What is length?

Length is the measurement of an object from end to end. In mathematics, length is only an interval between points. Previously, M(meter) was defined as the distance between two scratches on a bar of platinum-iridium alloy held in France. The meter has been defined in various different ways by the measurement techniques at that time.

Recently, The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.

Consequently, there is no an absolute standard of length in this world. Physicists has defined length because of their necessity. God and human beings cannot determine the standard of length. If we don't know the length of an object, we cannot enter further into the detalis of physics.

Under these situations, the relativity theory introduced the new understanding of object into Physics, but it omitted the concept of a body's length because of its difficulty and complexity. The theory gave birth to a strange results, like "Twins paradox and length contradict"

Until now, Physics has not known theoretically about the length of object .

picture1)

For example, If there is only one rod, we don't know whether the rod is long or short in the pic1

picture2)

In the picture2, we can know whether the rod is long or short. Such a relative comparison of the rods is easier to understand the concepts of length than when the rod is only one. If the rod C is a standard of other rods,

The mathematical expression can become a/c, b/c, d/c, when we know that a,b,d are longer or shorter than the standard rod C. It is the same as the rod (3m) is 1.5 times longer than the length of rod (2m)

However, if other peoples assert that a,b,d can become a standard of the rod length, we may be confused. The serious question does not stop here.

The fundermental question will be that "Where is the length of an object. ?" . We cannot reply this question.

Until now, human beings have commonly regarded the length of a rod as the interval between a and b. However, length of a rod can become the interval of line A and a diagonal line. Length is defined as a distance between ends of an object. Therefore, we can say that the shape of object is composed of countless lengths.. To know the length of object is the same as to know the mass of object. As we understand the length of object, we can know precisely the motion of object. (The standard of mass may be equally applied to the all place.)

The length of object A ( if radius is r ) is not a 2pir and diameter 2r. The length of object B is not the base , it's sides, height,diagonal line. The length of object C cannot be determinded as the object B. It is impossible to decide the length of a object under the condition which there is no an absolute standard of interval length. Length is a extension of interval.

In geometry, a line is a line which lies evenly with the points on itself. But in physics, length may be defined as a line , consisting of indivisible particles. Thus, the shape of object is formed by the numberless intervals which is a reduction of length.

Also, the extension of length( in geometry) is space. We must consider the given condition in space to understand the shape and length of a object. The space which is dominated by that object is a event and probability. Space is a only one, identical. Also space is infinite. The concepts of such a space, length, point, line, interval are well recognized by "Cartesian coordinate".

The object b dominates interval dx on the X-axis. Spacelength is a realistic interval, a line which pass through the object. Without a object, spacelength is impossible to exist. Spacelength is a extension of interval dx. Spacelength constitutes of dx)

Mathematicians have freely taken the coordinate-axis because they concentrates on a figure and body. But spacelength doesn't do that. Without a object, spacelength is impossible to exist. (Mathematicians proved that dx is not zero. )

Therefore, if there is only one spacelength , the length of a object is L=dx/X

If there are two spacelengths , the length of object is l=dx1/X (+) dx2/X

( (+) is a probability symbol. This symbol is needed to show all possible events .

For example, if we roll a fair dice, we obtain a 6 events. Let P be all events.

If we toss a fair coin, we will see the front and rear of the coin. Then, P= front (+) rear. If there are 3 spacelengths , the length of object is as follows.

The countless spacelengths can be existed ,therefore the length of object is.

Consequently, the formation of a length of general object shows that space and matter cannot be independently exist of each other. (Also, if dx1=dx2=dx3= ...........=dxn , then the place is a point because dx does not exist between continuous two points.)