The statement that someone moving at a speed close to that of light ages at a slower rate than an observer is based on the phenomenon known as time dilation in special relativity. In special relativity, time dilation occurs due to relative motion between two observers, specifically when one observer is moving at a significant fraction of the speed of light relative to the other observer.
According to special relativity, the passage of time is not absolute but is relative to the motion of the observers. When two observers are moving relative to each other, they will measure different durations of time. Specifically, an observer moving at a high velocity relative to another observer will experience time passing more slowly compared to the observer at rest.
This effect is a consequence of the Lorentz transformation, which describes how time and space coordinates change between different inertial frames of reference. As an object's velocity approaches the speed of light, the time dilation effect becomes more pronounced, and the moving object's clock appears to run slower relative to a stationary observer's clock.
It is important to note that this time dilation effect in special relativity is distinct from the time dilation due to gravity in general relativity. In the context of special relativity, the time dilation is solely a result of relative motion, while in general relativity, time dilation is influenced by both relative motion and gravitational fields.
So, while both time dilation due to motion in special relativity and time dilation due to gravity in general relativity can result in the perception of time running slower for certain observers, they arise from different physical principles.