Science of Discworld III

energy includes all these fluctuations, so you can get negative energy if you can calm the waves. One way to do this is the ‘Casimir effect’, discovered in 1948: if two metal plates are held very close together, then in between you find a negative energy state. This effect has been observed in experiments, but it’s very weak. To get enough negative energy, you need galaxy-sized plates. Rigid ones, to maintain the gap.
    Another possibility is a magnetic wormhole. In 1907 the geometer Tullio Levi-Civita proved that in general relativity a magnetic fieldcan warp space. Magnetism has energy, energy is equivalent to mass, and mass is spatial curvature. Moreover, he found an exact mathematical solution to Einstein’s field equations which he called ‘magnetic gravity’. The trouble was, this effect could only be observed using a magnetic field one quintillion times as large as anything that could be obtained in a laboratory. The idea languished until 1995, when Claudio Maccone realised that Levi-Civita had actually come up with a magnetic wormhole. The stronger the magnetic field, the more tightly curved the wormhole mouth is. A wormhole whose magnetic field was the strength you can get in a laboratory would be enormous – about 150 light-years across. And you’d need laboratories everywhere along it. It’s making a small wormhole that needs a gigantic magnetic field. Maccone suggested that the surface of a neutron star, where very strong magnetic fields can occur, might be a good place to look for magnetic wormholes. Why bother? Because a magnetic wormhole can stay open without any need for exotic matter.
    A better solution, though, might be to employ a rotating black hole, which has a ring singularity, not a point one. Passers-by can go through the ring and miss the singularity. The mathematics of Einstein’s equations tells us that a rotating black hole connects to infinitely many different regions of spacetime. One must be in our universe (assuming that we built the rotating black hole in our universe), but the others need not be. Beyond the ring singularity lie antigravity universes in which distances are negative and matter repels other matter. There are legal (slower-than-light) paths through the wormhole to any of its alternative exits. So, if we use a rotating black hole instead of a wormhole, and if we can find a way to tow its entrances and exits around at nearly lightspeed, we’ll get a much more practical time machine – one that we can get through without running into the singularity.
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    There are other time machines based on the twin paradox, but all of them are limited by the speed of light. They would work better, and perhaps be easier to build and operate, if you could follow Star Trek and engage your warp drive, travelling faster than light.
    But relativity forbids that, right?
    Wrong.
    Special relativity forbids that. General relativity, it turns out, permits it. The amazing thing is that the way it permits it turns out to be standard SF gobbledegook, invoked by innumerable writers who knew about relativistic limitations but still wanted their starships to travel faster than light. ‘Relativity forbids matter travelling faster than light,’ they would incant, ‘but it doesn’t forbid space travelling faster than light.’ Put your starship in a region of space, and leave it stationary relative to that region. No violation of Einstein there. Now move the entire region of space, starship inside, with superluminal (faster-than-light) speed. Bingo!
    Ha-ha, most amusing. Except …
    In the context of general relativity, that’s exactly what Miguel Alcubierre Moya came up with in 1994. He proved that there exist solutions of Einstein’s field equations involving a local ‘warping’ of spacetime to form a mobile bubble. Space contracts ahead of the bubble and expands behind it. Put a starship inside the bubble, and it can ‘surf’ a gravitational wave, cocooned inside a static shell of local spacetime. The speed of the starship relative to the bubble is zero. Only the bubble’s boundary moves, and that’s just empty space.
    The SF writers were right. There is no relativistic limit to the speed with which space can move.
    Warp drives have the same drawback as wormholes. You need exotic matter to create the gravitational repulsion needed to distort spacetime in this unusual way. Other schemes for warp drives have been proposed, which allegedly overcome this obstacle, but they have