Yes, time dilation occurs in the direction of velocity. According to the theory of special relativity, when an object moves at a significant fraction of the speed of light relative to another object, time dilation occurs along the direction of motion. This means that an observer moving relative to another observer will perceive time to pass more slowly for the stationary observer.
The time dilation effect arises from the constancy of the speed of light for all observers, regardless of their relative motion. As an object moves closer to the speed of light, its perception of time slows down relative to a stationary observer.
This phenomenon has been experimentally verified and is a fundamental aspect of special relativity. It has practical implications, particularly when dealing with high-speed spacecraft or particles traveling at relativistic speeds.
In summary, time dilation does occur in the direction of velocity. As an object's velocity approaches the speed of light, time appears to slow down for that object relative to a stationary observer.