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 Einsteinianphysics 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 – themovie 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,
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 Einsteinianphysics 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 – themovie 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,
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