Here is another basic principle of general relativity-equivalence principle.
Equivalence principle
Assuming that the spacecraft is completely closed and the astronaut has no contact with the outside world, then he has no way to judge whether the force that makes the object fall at a certain acceleration is gravity or inertia. In fact, not only the experiment of free fall, but also any physical process inside the spacecraft can't tell us whether the spacecraft is accelerating. Or moored on the planet's surface. The scene here is very similar to that in the Galileo spacecraft mentioned in the first section of this chapter. This fact makes us think that the uniform strong gravitational field is equivalent to the reference frame for uniform acceleration. Einstein regarded it as the second basic principle of general relativity, which is also the famous equivalence principle.
Some unexpected conclusions can be drawn directly from these two basic principles. Suppose a spaceship moves in a straight line with uniform acceleration in a space where gravity can be ignored, and a beam of light shoots into the spaceship perpendicular to the direction of motion. Of course, observers outside the spacecraft will see that the light beam propagates in a straight line, but observers inside the spacecraft will see different scenes with the spacecraft as the reference system. In order to record the trajectory of the light beam in the spacecraft, he placed some translucent screens (pictured) at equal distances in the spacecraft, so that the light could pass through these screens and leave light spots on the screens. As the spacecraft advances, the position where the light reaches the next screen is always closer to the stern than the position where it reached the last exhibition. If the spacecraft moves in a straight line at a uniform speed, the distance between any two adjacent screens is equal, and the observer on the spacecraft will still see that the light trajectory is a straight line (as shown by the dotted line). Although the direction of the straight line is not the same as that seen by the static observer outside the ship, if the spacecraft moves in a straight line at a uniform speed and the speed of the spacecraft increases while the light propagates to the right, then the trajectory of the light recorded by the observer on board is a parabola (solid line in the figure).
According to the equivalence principle, the observers in the spacecraft can also think that there is a huge object in the stern direction that does not accelerate, and its gravitational field affects the physical process in the spacecraft. Therefore, we come to the conclusion that the gravity of an object can bend light.
Usually, the gravitational field of objects is too weak, and only the light caused by the solar gravitational field can be observed at the beginning of the 20th century. Because of the gravitational field of the sun, we may see the stars behind the sun (pictured). But the bright sky usually prevents us from watching the stars, so the best time is the total solar eclipse. On May 29th, 2009, a total solar eclipse happened, and two British expeditions went to the Gulf of Guinea .5438+0919 respectively.
The time interval is related to the gravitational field. The existence of gravitational field makes the time process of different positions in space different. Let's examine a huge rotating disk (as shown in the picture). From the ground, all points on the disk are accelerating except the position of the rotating shaft. The closer to the edge, the greater the acceleration, and the direction points to the center of the disk. From the ground, we can also see that the closer to the edge, the greater the speed. According to the special theory of relativity, the more the same process happens.
Then take the disk itself as the frame of reference to study this phenomenon. People on the disk think that there is a gravitational field on the disk, and the direction points from the center of the disk to the edge. Because the time process near the edge is slow, people on the disk can conclude that the time process is slow at the position with low gravitational potential.
There is a kind of star in the universe, which is small in size but not small in mass. It's called a dwarf. The gravitational potential on the surface of dwarfs is much lower than that on the surface of the earth. The time process on the surface of dwarfs is slow, and the light emitted by atoms there is lower in frequency than that emitted by similar atoms on earth, and looks red. This phenomenon, called gravitational redshift, has been confirmed by astronomical observation. Modern technology can also verify the gravitational redshift on the earth.
The length of the rod is related to the gravity field. We still study rotating disks. The same rod is placed in different positions of the disc and moves with the disc at different speeds. According to special relativity, their lengths are different. The closer to the edge, the shorter the rod. The person on the disk also observed this difference, but he took the disk as a frame of reference and thought that the disk was static. At the same time, he also thinks that every point on the disk has gravity pointing to the edge of the disk, so he comes to the conclusion.
The length of the rod is related to the distribution of gravity field. This phenomenon reflects that due to the existence of matter, the actual space is not uniform, which is very different from our past ideas. For example, the grid on a piece of cloth is very neat (as shown in Figure A), and it will bend when pressed by hand (as shown in Figure B). Physics borrows the word "bending". Generally speaking, due to the existence of matter,
Planets orbit the sun in elliptical orbits, sometimes closer to the sun and sometimes farther away. The great mass of the sun bends the space around it. Therefore, the long axis of the planet's orbit will deviate from the previous period by an angle every time it makes one revolution. This phenomenon is called precession of planetary orbits. Theoretical analysis shows that only the precession of the orbit of Mercury is significant, reaching about 0.0 1 per century. This phenomenon was discovered long before the emergence of general relativity.
General relativity and geometry Finally, we return to the rotating disk. Special relativity tells us that only the length along the direction of motion changes, and the length perpendicular to the direction of motion will not change; If the disk is taken as the frame of reference, it can be said that the spatial scale along the direction of gravity has not changed, only the spatial scale perpendicular to the direction of gravity has changed. This is of great significance, because when measuring the circumference and diameter of a disk, their ratio is no longer 3. 14 1.59… but other values, and the sum of the inner angles of the triangle will not be 180.
Geometry reflects people's understanding of spatial relations. Historically, people have only been exposed to a weak gravitational field in a relatively small spatial scale. In this case, the curvature of the space can be ignored. On this basis, human beings developed Euclidean geometry, which reflects the reality of flat space. General relativity tells us that real space is curved, so it should be described by non-Euclidean geometry with more universal significance. However, as a special case of non-Euclidean geometry, Euclidean geometry is still correct within its scope of application.
After Einstein published his special theory of relativity in 1905, he began to think about how to bring gravity into the framework of special theory of relativity. From the ideal experiment of an observer's free fall, he began to explore the theory of gravitational relativity for eight years from 1907. After many detours and mistakes, he gave a speech at the Prussian Academy of Sciences in June191511,and its content was the famous Einstein gravitational field equation. This equation describes how the matter in space-time affects the surrounding space-time geometry and becomes the core of Einstein's general theory of relativity [1].
Einstein's gravitational field equation is a set of second-order nonlinear partial differential equations, and it is difficult to find the solution of the equation mathematically. Einstein used many approximate methods and got many initial predictions from the gravitational field equation. However, in 19 16, karl schwarzschild, a talented astrophysicist, got the first exact solution of the gravitational field equation-schwarzschild metric, which is the last stage of studying the gravitational collapse of stars, that is, the theoretical basis of black holes. In the same year, the research work of extending Schwarzschild geometry to charged mass began, and the final result was the Resler-Northstrom metric, which corresponds to the charged static black hole [2]. 19 17 Einstein applied general relativity to the whole universe, which initiated the research field of relativistic cosmology. Considering that the theory of the static universe is still widely accepted in cosmology research, Einstein added a new constant to his gravitational field equation, called the cosmological constant term, in order to get the consistency with the "observation" at that time [3]. But by 1929, Hubble and others' observations showed that our universe was in an expanding state. As early as 1922, the corresponding solution of the expanding universe was obtained by Alexander Friedman from his friedmann equations (also derived from Einstein's field equation), and this solution of the expanding universe did not need any additional cosmological constants. Belgian priest Lemaistre used these deconstructions to create the earliest BIGBANG model, which predicted that the universe evolved from a high temperature and high density state [4]. Einstein later admitted that adding cosmological constants was the biggest mistake he made in his life [5].
At that time, general relativity was still a mystery compared with other physical theories. Because it is in harmony with special relativity, it can explain many phenomena that Newton's gravity can't explain, so it is obviously superior to Newton's theory. Einstein himself proved in 19 15 how general relativity can explain the abnormal perihelion precession of mercury orbit, and this process does not need any additional parameters (so-called "perfunctory factors") [6]. Another famous experimental verification is the deflection of light in the solar gravitational field observed by the expedition led by Sir Arthur Eddington in principe island, Africa [7], and its deflection angle is completely consistent with the prediction of general relativity (twice that predicted by Newton's theory). This discovery was subsequently reported by newspapers all over the world, which made Einstein's theory famous for a time [8]. But it was not until 1960 to 1975 that general relativity really entered the mainstream research field of theoretical physics and astrophysics, which was called the golden age of general relativity. Physicists gradually understand the concept of black holes, and can identify black holes from quasars through the properties of astrophysics [9]. The more accurate experimental verification of general relativity in the solar system further proves the extraordinary prediction ability of general relativity [10], and the prediction of relativistic cosmology has withstood the test of experimental observation [1 1].