Well, for one piece of evidence, no confirmed time travelers attended the Time Traveler's Convention held at MIT in 2005 (http://web.mit.edu/adorai/timetraveler/ ). The organizers do note that some might have attended in disguise, to avoid questions about the future. More seriously, some philosophers have argued that time travel involves logical contradictions, and if that's right, then we can be sure that time travel doesn't happen. And certainly many time travel stories do seem to involve contradiction or incoherence. When Marty McFly travels back in time and then returns to the present day, the present day has been changed. So it looks as if 1985 the second time around differs from 1985 the first time around. But 1985 only occurs once, so it can only occur one way. You might think of this as "the second time around fallacy." Another famous contradiction discussed relative to time travel is the Grandfather Paradox. If time travel were possible, then you could go back in time and...

In addition to the points that Richard makes above, we might consider the fact that the expression "time" functions oddly in lots of constructions. Having too much time on your hands is quite different from having too much lotion on your hands, having time on your side is different from having Jack your side, and time's running out is different from Jill's running out. It might also be useful to remember that we should always be careful not to put too much weight on the surface grammar of our language. Lewis Carroll got a lot of mileage out of this, e.g., in Through the Looking Glass : "I see nobody on the road," said Alice. "I only wish I had such eyes," the King remarked in a fretful tone. "To be able to see Nobody! And at that distance too! Why, it's as much as I can do to see real people, by this light."

I don't think that we know the answer to this one yet. Leaving aside the question of whether travel back in time violates any physical laws, there are some reasons to think that it is conceptually incoherent. For one thing, there is the well-known "Grandfather Paradox." Suppose you were to travel back in time and kill your own grandfather before the time your mother was conceived, thus preventing her conception and obviously your own as well. This leads to a logical puzzle, since you would cause something to happen that would make it the case that you had never existed. It is very hard to tell a coherent time travel story. Science fiction representations of time travel often involve some kind of paradox. Very often, they fall victim to the "second time around" fallacy -- they depict events in some year, say 2005; our hero travels back in time and makes some crucial change; when he then returns to 2005 things are different. But this suggests that we have 2005-the-first-time-around and 2005-the...