I've long believed that time travel is impossible. One of the many reasons I have for it is: it violates the conservation of mass/energy (something disappears from the universe at moment A and something appears in the universe at moment B).
Recently, I've had to reconsider this problem.
I started with an observation: the conservation of mass/energy is not violated when something moves. Formalizing this statement, an object changing its X, Y and/or Z coordinates does not violate the conservation of mass/energy. Now, if I consider that the universe is actually a 4-coordinate system, it can be inferred by analogy that an object changing its X, Y, Z and/or T coordinates is not violating conservation either. (The fact that we don't currently know any such objects is irrelevant; there was a time when we didn't have airplanes or cars.)
Of course, this isn't proof, but I wasn't proving a theorem in the first case; all I had was a thought experiment, an apparent contradiction with the known laws of the universe. That contradiction is now gone.
I guess I'll have to think more about the other 100 reasons for my disbelief in time travel...