"time distortion" is an effect which is most "easily" observed at very very very high speeds, such as those approaching light. An example of it is, i think, the "Mount Washington" experiment conducted at MIT, Massachussets, and cited in the book "Special Relativity", AP French. Basically decaying cosmic ray mesons seem to "stay alive longer" due to their very high speeds. (I'd hate to see a train moving at relativistic speeds ... well, I probably wouldn't "see" it, thinking about it now.)
