The Science of Discworld II

gravitating bodies are unstable. Differences smaller than any specific level of coarse-graining not only can ‘bubble up’ into macroscopic differences as time passes, but do.
    Here lies the big difference between gravity and thermodynamics. The thermodynamic model that best fits our universe is one in which differences dissipate by disappearing below the level of coarse-graining as time marches forwards. The gravitic model that best fits our universe is one in which differences amplify by bubbling up from below the level of coarse-graining as time marches forwards. The relation of these two scientific domains to coarse-graining is exactly opposite when the same arrow of time is used for both.
    We can now give a completely different, and far more reasonable, explanation for the ‘entropy gap’ between the early and late universes, as observed by Penrose and credited by him to astonishingly unlikely initial conditions. It is actually an artefact of coarse-graining. Gravitational clumping bubbles up from a level of coarse-graining to which thermodynamic entropy is, by definition, insensitive. Therefore virtually any initial distribution of matter in the universe would lead to clumping. There’s no need for something extraordinarily special.
    The physical differences between gravitating systems and thermodynamic ones are straightforward: gravity is a long-range attractive force, whereas elastic collisions are short-range and repulsive. With such different force laws, it is hardly surprising that the behaviour should be so different. As an extreme case, imagine systems where ‘gravity’ is so short range that it has no effect unless particles collide, but then they stick together forever. Increasing clumpiness is obvious for such a force law.
    The real universe is both gravitational and thermodynamic. In somecontexts, the thermodynamic model is more appropriate and thermodynamics provides a good model. In other contexts, a gravitational model is more appropriate. There are yet other contexts: molecular chemistry involves different types of forces again. It is a mistake to shoehorn all natural phenomena into the thermodynamic approximation or the gravitic approximation. It is especially dubious to expect both thermodynamic and gravitic approximations to work in the same context, when the way they respond to coarse-graining is diametrically opposite.
    See? It’s simple. Not magical at all …
    Perhaps it’s a good idea to sum up our thinking here.
    The ‘laws’ of thermodynamics, especially the celebrated Second Law, are statistically valid models of nature in a particular set of contexts. They are not universally valid truths about the universe, as the clumping of gravity demonstrates. It even seems plausible that a suitable measure of gravitational complexity, like thermodynamic entropy but different, might one day be defined – call it ‘gravtropy’, say. Then we might be able to deduce, mathematically, a ‘second law of gravitics’, stating that the gravtropy of a gravitic system increases with time. For example, gravtropy might perhaps be the fractal dimension (‘degree of intricacy’) of the system.
    Even though coarse-graining works in opposite ways for these two types of system, both ‘second laws’ – thermodynamic and gravitic – would correspond rather well to our own universe. The reason is that both laws are formulated to correspond to what we actually observe in our own universe. Nevertheless, despite this apparent concurrence, the two laws would apply to drastically different physical systems: one to gases, the other to systems of particles moving under gravity.
    With these two examples of the misuse of information-theoretic and associated thermodynamic principles behind us, we can turn to the intriguing suggestion that the universe is made from information.
    Ridcully suspected that Ponder Stibbons would invoke ‘quantum’ to explain anything really bizarre, like the disappearance of the Shell Midden People. The quantum world is bizarre, and this kind of invocation is always tempting. In an attempt to make sense of the quantumuniverse, several physicists have suggested founding all quantum phenomena (that is, everything) on the concept of information. John Archibald Wheeler coined the phrase ‘It from Bit’ to capture this idea. Briefly, every quantum object is characterised by a finite number of