Traveling at the speed of light theoretically causes time to stop for the object in motion, but this only applies to massless particles, as massive objects cannot reach this speed. As an object approaches the speed of light, time for it slows significantly relative to an outside observer. Observers will see clocks on the fast-moving object ticking slowly, while the object itself perceives its own time normally. This phenomenon illustrates the relativity of time, where different frames of reference lead to varying perceptions of time flow. Understanding these concepts is crucial for grasping the implications of Einstein's theory of relativity.