Well, we already know how to travel forward in time -- get in a ship and come close to the speed of light. Outside the ship, time will "flow" more quickly than inside the ship (relatively speaking, both you inside the ship and everyone outside the ship would experience time flowing normally). The closer to the speed of light you get, the more pronounced the effect. So basically, going 99.99% the speed of light means you're traveling into the future.But I take it you mean traveling backward in time. Well the last I read, nothing we know outright prevents this from being possible... and if you actually were able to go faster than the speed of light, you'd be able to arrive at your destination before you actually left -- so I guess maybe you could do something with that and just repeat a whole bunch...I don't know; but if time is basically a fourth spatial dimension that we obviously experience very differently than the other 3, it can't be possible. I mean simply by virtue of traveling back in time, you would yourself travel back in time to the state you were in. As in, just like moving an object to the right of a table: the object moves to the right. You can't move it to the right and expect it to end up anywhere but right where it goes.... I'm explaining this incredibly poorly. But basically, time travel is always paradoxical. You don't even need to consider the grandfather paradox, that's just a weird human concept: the paradox arises the very moment matter "pops into existence" in the past. It wasn't there originally. It'll displace molecules that will be in different positions. Without alternate dimensions, it's always a paradox.