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 their own drawbacks. Sergei Krasnikov noticed one awkward feature of Alcubierre's warp drive: the inside of the bubble becomes causally disconnected from the front edge. The starship's captain, inside the bubble, can't steer it, and she can't even turn it on or off. He proposed a different method, a 'superluminal highway'. On the outward trip, the starship travels below lightspeed and leaves a tube of distorted spacetime behind it. On the way back, it travels faster than light along the tube. The superluminal highway also needs negative energy; in fact, Ken Olum and others have proved that any type of warp drive does.
There are limits to the lifetime of any given amount of negative energy. For wormholes and warp drives these limits imply that such structures must either be very small, or else the region of negative energy must be extremely thin. For example, a wormhole whose mouth is three feet (1m) across must confine its negative energy to a band whose thickness is one millionth of the diameter of a proton. The total negative energy required would be equivalent to the total output (in positive energy) of 10 billion stars for one year. If the mouth were one light year across, then the thickness of the negative energy band would still be smaller than a proton, and now the negative energy requirement would be that of 10 quadrillion stars.
Warp drives, if anything, are worse. To travel at 10 times lightspeed (a mere Star Trek Warp Factor 2) the thickness of the bubble's wall must be 10-32 metres. If the starship is 200 yards (200m) long, the energy required to make the bubble has to be 10 billion times the mass of the known universe.
Engage.
Roundworld narrativium can sometimes be documented. When Ronald Mallett was ten years old his 33-year-old father died of heart failure, brought on by drinking and smoking. `It completely devastated me,' he is reported to have said.' Soon after, he read Wells's The Time
[1] Michael Brooks, `Time Twister', New Scientist, 19 May 2001, 27-9.
Machine. And he reasoned that `If I could build a time machine, I might be able to warn him about what was going to happen.'
The childish idea faded, but the interest in time travel did not. As an adult, Mallett invented an entirely new type of time machine, one that uses bent light.
Morris and Thorne bent space to make a wormhole using matter. Mass is curved space. Levi-Civita bent space using magnetism. Magnetism has energy, energy is (so Einstein tells us) mass. Mallett prefers to bend space using light. Light, too, has energy. So it can act like mass. In 2000, he published a paper on the deformation of space by a circular beam of light. Then it hit him. If you can deform space, you ought to be able to deform time too. And his calculations showed that a ring of light could create a ring of time - a CTC.
With a Mallett bent-light time machine, you can walk into your past. A time traveller makes his or her way into the closed loop of light, space, and time. Walking round the loop has the same effect as moving backwards in time. The more times he walks round the loop, the further back he goes, tracing out a helical world-line. When he has gone sufficiently far into his past, he exits the loop. Easy.
Yes, but ... we've been here before. It takes huge amounts of energy to make a circular beam of light.
That's true ... unless you can slow the light down. A ring of really slow light, Discworld-speed, like that of sound on Roundworld, is much easier to make. The reason is that as light slows down, it gains inertia. This gives it more energy, and the warping effect is far greater for less effort on the part of the builder.
Relativity tells us that the speed of light is constant - in a vacuum. In other media, light slows down; this is why glass refracts light, for example. In the right medium, light can be slowed to walking pace, or even stopped altogether. Experiments by Lene Hau demonstrated this effect in 2001, using a medium known as a Bose-Einstein condensate. This is a furious, degenerate form of matter, occurring at temperatures near absolute zero; it consist of lots of atoms in exactly the same quantum state, forming a 'superfluid' with zero viscosity.
So maybe Wells's time traveller could have included some refrigeration equipment and a laser in his machine. But a Mallett bent-light time machine suffers from the same limitation as a wormhole one. You can't travel back to any time before the machine was constructed.
Wells was probably right to eliminate that encounter with a giant hippopotamus.
These are purely relativistic time machines, but the universe has quantum features too, and these should be taken into account. The search for a unification of relativity and quantum theory - respectably known as `quantum gravity' and often derided as a Theory of Everything - has turned up a beautiful mathematical proposal, string theory. In this theory, instead of fundamental particles being points, they are vibrating multidimensional loops. The best-known version uses six-dimensional loops, so its model of spacetime is really tendimensional. Why has no one noticed? Perhaps because the extra six dimensions are curled up so tightly that no one has observed them - very possibly, can observe them. Or perhaps - the Irishman again - we can't go that way from here.
Many physicists hope that string theory, as well as unifying relativity and quantum mechanics, will also supply a proof of Hawking's chronology protection conjecture - that the universe conspires to keep events happening in the same temporal order. In this connection, there is a five-dimensional string-theoretic rotating black hole called a BMPV [1] black hole. If this rotates fast enough, it has CTCs outside the black hole region. Theoretically, you can build one from gravitational waves and esoteric string-theoretic gadgets called 'D-branes'.
[1] Jason Breckenridge, Rob Myers, Amanda Peet, and Cumrun Vafa.
And here we see a hint of Hawking's cosmological time cops. Lisa Dyson took a careful look at just what happens when you put the gravitational waves and D-branes together. Just as the black hole is within a gnat's whisker of turning into a time machine, the components stop collecting together in the same place. Instead, they form a shell of gravitons (hypothetical particles of gravity, analogous to photons for light). The D-branes are trapped inside the shell. The gravitons can't be persuaded to come any closer, and the BMPV can't be made to spin rapidly enough to create an accessible CTC.
The laws of physics won't let you put this kind of time machine together, unless some clever kind of scaffolding can be invented.