Correct:
http://en.wikipedia.org/wiki/Second
Let's try this: imagine, instead of a vibrating 'caesium 133 atom', we have a beam of light bouncing back and forth between two mirrors within a vertical tube. Now let's say, for the sake of argument, that it takes precisely one second for the light beam to reach the top mirror (tic), reflect off it, reverse and reach the bottom mirror (toc).
Now let's say the light tube, or 'light clock', is resting on a flatbed train car, and on the flatbed is an observer who we will call "Observer A". To Observer A, who is moving along with the train and is therefore 'at rest' with respect to it, the light beam simply travels from the bottom of the tube *vertically* to the top of the tube and then straight back down again. From the relationship, speed equals distance over time, we get time equals distance over speed. So this is then how Observer A defines time (t=distance/speed). Important to note here is that light travels at the SAME SPEED for ALL observers.
Now let's say there is an observer B standing on the embankment alongside the train watching it pass by. From this observer's point of view, or frame of reference, the light beam does NOT simply travel vertically up and down. Rather, it travels on a slanted or diagonal path since the train is in motion, let's say from left to right as Observer B sees it. Now since the light beam travels a diagonal path between tic and toc, again, from OB's stationary point of view, the light beam therefore is traveling a LONGER distance (from OB's perspective). Therefore, since the light beam is traveling a longer distance (from OB's perspective) AND since light travels at the same speed for all observers, the light beam MUST take a longer time to bounce between the two mirrors (tic-toc). Therefore, the two observers (A and B) do NOT agree on what a "second" is.
http://galileo.phys.virginia.edu/classes/252/srelwhat.html
For anyone who has taken Physics in high school or college, you are probably aware of the "light clock" model for demonstrating Einstein's Special Relativity theory.