What is Special Relativity (4)
How did we get our formula?
First, we assumed the swimmer's motion is relative, and let him do a round trip along the bank, that is why the c-v and c+v are there.
Then, we assumed the swimmer's motion is absolute. That is to say, whether relative to the bank or to the river water, the swimmer's speed is always c.
In the end, to make up the difference between the average speed in relative motion and in absolute motion, we have no choice but to make the clock slower or to make the ruler shorter.
Einstein did exactly the same thing!
Just replace the swimmer with a beam of light, our illustration works exactly the same for Special Relativity.
First, Einstein assumed the motion of light is relative, and let light do a round trip along the x axises of the reference frames, that is where the c-v and c+v in his first equation came from.
Then, he assumed that the motion of light is absolute. That is, light moves at the same speed c in all reference frames.
To compensate for the speed loss caused by the relative motion, the observed distance and time were adjusted.