His error was to interpret perfectly good observational data in terms of a flawed theory. Scientists repeatedly return to established theories to test them in new ways, and tend towards testiness with those priests, religious or secular, who know the answers already – whatever the questions are. Science is not about building a body of known ‘facts’. It is a method for asking awkward questions and subjecting them to a reality-check, thus avoiding the human tendency to believe whatever makes us feel good.
* * *
From the earliest times, humans have been interested not just in the shape of the world, but in the shape of the universe. To begin with, they probably thought that these were the same question. Then they worked out, using roughly the same sort of geometry as Eratosthenes, that those lights in the sky were a very long way away. They came up with an amazing range of myths about the sun-god’s fiery chariot and so on, but after the Babylonians got the idea of making accurate measurements, their theories started to lead to surprisingly good predictions of things like eclipses and the motion of the planets. By the time of Ptolemy (Claudius Ptolemaeus, AD 100–160) the best model of planetary motion involved a series of ‘epicycles’ – the planets moved as if they were rotating round circles whose centres rotated round other circles whose centres rotated round …
Isaac Newton replaced this theory, and its more accurate successors, with a rule, the law of gravity; it describes how each body in the universe attracts every other body. It explained Johannes Kepler’s discovery that planetary orbits are ellipses, and in the fullness of time it explained a lot of other things too.
After a few centuries of stunning success, Newton’s theory ran into its first big failure: it made incorrect predictions about the orbit of Mercury. The place in its orbit at which Mercury came closest to the sun didn’t move quite the way Newton’s law predicted. Einstein came to the rescue with a theory based not on attractive forces, but on geometry – on the shape of spacetime. This was the celebrated Theory of Relativity. The theory came in two flavours: Special Relativity and General Relativity. Special Relativity is about the structure of space, time, and electromagnetism; General Relativity describes what happens when you throw in gravity too.
The main point to appreciate is that ‘Relativity’ is a silly name. The whole point of Special Relativity is not that ‘everything is relative’, but that one particular thing – the speed of light – is unexpectedly absolute. The thought experiment is well known. If you’re travelling in a car at 50 mph (80 kph) and you fire a gun forwards, so that the bullet moves at 500 mph (800 kph) relative to the car, then it will hit a stationary target at a speed of 550 mph (880 kph), adding the two components. However, if instead of firing the gun you switch on a torch, which ‘fires’ light at a speed of 670,000,000 mph (186,000 mps or 300,000 kps), then that light will not hit the stationary target at a speed of 670,000,050 mph. It will hit it at 670,000,000 mph, exactly the same speed as if the car had been stationary.
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 Poincaré – were working on the same idea, because electromagnetism 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 Anderson’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 su
rplus 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.
Recent work seems to have confirmed this remarkable discovery. But – as always – ingenious scientists have come up with alternative explanations. In 2001 Csaba Csáki, John Terning, and Nemanja Kaloper put forward a totally different theory to explain the observations. They suggest that the light from distant supernovas is dimmer than expected because some of the particles of light – photons – are changing into something else. Specifically, they are changing into ‘axions’, hypothetical particles predicted by several of the currently fashionable quantum-mechanical theories of particle physics. Axions are not expected to interact much with other matter, which makes it hard to detect them; but if they have a very small but non-zero mass, about one sextillionth of that of an electron, then they will interact with intergalactic magnetic fields. This interaction would convert a small fraction of photons into axions, and that would account for the missing light. In fact, the most distant supernovas could lose one third of their photons this way.
It is a sobering thought that such a tiny a modification of known physics, by introducing a particle whose mass ought to be negligible, could have such a big effect. At any rate, either gravity is not as we thought, or axions exist (as expected) and have mass (not as expected). Or there’s a third reason for the observations, which no one has yet thought of.
One theory of the repulsive force is an exotic form of matter, ‘quintessence’.2 This is a form of vacuum energy that pervades all of space, and exerts negative pressure. (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.) Curiously, Einstein originally included a repulsive force of this kind in his relativistic equations for gravity: he called it the cosmological 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.
Unless axions exist and have mass, of course.
In Einstein’s approach to the cosmological constant, quintessence is effectively spread uniformly throughout space. But suppose it isn’t? Ordinary matter is clumpy, not uniform. David Santiago has pointed out that if quintessence is clumpy too, then Einstein’s Equations predict that the universe could contain ‘anti-Black Holes’ that repel matter instead of swallowing it. These are not quite the same as hypothetical White Holes, time-reversed Black Holes, which spit matter out. However, it’s not yet clear that anti-Black Holes can be stable. Ordinary matter is clumpy because gravity is an attractive force – it likes to create clumps. Antigravity is a repulsive force, and by analogy it ought to destroy clumps. If that argument is right, then anti-Black Holes are unstable, and would not be able to form in the first place. They would be mathematical solutions of Einstein’s Equations, but not ones that could be physically realised. Until somebody does the necessary calculations, we can’t be sure.
1 ‘Most civilizations’ is admittedly not the same as ‘most people’. ‘Most people’ through the history of the planet have not needed to concern themselves with what shape the world is, provided it supports, somewhere, the next meal.
2 This word, meaning ‘fifth essence’, originally referred to a fifth ‘element’ after earth, air, fire and water. On Discworld this role is played by surprise.
ELEVEN
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 high-speed 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 narrativium.
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 narrativium, 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!’
The Science of Discworld Revised Edition Page 10