Build a space ship capable of near light speed. Put it into a long orbit like a comet that returns to earth every 100 years. Get in the ship and blast off. When you return you will have aged a few years and be 100 years into the earth's future.
Type 2
Build a space station in near orbit to a Black Hole. As long as you are in the space station you age very slowly. When you leave you could be 100s of years in the future.
Special and General Relativity makes either of these possible. The science is solid, the engineering will take some work.
Time Travel into the past:
The possibility of travel to the past hinges on: Does Free Will exist? If we have Free Will then we can change the past and thus the present. The Law of Causality does not allow this. All time travel paradoxes arise from the fact that causality does not allow us to change the present. But, IF everything is fixed and we can’t change it, then some of us, at least, could be time travelers caught in a loop stretching enough years to cover a life time or more maybe 1000s of years. Time Travel need only involve “quantum leaps” that prevent us from meeting ourselves and we live the same lives over and over with no memory of the last time we did it. Something like Joe Haldeman’s “The Accidental Time Machine” would work.
Modern Theoretical Physics offers another way out of the Time Travel to the Past Paradox trap. If there are an infinite number of parallel universes, we can travel back, violate causality and snap to a different universe that results from us changing the past. I.e.: Go ahead and kill your father. You snap to a universe where your father ain’t your father, but your father, he don’t know. Or, maybe he does and he does not care. Or, your mother was raped. Or, .........
See: “Closed Timelike Curves in Asymmetrically Warped Brane Universes,” Pas, Pakvasa, & Weiler
http://science-junkie.group.stumbleupon.…
If we live in a warped brane universe then Space-Time MIGHT be folded over itself like a sheet of paper. If so, our past or future is next to us. We could time travel by crossing the gap. Note: We cannot choose the time we travel to, only the time(s) next to us.
Grandfather Paradox: Assume time travel to the past. What happens to you, if you kill: yourself, your mother, your father, your grandfather, etc.?