According to the theory of special relativity, as formulated by Albert Einstein, time dilation occurs as an object approaches the speed of light relative to an observer. As an object's velocity increases, time slows down for that object as observed by a stationary observer.
However, it's important to note that the theory of special relativity applies to objects with mass, and it sets a limit on how close an object with mass can approach the speed of light. Specifically, as an object with mass accelerates and approaches the speed of light, its energy requirements also increase, and it would require an infinite amount of energy to accelerate a massive object to the exact speed of light.
So, in practice, it's not possible for an object with mass, such as a clock or a human, to reach or exceed the speed of light. Therefore, from the perspective of someone traveling at sub-light speeds, it would not be possible to observe a clock slowing down and stopping completely as it approached the speed of light.
However, it is worth mentioning that from the perspective of a hypothetical observer traveling at a speed close to the speed of light, time would appear to be passing differently for objects at rest relative to them. This phenomenon is known as time dilation, where time appears to be passing more slowly for objects in motion relative to the observer. So, from the perspective of a high-speed traveler, clocks on Earth or other slower-moving objects would appear to be running slower compared to their own local clocks.
It's important to emphasize that these effects are theoretical and have been experimentally confirmed in various ways, such as with atomic clocks on high-speed airplanes and in particle accelerators. However, they are only observed at speeds that approach the speed of light, which is not attainable by massive objects.