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How can we really know that time travel doesn't happen?

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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 kill your grandfather before your mother was conceived, which would in turn ensure that you'd never exist. But then how could you have killed your grandfather?

A good discussion of time travel and an attempt to resolve some of these issues is in David Lewis' paper "The Paradoxes of Time Travel."

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