Analysis:
Theory of relativity
/kloc-In the late 20th century, due to the establishment of the wave theory of light, scientists thought that space was full of a continuous medium called "ether". Just like sound waves in the air, light and electromagnetic signals are waves in the ether. However, the opposite result to the idea that space is full of "ether" soon appeared: according to the "ether" theory, the speed of light propagation should be a constant value relative to "ether", so if you are in line with the direction of light propagation, the speed of light you measure should be lower than that you measure at rest; On the contrary, if you travel in the opposite direction to the direction of light propagation, then the speed of light you measure should be higher than that you measure at rest. However, a series of experiments found no evidence of the difference in light speed.
Among these experiments, Ahlport Michelson and Eddie Ward Murray of the Case Institute in Cleveland, Ohio, USA made the most accurate and detailed measurement in 1887. They compared the propagation speeds of two right-angle beams. Because of the rotation around the rotation axis and the revolution around the sun, according to reasoning, the earth should pass through the "ether", so the two beams of light at right angles should be measured at different speeds due to the movement of the earth. Irish physicist George Fitzgerald and Dutch physicist Hen Zhuo Ke Lorenz first thought that the size of an object moving relative to the "ether" would shrink in the direction of motion, while the size of an object moving relative to the "ether" would shrink. Lorenz put forward the famous Lorentz transformation. As for "ether", Fitzgerald and Lorenz thought it was a real substance. Poincare, a French mathematician, expressed doubts about this and predicted that a brand-new mechanics would appear.
The philosophy of Mach and Hume had a great influence on Einstein. Mach believes that the measurement of space-time is related to the movement of matter. The concept of time and space is formed through experience. Absolute time and space, no matter what experience is based on, can't be grasped. More specifically, Hume said: Space and extension are just visible objects that are filled with space and distributed in a certain order. And time is always discovered through the perceptual changes of changeable objects. 1905, Einstein pointed out that Michelson and Morey's experiments actually showed that the whole concept of "ether" was redundant and the speed of light was constant. Newton's concept of absolute space-time is wrong. There is no absolutely static reference object, and the measurement of time varies with different reference frames. He put forward Lorentz transformation based on the principle of invariance of light speed and relativity. Created the special theory of relativity.
restricted theory of relativity
Special relativity applies to inertial reference system.
1, two basic principles of special relativity
(1) The principle of special relativity-the laws of physics have the same form in all inertial systems. All inertial systems should be equivalent, and there is no special inertial system. That is to say, the laws of things in each inertial system are the same. (in terms of rationality)
(2) The principle that the speed of light is constant-in all inertial systems, the speed of light in vacuum has the same value. The speed of light has nothing to do with extensive motion; The speed of light has nothing to do with frequency; The average round-trip speed of light is independent of direction. (This principle comes from Michelson-Morey experiment. )
2. Lorentz transformation, the core of special relativity kinematics.
With these two new axioms, the very important Lorentz transformation relation is naturally derived. A photon emitted from t=0 x=0 is discussed in σ system and σ' system (when t=0, σ' system coincides with σ system, and then σ' moves along X axis with V), according to:
1, spatiotemporal uniformity: x=γ(x'+vt')
2. Principle of relativity: x'=γ(x-vt)
3. Principle of constant speed of light: x=ct
x'=ct '
Among them, the condition of space-time consistency is not a new principle, and it is very intuitive that a fixed object is placed at any position in space whenever it has the same length. From simple reasoning, we can know that the coordinate transformation of uniform space-time is linear. Because if: x=ax'2+bt', the length of the object is measured at any time (dt'=0): dx=2ax'dx'. It can be seen that any Dx' placed in different X' is different for the sigma system. That is to say, the space of sigma system is not uniform and intuitive. Because ∑' and ∑ are equivalent, if the ∑' system becomes the ∑ system of x=γ(x'+vt'), then the ∑ system becomes the ∑ system of x'=γ(x-vt), which shows that the principle of relativity is fair to different inertial systems. Finally, the two relations given by the principle of light speed invariance seem puzzling, but they are supported by experiments. Solve the four equations in this way, and immediately get the Lorentz transformation:
Σ system →Σsystem →Σsystem
x=γ(x'+vt') x'=γ(x - vt)
y=y' y'=y
z=z' z'=z
t=γ(t'+vx'/c2) t'=γ(t-vx/c2)
Lorentz transformation unifies space-time and motion, and unifies the high-speed world and low-speed situation of classical mechanics research. When v
3. Space-time view of special relativity
① Relativity of simultaneity: δt =γ(δt '+δx '/C2), δt' = 0, generally δt≠0. X'/c2 is called the simultaneous coefficient.
② The moving clock slows down: from Δ t = γ (Δ t'+Δ x'/C2), because Δ δx' = 0 in the moving clock's own reference system, then Δ δt =γ(δt '+δx '/C2
③ Shorten the movement length: from Δ x = Δ x'/γ+Δ t, because Δ δt = 0 and Δ x =Δx'/γ = Δ x' ≤ when measuring the movement length, it is often called contraction factor and expansion factor.
4. Special Relativistic Mechanics
(1) relativistic mass
Discussion: A ball with a mass of m0 moves along the X direction with V in the ∑ system, while the same ball B in the ∑' system moves with V relative to the ∑' system ux'= -V, and the two balls collide completely elastically, as shown in the figure:
According to:
∑ system is momentum conservation;
(m+m0)ux=mv
For the Sigma system, through the conservation of momentum:
(m+m0)ux'= -mv
Speed conversion formula:
By solving these equations, we can get that m=γm0 should increase the velocity v (γ increases) and the mass m should also increase.
(2) Relativistic mass-energy relationship
Discussion: A single particle moves a certain distance under the action of external force F, so that the kinetic energy changes from 0 to 0→EK.
According to: kinetic energy theorem: A = δ ek
Newton's law:
Mass-velocity relationship: m=γm0
Deduction: ek = ek-0 = Δ ek =
Substitute → m2c2-p2= m02c2 → pdp= mc2dm into the above formula:
EK=
Obviously, the total energy of particles is: E=mc2.
The rest energy of the particle is E0=m0c2.
The kinetic energy of a particle is:
EK = mc2–m0c 2 =
Visible particle kinetic energy is not equal to the classical form, but when V
(3) Relativistic mechanical equation
Newton's law is often written in classical physics, but modern physics proves that it is only approximate at low speed. The general form is. This is actually the definition of force. Force is the reason for the change of the overall motion state of an object. It is more comprehensive to use p to represent the state parameters than v, because v only represents the relative motion factor of the object, and P=mv represents the complete number of motions when the whole object makes relative motion.
Theory of relativity
Although relativity is perfectly combined with the relevant laws of electromagnetic theory, it is incompatible with Newton's law of universal gravitation. Newton's theory of gravity shows that if you change the distribution of matter in space, the gravitational field of the whole universe changes at the same time, which not only means that you can send signals that travel faster than the speed of light (which is not allowed by relativity), but also requires an absolute or universal concept of time, which is abandoned by relativity. 19 1 1 year, Einstein thought deeply about this problem. Einstein realized the close relationship between acceleration and gravity field. A person in a sealed compartment can't tell whether his own pressure on the floor is because he is in the gravity field of the earth or because he is accelerated by a rocket in a weightless space. So he put forward the principle of equivalence between gravity and acceleration. Riemann geometry is used to deal with curved four-dimensional space, and general relativity is established.
19 15 Einstein extended the principle of special relativity to a more general case, that is, a non-inertial system, and established the general theory of relativity.
1. Equivalence principle-a non-inertial system is equivalent to a gravitational field.
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, the equality of gravitational mass and inertial mass is the third hypothesis in Einstein's argument.
Einstein has been looking for the explanation that "gravitational mass equals inertial mass". He believes that if an inertial system is uniformly accelerated relative to a Galileo system, then we can consider it (inertial system) to be static by introducing a uniformly accelerated gravitational field relative to it. 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. Therefore, 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. All objects in the gravitational field "fall at the same speed" is the equivalent result of inertial mass and gravitational mass (in classical mechanics)
2. The principle of general relativity-the laws of nature (the basic laws of physics) are the same in all departments.
This is Einstein's fourth hypothesis and a generalization of his first hypothesis. 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.
3. Description of general relativity
19 12 Einstein realized that if some adjustments were introduced into real geometry, the equivalent relationship between gravity and acceleration could be established. Einstein imagined that if the space-time entity formed by three-dimensional space plus the fourth-dimensional time was curved, what would be the result? His idea that mass and energy will bend space-time may have been proved in some ways. Like planets and apples, objects tend to move in straight lines, but their trajectories seem to be bent by gravity because space-time is bent by gravity.
19 13 With the help of his friend Marshall Glossmann, Einstein studied the theory of curved space and surface, namely Riemann geometry. When Bernhard Riemann developed these abstract theories, he never thought that they would be related to the real world. Gravity as we know it is only an expression of the fact that space-time is curved.
General relativity puts forward three testable predictions. The first is the perturbation of Mercury's perihelion, pointing out that the planet in orbit does not completely return to its original position in space every time it completes a cycle, but moves forward slightly. This fact was discovered as early as the middle of19th century, but the classical Newton celestial mechanics can not satisfactorily explain the perturbation phenomenon. The second prediction is that light will deflect in the gravitational field. According to this statement, when starlight passes near the sun, it will be deflected by the sun's gravity. The result is a change in the position of the star. This phenomenon can only be observed during the total solar eclipse, otherwise the strong light of the sun will make it impossible to observe the stellar light near the sun on the ground (Swiss astronomer M. Schwarzschild made a detailed quantitative description of this phenomenon). The third prediction is often called the "red shift" of spectral lines, that is, the stellar radiation always leaves us.
Shortly after the First World War, British astronomer Eddington organized a British solar eclipse observation team at 19 19 to detect the prediction that starlight would deflect when passing through the total solar eclipse. Two observation teams set out separately, one was sent to Sobral, Brazil, and the other was led by Eddington to principe island near the Spanish Guiana coast. The observation results were consistent with the prediction, which immediately shocked scientists and the public all over the world.