Time Dilation The time lapse between two events is not invariant from one observer to another, but is dependent on the relative speeds of the observers' reference frames (e.g., the twin paradox which concerns a twin who flies off in a spaceship traveling near the speed of light and returns to discover that his or her twin sibling has aged much more). Suppose a clock is at rest in the unprimed system S . The location of the clock on two different ticks is then characterized by Δ x = 0 . To find the relation between the times between these ticks as measured in both systems, the first equation can be used to find: {\displaystyle \Delta t'=\gamma \,\Delta t} for events satisfying {\displaystyle \Delta x=0\ .} This shows that the time (Δ t ′) between the two ticks as seen in the frame in which the clock is moving ( S ′), is longer than the time (Δ t ) between these ticks as measured in the rest frame of the clock ( S ). Time dilation explains a nu