Minkowski Diagram - Time Dilation

Time Dilation

Relativistic time dilation means that a clock moving relative to an observer is observed to run slower. In fact, time itself in the frame of the moving clock is observed to run slower. This can be read immediately from the adjoining Minkowski diagram. The observer whose reference frame is given by the black axes is assumed to move from the origin O towards A. The moving clock has the reference frame given by the blue axes and moves from O to B. For the black observer all events happening simultaneously with the event at A are located on a straight line parallel to its space axis. This line passes through A and B, so A and B are simultaneous from the reference frame of the observer with black axes. However, the clock that is moving relative to the black observer marks off time along the blue time axis. This is represented by the distance from O to B. Therefore, the observer at A with the black axes notices his or her clock as reading the distance from O to A while he or she observes the clock moving relative him or her to read the distance from O to B. Due to the distance from O to B being smaller than the distance from O to A, he or she concludes that the time passed on the clock moving relative to him or her is smaller than that passed on his own clock.

A second observer having moved together with the clock from O to B will argue that the other clock has reached only C until this moment and therefore this clock runs slower. The reason for these apparently paradoxical statements is the different determination of the events happening synchronously at different locations. Due to the principle of relativity the question of "who is right" has no answer and does not make sense.