wagenius -
Stephen Hawking has a neat resolution to the problem of "if time travel is possible, why haven't we been visited by travellers from the future?".
His argument is that if you are able to create a time machine, it will never be able to travel further back in time than to the date on which it was created. He sees this as some sort of built-in cosmic defence mechanism to avoid the paradoxes which arise from time travel.
However, it does not resolve the grandfather paradox. To do this, he says there is a possibility that when you travel back in time, you actually enter a universe which is very similar to ours, but not exactly the same - at the moment you arrive in time, the universe splits into two in some quantum fashion and from there the two variants branch off in different paths. So if you accidentally kill your grandfather before your father is born, you only kill him in this "new" universe, not your old one. So you still exist, even though you have killed your grandfather - because there are (well, were) two of him and you can never get back to the original one. As for your identical twin in the parallell universe, well, tough luck.
