Einstein's Second Theory of Relativity (19 16). This theory holds that gravity is caused by the distortion of space-time geometry (that is, the geometry that not only considers the distance between points in space, but also considers the distance between points in space-time), so the gravitational field affects the measurement of time and distance.
General relativity: Einstein's theory that all observers (no matter how they move) must have the same idea based on scientific laws. It explains gravity according to the curvature of four-dimensional space-time
General relativity? ) is Einstein's theory of gravity established in geometric language in 19 15. It combines special relativity with Newton's law of universal gravitation, and changes gravity to describe space-time bent by matter and energy to replace the traditional view that gravity is a force. Therefore, special relativity and the law of universal gravitation are only special cases of general relativity under special circumstances. Special relativity is the case that there is no gravity; The law of universal gravitation is the situation that the distance is close, the gravity is small and the speed is slow.
background
1907, Einstein published a paper on the influence of gravity and acceleration on light in special relativity, and the prototype of general relativity began to take shape. 19 12 years, Einstein published another paper to discuss how to describe gravity field in geometric language. At this point, the kinematics of general relativity appeared. 19 15 years, Einstein's field equation was published, and the dynamics of the whole general theory of relativity was finally completed.
After 19 15, the development of general relativity mostly focused on solving the field equation, and the physical explanation of the solution and the search for possible experiments and observations also accounted for a large part. However, because the field equation is a nonlinear partial differential equation, it is difficult to solve, so only a few solutions were solved before the computer was applied to science. There are three most famous solutions: Schwarzschild solution (19 16), Reissner-Nordstr? M solution and Kerr solution.
The observation of general relativity has also made a lot of progress. The precession of mercury is the first evidence to prove the correctness of general relativity. It was measured before the appearance of relativity, and it was not explained theoretically until Einstein discovered it. In the second experiment, 19 19 Eddington measured the starlight deflection caused by the solar gravitational field during the solar eclipse in Africa, which was completely consistent with the prediction of general relativity. At this time, the general theory of relativity has been widely accepted by the public and most physicists. After that, there were many experiments to test the theory of general relativity and confirm its correctness.
In addition, the expansion of the universe has also created another climax of general relativity. From 1922, researchers found that the solution of the field equation would be an expanding universe. Einstein naturally did not believe that the universe would rise or fall at that time, so he added a cosmological constant to the field equation, which made it possible to solve a solution that implicitly defined the universe. But there are two problems with this solution. Theoretically, the solution of a hidden universe is unstable in litigation. In addition, in 1929, Hubble discovered that the universe is actually expanding. This experimental result made Einstein give up the cosmological constant and declared that it was the biggest mistake in my life.
But according to the recent observation of a supernova, the expansion of the universe is accelerating. So the cosmological constant seems to have the possibility of resurrection, and the dark energy in the universe may be explained by the cosmological constant.
Basic hypothesis
Equivalence principle: Gravity and inertia force are completely equivalent.
Principle of general relativity: the form of physical laws is constant in all reference systems.
main content
Einstein put forward the "equivalence principle", that is, gravity and inertia 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 relativity in a narrow sense to the principle of relativity in a broad sense, that is, the form of physical laws is unchanged in all reference systems. The motion equation of an object is the geodesic equation in the reference system. Geodesic equation has nothing to do with the inherent properties of the object itself, but only depends on the local geometric properties of time and space. And gravity is the expression of local geometric properties of time and space. The existence of material mass will cause the bending of time and space. In curved space-time, objects still move along the shortest distance (that is, along the geodesic-in Euclidean space). For example, the geodesic movement of the earth in curved space-time caused by the sun actually revolves around the sun, resulting in a gravitational effect. Just like on the surface of the earth, if you move in a straight line, you actually walk around the great circle on the surface of the earth.
Gravity is the expression of local geometric properties of time and space. Although the general theory of relativity was founded by Einstein, its mathematical basis can be traced back to the axiom of Euclid geometry and the efforts made for centuries to prove Euclid's fifth postulate (that is, parallel lines are always equidistant). This effort culminated in the work of Lobachevsky, Bolyai and Gauss, who pointed out that Euclid's fifth postulate could not be proved by the first four postulates. Gauss's student Riemann developed the general mathematical theory of non-Euclidean geometry. So it is also called Riemannian geometry or surface geometry. Before Einstein developed general relativity, people thought that non-Euclidean geometry could not be applied to the real world.
Basic principles of general relativity
Because the inertial system cannot be defined, Einstein extended the principle of relativity to the non-inertial system and put forward the first principle of general relativity: the principle of general relativity. Its content is that all frames of reference are equivalent when describing the laws of nature. This is very different from the principle of relativity in a narrow sense. In different reference systems, all physical laws are completely equivalent, and there is no difference in description. But in all reference frames, this is impossible. It can only be said that different frames of reference can also effectively describe the laws of nature. This requires us to find a better description method to meet this requirement. Through the special theory of relativity, it is easy to prove that the pi of a rotating disk is greater than 3. 14。 So the general frame of reference should be described by Riemann geometry. The second principle is the principle that the speed of light is constant: the speed of light is constant in any reference system. The space-time point equivalent to light is fixed in four-dimensional space-time Space-time is straight, and light moves in a straight line at the speed of light in three-dimensional space. When space-time is curved, light moves along the curved space in three-dimensional space. It can be said that gravity can deflect light, but it cannot accelerate photons. The third principle is the most famous principle of reciprocity. There are two kinds of mass. Inertia mass is used to measure the inertia of an object, which was originally defined by Newton's second law. Gravitational mass is a measure of the gravitational charge of an object, which was originally defined by Newton's law of universal gravitation. These are two unrelated laws. Inertial mass is not equal to charge, and it is not even important so far. Then inertial mass and gravitational mass (gravitational charge) should have nothing to do with Newtonian mechanics. However, the difference between them cannot be discovered through the most sophisticated experiments. Inertia mass is strictly proportional to gravitational mass (it can be strictly equal if appropriate coefficients are selected). General relativity regards inertial mass and gravitational mass as the content of equivalence principle. Inertia mass is related to inertia force, and gravitational mass is related to gravity. In this way, the relationship between non-inertial system and gravity is established. Then a very small free-falling reference frame can be introduced at any point in the gravitational field. Because inertial mass is equal to gravitational mass, it is neither inertia nor gravity in this reference system, and all theories of special relativity can be used. When the initial conditions are the same, the orbits of particles with equal mass and different charges are different in the same electric field, but all particles have only one orbit in the same gravitational field. The principle of equivalence made Einstein realize that the gravitational field is probably not the outfield of space-time, but the geometric field, which is an attribute of space-time itself. Due to the existence of matter, the originally flat space-time has become a curved Riemannian space-time. At the beginning of the establishment of general relativity, there was a fourth principle, the law of inertia: an object that is not subjected to force (except gravity, because gravity is not real force) does inertial motion. In Riemann space-time, it moves along geodesic lines. Geodesic is a generalization of straight lines, the shortest (or longest) straight line between two points, and it is unique. For example, the geodesic of a sphere is an arc of a great circle cut by a plane passing through the center of the sphere and the sphere. But after the field equation of general relativity is established, this law can be deduced from the field equation, so the law of inertia becomes the law of inertia. It is worth mentioning that Galileo once thought that uniform circular motion was inertial motion, and uniform linear motion would always close into a circle. This is proposed to explain planetary motion. Naturally, he was criticized by Newtonian mechanics, but the theory of relativity revived it. Planets do inertial motion, but not the standard uniform circular motion.