An object in motion continues to move with constant velocity unless acted on by an external force. The equation Ft=mv well explains how the rest object begin to move. I will not debate this theory because Newton's motion law exactly explain the phenomena.

If there is one question, it is "where is the length of moving object?"

This question is very important in this chapter. In describing the motion of an object, the appearance of time "dt" is more difficult to explain than that of the Chapter 1. Also, what is the absolute standard of Time ? And where is the position that an observer has to be located for seeing?

If a motion occurs in space, that is, the occurred event is absolute but I don't know whether the speed of the body is fast or slow, where is the body?, how much time the motion has?". Futhermore, It is difficult to decide the motion's direction.

In classical physics, the observer seemed to be always located at the absolute position and he has described the motion as it was. The excellence of relativity theory is that can criticize the observing method of classical physics.

For example, if two bodys have a velocity v1,v2 respectively, then the observer can easily decide whether the velocity v1 is faster or slower than the velocity v2 .But the velocity v2 is not an absolute standard that can decide whether the velocity v1 is faster or slower.Because there is no absolute coordinates, there is no absolute standard of velocity. The necessity of absolute standard of velocity is because we must know whether the speed of moving object is faster or slower than any other.

If we profoundly think about that, we can find the absolutely unchangeable velocity in nature( empty space or vacuum). As shown in a result of The Michelson-Morley Experiment , it is that the speed of light C is the same in any inertial reference frame. Therefore, the speed of light can become an absolute standard of velocity. Using this principle, the relative comparison of velocity is A=v/C.

As we obtain the above formula, we can solve one by one the riddles which the classical physics omitted.

That is "How the comparison of the velocity of general object with the speed of light is possible?" Although the comparison of the velocity of a real object with the speed of light was at first appeared in Bradly's the aberration theory, he didn't know the important meaning of how the comparison is possible. Even though the C was appeared in the relativity theory, Einstein and Lorentz didn't know how the comparison of v/c is possible. This v/c only played an important role in supporting their main theory.

The description of motion, according to the observer's position,can be different in free space.

The V and C are analyzed as follows. If an object traveled the distance dx with the velocity v, when the speed of light traveled the total distance X during the time dt, then the velocity of an object is as follows.

The speed of light is as follows C=X/dt. But, the description of motion is changed by the position of observers in free space , when there is no an absolute coordinate system. The observers A, B, C, D, E have a different positions and coordinates of an object's velocity. No matter how the obsevers take the position where is well observed and seen, no one can assert that his place can become an absolute standard of coordinate . Therefore , as its usefulness was shown in the previous chapter, we have to analyze the moving object with n-th spacelength.

If we are not doing so, we cannot ignore the observer's arbitrary assertions.

The formula (1) may satisfy all of the observers and coordinates at the same time. We have to compare the formula (1) with the speed of light to know how the velocity is slower than light in the universe.

The form "A" is equal to the form "L" in the previous chapter. If this equivalence is not wrong, it means that the speed of light is a certain connection with the object. In the classical physics, it was a tendency that the object is not related to the speed of light. The background of these physical thoughts was because there was no connection between light and formula of an object's motion.

Only, light has been something that can see the object and stimulates the organs of light. Also, light had been accepted as an mediator to connect space to matter. Newton suggested that under certain circumstances, light and matter might be changed into each other. Light is not produced by itself but by matter. Besides light becomes an absolute standard of velocity, it gave rise to a guess that light might be connected with matter. These conjectures will be discussed in the next chapter. The new fact that the length of general object is equal to the length of moving object ,gives rise to a new debate.

But, If we correctly know the relativity of motion and the nature of object, this argument is a trivial thing. (L=dx/X, A=dx'/X'), where consequently the dx is not equal to the dx' because X is a spacelength and X' is a traveled distance during the time dt. The dx is an interval of object and dx' is a interval which the object traveled because X is spacelength and X' is the traveled distance during the time dt. Physics, however , has to accept the major premise as Elements. It is not to logically explain itself to obtain the results. This is only to narrow the gap between the theoretical space in mathematics and space, we really feel.

The experiment and observation are the first,but there are a some limits in it. The distance is invariant and the place where light doesn't reach during the time dt cannot be a space and the speed of light is always the same to all observers . Hence, the equivalence of X and X' is natural enough. When the observer and object are at stationary, they have no time.

To move, that is, the displacement of object is very different with the rest condition. There is a big difference between at rest and moving object . Maybe, The persons who cannot feel and perceive this difference may not understand the entire physics. . At a given time, the trace traveled by an object is the distance traveled by the object ,when the object is moving. But, the object at rest is not necessary to perceive time because there is no time.

All observers have to see the length of object moving at a given time. As time is eliminated , the form of the length of moving object must be equal to the length of object at rest. Because time is continuous and felt when an object is moving and the nature of matter is not dominated by time. If the length of object at rest is not equal to the length of object moving ,then this means that the object is not one but two.

Mathematics don't deal with time. Also, time is not mathematical concept. Time is only a concept of mind. Time is a physical habit .

For example, The observer A on earth exactly express that the rest object stays at rest. But the observer B in space express that the body at rest on earth is moving at the same velocity ,like earth. The passenger A inside the bus and the B on the station experience the same phenomenon. Without mutual communication, the observer A, B will assert that " you are wrong". The observer A insists on having his own way. The reasonable observer C( or you) will think that the observer B is much more right and clever than the observer A. In old times, the Copernican Revolution, proved that the ancient astronomy is wrong, said that the observer A is very stupid, unreasonable. This example states that the position of an observer is very important in the relativity of motion. Until now, I struggled to find out an length of moving object with different condition, situation, reasoning, logic; Nevertheless, the two observers obtained the same result.

The moving body has its length. But the length must be equal to the length of rest body when time is eliminated. The observer B exactly knows the process of the reasoning . The observer B's reasoning is right because he knew that the body on earth is continuously moving with the velocity V when the observer A only knew the body on earth is at rest.

Therefore, A=L Also, A=L is sufficient to prove the one among Einstein's two principles, based on the Special Relativity theory.

He stated that "All laws of nature take the same form for all observers moving with constant velocity." For example, the one observer standing at the apple tree and the other observer in a plane conclude that the apple falling toward earth is the same phenomenon. " The speed of light in a vacuum, measured in any inertial reference frame, always has the same value of c, no matter how fast the source of light and the observer are moving relative to each other" "The speed of light c in space is the same in all inertial reference frames." "If two events occur at the same time and at the same place in one reference frame, then they occur at the same time and place in all reference frames.