Is the cat alive or dead?
If the atom has decayed, then the cat’s dead. If not, it’s alive. However, the box is sealed, so you can’t observe what’s inside. Since unobserved quantum systems are waves, the quantum rules tell us that the atom must be in a ‘mixed’ state – half decayed and half not. Therefore the cat, which is a collection of atoms and so can be considered as a gigantic quantum system, is also in a mixed state: half alive, half dead. In 1935 Schrödinger pointed out that cats aren’t like that. Cats are macroscopic systems with classical yes/no physics. His point was that the Copenhagen interpretation does not explain – or even address – the link from microscopic quantum physics to macroscopic classical physics. The Copenhagen interpretation replaces a complex physical process (which we don’t understand) by a piece of magic: the wave collapses as soon as you try to observe it.
Most of the time this problem is discussed, physicists manage to turn Schrödinger’s point on its head. ‘No, quantum waves really are like that!’ And they’ve done lots of experiments to prove they’re right. Except … those experiments have no box, no poison gas, no alive, no dead, and no cat. What they have is quantum-scale analogues – an electron for a cat, positive spin for alive and negative for dead, and a box with Chinese walls, through which anything can be observed, but you take great care not to notice.
These discussions and experiments are lies-to-children: their aim is to convince the next generation of physicists that quantum-level systems do actually behave in the bizarre way that they do. Fine … but it’s got nothing to do with cats. The wizards of Unseen University, who know nothing about electrons but have an intimate familiarity with cats, wouldn’t be fooled for an instant. Neither would the witch Gytha Ogg, whose cat Greebo is shut in a box in Lords and Ladies. Greebo is the sort of cat that would take on a ferocious wolf and eat it.2 In Witches Abroad he eats a vampire by accident, and the witches can’t understand why the local villagers are so ecstatic.
Greebo has his own way of handling quantum paradoxes: ‘Greebo had spent an irritating two minutes in that box. Technically, a cat locked in a box may be alive or it may be dead. You never know until you look. In fact, the mere act of opening the box will determine the state of the cat, although in this case there were three determinate states the cat could be in: these being Alive, Dead, and Bloody Furious.’
Schrödinger would have applauded. He wasn’t talking about quantum states: he wanted to know how they led to ordinary, classical physics in the large, and he could see that the Copenhagen interpretation didn’t have anything to say about that. So how do classical yes/no answers emerge from quantum Ant Country? The closest we have to an answer is something called ‘decoherence’, which has been studied by a number of physicists, among them Anthony Leggett, Roland Omnés, Serge Haroche and Luis Davidovich. If you have a big collection of quantum waves and you leave it to its own devices, then the component waves get out of step and fuzz out. This is what a classical object is ‘really’ like from the quantum standpoint, and it means that cats do, in fact, behave like cats. Experiments show that the same is true even when the role of the detector is played by a microscopic quantum object: a photon’s wave function can collapse without any observers being aware, at the time, that it has done so. Even with a quantum cat, death occurs at the instant that the detector notices that the atom has decayed. It doesn’t require a mind.
In short, Archchancellor, the universe always notices the cat. And a tree in a forest does make a sound when it falls, even if no one is around. The forest is always there.
1 This rule does require some special assumptions, such as the chronic and irreversible stupidity of humanity.
2 As Nanny Ogg always says, ‘He’ just a big softy.’
THIRTEEN
NO, IT CAN’T DO THAT
ARCHCHANCELLOR RIDCULLY LOOKED around at his colleagues. They’d chosen the long table in the Great Hall for the meeting, since the HEM was getting too crowded.
‘All here? Good,’ he said. ‘Carry on, Mister Stibbons.’
Ponder sifted through his papers.
‘I’ve, er, asked for this meeting,’ he said, ‘because I’m afraid we’re doing things wrong.’
‘How can that be?’ said the Dean. ‘It’s our universe!’
‘Yes, Dean. And, er, no. It’s made up its own rules.’
‘No, no, it can’t do that,’ said the Archchancellor. ‘We’re intelligent creatures. We make the rules. Lumps of rock don’t make rules.’
‘Not exactly, sir,’ said Ponder, employing the phrase in its traditional sense of ‘absolutely wrong’. ‘There are some rules in the Project.’
‘How? Is someone else meddling with it?’ the Dean demanded. ‘Has a Creator turned up?’
‘An interesting thought, sir. I’m not qualified to answer that one. The point I’m trying to make is that if we want to do anything constructive, we’ve got to obey the rules.’
The Lecturer in Recent Runes looked down at the table in front of him. It had been laid for lunch.
‘I don’t see why,’ he said. ‘This knife and fork don’t tell me how to eat.’
‘Er … in fact, sir, they do. In a roundabout way.’
‘Are you trying to tell us that the rules are built in?’ said Ridcully.
‘Yes, sir. Like: big rocks are heavier than small rocks.’
‘That’s not a rule, man, that’s just common sense!’
‘Yes, sir. It’s just that the more I look into the Project, the more I’m not sure any more what common sense is. Sir, if we’re going to build a world it has to be a ball. A big ball.’
‘That’s a lot of outmoded religious nonsense, Mister Stibbons.’1
‘Yes, sir. But in the Project universe, it’s real. Some of the ba … the spheres the students have made are huge.’
‘Yes, I’ve seen them. Showy, to my mind.’
‘I was thinking of something smaller, sir. And … and I’m pretty sure things will stay on it. I’ve been experimenting.’
‘Experimenting?’ said the Dean. ‘What good does that do?’
The doors were flung open. Turnipseed, Ponder’s assistant, hurried across to the table in a state of some agitation.
‘Mister Stibbons! HEX has found something!’
The wizards turned to stare at him. He shrugged.
‘It’s gold,’ he said.
‘The Guild of Alchemists is not going to be happy about this,’ said the Senior Wrangler, as the entire faculty clustered around the project. ‘You know what they are for demarcation.’
‘Fair enough,’ said Ridcully, steering the omniscope. ‘We’ll just give them a few minutes to turn up, otherwise we’ll go on as we are, all right?’
‘How can we get it out?’ said the Dean.
Ponder looked horrified. ‘Sir! This is a universe! It is not a piggy-bank! You can’t just turn it upside down, stick a knife in the slot and rattle it around!’
‘I don’t see why not,’ said Ridcully, without looking up. ‘It’s what people do all the time.’ He adjusted the focus. ‘Personally I’m glad nothing can get out of the thing, though. Call me old fashioned, but I don’t intend to occupy the same room as a million miles of exploding gas. What happened?’
‘HEX says one of the new stars exploded.’
‘They’re too big to be stars, Ponder. We’ve been into this.’
‘Yes, sir,’ Ponder disagreed.
‘They’ve only been around for five minutes.’
‘A few days, sir. But millions of years in Project time. People have been dumping rubbish into it, and I think some just drifted in and … I don’t think it was a very well-made st – furnace in the first place.’
The exploding star was shrinking now, but flinging out a great halo of brilliant gases that even lit up one side of the rocky lumps the wizards had been making. Things want to come together and get big, Ponder thought. But when they’re big enough, they want to explode. Another law.
‘There’s lead and
copper here, too,’ said Ridcully. ‘We’re in the money now, gentlemen. Except that in this universe there’s nothing to spend it on. Even so, it seems we’re making progress. You’re looking peaky, Mister Stibbons. You ought to get some sleep.’
Progress, thought Ponder. Was that what they were making? But without narrativium, how did anything know?
It was day four. Ponder had been awake all night. He wasn’t sure, but he thought he’d probably been awake the previous night, too. He may have nodded off for a while, pillowing his head on the growing pile of screwed-up pieces of paper, with the Project winking and twinkling in front of him. If so, he’d dreamed of nothing.
But he’d decided that Progress was what you made it.
After breakfast, the wizards looked at the ball which currently occupied the centre of the omniscope.
‘Um, I used iron to start with,’ said Ponder. ‘Well, mostly iron. There’s quite a lot of it about. Some of the ices are really nasty things, and rock by itself just sits there. See this one here?’
A smaller ball of rock hung in space a little way away.
‘Yes, very dull,’ said the Senior Wrangler. ‘Why’s it got holes all over it?’
‘I’m afraid that when I was dropping rocks on the ball of iron there were a few that went out of control.’
‘Could happen to anyone, Stibbons,’ said the Archchancellor generously. ‘Did you add gold?’
‘Oh yes, sir. And other metals.’
‘Gold does give a crust some style, I think. Are these volcanoes?’
‘Sort of, sir. They are the, er, acne of young worlds. Only unlike ours, where the rock is melted in the internal magical fields generated in the sub-strata, the magma is kept molten by the heat trapped inside the sphere.’
‘Very smoky atmosphere. I can hardly see anything.’
‘Yes, sir.’
‘Well, I don’t call it much of a world,’ said the Dean, sniffing. ‘Practically red hot, smoke belching out everywhere …’
‘The Dean does have a point, young man,’ said Ridcully. He was extra kind, just to annoy the Dean. ‘It’s a brave attempt, but you just seem to have made another ball.’
Ponder coughed. ‘I just put this one together for demonstration purposes, sir.’ He fiddled with the controls of the omniscope. The scene flickered, and changed. ‘Now this,’ he said, and there was a twinge of pride in his voice, ‘is one I made earlier.’
They stared into the lens.
‘Well? Just more smoke,’ said the Dean.
‘Cloud, sir, in fact,’ said Ponder.
‘Well, we can all make clouds of gas –’
‘Er … it’s water vapour, sir,’ said Ponder.
He reached over and adjusted the omniscope.
The room was filled with the roar of the biggest rainstorm of all time.
By lunchtime it was a world of ice.
‘And we were doing so well,’ said Ridcully.
‘I can’t think what went wrong,’ said Ponder, wringing his hands. ‘We were getting seas!’
‘Can’t we just warm it up?’ said the Senior Wrangler.
Ponder sat down on his chair and put his head in his hands.
‘Bound to cool a world down, all that rain,’ said the Lecturer in Recent Runes, slowly.
‘Very good … er, rocks,’ said the Dean. He patted Ponder on the back.
‘Poor chap looks a bit down,’ hissed the Senior Wrangler to Ridcully. ‘I don’t think he’s been eating properly.’
‘You mean … not chewing right?’
‘No eating enough, Archchancellor.’
The Dean picked up a piece of paper from Ponder’s crowded desk.
‘I say, look at these,’ he said.
On the paper was written, in Ponder’s very neat handwriting:
THE RULES
1 Things fall apart, but centres hold.
2 Everything moves in curves.
3 You get balls.
4 Big balls tell space to bend.
5 There are no turtles anywhere.
6 … It’s so depressing.
‘Always been a bit of a one for rules, our Ponder,’ said the Senior Wrangler.
‘Number Six doesn’t sound incredibly well formulated,’ said Ridcully.
‘You don’t think he’s going a bit bursar, do you?’ said the Lecturer in Recent Runes.
‘He always thinks everything has to mean something,’ said Ridcully, who generally took the view that trying to find any deep meaning to events was like trying to find reflections in a mirror: you always succeeded, but you didn’t learn anything new.
‘I suppose we could simply heat the thing up,’ said the Senior Wrangler.
‘A sun should be easy,’ said Ridcully. ‘A big ball of fire should be no problem to a thinking wizard.’ He cracked his knuckles. ‘Get some of the students to put Mister Stibbons to bed. We’ll soon have his little world all warm or my name’s not Mustrum Ridcully.’
1 Omnianism had taught for thousands of years that the Discworld was in fact a sphere, and violently persecuted those who preferred to believe the evidence of their own eyes. At the time of writing, Omnianism was teaching that there was something to be said for every point of view.
FOURTEEN
DISC WORLDS
TO THE WIZARDS of Unseen University, the heavens include two obviously different types of body: stars, which are tiny pinpricks of light, and the sun, which is a hot ball, not too far away, and passes over the Disc during the day and under it at night. It’s taken humanity a while to realize that in our universe it’s not like that. Our Sun is a star, and like all stars it’s huge, so those tiny pinpricks must be a very long way off. Moreover, some of the pinpricks that seem to be stars aren’t: they betray themselves by moving differently from the rest. These are the planets, which are a lot closer and a lot smaller, and together with the Earth, Moon, and Sun they form the solar system. Our solar system may look like a lot of balls whizzing around in some kind of cosmic game of pool, but that doesn’t mean that it started out as balls or rock and ice. It is the outcome of a physical process, and the ingredients that went into that process are not obliged to resemble the result that comes out.
The more we learn about the solar system, the more difficult it is to give a plausible answer to the question: how did it start? It is not the ‘answer’ part that gets harder – it’s the plausibility. As we learn more and more about the solar system, the reality-check that our theories have to pass becomes more and more stringent. This is one reason why scientists have a habit of opening up old questions that everybody assumed were settled long ago, and deciding that they weren’t. It doesn’t mean that scientists are incompetent: it demonstrates their willingness to contemplate new evidence and re-examine old conclusions in its light. Science certainly does not claim to get things right, but it has a good record of ruling out ways to get things wrong.
What must a theory of the formation of the solar system explain? Principally, of course, the planets – nine of them, dotted rather randomly in space; Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto. It must explain their differences in size. Mercury is a mere 3,032 miles (4,878 km) in diameter, whereas Jupiter is 88,750 miles (142,800 km) in diameter – 29 times as big, 24,000 times the volume, an enormous discrepancy. It must explain their differences in chemical composition: Mercury is made of iron, nickel, and silicate rock; Jupiter is made from hydrogen and helium. It must explain why the planets near the Sun are generally smaller than those further out, with the exception of tiny Pluto, out in the cold and the dark. We don’t know a great deal about Pluto, but most of what we do know is strange. For instance, all the other planets lie pretty close to a single plane through the centre of the Sun, but Pluto’s orbit is inclined at a noticeable angle. All the other planets have orbits that are pretty close to circles, but Pluto’s orbit is much more elongated – to the extent that some of the time it is closer to the Sun than Neptune is.
But that’s not all that a
theory of the origin of the solar system has to get right. Most planets have smaller bodies in orbit around them – our own familiar Moon; Phobos and Deimos, the diminutive twin satellites of Mars; Jupiter’s 16 satellites; Saturn’s 17 … Even Pluto has a satellite, called Charon, and that’s weird too. Saturn goes one better and also has entire rings of smaller bodies surrounding it, a broad, thin band of encircling rocks that breaks up into a myriad distinct ringlets, with satellites mixed up among them as well as more conventional satellites elsewhere. Then there are the asteroids, thousands of small bodies, some spherical like planets, others irregular lumps of rock, most of which orbit between Mars and Jupiter – except for quite a few that don’t. There are comets, which fall in towards the Sun from the huge ‘Oort cloud’ way out beyond the orbit of Pluto – a cloud that contains trillions of comets. There is the Kuiper belt, a bit like the asteroid belt but outside Pluto’s orbit: we know over 30 bodies out there now, but we suspect there are hundreds of thousands.
These bodies are known as ‘Kuiper Belt Objects’ or KBOs. A few years back there was a big fuss because some astronomers wanted to redefine Pluto as a KBO rather than a planet. Pluto probably wouldn’t have minded either way, but an awful lot of textbook publishers would have. The scientific case was strong: Pluto is weird in almost every respect, as we’ve just seen, and it could easily be a KBO that accidentally strayed into the outer reaches of the solar system when disturbed by other bodies. If so, that would explain why it’s so weird. It doesn’t look like a planet because it isn’t one. Other astronomers disagreed strongly with this proposal – for sentimental reasons, for historical ones, or because we don’t know for sure that Pluto is a wandering KBO. In the end, Pluto remained on the list of planets. But whether it can hang on to that status for much longer is unclear.
Then there are meteorites, lumps of rock of various sizes that wander erratically through the whole thing …
The Science of Discworld Revised Edition Page 12