No, time dilation does not imply that faster-than-light travel leads to backward time travel. Special relativity, which incorporates time dilation, establishes that the speed of light in a vacuum, denoted by "c," is an absolute speed limit. According to our current understanding of physics, no object with mass can travel faster than the speed of light.
Time dilation occurs as a consequence of relative motion and the constancy of the speed of light. When an object moves at relativistic speeds, its perception of time slows down relative to a stationary observer. However, this effect does not enable backward time travel.
It is important to note that time dilation is a real and observed phenomenon. It has been experimentally confirmed in various ways, such as with high-speed particles or by comparing time measurements of clocks on satellites and on the ground. However, time dilation does not allow for traversing time in a backward direction.
The concept of backward time travel, where one could move back in time to events that have already occurred, is currently not supported by any accepted physical theories. It would involve violating fundamental principles of causality and lead to logical inconsistencies. While science fiction often explores the idea of time travel, the possibility of backward time travel remains speculative and outside the realm of our current scientific understanding.
In summary, time dilation does not imply that faster-than-light travel permits backward time travel. Time dilation is a well-established consequence of special relativity, but it does not allow for the reversal of time or the ability to travel back to events that have already taken place.