The novel had inauspicious beginnings. Wells studied biology, mathematics, physics, geology, drawing, and astrophysics at the Normal School of Science, which became the Royal College of Science and eventually merged with Imperial College of Science and Technology. While a student there, he began the work that led up to The Time Machine. His first time-travel story ‘The Chronic Argonauts’ appeared in 1888 in the Science Schools Journal, which Wells helped to found. The protagonist voyages into the past and commits a murder. The story offers no rationale for time travel and is more of a mad-scientist tale in the tradition of Mary Shelley’s Frankenstein, but nowhere near as well written. Wells later destroyed every copy of it he could locate, because it embarrassed him so much. It lacked even the paradoxical element of the 1891 Tourmalin’s Time Cheques by Thomas Anstey Guthrie, which introduced many of the standard time-travel paradoxes.
Over the following three years, Wells produced two more versions of his time-travel story, now lost, but along the way the storyline mutated into a far-future vision of the human race. The next version appeared in 1894 in the National Observer magazine, as three connected tales with the title ‘The Time Machine’. This version has many features in common with the final novel, but before publication was complete, the editor of the magazine moved to the New Review. There he commissioned the same series again, but this time Wells made substantial changes. The manuscripts include many scenes that were never printed: the hero journeys into the past, running into a prehistoric hippopotamus6 and meeting the Puritans in 1645. The published magazine version is very similar to the one that appeared in book form in 1895. In this version the Time Traveller moves only into the future, where he finds out what will happen to the human race, which splits into the languid Eloi and the horrid Morlocks – both equally distasteful.
Where did Wells get the idea? The standard SF writer’s reply to this question is that ‘you make it up’, but we have some fairly specific information in this case. In a foreword to the 1932 edition, Wells says that he was motivated by ‘student discussions in the laboratories and debating society of the Royal College of Science in the eighties’. According to Wells’s son, the idea came from a paper on the fourth dimension read by another student. In the introduction to the novel, the Time Traveller (he is never named, but in the early version he is Dr Nebo-gipfel, so perhaps it’s just as well) invokes the fourth dimension to explain why such a machine is possible:
‘But wait a moment. Can an instantaneous cube exist?’
‘Don’t follow you,’ said Filby.
‘Can a cube that does not last for any time at all, have a real existence?’
Filby became pensive.
‘Clearly,’ the Time Traveller proceeded, ‘any real body must have extension in four directions: it must have Length, Breadth, Thickness, and – Duration …
‘… There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives …
‘… But some philosophical people have been asking why three dimensions particularly – why not another direction at right angles to the three? – and have even tried to construct a Four-Dimensional geometry. Professor Simon Newcomb was expounding this to the New York Mathematical Society only a month or so ago.’
The notion of time as a fourth dimension was becoming common scientific currency in the late Victorian era. The mathematicians had started it, by wondering what a dimension was, and deciding that it need not be a direction in real space. A dimension was just a quantity that could be varied, and the number of dimensions was the largest number of such quantities that could all be varied independently. Thus the Discworld thaum, the basic particle of magic, is actually composed of resons, which come in at least five flavours: up, down, sideways, sex appeal, and peppermint. The thaum is therefore at least five-dimensional, assuming that up and down are independent, which is likely because it’s quantum.
In the 1700s the foundling mathematician Jean le Rond D’Alembert (his middle name is that of the church where he was abandoned as a baby) suggested thinking of time as a fourth dimension in an article in the Reasoned Encyclopaedia or Dictionary of Sciences, Arts, and Crafts. Another mathematician, Joseph-Louis Lagrange, used time as a fourth dimension in his Analytical Mechanics of 1788, and his Theory of Analytic Functions of 1797 explicitly states: ‘We may regard mechanics as a geometry of four dimensions.’
It took a while for the idea to sink in, but by Victorian times mathematicians were routinely combining space and time into a single entity. They didn’t (yet) call it spacetime, but they could see that it had four dimensions: three of space plus one of time. Journalists and the lay public soon began to refer to time as the fourth dimension, because they couldn’t think of another one, and to talk as if scientists had been looking for it for ages and had just found it. Newcomb wrote about the science of four-dimensional space from 1877, and spoke about it to the New York Mathematical Society in 1893.
Wells’s mention of Newcomb suggests a link to one of the more colourful members of Victorian society, the writer Charles Howard Hinton. Hinton’s primary claim to fame is his enthusiastic promotion of ‘the’ fourth dimension. He was a talented mathematician with a genuine flair for four-dimensional geometry, and in 1880 he published ‘What is the Fourth Dimension?’ in the Dublin University Magazine, which was reprinted in the Cheltenham Ladies’ Gazette a year later. In 1884 it reappeared as a pamphlet with the subtitle ‘Ghosts Explained’. Hinton, something of a mystic, related the fourth dimension to pseudoscientific topics ranging from ghosts to the afterlife. A ghost can easily appear from, and disappear along, a fourth dimension, for instance, just as a coin can appear on, and disappear from, a tabletop, by moving along ‘the’ third dimension.
Charles Hinton was influenced by the unorthodox views of his surgeon father James, a collaborator of Havelock Ellis, who outraged Victorian society with his studies of human sexual behaviour. Hinton the elder advocated free love and polygamy, and eventually headed a cult. Hinton the younger also had an eventful private life: in 1886 he fled to Japan, having been convicted of bigamy at the Old Bailey. In 1893 he left Japan to become a mathematics instructor at Princeton University, where he invented a baseball-pitching machine that used gunpowder to propel the balls, like a cannon. After several accidents the device was abandoned and Hinton lost his job, but his continuing efforts to promote the fourth dimension were more successful. He wrote about it in popular magazines like Harper’s Weekly, McClure’s, and Science. He died suddenly of a cerebral haemorrhage in 1907, at the annual dinner of the Society of Philanthropic Enquiry, having just completed a toast to female philosophers.
It was probably Hinton who put Wells on to the narrative possibilities of time as the fourth dimension. The evidence is indirect but compelling. Newcomb definitely knew Hinton: he once got Hinton a job. We don’t know whether Wells ever met Hinton, but there is circumstantial evidence of a close connection. For example, the term ‘scientific romance’ was coined by Hinton in titles of his collected speculative essays in 1884 and 1886, and Wells later used the same phrase to describe his own stories. Moreover, Wells was a regular reader of Nature, which reviewed Hinton’s first series of Scientific Romances (favourably) in 1885 and summarised some of his ideas on the fourth dimension.
In all likelihood, Hinton was also partially responsible for another Victorian transdimensional saga, Edwin A. Abbott’s Flatland of 1884. The tale is about A. Square, who lives in the Euclidean plane, a two-dimensional society of triangles, hexagons and circles, and doesn’t believe in the third dimension until a passing sphere drops him in it. By analogy, Victorians who didn’t believe in the fourth dimension were equally blinkered. A subtext is a satire on Victorian treatment of women and the poor. Many of Abbott’s ingredients c
losely resemble elements found in Hinton’s stories.7
Most of the physics of time travel is general relativity, with a dash of quantum mechanics. As far as the wizards of Unseen University are concerned, all this stuff is ‘quantum’ – a universal intellectual get-out-of-jail card – so you can use it to explain virtually anything, however bizarre. Indeed, the more bizarre, the better. You’re about to get a solid dose of quantum in Chapter 8. Here we’ll set things up by providing a quick primer on Einstein’s theories of relativity: special and general.
As we explained in The Science of Discworld, ‘relativity’ is a silly name. It should have been ‘absolutivity’. The whole point of special relativity is not that ‘everything is relative’, but that one thing – the speed of light – is unexpectedly absolute. Shine a torch from a moving car, says Einstein: the extra speed of the car will have no effect on the speed of the light. This contrasts dramatically with old-fashioned Newtonian physics, where the light from a moving torch would go faster, acquiring the speed of the car in addition to its own inherent speed. If you throw a ball from a moving car, that’s what happens. If you throw light, it should do the same, but it doesn’t. Despite the shock to human intuition, experiments show that Roundworld really does behave relativistically. We don’t notice because the difference between Newtonian and Einsteinian physics becomes noticeable only when speeds get close to that of light.
Special relativity was inevitable; scientists were bound to think of it. Its seeds were already sown in 1873 when James Clerk Maxwell wrote down his equations for electromagnetism. Those equations make sense in a ‘moving frame’ – when observations are made by a moving observer – only if the speed of light is absolute. Several mathematicians, among them Henri Poincaré and Hermann Minkowski, realised this and anticipated Einstein on a mathematical level, but it was Einstein who first took the ideas seriously as physics. As he pointed out in 1905, the physical consequences are bizarre. Objects shrink as they approach the speed of light, time slows to a crawl, and mass becomes infinite. Nothing (well, no thing) can travel faster than light, and mass can turn into energy.
In 1908 Minkowski found a simple way to visualise relativistic physics, now called Minkowski spacetime. In Newtonian physics, space has three fixed coordinates – left/right, front/back, up/down. Space and time were thought to be independent. But in the relativistic setting, Minkowski treated time as an extra coordinate in its own right. A fourth coordinate, a fourth independent direction … a fourth dimension. Three-dimensional space became four-dimensional spacetime. But Minkowski’s treatment of time added a new twist to the old idea of D’Alembert and Lagrange. Time could, to some extent, be swapped with space. Time, like space, became geometrical.
We can see this in the relativistic treatment of a moving particle. In Newtonian physics, the particle sits in space, and as time passes, it moves around. Newtonian physics views a moving particle the way we view a movie. Relativity, though, views a moving particle as the sequence of still frames that make up that movie. This lends relativity an explicit air of determinism. The movie frames already exist before you run the movie. Past, present and future are already there. As time flows, and the movie runs, we discover what fate has in store for us – but fate is really destiny, inevitable, inescapable. Yes – the movie frames could perhaps come into existence one by one, with the newest one being the present, but it’s not possible to do this consistently for every observer.
Relativistic spacetime = geometric narrativium.
Geometrically, a moving point traces out a curve. Think of the particle as the point of a pencil, and spacetime as a sheet of paper, with space running horizontally and time vertically. As the pencil moves, it leaves a line behind on the paper. So, as a particle moves, it traces out a curve in spacetime called its world-line. If the particle moves at a constant speed, the world-line is straight. Particles that move very slowly cover a small amount of space in a lot of time, so their world-lines are close to the vertical; particles that move very fast cover a lot of space in very little time, so their world-lines are nearly horizontal. In between, running diagonally, are the world-lines of particles that cover a given amount of space in the same amount of time – measured in the right units. Those units are chosen to correspond via the speed of light – say years for time and light-years for space. What covers one light-year of space in one year of time? Light, of course. So diagonal world-lines correspond to particles of light – photons – or anything else that can move at the same speed.
Relativity forbids bodies that move faster than light. The world-lines that correspond to such bodies are called timelike curves, and the timelike curves passing through a given event form a cone, called its ‘light cone’. Actually, this is like two cones stuck together at their sharp tips, one pointing forward, the other backward. The forward-pointing cone contains the future of the event, all the points in spacetime that it could possibly influence. The backward-pointing cone contains its past, the events that could possibly influence it. Everything else is forbidden territory, elsewheres and elsewhens that have no possible causal connections to the chosen event.
Minkowski spacetime is said to be ‘flat’ – it represents the motion of particles when no forces are acting on them. Forces change the motion, and the most important force is gravity. Einstein invented general relativity in order to incorporate gravity into special relativity. In Newtonian physics, gravity is a force: it pulls particles away from the straight lines that they would naturally follow if no force were acting. In general relativity, gravity is a geometric feature of the universe – a form of spacetime curvature.
In Minkowski spacetime, points represent events, which have a location in both space and time. The ‘distance’ between two events must capture how far apart they are in space, and how far apart they are in time. It turns out that the way to do this is, roughly speaking, to take the distance between them in space and subtract the distance between them in time. This quantity is called the interval between the two events. If, instead, you did what seems obvious and added the time-distance to the space-distance, then space and time would be on exactly the same physical footing. However, there are clear differences: free motion in space is easy, but free motion in time is not. Subtracting the time-difference reflects this distinction; mathematically it amounts to considering time as imaginary space – space multiplied by the square root of minus one. And it has a remarkable effect: if a particle travels with the speed of light, then the interval between any two events along its world-line is zero.
Think of a photon, a particle of light. It travels, of course, at the speed of light. As one year of time passes, it travels one light-year. The sum of 1 and 1 is 2, but that’s not how you get the interval. The interval is the difference 1 – 1, which is 0. So the interval is related to the apparent rate of passage of time for a moving observer. The faster an object moves, the slower time on it appears to pass. This effect is called time dilation. As you travel closer and closer to the speed of light, the passage of time, as you experience it, slows down. If you could travel at the speed of light, time would be frozen. No time passes on a photon.
In Newtonian physics, particles that move when no forces are acting follow straight lines. Straight lines minimise the distance between points. In relativistic physics, freely moving particles minimise the interval, and follow geodesics. Finally, gravity is incorporated, not as an extra force, but as a distortion of the structure of spacetime, which changes the size of the interval and alters the shapes of geodesics. This variable interval between nearby events is called the metric of spacetime.
The usual image is to say that spacetime 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 cones to deform.
One result is ‘gravitational lensing’, the bending of light by massive objects, which Einstein discovered in 1911 and published in 1915. He
predicted that gravity should bend light by twice the amount that Newton’s Laws imply. In 1919 this prediction was confirmed, when Sir Arthur Stanley Eddington led an expedition to observe a total eclipse of the Sun in West Africa. Andrew Crommelin of Greenwich Observatory led a second expedition to Brazil. The expeditions observed stars near the edge of the Sun during the eclipse, when their light would not be swamped by the Sun’s much brighter light. They found slight displacements of the stars’ apparent positions, consistent with Einstein’s predictions. Overjoyed, Einstein sent his mum a postcard: ‘Dear Mother, joyous news today … the English expeditions have actually demonstrated the deflection of light from the Sun.’ the Times ran the headline: REVOLUTION IN SCIENCE. NEW THEORY OF THE UNIVERSE. NEWTONIAN IDEAS OVERTHROWN. Halfway down the second column was a subheading: SPACE ‘WARPED’. Einstein became an overnight celebrity.
It would be churlish to mention that to modern eyes the observational data are decidedly dodgy – there might be some bending, and then again, there might not. So we won’t. Anyway, later, better experiments confirmed Einstein’s prediction. Some distant quasars produce multiple images when an intervening galaxy acts like a lens and bends their light, to create a cosmic mirage.
Science of Discworld III Page 8
