The Science of Discworld I tsod-1

by Terry Pratchett

  There are practical problems in staging that experiment, but less graphic and dangerous ones have indicated what the result would be.

  Einstein published Special Relativity in 1905, along with the first serious evidence for quantum mechanics and a ground-break­ing paper on diffusion. A lot of other people, among them the Dutch physicist Hendrik Lorentz and the French mathematician Henri Poincare, were working on the same idea, because electro-magnetism didn't entirely agree with Newtonian mechanics. The conclusion was that the universe is a lot weirder than common sense tells us, although they probably didn't use that actual word. Objects shrink as they approach the speed of light, time slows down to a crawl, mass becomes infinite ... and nothing can go faster than light. Another key idea was that space and time are to some extent interchangeable. The traditional three dimensions of space plus a separate one for time are merged into a single unified spacetime with four dimensions. A point in space becomes an event in spacetime.

  In ordinary space, there is a concept of distance. In Special Relativity, there is an analogous quantity, called the interval between events, which is related to the apparent rate of flow of time. The faster an object moves, the slower time flows for an observer sitting on that object. This effect is called time dilation.

  If you could travel at the speed of light, time would be frozen.

  One startling feature of relativity is the twin paradox, pointed out by Paul Langevin in 1911. Again, it is a classic illustration. Suppose that Rosencrantz and Guildenstern are born on Earth on the same day. Rosencrantz stays there all his life, while Guildenstern travels away at nearly lightspeed, and then turns round and comes home again. Because of time dilation, only one year (say) has passed for Guildenstern, whereas 40 years have gone by for Rosencrantz. So Guildenstern is now 39 years younger than his twin brother. Experiments carrying atomic clocks around the Earth on jumbo jets have verified this scenario, but aircraft are so slow compared to light that the time difference observed (and pre­dicted) is only the tiniest fraction of a second.

  So far so good, but there's no place yet for gravity. Einstein racked his brains for years until he found a way to put gravity in: let spacetime be curved. The resulting theory is called General Relativity, and it is a synthesis of Newtonian gravitation and Special Relativity. In Newton's view, gravity is a force that moves particles away from the perfect straight line paths that they would otherwise follow In General Relativity, gravity is not a force: it is a distortion of the structure of spacetime. The usual image is to say that space-time becomes 'curved', though this term is easily misinterpreted. In particular, it doesn't have to be curved round anything else. The cur­vature is interpreted physically as the force of gravity, and it causes light rays to bend. One result is 'gravitational lensing', the bending of light by massive objects, which Einstein discovered in 1911 and published in 1915. The effect was first observed during an eclipse of the Sun. More recently it has been discovered that some distant quasars produce multiple images in telescopes because their light is lensed by an intervening galaxy.

  Einstein's theory of gravity ousted Newton's because it fitted observations better, but Newton's remains accurate enough for many purposes, and is simpler, so it is by no means obsolete. Now it's beginning to look as if Einstein may in turn be ousted, possibly by a theory that he rejected as his greatest mistake.

  In 1998 two different observations called Einstein's theory into question. One involved the structure of the universe on truly mas­sive scales, the other happened in our own backyard. The first has survived everything so far thrown at it; the second can possibly be traced to something more prosaic. So let's start with the second curious discovery.

  In 1972 and 1973 two space probes, Pioneer 10 and 11, were launched to study Jupiter and Saturn. By the end of the 1980s they were in deep space, heading out of the known solar system. There has long been a belief, a scientific legend waiting to happen, that beyond Pluto there may be an as yet undiscovered planet, Planet X. Such a planet would disturb the motions of the two Pioneers, so it was worth tracking the probes in the hope of finding unexpected deviations. John Andersen's team found deviations, all right, but they didn't fit Planet X, and they didn't fit General Relativity either. The Pioneers are coasting, with no active form of propul­sion, so the gravity of the Sun (and the much weaker gravity of the other bodies of the known solar system) pulls on them and gradu­ally slows them down. But the probes were slowing down a tiny bit more than they should have been. In 1994 Michael Martin sug­gested that this effect had become sufficiently well established that it cast doubt on Einstein's theory, and in 1998 Anderson's team reported that what was observed could not be explained by such effects as instrument error, gas clouds, the push of sunlight, or the gravitational pull of outlying comets.

  Three other scientists quickly responded by suggesting other things that might explain the anomalies. Two wondered about waste heat. The Pioneers are powered by onboard nuclear generators, and they radiate a small amount of surplus heat into space. The pressure of that radiation might slow the craft down by the observed amount. The other possible explanation is that the Pioneers may be venting tiny quantities of fuel into space. Anderson thought about these explanations and found problems with them both.

  The strangest feature of the observed slowing down is that it is precisely what would be predicted by an unorthodox theory sug­gested in 1983 by Mordehai Milgrom. This theory changes not the law of gravity, but Newton's law of motion: force equals mass times acceleration. Milgrom's modification applies when the acceleration is very small, and it was introduced in order to explain another gravitational puzzle, the fact that galaxies do not rotate at the speeds predicted by either Newton or Einstein. This discrepancy is usually put down to the existence of 'cold dark matter' which exerts a grav­itational pull but can't be seen in telescopes. If galaxies have a halo of cold dark matter then they will rotate at a speed that is inconsis­tent with the matter in the visible portions. A lot of theorists dislike cold dark matter (because you can't observe it directly, that's what 'cold dark' means) and Milgrom's theory has slowly gained in pop­ularity. Further studies of the Pioneers may help decide.

  The other discovery is about the expansion of the universe. The universe is getting bigger, but it now seems that the very distant universe is expanding faster than it ought to. This startling result -confirmed by later, more detailed studies, comes from the Supernova Cosmology project headed by Saul Perlmutter and its arch-rival High-Z Supernova Search Team headed by Brian Schmidt. It shows up as a slight bend in a graph of how a distant supernova's apparent brightness varies with its red shift. According to General Relativity, that graph ought to be straight, but it's not. It behaves as if there is some repulsive component to gravity which only shows up at extremely long distances, say half the radius of the universe. A form of antigravity, in fact.

  Curiously, Einstein originally included a repulsive force of this kind in his relativistic equations for gravity: he called it the cosmo-logical constant. Later he changed his mind and threw the cosmological constant out, complaining that he'd been foolish to include it in the first place. He died thinking it was a blemish on his record, but maybe his original intuition was spot on after all.

  There is also a possible link to the other deep physical theory, quantum mechanics. At first this looked unlikely. If there is an antigravity effect, then it should stem from Vacuum energy', a form of energy that, if it exists, is stored in empty space ... (As we write this, we can picture Ridcully's expression. We shall have to ignore it. This isn't something sensible, like magic. This is science. Empty space can be full of interest.)

  However, quantum theory predicts that if vacuum energy exists in today's universe, then it would produce an antigravity effect 10119 (1 followed by 119 zeros) times as big as what's observed. Although astronomers are accustomed to larger experimental errors than you find in most other sciences, this is too much for even them to swal­low. But late in 1998 Robert Matthews wondered w
hether the antigravity effect might come from a relic of the vacuum energy of an earlier phase of the universe. His idea is related to a sixty-year-old piece of speculation by Paul Dirac, one of the founders of quantum theory. Dirac noticed a strange coincidence. The electro­magnetic force between a proton and an electron is 1040 (1 followed by 40 zeros) times as great as the gravitational force between them. The age of the universe is also 1040 times as great as the time it takes light to cross one atom. It's not hard to come up with numerologi-cal accidents of this kind, but Dirac had a hunch that this one might indicate some deep connection between the expansion of the uni­verse and the microscopic quantum realm. Now Matthews has come up with a possible explanation of the coincidence, and it fits the antigravity effect.

  According to the Big Bang theory, the early history of the uni­verse involves a number of 'phase transitions', dramatic changes of state which result in big qualitative changes in how the universe works. The earliest one occurred when the strong nuclear force sep­arated from the electromagnetic forces and the weak nuclear force. The last in this series of phase transitions was the quark-hadron transition, in which quarks grouped together to produce the more familiar protons and neutrons. If the universe has somehow retained the vacuum energy from this phase transition, then it will exhibit an antigravity effect of just the right size. So these curious observations may be telling us something rather curious about the early universe.

  11. NEVER TRUST A CURVED UNIVERSE

  PONDER STIBBONS HAD SET UP A DESK a little separate from the others and surrounded it with a lot of equipment, primarily in order to hear himself think.

  Everyone knew that stars were points of light. If they weren't, some would be visibly bigger than others. Some were fainter than others, of course, but that was probably due to clouds. In any case their purpose, according to established Discworld law, was to lend a little style to the night.

  And everyone knew that the natural way for things to move was in a straight line. If you dropped something, it hit the ground. It didn't curve. The water fell over the edge of the world, drifting sideways just a tiny bit to make up for the spin, but that was com­mon sense. But inside the Project, spin was everything. Everything was bent. Archchancellor Ridcully seemed to think this was some sort of large-scale character flaw, akin to shuffling your feet or not owning up to things. You couldn't trust a universe of curves. It was­n't playing a straight bat.

  At the moment Ponder was rolling damp paper into little balls. He'd had the gardener push in a large stone ball that had spent the last few hundred years on the university's rockery, relic of some ancient siege catapult. It was about three feet across.

  He'd hung some paper balls of string near it. Now, glumly, he threw others over it and around it. One or two did stick, admittedly, but only because they were damp. He was in the grip of some thought, You had to start with what you were certain of. Things fell down. Little things fell down on to big things. That was common sense.

  But what would happen if you had two big things all alone in the universe?

  He set up two balls of ice and rock, in an unused corner of the Project, and watched them bang into each other. Then he tried with ball of different sizes. Small ones drifted towards big ones but, oddly enough, the big ones also drifted slightly towards the small ones.

  So ... if you thought that one through ... that meant that if you dropped a tennis ball to the ground it would certainly go down, but in some tiny, immeasurable way the world would, very slightly, come up.

  And that was insane.

  He also spent some time watching clouds of gas swirl and heat in the more distant regions of the Project. It was all so ... well, god­less.

  Ponder Stibbons was an atheist. Most wizards were. This was because UU had some quite powerful standing spells against occult interference, and knowing that you're immune from lightning bolts does wonders for an independent mind. Because the gods, of course, existed. Ponder wouldn't even attempt to deny it. He just didn't believe in them. The god currently gaining popularity was Om, who never answered prayers or manifested himself. It was easy to respect an invisible god. It was the ones that turned up every­where, often drunk, that put people off.

  That's why, hundreds of years before, philosophers had decided that there was another set of beings, the creators, that existed inde­pendently of human belief and who had actually built the universe. They certainly couldn't have been gods of the sort you got now, who by all accounts were largely incapable of making a cup of coffee.

  The universe inside the Project was hurtling through its high­speed time and there was still nothing in there that was even vaguely homely for humans. It was all too hot or too cold or too empty or too crushed. And, distressingly, there was no sign of nar-rativium.

  Admittedly, it has never been isolated on Discworld either, but its existence had long ago been inferred, as the philosopher Lye Tin Wheedle had put it: 'in the same way that milk infers cows'. It might not even have a discrete existence. It might be a particular way in which every other element spun through history, something that they had but did not actually possess, like the gleam on the skin of a polished apple. It was the glue of the universe, the frame that held all the others, the thing that told the world what it was going to be, that gave it purpose and direction. You could detect narra-tivium, in fact, by simply thinking about the world.

  Without it, apparently, everything all was just balls spinning in circles, without meaning.

  He doodled on the pad in front of him:

  There are no turtles anywhere.

  'Eat hot plasma! Oh ... sorry, sir.'

  Ponder peered over his defensive screen.

  'When worlds collide, young man, someone is doing something wrong!'

  That was the voice of the Senior Wrangler. It sounded more petulant than usual.

  Ponder went to see what was going on.

  12. WHERE DO RULES COME FROM?

  SOMETHING IS MAKING ROUNDWORLD DO STRANGE THINGS...

  It seems to be obeying rules. Or maybe it's just making them up as it goes along.

  Isaac Newton taught us that our universe runs on rules, and they are mathematical. In his day they were called 'laws of nature', but 'law' is too strong a word, too final, too arrogant. But it does seem that there are more or less deep patterns in how the universe works. Human beings can formulate those patterns as mathematical rules, and use the resulting descriptions to work out some aspects of nature that would otherwise be totally mysterious, and even exploit them to make tools, vehicles, technology.

  Thomas Malthus changed a lot of people's minds when he found a mathematical rule for social behaviour. He said that food grows arithmetically (1-2-3-4-5), but populations grow geometri­cally (1-2-4-8-16). Whatever the growth rates, eventually population will outstrip food supply: there are limits to growth[20]. Malthus's law shows that there are rules Down Here as well as Up There, and it tells us that poverty is not the result of evil or sin. Rules can have deep implications.

  What are rules? Do they tell us how the universe 'really' works, or do our pattern-seeking brains invent or select them?

  There are two main viewpoints here. One is fundamentalist at heart, as fundamentalist as the Taliban and Southern Baptists -indeed, as fundamentalist as the exquisitor Vorbis in Small Gods who states his position thus: '... that which appears to our senses is not the fundamental truth. Things that are seen and heard and done by the flesh are mere shadows of a deeper reality.'

  Scientific fundamentalism holds that there is one set of rules, the Theory of Everything, which doesn't just describe nature rather well, but is nature. For about three centuries science seems to have been converging on just such a system: the deeper our theories of nature become, the simpler they become too. The philosophy behind this view is known as reductionism, and it proceeds by tak­ing things to bits, seeing what the bits are and how they fit together, and using the bits to explain the whole. It's a very effective research strategy, and it's served us well
for a long time. We've now managed to reduce our deepest theories to just two: quantum mechanics and relativity.

  Quantum mechanics set out to describe the universe on very small scales, subatomic scales, but then became involved in the largest scales of all, the origin of the universe in the Big Bang. Relativity set out to describe the universe on very large scales, supergalactic ones, but then became involved in the smallest scales of all, the quantum effects of gravity. Despite this, the two theories disagree in fundamental ways about the nature of the universe and what rules it obeys. The Theory of Everything, it is hoped, will sub­tly modify both theories in such a way that they fit seamlessly together into a unified whole, while continuing to work well in their respective domains. With everything reduced to one Ultimate Rule, reductionism will have reached the end of its quest, and the uni­verse will be completely explained.

  The extreme version of the alternative view is that there are no ultimate rules, indeed that there are no totally accurate rules either. What we call laws of nature are human approximations to regulari­ties that crop up in certain specialized regions of the universe -chemical molecules, galaxy dynamics, whatever. There is no reason why our formulations of regularities in molecules and regularities in galaxies should be part of some deeper set of regularities that explains both, any more than chess and soccer should somehow be aspects of the same greater game. The universe could perfectly well be patterned on all levels, without there being an ultimate pattern from which all the others must logically follow. In this view, each set of rules is accompanied by a statement of which areas it can safely be used to describe, 'use these rules for molecules with fewer than a hundred atoms' or 'this rule works for galaxies provided you don't ask about the stars that make them up'. Many such rules are con­textual rather than reductionist: they explain why things work the way they do in terms of what is outside them.