained a sense of mystery compared to other physical theories. Because it is harmonious with special theory of relativity, and can explain many phenomena that Newton's gravity cannot explain, it is obviously better than Newton's theory. Einstein himself proved in 1915 how the theory of general relativity explains the phenomenon of the abnormal perihelion precession of Mercury's orbit. The process does not require any additional parameters (the so-called "perfunctory factor") [6]. Another well-known experimental verification is the deflection of the solar eclipse in the gravitational field of the solar eclipse observed by the expedition led by Sir Arthur Eddington on the island of Principe in Africa [7]. The angle is in complete agreement with the predictions of general relativity (twice the deflection angle predicted by Newton's theory), and this discovery was subsequently reported by newspapers around the world, making Einstein's theory famous for a while [8]. But it wasn't until 1960-1975 that general relativity really entered the field of view of mainstream research in theoretical physics and astrophysics. This period was called the golden age of general relativity. Physicists gradually understood the concept of black holes and were able to identify black holes from quasars through the properties of astrophysics [9]. The more accurate experimental verification of general relativity that can be performed in the solar system has further demonstrated the extraordinary prediction ability of general relativity [10], and the predictions of relativistic cosmology have also stood the test of experimental observations [11].