Let me explain why I believe effective time travel is impossible.
If you were to go forward or backwards in time, to what spatial reference would you travel.? In other words, if you go back in time from this position of the earth in space, where was the earth at that time? In the middle of space someplace, right? So you go back to the time/place where the earth was--which means you're dead, dead, dead.
At any moment we're flying through space, the sum total of a lot of velocity vectors--the earth is spinning, it's revolving around the sun, the sun is moving around the galaxy, the galaxy is moving in relation to other bodies.
So to plausibly move in time, you'd have to account for not only place but also time and velocity vectors. And since there is no absolute location to serve as a reference for any of that....
In other words, you'd have to travel in time AND space if you wanted to go back or forward to any particular location on the earth or anywhere else. In fact, if you could do that, you'd have effectively a Star-Trek transporter. And that is why I don't believe effective time travel will ever be possible, even if time travel becomes so.
That's me getting my nerd on.
“Effective” time travel at least into the future is super simple and probably requires the least futuristic technology through suspended animation like Buck Rodgers. Going back in time however would be more difficult although consider suspending our galaxy right when a colony ship leaves to another galaxy, then they could come back and visit earth thousands of years in the past. One issue for any type of suspended animation is that as things go on around what is in statsis preservation is key to have the time travel work.