Science of Discworld III

key to wormhole time travel is the notorious twin paradox, pointed out by the physicist Paul Langevin in 1911. Recall that in relativity, time passes more slowly the faster you go, and stops altogether at the speed of light. This effect is known as time dilation. We quote from The Science of Discworld :
    Suppose that Rosencrantz and Guildenstern are born on Earth on the same day. Rosencrantz stays there all his life, while Guildenstern travels away at nearly lightspeed, and then turns round and comes home again. Because of time dilation, only one year (say) has passed for Guildenstern, whereas 40 years have gone by for Rosencrantz. So Guildenstern is now 39 years younger than his twin brother.
    It’s called a paradox because there seems to be a puzzle: from Guildenstern’s frame of reference, it is Rosencrantz who has whizzed off at near-lightspeed. Surely, by the same token, Rosencrantz should be 39 years younger, not Guildenstern? But the apparent symmetry is fallacious. Guildenstern’s frame of reference is subjectto acceleration and deceleration, especially when he turns round to head for home; Rosencrantz’s isn’t. In relativity, accelerations make a big difference.
    In 1988 Michael Morris, Kip Thorne, and Ulvi Yurtsever realised that combining a wormhole with the twin paradox yields a CTC. The idea is to leave the white end of the wormhole fixed, and to zigzag the black one back and forth at just below the speed of light. As the black end zigzags, time dilation comes into play, and time passes more slowly for an observer moving with that end. Think about world-lines that join the two wormholes through normal space, so that the time experienced by observers at each end are the same. At first those lines are almost horizontal, so they are not timelike, and it is not possible for material particles to proceed along them. But as time passes, the line gets closer to the vertical, and eventually it becomes timelike. Once this ‘time barrier’ is crossed, you can travel from the white end of the wormhole to the black through normal space – following a timelike carve. Because the wormhole is a short cut, you can do so in a very short period of time, effectively travelling instantly from the black end to the corresponding white one. This is the same place as your starting point, but in the past.
    You’ve travelled in time.
    By waiting, you can close the path into a CTC and end up at the same place and time that you started from. Not back to the future, but forward to the past. The further into the future your starting point is, the further back in time you can travel from that point. But there’s one disadvantage of this method: you can never travel back past the time barrier, and that occurs some time after you build the wormholes. No hope of going back to hunt dinosaurs. Or to tread on Cretaceous butterflies.
    Could we really make one of these devices? Could we really get through the wormhole?
    In 1966 Robert Geroch discovered a theoretical way to warp spacetime, smoothly, without tearing it, to create a wormhole. There’s a snag, though: at one stage in the construction, time becomes so twisted that the wormhole turns into a temporary time machine, and equipment from late in the construction gets carried back to the beginning. The builders’ tools might vanish into the past, just as they thought they had finished. Still, with the right work schedule, that might not matter. Perhaps a technologically advanced civilisation could build black and white holes, and move them around, by creating intense gravitational fields.
    But building a wormhole is not the only obstacle. Keeping it open is another. The main trouble is the ‘catflap effect’: when you move a mass through a wormhole, the hole tends to shut on your tail. It turns out that in order to get through without getting your tail trapped, you have to travel faster than light, so that’s no good. Any timelike path that starts at the wormhole entrance must run into the future singularity. There’s no way to get across to the exit without exceeding the speed of light.
    The traditional way round this difficulty is to thread the wormhole with ‘exotic’ matter, which exerts enormous negative pressure like a stretched spring. It is a form of negative energy, and is thus different from antimatter, which has positive energy. In quantum mechanics, a vacuum is not empty – it is a turbulent sea of particles, coming into being and disappearing again. Zero