According to our current understanding of physics, it is not possible for an object with mass, such as a spaceship, to travel at the speed of light. The theory of relativity, proposed by Albert Einstein, tells us that as an object with mass approaches the speed of light, its energy requirements become infinite. Therefore, it is impossible for a massive object to reach or exceed the speed of light.
However, let's consider a scenario where two observers are in a spaceship moving at a significant fraction of the speed of light relative to other galaxies. In this case, we can explore the concept of relativistic effects.
According to the theory of relativity, space and time are interconnected, forming what is known as spacetime. When an object moves at high speeds relative to an observer, the effects of time dilation and length contraction come into play.
Time dilation means that as an object moves faster relative to another observer, time appears to pass more slowly for the moving object. This effect becomes significant as the speed of the object approaches the speed of light. As a result, if one person in the spaceship sees other galaxies rushing towards them, it would be due to the time dilation effect caused by their high relative velocity.
On the other hand, the person who sees nothing coming towards them is likely in a reference frame at rest relative to the galaxies or moving at a significantly slower velocity relative to them. In their reference frame, the galaxies may appear relatively motionless or moving at different velocities.
It's important to note that these scenarios involve significant fractions of the speed of light, which is currently beyond our technological capabilities. Additionally, the effects of relativity become more pronounced as velocities approach the speed of light, making the situations described highly theoretical.
In reality, our observations of galaxies and their motion are based on the expansion of the universe, gravitational effects, and the relative motion of galaxies within galaxy clusters. These observations are not dependent on individual observers' velocities or relative speeds.