There are 2 fundamental issues with the whole idea.
One, everything in Einstein's theory of Special Relativity is based on relative frames of reference; that is, there is no point in the universe which is completely stationary, and everyone has the right to call the shots based on "their" frame of reference. For instance, if train X is moving toward train Y then to the passenger on train Y it would appear thus, but to a passenger on train X it would appear that train Y is moving toward them.
Special Relativity is comprised of 2 postulates: One says that the laws of physics are true for all frames of reference. The other says that based on this, the speed of light is the same in all frames of reference. Here's where it gets goofy...this means the speed of light is the same no matter what speed the object generating it is moving. If someone throws a ball from train X at train Y at, say, 30 MPH, then the ball itself would be traveling at 30MPH plus whatever speed the train is doing, so if that train is going 50, then the ball will hit you at 80 MPH (ouch!)
With this in mind, you'd think the light (which travels about 670,000,000 MPH) coming from the front of the train would be going 670,000,050. HOWEVER, the second postulate of Einstein's theory says that isn't the case; the light is still going 670,000,000MPH regardless. Remember that speed is distance x time; then remember that whole frame-of-reference thing in the first paragraph...
the way we measure it is the problem, which leads me to the second issue with time travel.
Hasn't anyone stopped to consider the idea that time is a uniquely human invention? It's in our nature to measure things; it's how we orient ourselves in the universe. We need to know "when" something happened--or will happen--therefore we need a scale on which to place events relative (there's that word again) to each other. Think of it this way: Would a tree measuring 30m still be 30m tall if humans weren't around to measure it?
Think about that for a second...or however long you like, since this is about time
Yes, the tree would still be the same height, but would it be 30m? Put another way: Yes, the dinosaurs would have become extinct at the same point in time, but if we weren't here to measure that period of time (much less develop the technology to determine it), it would be just another event that happened after something but before something else.
To me--from my frame of reference, if you will--the pursuit of a unification-theory of time and space resembles that of Zeno's Paradox, wherein science will get closer and closer, but technically never get there.