The wizards would have to go in. They could do that. They'd done it before. No trouble is too much if it saves some excellent chefs from extinction.
Clothing, at least, would not be a problem. Give or take the odd pointy hat and staff, the wizards would be able to walk the Roundworld streets without attracting a second glance.
`How do we look?' said the Archchancellor, as they reassembled.
`Very ... Victorian,' said Ponder. `Although technically, at the moment, very Georgian. Very ... tweedy, anyway. Are you totally happy with the bishop look, Dean?'
`Isn't that appropriate for the time?' said the Dean, looking worried. `We looked through the book on costumes and I thought...' His voice trailed off. `It's the mitre, isn't it ...'
`And the crozier,' said Ponder.
'I wanted to fit in, you see.'
`In a cathedral, yes.. I'm afraid it's plain black suit with gaiters for street wear. However, you can do anything you like with your beard and you can wear hats a small child could stand up inside. But on the streets, bishops are quite dull.'
`Where's the fun in that?' said the Dean, sulkily.
Ponder turned to Rincewind.
`As for you, Rincewind, can I ask why you are wearing nothing but a loincloth and a pointy hat?
'Ah, well, you see, if you don't know what you're getting into, naked always works,' said Rincewind. `It's the all-purpose suit. At home in every culture. Admittedly you sometimes get-'
`In tweed, that man!' barked Ridcully. `And no pointy hat!' Against a background of grumbling he turned then to the Librarian. `And as for you, sir ... a suit too. And a stovepipe hat. You need the height!'
'Ook!' said the Librarian.
`I am the Archchancellor, sir! I insist! And a false beard, I think. False eyebrows, too. Let Mr Darwin be your model here! These Victorians were very civilised people! Hair everywhere! Keep the knuckling to a minimum and they'll make you Prime Minister! Very well, gentlemen. Back here in half an hour!
The wizards assembled. A circle of white light appeared on the floor. They stepped inside, there was a change in the sounds made by Hex, and they vanished.
They landed knee-deep in the mire of a peat bog, causing bubbles of foul air to burst around them.
`Mr Stibbons!' Ridcully bellowed.
`Sorry, sir, sorry,' said Ponder quickly. `Hex, raise us by two feet, please.'
`Yes, but we're still soaked,' grumbled the Dean, as they floated up in the air. `You seem to have, ah, "mucked up", Mr Stibbons!' 'No, sir, I wanted to show you a Charles Darwin in the wild,' said Ponder. 'Here he comes now ...
A large and energetic young man bounded out of the weeds and went to clear a black pool with a vaulting pole. The pole immediately sank one-third of its length into the sucking ground and its athletic owner sailed off into the mud. He came up holding a small water plant. Oblivious of the noisome bubbling around him, he waved the plant triumphantly at some distant companions, pulled his pole out of the peat with some effort, and splashed away.
`Did he see us?' said Rincewind.
`No, not yet. That's young Darwin,' said Ponder. `Very keen on collecting all sorts of wildlife. Collecting was enormous popular among the English of this century. Bones, shells, butterflies, birds, other people's countries ... all sorts of things.'
`Man after my own heart!' said Ridcully, cheerfully. `I had the best pressed lizard collection ever when I was that age!'
`Can't see a beagle anywhere, though,' said Rincewind, gloomily. He got edgy in the absence of his hat, and tried to stand under things.
The Chair of Indefinite Studies looked up from the thaumometer in his hand.
`No magic disturbance, no nothing,' he said, looking around at the marshes. `Is Hex sure? The only strange thing here is us.'
`Let's get started, shall we?' said Ridcully. `Where to next?' `Hex, move us to London, will you?' said Ponder. `Location 7.' The wizards didn't apparently move, but the landscape around them wavered and changed.
It became an alleyway. There were a lot of street noises nearby. `I'm sure you all read the briefing I prepared this morning.' said Ponder, brightly.
`Are you also sure were not back in Ankh-Morpork?' said Ridcully loudly. `I'd swear I can smell the river!'
`Ah, then perhaps I'd better just remind you of the important points,' said Ponder wearily. `The list of major things that might impede Darwin's progress-'
`I remember about the giant squid,' Rincewind volunteered.
`Hex can handle the giant squid,' said Ponder.
`Oh, shame. I was looking forward to that,' said Ridcully.
`No, sir,' said Ponder, as patiently as possible. `We have to deal with people. Remember? We agreed last time it's not ethical to leave that to Hex. Remember the rain of fat women[22]?
`That never actually happened,' said the Lecturer in Recent Runes, wistfully.
`Quite so,' said Ridcully, firmly. `And just as well. Lead on, Mr Stibbons.'
`So much to do, so much to do,' muttered Ponder, leafing through the paperwork. `I suppose we'd better do things in order ... so first, we must see that Mr Habbakuk Souser's cook throws away the fish.'
It was a scullery boy who opened the back door, in a street of quite prosperous-looking houses. Ponder Stibbons raised his very tall hat.
`We wish to see - ' he consulted the clipboard ` - Mrs Boddy,' he said. `She is the cook here, I believe? Tell her we are the Committee for Public Sanitation, and the matter is urgent, so look sharp about it!'
`I hope you know what you're doing, Stibbons,' hissed Ridcully as the boy scurried away.
`Totally, Archchancellor. Hex says the line of causality is - ah, Mrs Boddy?'
This was to a skinny, worried woman who was advancing on them from the dim interior, wiping her hands on her apron.
'I am, sir,' said the cook. `The boy said you gentlemen was Hygienic?'
`Mrs Boddy, you had some fish delivered this morning?' said Ponder, sternly.
`Yes sir. Nice piece o' hake.' Sudden uncertainty seized her features. `Er ... that was all right, wasn't it?
'Alas it was not, Mrs Boddy!' said Ponder. `We have just come from the fishmonger. All his hake is completely off. We have had many complaints. Some of them were from next of kin, Mrs Boddy!'
`Oh, what shall we do to be saved!' the cook burst out. `I've got it cookin'! It smelled all right, sir!'
`Thankfully, then, there is no harm done,' said Ponder. `Shall I give it to the cat?
'Do you like the cat?' said Ponder. `No, wrap it in some paper and bring it out to us right now! I'm sure Mr Souser will understand when you give him some of the cold ham from yesterday.'
`Yessir!' The cook scurried away, and returned shortly with a parcel of very hot, very damp fish. Ponder grabbed it from her and thrust it into Rincewind's arms.
`Scour the pan thoroughly, Mrs Boddy!' said Ponder, as Rincewind tried to juggle hake. `Gentlemen, we must hurry!'
He started to walk very fast towards the end of the street, the wizards jogging along behind him, and turned sharply into an alleyway just ahead of a shout of `Sir? Sir? How did you know about the cold ham?'
`Location 9, Hex,' said Ponder. `And remove the fish, please!'
`Was all that about?' said Ridcully. `Why did we take that poor woman's fish?'
Rincewind said `ow!' as the fish disappeared.
`Mr Souser will travel, er, tomorrow to meet some businessmen,' said Ponder, as a circle formed on the ground around the wizards. `One of them will be a man called Josiah Wedgwood, a famous industrialist. Mr Souser will tell him about his son James, who is currently working with the Navy. It has made a man of him, Mr Souser will say. Mr Wedgwood will listen with interest, and form the opinion that the adventure of a long sea voyage in respectable company may well be of benefit to a young man on the verge of adult life. At least, he will now. If Mr Souser had eaten that fish, he would have been too ill to travel tomorrow.'
`Well, that's good news for Mr Souser, but what's it got to do wit
h us?' said the Dean.
'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.'
8. 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, i
f you must know.
The Schwarzschild radius for the Sun is 1.2 miles (2 km), and for the Earth 0.4 inches (1 cm) - both buried inaccessibly deep where they can't cause trouble. So it wasn't entirely clear how significant the strange mathematical behaviour was ... or even what it meant.
What would happen to a star that is so dense that it lies inside its own Schwarzschild radius?
In 1939 Robert Oppenheimer and Hartland Snyder showed that it would collapse under its own gravitational attraction. Indeed a whole portion of spacetime would collapse to form a region from which no matter, not even light, could escape. This was the birth of an exciting new physical concept. In 1967 John Archibald Wheeler coined the term black hole, and the new concept was christened.
How does a black hole develop as time passes? An initial clump of matter shrinks to the Schwarzschild radius, and then continues to shrink until, after a finite time, all the mass has collapsed to a single point, called a singularity. From outside, though, we can't observe the singularity: it lies beyond the `event horizon' at the Schwarzschild radius, which separates the observable region, from which light can escape, and the unobservable region where the light is trapped.
If you were to watch a black hole collapse from outside, you would see the star shrinking towards the Schwarzschild radius, but you'd never see it get there. As it shrinks, its speed of collapse as seen from outside approaches that of light, and relativistic timedilation implies that the entire collapse takes infinitely long when seen by an outside observer. The light from the star would shift deeper and deeper into the red end of the spectrum. The name should be `red hole'.
Black holes are ideal for spacetime engineering. You can cut-andpaste a black hole into any universe that has asymptotically flat regions, such as our own[23]. This makes black hole topology physically plausible in our universe. Indeed, the scenario of gravitational collapse makes it even more plausible: you just have to start with a big enough concentration of matter, such as a neutron star or the centre of a galaxy. A technologically advanced society could build black holes.
The Science of Discworld III - Darwin's Watch tsod-3 Page 9
