Constancy of Speed of Light in Minkowski Diagram

∟Constancy of Speed of Light in Minkowski Diagram

This section provides a demonstration of constancy of speed of light using a Minkowski diagram.

The main assumption of the special theory of relativity is that the speed of light has the same value c measured in all inertial frames.

This assumption can be easily demonstrated by the Minkowski diagram. Let's follow a simple thought experiment described below:

A light pulse travels from Bob's location for 6 seconds.
The trajactory of the light pulse can be represented by a diagonal line between event O and event E, (X,cT)=(6,6), in Bob's stationary frame.
So according to Bob's stationary frame, the speed of the light pulse is X/cT = 6/6 = 1 (c).

Now let's assume that Amy's frame is moving at a speed of v=0.6*c:

The event E would be observed at (X',cT')=(3,3) in Amy's moving frame based on the Minkowski diagram given below.
So according to Amy's moving frame, the speed of the light pulse is X'/cT' = 3/3 = 1 (c).