Relativity of Simultaneity

The two movies below show a railroad car (boxcar) that is moving to the right at half the speed of light.  On the side of the track is a telegraph pole.  When the center of the boxcar is alligned with the telegraph pole a spark jumps between the pole and boxcar.  This produces a flash of light, which travels towards both ends of the boxcar.

Pole Frame

When this scene is viewed from the reference frame of the telegraph pole (upper movie), the light reaches the back end of the boxcar before the front end.  This is because the boxcar is moving, so the light has a shorter distance to travel to get to the back of the boxcar than to the front. 

Boxcar Frame

The movie below shows the same situation from the frame of reference of the boxcar.  In this frame the boxcar is stationary, and the light has the same distance to travel to the two ends of the car.  Since the speed of light is the same in both directions the light arrives at both ends of the car at the same time.      
Thus, two events -- light reaching the back of the boxcar and light reaching the front of the boxcar -- that are simultaneous in one inertial frame (boxcar frame) are not simultaneous in another intertial frame (pole frame).