The classic time travel paradox is 'what if I went back and killed my grandfather?' The logic of the situation, of course, is that with granddad dead, you wouldn't have been born, so you wouldn't be able to go back and kill him, so he'd have lived, so you would have been born ... All attempts to resolve this self-contradictory causal loop are cheats: perhaps granddad dies, but you get born anyway with different grandparents, but then it wasn't really granddad that you killed. In the 'many worlds' interpretation of quantum mechanics, the causal logic of the universe holds together provided the grandfather that gets killed was in a different parallel universe from that of the killer. But then he wasn't your real granddad, either, just a parallel version in some other universe.

A slightly more subtle time paradox is the Cumulative Audience Paradox. If people in the future have access to time machines, then they are bound to want to go back and witness all of the great historical events, like the crucifixion. But we know, from existing descriptions of these events, that they did not happen in front of crowds of thousands of visitors from the future. So where were they? This is a temporal analogue of the Fermi Paradox74 about intelligent aliens: if they're all over the galaxy, then why aren't they here? Why haven't they visited us? Other time paradoxes are used as essential plot elements in Robert A. Heinlein's short stories 'By his bootstraps' and 'All you zombies', fn the latter, a time-traveller manages to be his own father, son, and - via a sex change - mother. When asked where he comes from, he replies that he knows exactly where he comes from. The big puzzle is: where does everybody else come from? This idea is taken to serious extremes by David Gerrold in The Man Who Folded Himself.

Over the last few decades, serious physicists have started thinking about the possibility of time travel and the resolution of any associated paradoxes. Their work is a tribute to narrative imperative on Roundworld. The reason they are asking such questions is no doubt that as children they read stories like those of Wells, Silverberg, Heinlein and Gerrold. When they became professional physicists, the stories bubbled up from their subconscious, and they began to take the idea seriously - not as a practical engineering issue, but as a theoretical challenge.

Do the laws of physics permit time travel, or not? You'd expect the answer to be 'no', but the remarkable consequence of the theorists' research is that it is 'yes'. A working time machine is still a long way off, and it may be that we're missing some basic physical principle that would change the answer to 'no', but the fact is that today's accepted frontier physics does not forbid time travel. It even offers a few scenarios in which it could occur.

The context for such research is general relativity, in which the continuum of space and time can be distorted by gravity. Or, more accurately, in which gravity is caused by such distortions,

'curved spacetime'. In place of a time machine, the physicists look for a 'closed timelike curve'.

Such a curve corresponds to an object that travels into the future and ends up in its own past, and so becomes trapped in a closed 'time loop'.

The best known way to generate a closed timelike curve is to use a wormhole. A wormhole is a short-cut through space, obtained by fusing a Black Hole to its time-reversal, a White Hole. Just as Black Holes suck in anything that comes near them, White Holes spit things out. A wormhole sucks things in at its black end and spits them out at its white end. Of itself, a wormhole is more a matter-transmitter than a time machine, but it becomes a time machine when allied to the famous Twin Paradox. In relativity, time slows down for objects moving at very high speeds. So if one member of a pair of twins heads out to a distant star at very high speed, and then returns, she will have aged less than the other twin who stayed at home. Suppose that the travelling twin takes with her the white end of a wormhole, while her sister keeps the black end. Then when the travelling twin returns, the white end is younger than the black end: the exit from the wormhole lies in the past of the entrance. So anything that is sucked into the black end is spat out in its own past. Because the white end is now right next to the black one -the twin has come back home the object can hop across to the Black Hole and go round and round this closed loop in spacetime, tracing a closed timelike curve.

There are practical problems in making such a gadget, the main one(!) being that the wormhole will collapse too quickly for an object to pass through it, unless it is held open by threading

'exotic matter' with negative energy through it. Nonetheless, none of this is forbidden by the current laws of physics. So what of the paradoxes? It turns out that the laws of physics forbid genuine paradoxes, although they permit many apparent paradoxes. A useful technique for understanding the difference is known as a Feynman diagram, which is a picture of the motion of an object (usually a particle) in space and time.

For example, here is an apparent time travel paradox. A man is imprisoned in a concrete cell, locked from the outside, with no food, no water and no possibility of escape. As he sits in a corner in despair, waiting for death, the door opens. The person who has opened it is ... himself.

He has returned in a time machine from the future. But how (the paradox) did he get to the future in the first place? Well, a kind person opened the door and set him free ...

There seems to be something very odd about the causality in the story, but the corresponding Feynman diagram shows that it violates none of the laws of physics. First, the man follows a space-time path that puts him inside the cell and then removes him from it through opened door.

This time-line continues into his future until he encounters a time machine. Then the time-line reverses direction, heading into the past, until he encounters a locked cell. He opens it, and his time-line reverses again, propelling him into his own future. So the man follows a single zig-zag path through time, and at every step the laws of physics hold good. Provided his time machine violates no physical law, of course.

If you try to 'explain' the grandfather paradox by this method, it doesn't work. The time-line leading from grandfather to killer is severed when the killer returns; there is no consistent scenario, even in a Feynman diagram. So some stories of time travel are consistent with the laws of physics, and have their own kind of causal logic, albeit twisted; but other equally plausible stories are inconsistent with the laws of physics. You can rescue the Grandfather Paradox by assuming that changing the past in a logically inconsistent way switches you into a different alternate universe -say a quantum-mechanical parallel world. But then it wasn't your grandfather that you killed, but the grandfather of an alternate you. So this 'resolution' of the Grandfather Paradox is a cheat.

Faced with all this, the way that the wizards handle the complications of time travel seems quite reasonable!