I have seen a lot of shows that feature the premise of time travel. Many Sci-Fi shows like Star Trek sometimes have this in its storyline. And shows sometime feature time travel as the main premise of the entire series, or the entire movie. Like a show I'm watching now. The Lazarus Project.
It's a great premise for a fictional show. Why not? But there is one catch. Time travel to the past, like in The Lazarus Project, (and The Time Tunnel from the 60s,) is not possible. Ever. Time travel to the past just cannot happen. However, time travel into the future is a different story.
I read about real life experiments that have shown that time travel into the future CAN happen. It's been proven that when an object is traveling close to the speed of light, time, for that object, is moving more slowly. But, of course, time on earth is still moving at the normal speed, ie, seconds, minutes, hours, days.
For example. It could be day one on Earth when a spaceship is launched. It goes very fast into space. And for the people inside that spaceship, time is moving more slowly compared to the time that goes by on earth. Then, say, the spaceship returns to earth on day three for the people inside the spaceship. But for the people on earth, it's day four, five, or six.
So that means the people inside the spaceship actually time traveled into the future. It's a poor example of what I'm trying to point out, but it is still proof that time travel into the future is possible.
One of the first stories ever written that had time travel as a premise was H.G. Wells' The Time Machine. Wells had it right, that the main character traveled into the future. Okay, that was something possible. However, Wells wrote in the story, that the character managed to travel back to his own time after he had gone into the future. Then of course, those who have read the book know that he once again returned to the future where had a a girlfriend waiting for him and it's where he preferred to be.
So if that one part where he returned to his own time didn't happen. Wells would have nailed it on the world's first time travel book. But so what. It's fiction. Enjoy it and move on.