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Even if you could get past these difficulties, the physics of both types of time machine dictate that you can't go back in time to an epoch before the time machine was created. So you couldn't meet and perhaps kill your own ancestor. But if such a machine were built today, your descendants might come and kill you, changing their own past.
Some argue conservatively that time travelers don't change the past; they were always part of it. On the other hand, paradoxical though this sounds, a version of the many-worlds theory of quantum mechanics (see "Will We Discover Another Universe?" in this issue) devised by Oxford physicist David Deutsch might allow such history-changing visits. In this picture, there are many interlacing world histories, so that if you went back in time and killed your grandmother when she was a young girl, this would simply cause space-time to branch off into a new parallel universe that doesn't interfere with the familiar one.
Stephen Hawking has addressed the problem in a different way, proposing what he calls a chronology-protection conjecture. Somehow, he argues, the laws of physics must always conspire to prevent travel into the past. He believes that quantum effects, coupled with other constraints, will always step in to prevent time machines. The jury is still out on this question. We may need to develop a theory of quantum gravity to learn whether Hawking is right.
So, will we time-travel in the next century? Travel to the future--yes, but only in short hops, I suspect. To the past--very likely not. Such travel is expensive, dangerous and subject to quantum effects that may or may not spoil your chances of coming back alive. Those of us working in this field aren't rushing to the patent office with time-machine blueprints. But we are interested in knowing whether time machines are possible, even in principle, because answering that question will tell us where the boundaries of physics lie and provide clues to how the universe works.
J. Richard Gott III is a professor of astrophysics at Princeton, where he does research on general relativity and cosmology