According to the principles of special relativity, if you were to travel away from Earth at close to the speed of light for an extended period, you would experience certain relativistic effects, but you would not see things moving backward relative to you.
One of the key consequences of special relativity is time dilation. As you approach the speed of light, time slows down for you relative to an observer at rest. This means that while you would perceive time passing normally for yourself, observers on Earth would perceive time passing more quickly.
As a result, if you were to travel away from Earth and then return, you would find that less time has passed for you compared to those who remained on Earth. This effect is often referred to as the "twin paradox" because if you had a twin sibling on Earth, they would age more quickly than you.
However, it's important to note that the concept of seeing things "moving backward" is not a direct consequence of time dilation or traveling at high speeds. Relative motion does not change the direction of time or cause objects to appear reversed in their movement.
The effects of special relativity primarily involve differences in the passage of time and length contraction, where objects in motion appear shorter in the direction of motion. These effects are described by mathematical equations and are supported by experimental evidence, but they do not lead to a perception of objects moving backward.
In summary, traveling at close to the speed of light would result in time dilation and other relativistic effects, but it would not cause you to see things moving backward relative to you.