Imagine a ball tossed back and forth in a car moving at a constant
velocity. To an observer in the car's frame, the car's motion is
irrelevant. The motion appears as it would to the observer if he and
the ball were in the Earth frame:
To an observer in the Earth frame, the ball moves back and forth
inside the car. The ball's speed adds to the car's when the ball moves
to the right, it subtracts when the ball moves to the left:
When all references to the car are removed, the motion of the ball
appears quite different to the Earth-bound observer than it did to the
Galilean relativity says that you cannot distinguish inertial reference frames from on another by the motion of objects in them. The observer in the car experiences the same motion of the ball as he would if he and the ball were in the Earth frame. This rather obvious notion was extended and modified by Einstein.
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