In special relativity, an observer in inertial (i.e., nonaccelerating) motion has a well-defined means of determining what events occur simultaneously with a given event. A second inertial observer, who is in relative motion with respect to the first, however, will disagree with him regarding which events are simultaneous with that given event. (Neither observer is wrong in his determination; rather, their disagreement merely reflects the fact that simultaneity is an observer-dependent notion in special relativity.) A notion of simultaneity is required in order to make a comparison of the rates of clocks carried by the two observers. If the first observer's notion of simultaneity is used, it is found that the second observer's clock runs slower than his. Similarly, using the second observer's notion of simultaneity, it is found that the first observer's clock runs slower by the same factor. Thus each inertial observer determines that all clocks in motion relative to him run slower than his own clock.

Excerpt from the Encyclopedia Britannica without permission.