I read the Grandfather Paradox link that buen posted and correct me if I'm wrong here, but I think I see a flaw. Assuming that there is only one time line, some time in the future someone travels back in time, then kills their grandfather. Ok. Now that person will never be born. However the single time line can surely remain, however now the time traveller never existed. Any takers?
pmsl@Butch ... Imagine when MarkRae actually does invent the time-machine and all people use it for is going back to killl their Grandfathers ... hahahaaa.
One of the best time travel short stories is 'By His Bootstraps' by Robert Heinlin. Still one of my favourites, with more twists than you can count! Luckily, it's actually available online. Scroll down here...)
A lot of the so called paradoxs regarding time travel come from the attachment that people have with the idea of cause and effect.
We see it all around but then we're not in the sort of extreme environments where this sort of thing might break down so I don't think flobadob's argument is bad - In fact I've considered it before.
I do think Loosehead's aregument is fundamentally flawed.
Small changes rapidly multiply and cause large scale changes - small air pressure changes cause large scale differences - the famous butterfly effect.
There are many random events in the form of radiaoctive decays all the time so I think a time traveller with a history of Lottery results would be sorely disappointed!
I'm more troubled by the "new knowledge" paradox whereby a time traveller brings new knowledge to the past - this may be the informational equivilent of breaking the third law of thermodynamics.
Of course it's entirely possible that if you could go back in time a consequence would be that all information of later times would be distroyed in the process - In which case travelling earlier than your date of birth would be suicide and a lot of these paradoxes would not arise
If your personal spacetime trajectory can take you to the paradoxical situation where you exist before you are born then subsequent actions by you are not going to retrospectively affect that events determining that trajectory.