One Big Problem with Time Travel
There is one aspect of time travel that nobody considers, whether in science or science-fiction (at least, i am not aware of it), something that has the potential of rendering time travel, even if it is possible, totally futile. So, what is it? In time-travel, we are only moving through time, and not through space. So, if we are at a given set of co-ordinates X, Y, Z at the present time A, and we go back in the past to some moment B, we would still, essentially, be at the same co-ordinates XYZ. Now, here's the point. Earth is moving through space; moving with velocities we might not even have a clear idea of. For definite, we know the earth is moving around the sun, the sun is moving around the centre of the galaxy, and the galaxy itself is moving. That makes up a lot of motion. So that at any given two instants earth would be at two different places. So, if i travel in time, whether in past or future, while retaining my location in space, i would end up in empty space, cause earth would be somewhere far far away...
[Edit: Since JesseM resolved this issue and clarified the problem in her comment, i am posting it under the post for the convenience of future readers:
JesseM: None of the time travel schemes proposed in general relativity actually involve the sci-fi idea of dematerializing in one time and rematerializing in another, instead they involve travel through a warped region of spacetime like a wormhole--and with a wormhole, where you end up in the past would just depend on where the "mouth" of the wormhole happened to be located at the time you exit. For example, if the mouth was in orbit around the Earth then you'd end up near Earth no matter what time you travelled to.
That said, the idea that there is some objective truth about which point in space in the past is the "same position" that the Earth is in today is in total contradiction with relativity. See this section of the wikipedia time travel article:
An objection that is sometimes raised against the concept of time machines in science fiction is that they ignore the motion of the Earth between the date the time machine departs and the date it returns. The idea that a traveler can go into a machine that sends him or her to 1865 and step out into the exact same spot on Earth might be said to ignore the issue that Earth is moving through space around the Sun, which is moving in the galaxy, and so on, so that advocates of this argument imagine that "realistically" the time machine should actually reappear in space far away from the Earth's position at that date. However, the theory of relativity rejects the idea of absolute time and space; in relativity there can be no universal truth about the spatial distance between events which occurred at different times (such as an event on Earth today and an event on Earth in 1865), and thus no objective truth about which point in space at one time is at the "same position" that the Earth was at another time. In the theory of special relativity, which deals with situations where gravity is negligible, the laws of physics work the same way in every inertial frame of reference and therefore no frame's perspective is physically better than any other frame's, and different frames disagree about whether two events at different times happened at the "same position" or "different positions". In the theory of general relativity, which incorporates the effects of gravity, all coordinate systems are on equal footing because of a feature known as "diffeomorphism invariance". ]