The slowing down of time, as observed from the perspective of an observer in a relatively stationary frame, when an object approaches the speed of light is a consequence of the theory of special relativity. This phenomenon is known as time dilation.
According to special relativity, the speed of light in a vacuum is constant and the same for all observers, regardless of their relative motion. However, the theory also states that space and time are interconnected in a four-dimensional framework known as spacetime. When an object moves at high speeds relative to an observer, both space and time are affected.
As an object accelerates and approaches the speed of light, several effects come into play. One of them is time dilation. Time dilation occurs because the speed of light is constant and the same for all observers. As an object moves faster, its time appears to slow down from the perspective of an observer in a relatively stationary frame.
This effect can be explained by considering the spacetime interval, which is an invariant quantity in special relativity. As an object moves faster, its motion through space increases, which causes its motion through time to slow down. In other words, the more an object "uses" its motion for spatial travel, the less it "uses" it for time travel.
From the perspective of the moving object itself, time would appear to pass normally. However, for an observer in a relatively stationary frame, time would appear to slow down for the moving object.
This phenomenon has been experimentally verified through various experiments, such as the observation of high-speed particles or the use of atomic clocks on fast-moving objects like satellites. Time dilation is a fundamental consequence of the theory of special relativity and is a well-established aspect of our understanding of the universe.