3) You can't kill your own grandfather.
Supposing you've inherited a time machine from your grandfather. Presumably, you could pop back for a visit to thank him and/or commit retro-grand-patricide, couldn't you? Not so fast. To make the logic blindingly obvious, if you kill your grandfather, then you won't have been born, which means you couldn't have killed your grandfather, which (logically) means that you will be born.
If history is to have any consistency in a world with time travel, then the "grandfather paradox" (so named by writer René Barjavel) must be resolved. Physicists had little to say on this topic until the mid-1980s, when Igor Novikov of the University of Moscow used quantum mechanical arguments to develop what has become known as the "self-consistency theorem." Quantum randomness must obey well-established laws, and Novikov showed that the probability of producing a different future with a time machine was zero. To put it more simply: You cannot alter history in any way that changes it from what it always was.
So, try as you might, you can't kill your own grandfather, nor can you change history at all. The Terminator learned this the hard way, going back in time to prevent John Connor's birth by killing his mother. When a human travels back in time to protect her, the two fall in love—and she becomes pregnant with … John Connor. Ta-da.
There's no need for such finagling in The Time Traveler's Wife. Since Henry DeTamble serves as his own time machine, there's little chance of his preventing his own birth. Cf. rule No. 2.
4) You don't have nearly as much free will as you think you do.
Novikov's theorem can feel somewhat unsatisfying. As Kip Thorne writes, "something has to stay your hand as you try to kill your grandmother. What? How? The answer (if there is one) is far from obvious, since it entails the free will of human beings." The concept may be easier to grasp if you think about it in terms of inanimate objects: Imagine you shot a pool ball into a time machine and it emerged a moment beforeyou made the shot. Now suppose that you aimed the shot just right, so the outgoing ball (your ball, a second earlier) would block the original shot and prevent it from going into the time machine. This paradox, proposed by Joe Polchinski, then at the University of Texas, * turns out to be the same as the grandfather paradox, albeit with less profound implications.
Kip Thorne and his students worked out what looks like a compromise solution for the impossible pool shot. They argue that you'd line up your shot exactly, but as your ball headed toward the time machine, another one would fly out at a slight angle and graze its side. The first ball would still travel into the time machine but at a slightly different angle than you'd intended. Then it would come back out of the machine, a moment earlier, at the same barely skewed angle—and the Terminator-style loop would be complete.
If pool balls can be forced to succumb to their destiny, so can people. This fact is very easy to ignore if you don't know what the future will bring; it certainly seems like you've got free choice. But if you've already seen what your destiny is, then the future is already written. Making that self-consistent future play out is one of the great challenges of time-travel fiction.
In The Time Traveler's Wife, Henry and Clare enforce the (predetermined) future by giving each other instructions and hints about how things are supposed to happen. That gives them a feeling of free choice where none really exists. In a letter to Clare about their future, Henry explains, "I won't tell you any more, so you can imagine it, so you can have it unrehearsed when the time comes, as it will, as it does come."
Correction, Aug. 13, 2009: The original version of this article misspelled Joe Polchinski's name and suggested that he was still on the faculty at the University of Texas. (Return to the corrected sentence.)