The Science of Discworld Revised Edition

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