The Science of Discworld IV

collisions of even
higher
energy. This requires erecting an LHC (Large Hotel Collapser) forty storeys high, and pushing the piano out of a top-floor window in the time-honoured fashion of visiting rock stars. The results are impressive, but hard to interpret. Careful analysis decomposes the resulting sound into a cacophony of a hundred or so different twangons, several variants of the slamon … and a bit left over. This bit, obtained by deducting from the overall sound every known component, is of course the long-sought proof of the existence of the Bigg Bashon – which journalists insist on calling the Thud pianicle, a name given to the sound created when a piano encounters a hypothetical field … or maybe a car park.
    This proves that a piano has mass.
    Because the procedure that confirms the new pianicle is so complex and error-prone, several billion pianos need to be launched into oblivion before the results become statistically significant. They are, and the discovery is published, months after the first experiment hit the headlines.
    The big question here, which is where Ian and Jack tend to differ, though not by a lot, is whether particle physicists are misinterpreting the nature of matter in a similar way to pianologists resolutely failing to understand a piano. Bashing things 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 canpull 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