The Science of Discworld IV Judgement Da - By Terry Pratchett, Ian Stewart Page 0,70

to see what happens can break them into constituent parts, but it can also excite new modes of behaviour that can’t sensibly be thought of as components. Are particle physicists really finding out what matter is made of, or are they just causing it to behave in ever wilder ways?

Less facetiously, think about how we analyse sounds themselves. Scientists and engineers like to break a complex sound into simple ‘components’, sinusoidal vibrations with specific frequencies. ‘Sinusoidal’ refers to the mathematical sine curve, the simplest pure sound. This technique is called Fourier analysis, after Joseph Fourier, who used it to study heat flow in 1807. The sound produced by a clarinet, for example, has three main Fourier components: a vibration at the dominant frequency (the note that it sounds like), a slightly softer vibration at three times that frequency (the third harmonic), and an even softer vibration at five times that frequency (the fifth harmonic). This pattern continues with only odd-numbered harmonics, until the components reach such a high pitch that the human ear can’t hear them.

The sound of a clarinet can be synthesised, digitally, by adding together all of these Fourier components.fn3 But do those components ‘exist’ as physical things? That’s a moot point, even though we can pull the sound apart into those ‘things’ and reassemble them. On the one hand, we can detect them by applying the right mathematics to the sound that the clarinet emits. On the other hand, a clarinet does not emit pure sinusoidal tones at all, at least not without an awful lot of fiddling about to damp out unwanted components – in which case it’s not exactly a clarinet any more. Mathematically, a clarinet’s vibrations are best described by a nonlinear equation, which generates the complex waveform only, not its individual Fourier components. In that sense, a clarinet does not generate the components and then add them together. Instead, they come as a single, indivisible package.

You can learn a lot about the sound a clarinet makes from these mathematical constructs – but that doesn’t imply that the constructs are real, just that the mathematical technique is useful in its own right. A similar method is used to compress the data in digital images, using grey-scale patterns in place of sound waves – but in the real world the image is not formed by adding these components.

Are physicists just picking up mathematical constructs – in a sense, creating them by the way they analyse their data – and interpreting them as fundamental particles? Are fancy high-energy particles real, or artefacts of complex excitations in something else? Even if they are, does this make any important scientific or philosophical difference? Now we are venturing into questions about the nature of reality, of which the most crucial is whether such a thing exists at all. We aren’t sure of the answers, so we’ll content ourselves with raising the questions. But we suspect that several different interpretations of the same physics may be equally valid,fn4 and which one is best depends on what you want to do with it.

Evidentially, the Higgs is a small bump on an otherwise smooth curve. With the mind-set and traditions of particle physics, it is interpreted as a particle. What’s interesting to us is how the bump becomes the object of attention, while the much larger quantity of data representing the smooth curve is relegated to the background.

A more familiar example has the same features. Our view of the solar system, with all the planets, all the asteroids and comets, behaving as they should, would be upset if we spotted a spaceship rocketing about but thought it was just another regular body. It would be a malefactor, not obeying the law of gravity. Indeed, the law tells us what is natural, so the spaceship becomes an anomaly.

Think of all the fuss about the Pioneer anomaly, an unexplained deceleration discovered when observing the spacecraft Pioneer 10 and Pioneer 11. These were the first space probes to reach the outer planets of the solar system, from Jupiter to Neptune. Because of the gravitational pull of the Sun, their speed continually decreased, but they were travelling fast enough to escape the solar system entirely, given enough time. However, when they were at about the same distance from the Sun as Uranus, observations showed that they were slowing down a little bit faster than gravity alone could explain – by about one billionth of a metre per second per second. After much head-scratching, an analysis published