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General relativity (generalized? Relativity? ), Einstein's theory of gravity, which was established in geometric language in 19 15, integrated the special theory of relativity and Newton's law of universal gravitation, and changed gravity into a description of space-time bent by matter and energy to replace the traditional view that gravity is a force. This also explains why Mercury's orbit is unstable.

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Basic information

Chinese name

Theory of relativity

Foreign name

general theory of relativity

Another name

Theory of relativity

express

R_uv- 1/2×R×g_uv=κ×T_uv

presenter

Albert. Albert Einstein

Show time

19 15

Applied discipline

Modern physics

area of application

Gravitational physics, astrophysics, cosmic physics

thesis

Fundamentals of general relativity

catalogue

1 Basic introduction

2 basic concepts

3 birth background

4 related introduction

Five basic assumptions

6 main contents

7 scientific research application

8 experimental examination

9 The fourth hypothesis

10 physical application

The advanced concept of 1 1

12 theoretical relationship

13 Current progress

14 Example of Teaching Plan

Basic introduction of folding editing this paragraph.

General relativity is Einstein's theory of gravity described in geometric language published in 19 15, which represents the highest level of theoretical research on general relativity of gravity in modern physics. General relativity contains the classical Newton's law of universal gravitation under the framework of special relativity, which is based on the principle of equivalence. In general relativity, gravity is described as the geometric property (curvature) of space-time; This curvature of space-time is directly related to the energy and momentum tensor of matter and radiation in space-time, and its relationship is Einstein's gravitational field equation (second-order nonlinear partial differential equation group).

The predictions obtained from general relativity are quite different from those in classical physics, especially about the passage of time, space geometry, the movement of free falling bodies and the propagation of light, such as time expansion in gravitational field, gravitational redshift of light and gravitational time delay effect. The prediction of general relativity has been verified by all the observations and experiments so far-although general relativity is not the only theory describing gravity today, it is the most concise theory that can be consistent with experimental data. However, there are still some problems that have not been solved. Typical is how to unify the laws of general relativity and quantum physics, so as to establish a complete and self-consistent theory of quantum gravity.

Einstein's general theory of relativity has a very important application in astrophysics: it directly deduces that some massive stars will eventually become black holes-some areas in space-time are distorted so that even light cannot escape. There is evidence that stellar mass black holes and supermassive black holes are the direct causes of high-intensity radiation emitted by some celestial bodies, such as active galactic nuclei and micro quasars. The deflection of light in the gravitational field will form a gravitational lens phenomenon, which enables people to observe multiple images of the same celestial body at a far distance. General relativity also predicts the existence of gravitational waves. 20 15 Beijing time on September 14 17: 50: 45, two detectors of the laser interferometer gravitational wave observatory (LIGO) in Livingston, Louisiana, USA and hanford, Washington, respectively, observed a gravitational wave event with a confidence of 5. 1 multiple standard deviation. According to LIGO data, gravitational wave events occur in distant galaxies that are more than 10 billion light years away from the Earth. Two black holes with solar mass of 36 and 29 are merged into a black hole with solar mass of 62. The peak intensity of gravitational waves radiated by the merger of two black holes at the last moment is more than ten times higher than the electromagnetic radiation intensity of the whole Hubble volume. The detailed results will be published in Physics Review Letters (phys.rev.lett,116,061102) in the near future. This extraordinary discovery marks that astronomy has entered a new era, and mankind has since opened a brand-new window to observe the universe. In addition, general relativity is the theoretical basis of modern cosmology. [ 1]

Fold and edit the basic concepts of this paragraph.

General relativity is based on special relativity. If the latter is proved wrong, the whole theory will collapse.

Two Different Expressions of Folding Quality

In order to understand general relativity, we must know how mass is defined in classical mechanics.

First of all, let's think about what quality stands for in our daily life. "Weight"? In fact, we think that mass is something that can be weighed, just like we measure it: we put the object that needs to be measured on the balance. What kind of quality do we use to do this? It is the fact that the earth and the measured object attract each other. This kind of mass is called "gravitational mass when the ball falls to the acceleration floor and falls to the earth". We call it "gravity" because it determines the motion of all stars in the universe: the gravitational mass between the earth and the sun drives the earth to move around the latter in a nearly circular motion.

Now, try to push your car on a flat ground. You can't deny that your car strongly resists the acceleration you want to give it. This is because your car is of great quality. It is easier to move light objects than heavy ones. Mass can also be defined in another way: "It opposes acceleration". This mass is called "inertial mass".

The frequency of light waves emitted from the surface of a massive object is red-shifted, so we come to the conclusion that we can measure quality in two ways. Either we weigh it (very simply) or we measure its resistance to acceleration (using Newton's law).

Many experiments have been done to measure the inertial mass and gravitational mass of the same object. All experimental results come to the same conclusion: inertial mass is equal to gravitational mass.

Newton himself realized that this kind of mass equivalence was caused by some reason that his theory could not explain. But he thinks this result is a simple coincidence. On the contrary, Einstein found that there is a channel in this equation that can replace Newton's theory.

Everyday experience proves this equivalence: two objects (one light and one heavy) will "fall" at the same speed. However, heavy objects are subject to greater gravity than light objects. So why didn't it "fall" faster? Because it is more resistant to acceleration. The conclusion is that the acceleration of an object in the gravitational field has nothing to do with its mass. Galileo was the first person to notice this phenomenon. It is important for you to understand that all objects in the gravitational field "fall at the same acceleration" is the equivalent result of inertial mass and gravitational mass (in classical mechanics).

Now let's pay attention to the expression "whereabouts". Objects "fall" because the gravitational mass of the earth produces the gravitational field of the earth. Two objects have the same acceleration in the same gravitational field. Whether it's the moon or the sun, their acceleration speed is the same. In other words, their speed increases by the same amount every second. (Acceleration is the increment of speed per second)

Equivalence between folded gravitational mass and inertial mass

Light cone Einstein has been looking for the explanation that "gravitational mass equals inertial mass". To this end, he put forward a third hypothesis, called "equivalence principle". It shows that if an inertial system is uniformly accelerated relative to a Galileo system, then we can consider it (inertial system) to be stationary by introducing a uniformly accelerated gravitational field relative to it.

Let's examine an inertial system K', which has a uniform acceleration motion relative to Galileo system. There are many objects around k and k'. This object is stationary with respect to K, so these objects have the same accelerated motion with respect to K'. This acceleration is the same for all objects, contrary to the acceleration direction of K' relative to K. As we have said, the acceleration of all objects in a gravitational field is the same, so the effect is equivalent to that K' is static and has a uniform gravitational field.

Therefore, if the equivalence principle is established, it is only a simple inference that two masses of an object are equal. This is why (quality) equivalence is an important argument to support the principle of equivalence.

Assuming that K' is static and the gravitational field exists, we can understand K' as a Galileo system, in which we can study the laws of mechanics. Therefore, Einstein established his fourth principle.

Fold and edit the birth background.

The title page of Einstein's manuscript explaining general relativity Einstein published a paper in 1905 to discuss 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 &; Oumlm 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 stable universe. But there are two problems with this solution. Theoretically, the solution of a stable universe is mathematically unstable. 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 career.

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.

Fold and edit the related introduction of this paragraph.

Title page of Einstein's manuscript explaining general relativity. Relativity is one of the theoretical foundations of modern physics. Discuss the theory of the relationship between material movement and time and space. Founded by Einstein in the early 20th century, and developed with other physicists, the special theory of relativity was founded in 1905, and the general theory of relativity was completed in 19 16. At the end of 19, due to the perfection of Newtonian mechanics and Maxwell's electromagnetic theory (183 1~ 1879), some physicists thought that "the development of physics is actually over", but when people used galilean transformation to explain the propagation of light and other issues, they found a series of sharp contradictions and put forward the classical view of time and space. Einstein put forward a new concept of time and space in physics, established the law of high-speed moving objects equivalent to the speed of light, and founded the theory of relativity. Special relativity puts forward two basic principles. (1) principle of light speed invariance: that is, in any inertial system, the light speed c in vacuum is the same, regardless of the movement of the light source and the observer. (2) The special principle of relativity refers to the basic laws of physics, even the laws of nature, which are the same for all inertial reference systems.

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 and time), so the gravitational field affects the measurement of time and distance.

General relativity: Einstein's theory based on the fact that all observers must have the same speed of light, no matter how they move. It explains gravity according to the curvature of four-dimensional space-time

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.

Fold and edit the basic assumptions of this paragraph.

To put it simply, the two basic principles of general relativity are: first, the equivalence principle: gravity and inertia force are equivalent; Second, the principle of general relativity: all physical laws take the same form in any reference system.

Folding equivalence principle

Principle of reciprocity: it can be divided into weak principle and strong principle. The weak equivalence principle holds that gravitational mass and inertial mass are equivalent. According to the principle of strong equivalence, two spaces are subjected to gravity and equal inertial force respectively, and all experiments in these two spaces will get the same physical laws. At present, many scholars are engaged in the demonstration and research of the equivalence principle, but at least as far as the accuracy can be achieved at present, the equivalence principle has not been proved by experiments.

Folding generalized relativity principle

Principle of general relativity: the form of physical laws is constant in all reference systems.

In general physics (college textbooks), these two principles are described as follows:

Equivalence principle: all physical phenomena in inertial system under the action of uniform and constant gravitational field can be exactly the same as those in non-inertial system that is not affected by gravitational field but moves with constant acceleration.

Relativity principle of general relativity: all non-inertial systems and inertial systems existing in the gravitational field are equivalent, which are used to describe physical phenomena.

The law of universal gravitation was replaced by Einstein's field equation;

R_uv- 1/2*R*g_uv=κ*T_uv

(Rμν-( 1/2)gμνR = 8gπTμν/(c * c * c * c)-gμν)

Where g is Newton's gravitational constant.

The equation is a second-order hyperbolic partial differential equation with elliptic constraints, with time and space as independent variables and measurement as dependent variables. It is famous for its complexity and beauty, but it is not perfect, and only approximate solutions can be obtained in calculation. Finally, people get the exact solution of true spherical symmetry-Schwartz solution.

The field equation after adding the cosmological constant is:

R _ uv- 1/2 * R * g _ uv+λ* g _ uv =κ* T _ uv

Scientific research application folding editing this paragraph

According to the general theory of relativity, there is no gravity in the local inertial system, and one-dimensional time and three-dimensional space form a four-dimensional flat Euclidean space; In any frame of reference, there is gravity, which leads to the curvature of space-time, so space-time is a four-dimensional curved non-Euclidean space. Einstein discovered the gravitational field equation that the distribution of matter affects the space-time geometry. The bending structure of time space depends on the distribution of material energy density and momentum density in time space, and the bending structure of time space determines the motion trajectory of objects. When gravity is weak and curvature of spacetime is small, the predictions of general relativity tend to be consistent with those of Newton's law of universal gravitation and Newton's law of motion. But there is a difference between strong gravity and large curvature of spacetime. Since the general theory of relativity was put forward, the abnormal precession of Mercury's perihelion, gravitational redshift of light frequency, gravitational deflection of light and delay of radar echo have been predicted, which have been confirmed by astronomical observations or experiments. In recent years, the observation of pulse binary stars also provides strong evidence that the light emitted by the light source is deflected when passing through the dense star.

The general theory of relativity is quickly recognized and appreciated by people because of its amazing confirmation and theoretical beauty. However, because Newton's gravity theory is accurate enough for most gravity phenomena, general relativity only provides a very small correction, which people do not need in practice. Therefore, the general theory of relativity has not been fully valued and developed rapidly in the half century after its establishment. In the 1960s, the situation changed, and the background radiation of strong gravitational celestial bodies (neutron stars) and the 3K universe was discovered, which made the research of general relativity flourish. General relativity is of great significance for studying the structure and evolution of celestial bodies and the structure and evolution of the universe. The formation and structure of neutron stars, black hole physics and black hole detection, gravitational radiation theory and gravitational wave detection, big bang cosmology, quantum gravity and topological structure of large-scale spacetime are being deeply studied, and general relativity has become an important theoretical basis for physical research.

Fold and edit this paragraph for experimental inspection.

At the beginning of the establishment of general relativity, Einstein put forward three experimental tests, one is the precession of Mercury's perihelion, the other is the bending of light in the gravitational field, and the third is the gravitational red shift of spectral lines. Among them, only the precession of Mercury's perihelion is a definite fact, and the other two items were determined later. After 1960s, some people put forward plans to observe radar echo delay and gravitational waves.

Precession of folding mercury perihelion

1859, astronomer le Villier found that the observed precession of Mercury's perihelion is 38 seconds faster than the theoretical value calculated every hundred years according to Newton's law. He speculated that there might be an asteroid inside Mercury, and the attraction of this asteroid to Mercury led to the deviation between the two. But after years of searching, this asteroid has never been found. Newcomb Street 1882

After recalculation, it is concluded that the excess annual difference of mercury perihelion is 43 seconds every hundred years. He suggested that it was possible that the diffusion material emitted by zodiacal light hindered the movement of mercury. But this does not explain why several other planets have similar redundant precession. Newcomb wants to know whether gravity obeys inverse square law. Later, some people used electromagnetic theory to explain the abnormal phenomenon of mercury perihelion precession, but none of them succeeded.

19 15 years, Einstein regarded the motion of the planet around the sun as its motion in the gravitational field of the sun according to the general theory of relativity, and the surrounding space was bent due to the mass of the sun, so that the precession of the perihelion of each revolution of the planet was as follows:

ε=24π2a2/T2c2( 1-e2)

Where a is the long semi-axis of the planetary orbit, c is the speed of light, expressed in cm/s, e is eccentricity, and t is period of revolution. For mercury, ε=43″/ century is calculated, which coincides with Newcomb's result, and solves the unsolved problem of Newton's gravity theory for many years. This result became the most powerful evidence of general relativity at that time. Mercury is the closest inner planet to the sun. The closer to the central celestial body, the stronger the gravitational field and the greater the curvature of space-time bending. In addition, the orbit eccentricity of Mercury is large, so the precession correction value is larger than that of other planets. The excess precession of Venus, Earth and Icarus measured later is basically consistent with the theoretical calculation.

Bending of folded light in gravitational field

In 19 1 1, Einstein discussed that when light passes near the sun, it will bend under the action of the sun's gravity. He calculated that the deflection angle was 0.83 ",and pointed out that this phenomenon could be observed in the total solar eclipse. 19 14 German astronomer E.F.Freundlich led a team to Klimu Peninsula to observe the total solar eclipse in August of that year, when World War I broke out and the observation failed. Fortunately, this is the case, because Einstein only considered the equivalence principle at that time, and the calculation result was half smaller. 19 16 Einstein recalculated the bending of light in the gravitational field according to the complete general relativity. He not only considered the gravity of the sun, but also considered the spatial geometric deformation caused by the mass of the sun. The deflection angle of light is α =1".75R0/r, where r0 is the radius of the sun and r is the distance from the light to the center of the sun.

During the total solar eclipse of 19 19, the Royal Society and the Royal Astronomical Society sent two observation teams led by A.S. Feddington and others to principe island in the Gulf of Guinea in West Africa and Sobral in Brazil for observation. After comparison, the observation results of the two places are 1 ". 6 1 ".30 and1". 980 ".They are 12 respectively. Comparing the deflection angle data measured at that time with Einstein's theoretical expectation, it is basically consistent. This kind of observation accuracy is too low, and it will be interfered by other factors. People have been looking for possibilities other than total solar eclipse. The development of radio astronomy in the 1960s brought hope. A radio source similar to a star was discovered with a radio telescope. The results of observing quasars at 1974 and 1975 show that the deviation between the theoretical values and the observed values is less than 1%.

Gravitational redshift of folded spectral lines

The comparative general relativity of planets revolving around stars points out that the clock moves slowly in a strong gravitational field, so the light emitted from the surface of a massive star to the earth will move to the red end of the spectrum. Einstein discussed this problem in the article 19 1 year. He expressed the gravitational potential difference between the surface of the sun and the earth with φ, and ν0 and ν respectively expressed the frequency of light on the surface of the sun and when it reached the earth, so:

(ν0-ν)/ν=-φ/C2 = 2× 10-6。

Einstein pointed out that this result is consistent with the observation of C.Fabry and others, and Fabry originally thought it was influenced by other reasons.

1925, W.S. Adams of Mount Wilson Observatory observed Sirius A, the companion of Sirius. This companion star is a so-called white dwarf star, which is 2000 times denser than platinum. By observing its spectral lines, the frequency shift obtained is basically consistent with the expectation of general relativity.

1958, Mossbauer effect was discovered. By using this effect, high-resolution R-ray vibration absorption can be measured. 1959, Pound (R.V.Pound) and Rybka (G.Rebka) first proposed a scheme to detect gravitational frequency shift by using Mossbauer effect. Then, they successfully carried out the experiment, and the difference between the results and the theoretical values was about 5%.

Good results can also be obtained by measuring gravitational frequency shift with atomic clock. In 197 1, J.C. Havler and R.E. Keating used several cesium atomic clocks to compare the timing rates at different heights. One of them was placed on the ground as a reference clock, and the others were carried into space by civil aviation planes, flying around the earth along the equator at an altitude of 65438+100000 meters. The experimental results are consistent with the theoretical expected values in the range of 65438 00%. 1980, R.F.C viso et al. did experiments with hydrogen maser. They launched the hydrogen maser rocket into the space of 10000 km, and the difference between the results obtained and the theoretical value was only 7× 10-5.

Folding radar echo delay

The bending phenomenon of light passing near a massive object can be regarded as a kind of refraction, which is equivalent to slowing down the speed of light. Therefore, if the signal from a certain point in space passes near the sun, the time to reach the earth will be delayed. In 1964, I.I.Shapiro first put forward this proposal. His team conducted radar experiments on Mercury, Venus and Mars successively, which proved that the radar echo did have a delay. In recent years, the experimental accuracy has been improved by taking artificial celestial bodies as reflection targets. Compared with the theoretical value of general relativity, the difference between the results of such experiments is about 65438 0%. There are many examples of testing general relativity with astronomical observations. For example: gravitational wave observation and binary star observation, Hubble's law on the expansion of the universe, the discovery of black holes, the discovery of neutron stars, the discovery of microwave background radiation and so on. Through various experiments, the general theory of relativity is more and more convincing. But there is one thing to emphasize: we can deny a theory with one experiment, but we can't prove a theory with a limited number of experiments; An experiment with low accuracy may overturn a theory, but a series of experiments with high accuracy cannot finally confirm a theory. Whether the general theory of relativity is correct or not, people must take a very cautious attitude and draw reasonable conclusions strictly and cautiously.

Fold and edit the fourth assumption in this paragraph.

Four images of the same celestial body under the gravitational lens effect Einstein's fourth hypothesis is a generalization of his first hypothesis. It can be said that the laws of nature are the same in all departments.

It is undeniable that 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 only in Galileo. But we don't know whether there is a Galileo system.

This principle is called "the principle of general relativity"