First, Galileo's relativity principle and the time-space view of classical mechanics

Inertia system: an object that is not acted by external force or whose resultant force is zero remains stationary or moves in a straight line at a constant speed. Such a reference system is called inertial reference system, or inertial system for short.

(New thinking: If we recognize the causes of non-uniform force in physical experiments and calculate this force (inertia force), we can get the same conclusion as jumping out of the non-inertial system and doing experiments in the inertial system, and we can treat the non-inertial system as an inertial system-this is similar to the relativity principle of general relativity).

The inertial system of all uniform linear motion is completely equivalent to describing the mechanical laws of mechanical motion. Any mechanical experiment done "inside" the inertial system cannot determine whether the inertial system itself is static or moving in a straight line at a constant speed. This principle is called mechanical relativity principle, or Galileo relativity principle.

Newton said: "Absolute, real and mathematical time passes by itself, and it passes evenly and independently of any external object because of its nature." "Absolute space, by its very nature, has nothing to do with anything outside, but is always constant and motionless." (See Newton's book Mathematical Principles of Natural Philosophy)

Second, the background of special relativity

At the end of 19, people knew that the speed of light was limited. When measuring the speed of light, it is found that the light emitted by Jupiter's satellite reaches the earth at the same time, no matter whether the earth moves towards or away from the satellite. This does not conform to the velocity superposition principle of object motion (the velocity of frame A relative to frame B is V 1, the velocity of object relative to frame A is V2, and the velocity of object relative to frame B is V 1+V2), but it conforms to the essence of fluctuation. Because all the waves known at that time had a medium, people assumed that light also had a medium, so it was named "ether", and light propagated stably in the ether, so it was similar to.

Because the earth is not a special celestial body in the universe, the ether should be moving relative to the earth, and the famous experiments of A.A. Michelson and E.W. Molly prove that the ether moving relative to the earth does not exist, that is, if there is ether, it is static to the earth. This is a little different from some people who think that ether does not exist.

1905, Einstein put forward two hypotheses:

1。 Principle of Relativity: Physics has the same mathematical expression in all inertial reference frames, that is, all inertial reference frames are equivalent to describing physical phenomena. (absolutely enough)

2。 Principle of invariability of light speed: In any inertial reference system that makes uniform linear motion relative to each other, the measured light travels at the same speed in vacuum.

From 1964 to 1966, CERN made accurate experimental measurements of the speed of light in the proton synchrotron, which directly verified the principle that the speed of light is constant. The experimental results show that a meson generated in the synchrotron (recorded as a power of 0) flies at a high speed of 0.99975c, and it decays in flight, radiating photons with energy of 60000000000 EV, and the measured photon laboratory speed is still C.

Third, the space-time view of special relativity.

Special relativity provides people with a view of time and space different from classical mechanics. According to classical mechanics, two events that occur at the same time in different places relative to one inertial system also occur at the same time relative to another relatively moving inertial system. But the theory of relativity points out that the problem of simultaneity is relative, not absolute. Two events that occur at the same time in different places in one inertial system may not happen at the same time in another inertial system. Classical mechanics holds that the measurement of time and space does not change with the choice of inertial system, that is to say, the measurement of time and space is absolute. Relativity holds that the measurement of space-time is relative, not absolute, and they will be different because of the choice of inertial system. All these are the concrete embodiment of the space-time view of special relativity.

Relativity of simultaneity

Let's do a hypothetical experiment. A train running at a constant speed has two signs, A 1 and B 1, at the front and rear respectively. When they coincide with the two marks A and B on the ground, they flash respectively. The receivers are installed at the midpoint of C of A and b and at the midpoint of A 1 and B 1 respectively. Point C will receive signals from both ends at the same time, and the signal transmission will take time. During this period, the train moves forward, so C 1 first receives the signal from the front, and then receives the signal from the back. In other words, different frames of reference do not think that two events happen at the same time. "At the same time" is relative.

Fourthly, Lorentz coordinate transformation.

Lorenz formula was established by Lorenz to make up for the defects exposed in classical theory. Lorenz is a theoretical physicist and the founder of classical electronic theory.

The coordinate system K 1(O 1, X 1, Y 1, Z 1) moves in a straight line at a constant speed relative to the coordinate system K(O, x, y, z); The three pairs of coordinates are parallel, and V is along the positive direction of the X axis. Let the X axis coincide with the X 1 axis, and the origin O 1 coincides with O when T 1=T=0. Let P be an observed event, and the observer "sees" it in the K system. At time t, it occurs at (x, y, z), but it occurs at time T 1 (X 1, Y 1, Z 1) according to the observer of the K 1 system. This transformation between two coordinate systems is called Lorentz coordinate transformation.

Before deriving Lorentz transformation, as postulate, we must assume that time and space are unified, so the transformation relationship between them must be linear. If the equation is not linear, the measurement results of the spatial interval and time interval of two specific events will be related to the position and time of the interval in the coordinate system, thus destroying the unity of time and space. For example, if X 1 is related to the square of x, that is, x1= ax 2, then the relationship between the distance of two K 1 systems and their coordinates in the k system is expressed as x1a-x1b = a (xa 2 Now, let's assume that there is a rod with unit length in the K series, and its end points fall at Xa=2m, Xb= 1m, then X 1a-X 1b=3Am. If the endpoint Xa=5m and Xb=4m of the same rod, then we get X 1a-X 1b=9Am. In this way, the measurement results of the same rod will change with the position of the rod in space. In order not to make the selection of the origin of our space-time coordinate system have some physical particularity relative to other points, the transformation formula must be linear.

Write galilean transformation first: x = x1+vt1; X 1=X-VT

Increase the coefficient k, x = k (x1+vt1); X 1=k 1

According to the relativity principle of special relativity, k and K 1 are equivalent, and the forms of the above two equations should be the same (except the sign), so the proportional constants k and k 1 in the two equations should be equal, that is, there is k=k 1.

Therefore, X 1=k(X-VT).

In order to get certain transformation rules, we must find the constant k. According to the principle that the speed of light is constant, assuming that when o and O 1 coincide (T=T 1=0), the optical signal will advance along the OX axis from the coincidence point, then at any time t (measured by coordinate system K 1, that is, T 1), the coordinates of the optical signal's arrival point will be in two coordinate systems. X 1=CT 1

xx 1=k^2(x-vt)(x 1+vt 1)

c^2 tt 1=k^2 TT 1(c-v)(c+v)

From this

k = 1/( 1-v^2/c^2)^( 1/2)

therefore

t 1=(t-vx/c^2)/( 1-v^2/c^2)^( 1/2)

t 1+vx/c^2)/( 1-v^2/c^2)^( 1/2)

Einstein's hypothesis:

1. The laws followed by the state changes of physical systems have nothing to do with which of the two coordinate systems with uniform motion is used to describe these state changes.

2. Any light moves at a certain speed c in the "stationary" coordinate system, no matter whether it is emitted by a stationary or moving object. "