We can travel through the three dimensions of space pretty much at will — moving forward or back, left or right, up or down — without even thinking about it. When it comes to the fourth dimension, though, we appear to be stuck. Time flows on in one direction only, and we flow with it like corks bobbing helplessly in a river. So the idea of traveling through time, as opposed to with time, is immensely seductive. Who wouldn't want to know what technology will look like in the year 3000, or witness the assassination of Julius Caesar?

Not only does such a thing seem extremely difficult, but it could also be a little risky. What if you prevented Caesar's assassination and changed history? What if you accidentally killed someone who happened to be your own ancestor? Then you wouldn't have been born, and couldn't have killed your ancestor, so you could be born after all to go back and ... well, you get the idea.

We physicists are mindful of all these difficulties, of course. But we can't resist exploring the notion of time travel — not necessarily for practical reasons, but to understand the limits of our theories.

Do the laws of physics permit time travel, even in principle? They may in the subatomic world. A positron (the antiparticle associated with the electron) can be considered to be an electron going backward in time. Thus, if we create an electron-positron pair and the positron later annihilates in a collision with another, different electron, we could view this as a single electron executing a zigzag, N-shaped path through time: forward in time as an electron, then backward in time as a positron, then forward in time again as an electron.

The probability of a macroscopic object — like a human — doing this trick is infinitesimal. But thanks to Albert Einstein we know that time travel of a different sort does happen in the macroscopic world. As he showed back in 1905 with his special theory of relativity, time slows down for objects moving close to the speed of light, at least from the viewpoint of a stationary observer. You want to visit the earth 1,000 years from now? Just travel to a star 500 light-years away and return, going both ways at 99.995% the speed of light. When you return, the earth will be 1,000 years older, but you'll have aged only 10 years. I already know a time traveler. My friend, astronaut Story Musgrave, who helped repair the Hubble Space Telescope, spent 53.4 days in orbit. He is thus more than a millisecond younger than he would have been if he had stayed home. The effect is small, because he traveled very slowly relative to the speed of light, but it's real.

With more money, we could do better in the next century — but only a little. If we sent an astronaut to the planet Mercury and she lived there for 30 years before returning, she would be about 22 seconds younger than if she had stayed on Earth. Clocks on Mercury tick more slowly than those on Earth because Mercury circles the sun at a faster speed (and also because Mercury is deeper in the sun's gravitational field; gravity affects clocks much as velocity does). Astronauts traveling away from Earth to a distance of 0.1 light years and returning at 1% the speed of light would arrive back 8.8 hours younger than if they hadn't gone.

The downside of traveling into the future this way is that you might be stuck there. Is there any way of going backward in time? Once again, Einstein may have provided the answer. His 1915 theory of general relativity showed that space and time are curved, and that the curvature can be large in the neighborhood of very massive objects. If an object is dense enough, the curvature can become nearly infinite, perhaps opening a tunnel that connects distant regions of space-time as though they were next door. Physicists call this tunnel a wormhole, in an analogy to the shortcut a worm eats from one side of a curved apple to the other.

In 1988, Kip Thorne, a physicist at Caltech, and several colleagues suggested that you could use such a wormhole to travel into the past. Here's how you do it: move one mouth of the wormhole through space at nearly the speed of light while leaving the other one fixed. Then jump in through the moving end. Like a moving astronaut, this end ages less, so it connects back to an earlier time on the fixed end. When you pop out through the fixed end an instant later, you'll find that you've emerged in your own past.

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