Special theory of relativity (in terms of time)

[Axiom]

It was definitely shown that speed of light is 300,000 km/s.
In other words, it will lead to No matter how an object is moving, the speed of light coming from the object is constantly 300,000 km/s.

[Thought experiment]

According to understanding from Newtonian mechanics, when a man walks at 4 km/h in tha train running at 40 km/h, his speed will be
40 km/h + 4 km/s = 44 km/s.

When a rocket flies over the earth at half speed of light 150,000 km/s and emits light forward, the speed of light ought to be
150,000 km/s + 300,000 km/s = 450,000 km/s.

However, since speed of light must be 300,000 km/s without exception, the right understanding ought to be
150,000 km/s + 300,000 km/s = 300,000 km/s.
The method of calculation according to Newtonian mechanics may be wrong.

Here, taking into account speed = length / time, we can get
speed of rocket = 150,000 km/s
speed of light emitted from rocket = 300,000 km/s, and
speed of light as observed = 300,000 km/s.

[Conclusion]

The reason why the expression 150,000 km/s + 300,000 km/s = 300,000 km/s contradicts itself may be explained if we understand as follows:
A world in which the left side is moving and one in which the right side is at rest have their different lengths and time.

[Formula of time shift]


When light is emitted from the bottom to the top in a rocket, time interval during which the light arrives at the top is defined as t second. Then, a length between A and B will be ct as shown in the figures.


If the rocket is moving at a speed v, a position B ought to have shifted until the light will arrive at B.
In order to study the "shift," we fix our eyes upon the motions of A and B.


Those who are in the rocket will insist that the time interval during which the light arrives at the top B is t second. For those who are on the earth, the light trajectory will be longer than AB, that is, A'B along which light (300,000 km/s) will pass, so needing the more time that is defined as T second. The length then will be cT.


Suppose the rocket is moving at the speed v. The shift distance then is vT.

According to Pythagorean theorem, we have
(ct)2+(vT)2=(cT)2
Upon transforming this, we therefore have

This means that t second as in the rocket will seem to be a greater time T second than as from the earth.
However, those who are in the rocket can understand "the earth is moving", and so both methods of thinking are the same for those looking at the rocket from the earth and those looking at the earth from the rocket.
One ought to seem that the other has the greater speed and time.

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