No, the phenomenon you would observe in this scenario is known as time dilation, not time contraction. According to the theory of relativity, as an object approaches the speed of light, time for that object appears to slow down relative to an outside observer.
If a spaceship were to travel at close to the speed of light relative to Earth, observers on Earth would perceive time on board the spaceship to be running slower compared to their own time. This means that astronauts on the spaceship would experience time passing more slowly compared to people on Earth.
This effect is a consequence of the fundamental principles of relativity, which include the constancy of the speed of light in all inertial reference frames. It is important to note that the time dilation effect is mutual. From the perspective of the astronauts on board the spaceship, they would see time on Earth running slower while their own time appears to pass normally.
Therefore, the phenomenon is commonly referred to as time dilation, as it describes the stretching or slowing down of time relative to an outside observer due to relative motion and high speeds.