'Mr Wedgwood is Charles Darwin's uncle,' said Ponder, as the air wavered. `He will have an influence on his nephew's career. And now for our next call ...'
`Good morning! Mrs Nightingale?'
`Yes?' said the woman, as if she was now doubting it. She took in the group of people in front of her, her eye resting on the very bearded one whose knuckles touched the ground. Beside her, the housemaid who'd opened the door looked on nervously.
`My name is Mr Stibbons, Mrs Nightingale. I am the secretary of The Mission to Deep Sea Voyagers, a charitable organisation. I believe Mr Nightingale is shortly to embark on a perilous mission to the storm-tossed, current-mazed, ship-eating giant-squid infested waters of the South Americas?'
The woman's gaze tore itself away from the Librarian and her eyes narrowed.
`He never said anything to me about giant squid,' she said.
`Indeed? I'm very sorry to hear that, Mrs Nightingale. Brother Bookmeister here,' Ponder patted the Librarian on the shoulder, `would tell you about them himself were it not that the dire experience quite robbed him of the power of speech.'
'Ook!' said Brother Bookmeister plaintively.
`Really?' said the woman, setting her jaw firmly. `Would you gentlemen care to step into the parlour?'
`Well, the biscuits were nice,' said the Dean, as the wizards strolled out into the street half an hour later. `And now, Stibbons, would you care to tell us what all that was about?'
`Gladly, Dean, and may I say your story about the sea snake was very useful?' said Ponder. `But Rincewind, that tale about the killer flying fish was rather over the top, I thought.'
`I didn't make it up!' Rincewind said. `They had teeth on them like-'
`Well, anyway ... Darwin was the second choice for the post on the Beagle,' said Ponder. 'Mr Nightingale was the captain's initial choice. History will record that after his wife's pleading he declined the offer. This he will do within about five minutes of when he gets home tonight.'
`Another fine ruse?' said Ridcully.
`I'm rather pleased with it, as a matter of fact,' said Ponder.
'Hmm,' said Ridcully. Cunning in younger wizards is not automatically applauded in their elders. `Very clever, Stibbons. You are a wizard to watch.'
`Thank you, sir. My next question is: does anyone here know anything about shipbuilding? Well, perhaps that won't be necessary. Hex, take us to Portsmouth, please. The Beagle is being refitted. You will need to be naval inspectors which, ahaha, I'm sure you'll be good at. In fact you will be the most observant inspectors there have ever been. Location 3, please, Hex.'
FORWARD TO THE PAST
WELL, THE WIZARDS HAVE MADE a good start. And with the might of Hex behind them, the wizards can travel at will along the Roundworld timeline. We're happy for them to do that, in a fictional context - but could we do the same thing, in a factual one?
To answer that, we must decide what a time machine looks like within the framework of general relativity. Then we can talk about building one.
Travel into the future is easy: wait. It's getting back that's hard. A time machine lets a particle or object return to its own past, so its world-line, a timelike curve, must close into a loop. So a time machine is just a closed timelike curve, abbreviated to CTC. Instead of asking, `Is time travel possible?' we ask, `Can CTCs exist?'
In flat Minkowski spacetime, they can't. Forward and backward light cones - the future and past of an event - never intersect (except at the point itself, which we discount). If you head off across a flat plane, never deviating more than 45° from due north, you can never sneak up on yourself from the south.
But forward and backward light cones can intersect in other types of spacetime. The first person to notice this was Kurt Godel, better known for his fundamental work in mathematical logic. In 1949 he worked out the relativistic mathematics of a rotating universe, and discovered that the past and future of every point intersect. Start wherever and whenever you like, travel into your future, and you'll end up in your own past. However, observations indicate that the universe is not rotating, and spinning up a stationary universe (especially from inside) doesn't look like a plausible way to make a time machine. Though, if the wizards were to give Roundworld a twirl ...
The simplest example of future meeting past arises if you take Minkowski spacetime and roll it up along the `vertical' time direction to form a cylinder. Then the time coordinate becomes cyclic, as in Hindu mythology, where Brahma recreates the universe every kalpa, a period of 4.32 billion years. Although a cylinder looks curved, the corresponding spacetime is not actually curved - not in the gravitational sense. When you roll up a sheet of paper into a cylinder, it doesn't distort. You can flatten it out again and the paper is not folded or wrinkled. An ant that is confined purely to the surface won't notice that spacetime has been bent, because distances on the surface haven't changed. In short the local metric doesn't change. What changes is the global geometry of spacetime, its overall topology.
Rolling up Minkowski spacetime is an example of a powerful mathematical trick for building new spacetimes out of old ones: cut-and-paste. If you can cut pieces out of known spacetimes, and glue them together without distorting their metrics, then the result is also a possible spacetime. We say `distorting the metric' rather than `bending', for exactly the reason that we say that rolled-up Minkowski spacetime is not curved. We're talking about intrinsic curvature, as experienced by a creature that lives in the spacetime, not about apparent curvature as seen by some external viewer.
The rolled-up version of Minkowski spacetime is a very simple way to prove that spacetimes that obey the Einstein equations can possess CTCs - and thus that time travel is not inconsistent with currently known physics. But that doesn't imply that time travel is possible. There is a very important distinction between what is mathematically possible and what is physically feasible.
A spacetime is mathematically possible if it obeys the Einstein equations. It is physically feasible if it can exist, or could be created, as part of our own universe or an add-on. There's no very good reason to suppose that rolled-up Minkowski spacetime is physically feasible: certainly it would be hard to refashion the universe in that form if it wasn't already endowed with cyclic time, and right now very few people (other than Hindus) think that it is. The search for spacetimes that possess CTCs and have plausible physics is a search for more plausible topologies. There are many mathematically possible topologies, but, as with the Irishman giving directions, you can't get to all of them from here.
However, you can get to some remarkably interesting ones. All you need is black hole engineering. Oh, and white holes, too. And negative energy. And - One step at a time. Black holes first. They were first predicted in classical Newtonian mechanics, where there is no limit to the speed of a moving object. Particles can escape from an attracting mass, however strong its gravitational field, by moving faster than the appropriate `escape velocity'. For the Earth, this is 7 miles per second (11 kps), and for the Sun, it is 26 miles per second (41 kps). In an article presented to the Royal Society in 1783, John Michell observed that the concept of escape velocity, combined with a finite speed of light, implies that sufficiently massive objects cannot emit light at all - because the speed of light will be lower than the escape velocity. In 1796 Pierre Simon de Laplace repeated these observations in his Exposition of the System of the World. Both of them imagined that the universe might be littered with huge bodies, bigger than stars, but totally dark.
They were a century ahead of their time.
In 1915 Karl Schwarzschild took the first step towards answering the relativistic version of the same question, when he solved the Einstein equations for the gravitational field around a massive sphere in a vacuum. His solution behaved very strangely at a critical distance from the centre of the sphere, now called the Schwarzschild radius. It is equal to the mass of the star, multiplied by the square of the speed of light, multiplied by twice the gravitational constant, if you must know.