According to our current understanding of physics, which is based on Einstein's theory of relativity, it is not possible to travel faster than the speed of light in a vacuum. The theory of relativity establishes the speed of light as an absolute speed limit beyond which it is not possible to go. As an object with mass approaches the speed of light, its energy and momentum increase without bound, making it increasingly difficult to accelerate further.
The idea of time travel, specifically going backward in time, is a topic that has been explored in science fiction and is subject to speculation. However, it is important to note that there is no scientific consensus or evidence supporting the possibility of traveling backward in time, even if one were to surpass the speed of light.
The concept of time dilation, which is a consequence of special relativity, does allow for a kind of "time travel" into the future. As an object approaches relativistic speeds, time appears to pass more slowly for that object relative to a stationary observer. This effect is well-established and has been experimentally confirmed through various experiments involving fast-moving particles.
However, it is crucial to distinguish this time dilation effect from the idea of "time travel" as commonly depicted in science fiction, which typically involves consciously moving backward in time. At present, there is no scientific basis or theoretical framework that supports such backward time travel within our current understanding of physics.