1. The time interval between two events has nothing to do with the movement state of the clock used to measure time;
2. The spatial distance between two points has nothing to do with the motion state of the ruler used to measure the distance.
Einstein found that if the principle of light speed invariance and the principle of relativity are recognized to be compatible, then both hypotheses must be abandoned. At this time, the simultaneous events of one clock are not necessarily simultaneous for another clock, and they are relative at the same time. In two coordinate systems with relative motion, the values obtained by measuring the distance between two specific points are no longer equal. Distance is also relative.
If an event in the K coordinate system can be determined by three spatial coordinates X, Y, Z and a time coordinate T, and the same event in the K coordinate system is determined by X', Y', Z' and T', Einstein found that X', Y', Z' and T' can be solved by a set of equations. The relative velocity of the two coordinate systems and the speed of light c are the only parameters of the equation. This equation was first derived by Lorentz, so it is called Lorentz transformation.
Using Lorentz transformation, it is easy to prove that the clock will slow down because of movement, the ruler will be shorter when it is moving than when it is at rest, and the sum of speeds satisfies a new law. The principle of relativity is also expressed as a clear mathematical condition, that is, under the Lorentz transformation, the space-time variables X', Y', Z' and T' with apostrophes will replace the space-time variables X, Y, Z and T, and any expression of natural laws will still take the same form as before. What people call the universal law of nature is covariant for Lorentz transformation. This is very important for us to explore the universal laws of nature.
Besides, in classical physics, time is absolute. It has always played an independent role different from the three spatial coordinates. Einstein's theory of relativity involves time and space. It is believed that the real world of physics is composed of various events, and each event is described by four numbers. These four numbers are its space-time coordinates T and X, Y and Z, which form a four-dimensional continuous space, usually called Minkowski four-dimensional space. In relativity, it is natural to examine the real world of physics in a four-dimensional way. Another important result caused by special relativity is about the relationship between mass and energy. Before Einstein, physicists always thought that mass and energy were completely different and were separately conserved quantities. Einstein found that in the theory of relativity, mass and energy are inseparable, and the two conservation laws are combined into one. He gave a famous formula of mass and energy: e = MC? , where c is the speed of light. So quality can be regarded as a measure of its energy. Calculations show that tiny masses contain enormous energy. This wonderful formula has laid a theoretical foundation for mankind to obtain huge energy, make atomic bombs and hydrogen bombs, and use atomic energy to generate electricity.
Einstein further established the general theory of relativity in 19 15. The principle of relativity in a narrow sense is limited to two coordinate systems with uniform motion, while the principle of relativity in a broad sense cancels the restriction of uniform motion. He introduced an equivalence principle, arguing that it is impossible for us to distinguish between gravitational effect and non-uniform motion, that is, non-uniform motion and gravity are equivalent. He further analyzed the phenomenon that light will be bent by gravity when passing near a planet, and thought that the concept of gravity itself was completely unnecessary. It can be considered that the mass of the planet makes the space around it curved, and the light takes the shortest path. Based on these discussions, Einstein derived a set of equations, which can determine the curved space geometry caused by the existence of matter. Using this equation, Einstein calculated the displacement of the perihelion of Mercury, which was completely consistent with the experimental observation, and solved a long-term unexplained problem, which made Einstein excited. In his letter to Erenfest, he wrote that this equation gives the correct value of perihelion. You can imagine how happy I am! For days, I was so happy that I didn't know what to do. "
1915165438+1On October 25th, Einstein submitted a paper entitled "Equation of Gravitation" to the Prussian Academy of Sciences in Berlin, which fully discussed the general theory of relativity. In this article, he not only explained the mystery of the perihelion motion of Mercury's orbit found in astronomical observation, but also predicted that the starlight would deflect after passing through the sun, and the deflection angle was twice that predicted by Newton's theory. The first world war delayed the determination of this value. 19 19 The total solar eclipse on May 25th provided people with the first observation opportunity after the war. Eddington, an Englishman, went to principe island on the west coast of Africa and made this observation. 165438+1On October 6th, Thomson solemnly announced at the joint meeting of the Royal Society and the Royal Astronomical Society that Einstein, not Newton, had proved this result. He praised "this is one of the greatest achievements in the history of human thought." Einstein discovered not an island, but a brand-new continent of scientific ideas. "The Times reported this important news under the title of" Revolution in Science ". The news spread all over the world, and Einstein became a world-famous celebrity. General relativity has also been elevated to a mythical sacred position.
Narrow sense theory
Narrow sense principle
Matter moves forever in interaction, and there is no matter that does not move and there is no matter that does not move. Because matter moves in interaction, it is necessary to describe motion in the relationship of matter, and it is impossible to describe motion in isolation. In other words, motion must have a reference object, and this reference object is the frame of reference.
Relativity requires that the laws of physics remain unchanged under coordinate transformation (Lorentz change). Classical electromagnetic theory can be incorporated into the framework of relativity without modification, while Newtonian mechanics remains unchanged only under galilean transformation, and the original simple form becomes extremely complicated under Lorentz transformation. Therefore, classical mechanics needs to be revised, and the revised mechanical system remains unchanged under Lorentz transformation, which is relativistic mechanics.
Second, special relativity mechanics
(Note: "γ" is a relativistic factor, γ = 1/sqr (1-u 2/c 2), β=u/c, and u is the velocity of inertial system. )
1. Basic principle: (1) Principle of relativity: All inertial systems are equivalent.
(2) The principle of invariability of the speed of light: the speed of light in vacuum is a constant that has nothing to do with the inertial system.
(Give the formula first and then give the proof)
2. Lorentz coordinate transformation;
X=γ(x-ut)
Y=y
Z=z
T=γ(t-ux/c^2)
3. Speed conversion:
v(x)=(v(x)-u)/( 1-v(x)u/c^2)
V(y)=v(y)/(γ( 1-v(x)u/c^2))
V(z)=v(z)/(γ( 1-v(x)u/c^2))
4. Scaling effect: △L=△l/γ or dL=dl/γ.
5. Clock slowness effect: △t=γ△τ or dt=dτ/γ.
6. Doppler effect of light: ν (a) = sqr ((1-β)/(1+β)) ν (b)
(The light source and detector move in a straight line. )
7. Momentum expression: P=Mv=γmv, that is, m = γ m
8. Basic equation of relativistic mechanics: F=dP/dt.
9. mass-energy equation: E = MC 2
10. Relationship between energy and momentum: E 2 = (E0) 2+P 2C 2.
Note: There are two ways to prove it, one is in three-dimensional space and the other is in four-dimensional space-time. In fact, they are equivalent. )
Three-dimensional proof
The axiom summarized by 1. experiment cannot be proved.
2. Lorentz transformation:
Let the coordinate system (A system) where (x, y, z, t) is located be constant, while the coordinate system (B system) where (x, y, z, t) is located has a speed of U and is positive along the X axis. At the origin of series A, x=0, and the origin coordinate of series B is X=-uT, that is, X+uT=0.
Ke Ling
x=k(X+uT) ( 1)。
Moreover, because the positions of each point in the inertial system are equivalent, K is a constant related to U (in general relativity, due to the curvature of space-time, each point is no longer equivalent, so K is no longer a constant. ) Similarly, there is X=K(x-ut) at the origin of system B. According to the principle of relativity, the two inertial systems are equivalent, and the two formulas should take the same form, that is, k=K, but the speeds are opposite.
So there is
X=k(x-ut) (2)。
For y, z, y, z, regardless of speed, you can get.
Y=y (3)。
Z=z (4)。
Substituting (2) into (1) gives: x = k 2 (x-ut)+Kut, i.e.
T=kt+(( 1-k^2)/(ku))x (5)。
(1)(2)(3)(4)(5) The principle of relativity is satisfied, and the principle of invariability of the speed of light is needed to determine k. When the origins of the two systems coincide, an optical signal is emitted from the coincidence point, and there are x=ct and X=cT for the two systems respectively.
Substitute into the formula (1)(2): ct=kT(c+u), cT=kt(c-u). Multiply two formulas to eliminate t and t:
K = 1/sqr ( 1-u 2/c 2) = γ。 Substituting γ into the coordinate transformation of (2) and (5):
X=γ(x-ut)
Y=y
Z=z
T=γ(t-ux/c^2)
3. Speed conversion:
v(x)=dx/dt=γ(dx-ut)/(γ(dt-udx/c^2))
=(dx/dt-u)/( 1-(dx/dt)u/c^2)
=(v(x)-u)/( 1-v(x)u/c^2)
The expressions of v (y) and v (z) can be obtained in the same way.
4. Scaling effect:
In system B, there is a thin rod with a length of L parallel to the X axis, then it is obtained from X=γ(x-ut): △X=γ(△x-u△t), and △t=0 (measuring the coordinates at both ends at the same time), then △X=γ△x, that is, △ L = γ△ L, △ L.
5. Clock slow effect:
According to the inverse transformation of coordinate transformation, t = γ (t+xu/c 2), so △ t = γ (△ t+△ xu/c 2) and △X=0 (the same location to be measured), so △ t = γ△ t 。
(Note: The length, mass and time interval of an object that is relatively stationary with the coordinate system are called intrinsic length, static mass and intrinsic time, which are objective quantities that do not change with the coordinate transformation. )
6. Doppler effect of light: (Note: Doppler effect of sound is: ν(a)=((u+v 1)/(u-v2))ν(b). )
A light source at the origin of system B emits light signals, while the origin of system A has a detector, and the two systems have two clocks respectively. When the origins of the two systems coincide, the calibration clock starts timing. The frequency of light source in system B is ν(b), the wave number is n, and the time measured by system B clock is △t(b). According to the slow effect of the clock, the time delta measured by the clock in system A is
△t(a)=γ△t(b) ( 1)。
The detector starts receiving at t 1+x/c and ends at t2+(x+v△t(a))/c, and then
△t(N)=( 1+β)△t(a) (2)。
Relative motion does not affect the wave number of the optical signal, so the wave number emitted by the light source is the same as that received by the detector, that is,
ν(b)△t(b)=ν(a)△t(N) (3)。
Can be obtained from the above three formulas:
ν(a)= sqr(( 1-β)/( 1+β))ν(b)。
7. Momentum expression: (Note: dt=γdτ, at this time γ = 1/sqr (1-V 2/C 2) Because the dynamic particle can choose itself as the reference system, β=v/c)
Newton's second law remains unchanged under galilean transformation, that is, Newton's second law holds in any inertial system, but under Lorentz transformation, the original concise form becomes messy, so Newton's law needs to be revised, and the requirement is to keep the original concise form under coordinate transformation.
In Newtonian mechanics, the forms of v=dr/dt and R are invariant under coordinate transformation ((x, y, z) in the old coordinate system and (x, y, z) in the new coordinate system). As long as the denominator is changed into an invariant (of course, it belongs to dτ when it is not fixed), the concept of speed can be corrected. Let V=dr/dτ=γdr/dt=γv be the relativistic velocity. Newton's momentum is p=mv, and replacing v with v can correct the momentum, that is, p=mV=γmv. Define M=γm (relativistic mass) and then p=Mv. This is the basic quantity of relativistic mechanics: relativistic momentum. (Note: We generally use Newton's velocity instead of relativistic velocity to participate in the calculation)
8. Basic equations of relativistic mechanics;
According to the expression of relativistic momentum, the definition of force F=dp/dt is exactly the same as Newton's second law, but the connotation is different. Mass is a variable in the theory of relativity.
9. Mass-energy equation:
ek =∫Fdr =∫(DP/dt)* dr =∫DP * dr/dt =∫vdp = PV-∫pdv
=mv^2-∫mv/sqr( 1-v^2/c^2)dv=mv^2+mc^2*sqr( 1-v^2/c^2)-mc^2
=mv^2+mc^2( 1-v^2/c^2)-mc^2
=Mc^2-mc^2
That is, e = MC 2 = ek+MC 2.
10. Energy momentum relation:
E = MC 2, p=Mv, γ =1/sqr (1-v 2/c 2), E0 = MC 2, we can get: E2 = (E0) 2+p 2c 2.
Four-dimensional proof
The axiom 1. cannot be proved.
2. Coordinate transformation: dl=cdt, that is, DX 2+DY 2+DZ 2+(ICDT) 2 = 0 holds in any inertial system. Define dS as a four-dimensional interval,
ds^2=dx^2+dy^2+dz^2+(icdt)^2( 1)。
Then the optical signal dS is always equal to 0, and the dS at any two time and space points is generally not 0. ds^2>； 0 is called class space partition, DS 2
The mathematical rotation transformation formula is: (keep the Y axis and Z axis fixed, and rotate the X axis and ict axis)
X=xcosφ+(ict)sinφ
icT=-xsinφ+(ict)cosφ
Y=y
Z=z
When X=0 and x=ut, then 0=utcosφ+ictsinφ.
So: tanφ=iu/c, then cos φ = γ and sin φ = iu γ/c are substituted into the above formula:
X=γ(x-ut)
Y=y
Z=z
T=γ(t-ux/c^2)
3.4.5.6. Omit.
7. Momentum expression and four vectors: (Note: γ = 1/sqr (1-V 2/C 2), where dt=γdτ).
Let r=(x, y, z, ict) and replace dt in v=dr/dt with dτ, and V=dr/dτ is called four-dimensional velocity.
Then V=(γv, icγ)γv is a three-dimensional component, V is a three-dimensional velocity, and icγ is a four-dimensional component. (The same is true below)
Four-dimensional momentum: P=mV=(γmv, icγm)=(Mv, icM)
Four-dimensional force: f=dP/dτ=γdP/dt=(γF, γicdM/dt)(F is three-dimensional force).
Four-dimensional acceleration: ω =/dτ = (γ 4a, γ4va/c)
Then f=mdV/dτ=mω.
8. Omit.
9. Mass-energy equation:
fV=mωV=m(γ^5va+i^2γ^5va)=0
So four-dimensional force and four-dimensional velocity are always "vertical" (similar to Lorentz magnetic field force)
From Fv = 0: γ 2mfv+γ IC (DM/DT) (IC γ M) = 0 (F, V is a three-dimensional vector, Fv=dEk/dt (power expression)).
So dek/dt = c 2dm/dt means ∫ dek = c 2 ∫ DM, that is, ek = MC 2-MC 2.
So e = MC 2 = ek+MC 2.
Paradox problem
Clock twinning paradox
After the birth of the theory of relativity, there is a very interesting and difficult problem-twin paradox. A pair of twins, A and B, are on the earth, and B travels in a rocket and returns to the earth after a long time. Einstein asserted from the theory of relativity that the two experienced different times, and B would be younger than A when they met again. Many people have doubts, thinking that A watches B exercise and B watches A exercise. Why can't A be smaller than B? Because the earth can be approximated as an inertial system, and B has to go through the process of acceleration and deceleration, and it is a reference system with variable acceleration, so it is really complicated to discuss. So this problem that Einstein has discussed clearly is mistaken by many people as contradictory relativity. It is much easier to discuss this problem with the concepts of Shi Kongtu and World Line, but it requires a lot of mathematical knowledge and formulas. Here, we just use language to describe the simplest situation. However, it is impossible to explain the details in more detail by language alone. If you are interested, you can refer to some books on relativity. Our conclusion is that B is younger than A in any frame of reference. Because B is accelerated, you see that at first on the earth, the relative speed of A is zero, and then the speed is close to the speed of light (note that it is close). Obviously, this is a speed-changing exercise, so we can't say "I think A is watching B and B is watching A". Why can't A be smaller than B? " This sentence is simply a misunderstanding of relativity. Moreover, B's youth is relative to A's, and there is no question of how long he can live.
In order to simplify the problem, we will only discuss this situation. After a while, the rocket accelerated to sub-light speed. Fly for a while, turn around for a short time, fly for a short time, and slow down for a short time to meet the earth. The purpose of this treatment is to ignore the effects of acceleration and deceleration. It is easy to discuss in the earth reference system that the rocket is always a moving clock, and B is younger than A when we meet again. In the rocket reference system, the earth is the moving clock in the process of uniform motion, and the time process is slower than that in the rocket, but the most critical place is the process of rocket rotation. In the process of U-turn, the earth crossed half a circle from the distance behind the rocket in a very short time and reached the distance in front of the rocket. This is a "superluminal" process. It's just that this superluminal and relativity are not contradictory. This superluminal can't transmit any information, and it's not superluminal in the real sense. Without this u-turn process, the rocket and the earth would not meet. Because there is no uniform time in different reference systems, it is impossible to compare their ages. Only when they meet can they be compared. After the rocket turns around, B can't accept the message from A directly, because it takes time to transmit it. The actual process that B saw was that during the U-turn, the earth's time schedule accelerated sharply. In B's view, A was younger than B at first, then aged rapidly when he turned around, and aged faster than himself when he returned to China. When we meet again, we are still younger than A. In other words, there is no logical contradiction in the theory of relativity.
Generalized theory
The concept of general relativity
When the theory of relativity came out, people saw the following conclusions: four-dimensional curved space-time, finite boundless universe, gravitational wave, gravitational lens, big bang cosmology, black hole, the main theme of 2 1 century, and so on. All this comes too suddenly, which makes people feel that the theory of relativity is mysterious. Therefore, in the early years of the advent of the theory of relativity, some people threatened that "only twelve people in the world understand the theory of relativity." Some people even say that "only two and a half people in the world understand the theory of relativity". What's more, the theory of relativity is compared with spiritualism and idealism. In fact, the theory of relativity is not mysterious. It is the most down-to-earth theory, a truth that has been tested thousands of times, and not unattainable.
The geometry applied by relativity is not ordinary Euclidean geometry, but Riemann geometry. I believe many people know non-Euclidean geometry, which can be divided into Roche geometry and Riemannian geometry. Riemann unified three kinds of geometry from a higher angle, which is called Riemann geometry. Non-Euclidean geometry has many strange conclusions. The sum of the internal angles of a triangle is not 180 degrees, and the pi is not 3. 14. So when it was first put forward, it was ridiculed as the most useless theory. It was not until its application was found in spherical geometry that it was paid attention to.
If there is no matter in space and space-time is flat, then Euclidean geometry is enough. For example, the application in special relativity is four-dimensional pseudo-Euclidean space. Because there is an imaginary unit I in front of the time coordinate, a pseudo word is added. When matter exists in space, the interaction between matter and space-time bends space-time, which means using non-Euclidean geometry. Without matter, there is no space, because even if there is, you will never find it, because when you see it, it has matter, at least light.
Relativity predicted the existence of gravitational waves, and found that both gravitational fields and gravitational waves travel at the speed of light, denying the distance effect of the law of universal gravitation. When light comes from a star and meets a massive celestial body, it will converge again, that is, we can observe the stars blocked by celestial bodies. Generally speaking, what you see is a ring called Einstein ring. When Einstein applied the field equation to the universe, he found that the universe was not stable, and it either expanded or contracted. Cosmology at that time believed that the universe was infinite, static and the stars were infinite. So he did not hesitate to modify the field equation, added the universe term, got the stable solution, and put forward the finite infinite universe model. Soon Hubble discovered the famous Hubble law and put forward the theory of cosmic expansion. Einstein regretted this and gave up the cosmological term, calling it the biggest mistake in his life. In later research, physicists were surprised to find that the universe was not only expanding, but also exploding. The very early universe was distributed in a very small area. Cosmologists need to study the content of particle physics to put forward a more comprehensive model of the evolution of the universe, and particle physicists need cosmologists' observations and theories to enrich and develop particle physics. In this way, the two most active branches of physics-particle physics and cosmology-are combined with each other. As the preface of high school physics says, it's like a strange python biting its tail. It is worth mentioning that although Einstein's static universe has been abandoned, its finite boundless universe model is one of the three possible fates of the future universe and the most promising. In recent years, the cosmological term has been revalued. The problem of black holes will be discussed in a future article. Although black holes and big bang are predictions of relativity, their contents have gone beyond the limitation of relativity and are closely combined with quantum mechanics and thermodynamics. I hope the future theory can find a breakthrough here.
Generalized theoretical formula
According to the general theory of relativity, "the motion of all substances in the universe can be described by curvature, and the gravitational field is actually a curved space-time", Einstein gave the famous Einstein field equation:
Where g is Newton's gravitational constant, which is called Einstein's gravitational field equation, also called Einstein's field equation. 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:
Principle of generalized theory
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 move in inertia, but it is not a standard uniform motion.
Verification of generalized theory
When Einstein established the general theory of relativity, he put forward three experiments, which were quickly verified: (1) gravitational redshift (2) light deflection (3) Mercury perihelion precession. Until recently, the fourth verification was added: (4) the time delay of radar echo.
(1) Gravitational redshift: The general theory of relativity proves that the inherent time passes slowly where the gravitational potential is low. In other words, the closer to the celestial body, the slower the time. In this way, the period of light emitted by atoms on the surface of celestial bodies becomes longer, and the corresponding frequency becomes smaller because of the constant speed of light, and moves in the direction of red light in the spectrum, which is called gravitational redshift. There are many dense celestial bodies in the universe. We can measure the frequency of the light they emit and compare it with the light emitted by the corresponding atoms on the earth. It is found that the red shift is consistent with the prediction of relativity. In the early 1960s, people used the recoil-free vibration absorption effect (Mossbauer effect) of gamma rays in the earth's gravitational field to measure the vertical propagation of light. 5M, the result is consistent with the prediction of relativity.
(2) Light deflection: According to the fluctuation of light, light should not be deflected in the gravitational field. According to the mixed product of semi-classical "quantum theory plus Newton's gravity theory", the mass of photons is calculated by Planck formula E=hv and mass-energy formula e = MC 2. The deflection angle of light near the sun obtained by Newton's law of universal gravitation is 0.87 seconds, and that calculated by general relativity is 65438. 19 19, just after the first world war, British scientist Eddington sent two expeditions to take advantage of the solar eclipse to observe, and the observation result was about 1.7 seconds, which was just within the error range of the relativistic experiment. The main reason for the error is the deflection of light by the sun's atmosphere. Recently, radio telescopes can be used to observe the deflection of quasar waves in the solar gravitational field, without waiting for the rare opportunity of solar eclipse. Accurate measurement further confirms the conclusion of relativity.
(3) Precession of Mercury Perihelion: Astronomical observation records that Mercury Perihelion moves for 5600 seconds every hundred years. People have considered various factors, and according to Newton's theory, only 5557 seconds can be explained, leaving only 43 seconds. The calculation result of general relativity deviates from the law of universal gravitation (inverse square law), which just makes the perihelion of Mercury move for 43 seconds every 100 years.
(4) Radar echo experiment: transmit radar signals from the earth to the planet, receive the signals reflected by the planet, measure the round-trip time of the signals, and check whether the space is bent (check the sum of the angles in the triangle). In 1960s, American physicists did this experiment despite many difficulties, and the result was consistent with the prediction of relativity.
Einstein put forward the famous formula of mass and energy in the special theory of relativity: e = MC 2 (where e represents the energy of an object, m represents the mass of an object, and c represents the speed of light, that is, 300,000 kilometers per second. )
Einstein's formula of mass-energy relationship correctly explains all kinds of nuclear reactions: take helium 4 as an example, its nucleus consists of two protons and two neutrons. In principle, the mass of helium 4 nucleus is equal to the sum of the masses of two protons and two neutrons. In fact, this arithmetic doesn't hold water. The mass of helium nucleus is 0.0302 atomic mass unit less than the sum of the mass of two protons and two neutrons [57]! Why is this? Because when two deuterium [dao] nuclei (each deuterium contains 1 proton and 1 neutron) are polymerized into 1 helium 4 nuclei, a large amount of atomic energy is released. When 1 g helium 4 atom is generated, about 27000000000000 joules of atomic energy are released. Because of this, the mass of helium 4 nucleus decreases.