Science of Discworld III

anyone asserting that there must therefore exist a corresponding set of parallel clarinets, each producing one of the pure notes. The mathematical decomposition need not have a literal physical analogue.
    What about paradoxes of genuine time travel, no faffing about with parallel worlds? In the relativistic setting, which is where such questions most naturally arise, there is an interesting resolution. If you set up a situation with paradoxical possibilities, it automatically leads to consistent behaviour.
    A typical thought-experiment here is to send a billiard ball through a wormhole, so that it emerges in its own past. With care, you can send it in so that when it comes (came) out it bashes into its earlier incarnation, deflecting it so that it never enters the wormhole in the first place. This is the grandfather paradox in less violent form. The question for a physicist is: can you actually set such paradoxical statesup? You have to do so before the time machine is built, then build it, and see what physical behaviour actually occurs.
    It turns out that, at least in the simplest mathematical formulation of this question, the usual physical laws select a unique, logically consistent behaviour. You can’t suddenly plonk a billiard ball down inside a pre-existing system – that act involves human intervention, ‘free will’, and its relation to the laws of physics is moot. If you leave it up to the billiard ball, it follows a path that does not introduce logical inconsistencies. It is not yet known whether similar results hold in more general circumstances, but they may well do.
    This is all very well, but it does beg the ‘free will’ question. It’s a deterministic explanation, valid for idealised physical systems like billiard balls. Now, it is possible that the human mind is actually a deterministic system (ignoring quantum effects to keep the discussion within bounds). What we like to think of as making a free choice may actually be what it feels like when a deterministic brain works its way towards the only decision that it can actually reach. Free will may be the ‘quale’ of decision-making – the vivid feeling we get, like the vivid sense of colour we get when we look at a red flower. 5 Physics does not yet explain how these feelings arise. So it is usual to dismiss effects of free will when discussing possible temporal paradoxes.
    This sounds reasonable, but there’s a catch. The whole discussion of time machines, in physics terms, is about the possibility of people constructing the various warped spacetimes that are involved. ‘Get a black hole, join it to a white one …’ Specifically, it is about people choosing or deciding to construct such a device. In a deterministic world, either they are bound to construct it from the beginning, in which case ‘construct’ isn’t a very appropriate word, or the thing just puts itself together, and you find out what sort ofuniverse you are in. It’s just like Gödel’s rotating universe: either you’re in it, or you’re not, and you don’t get to change anything. You can’t bring a time machine into being unless it was already implicit in the unfolding of that universe anyway.
    The standard physics viewpoint really only makes sense in a world where people have free will and can choose to build, or not to build, as they see fit. So physics, not for the first time, has adopted inconsistent viewpoints for different aspects of the same question, and has got its philosophical knickers in a twist as a result.
    For all the clever theorising, the dreadful truth is that we do not yet have the foggiest idea how to make a practical time machine. The clumsy and energy-wasteful devices of real physics are a pale shadow of the elegant machine of Wells’s Time Traveller, whose prototype was described as ‘a glittering metallic framework, scarcely larger than a small clock, very delicately made. There was ivory in it, and some transparent crystalline substance.’
    There’s still some R&D needed.
    Probably this is a Good Thing.
    1 This is a mathematician’s way of saying that you can put a black hole anywhere you want. (Or, like a gorilla in a Mini, it can go anywhere it wants.)
    2 Michael Brooks, ‘Time Twister’, New Scientist , 19 May 2001, 27–9.
    3 Jason Breckenridge, Rob Myers, Amanda Peet, and Cumrun Vafa.
    4 It’s OK for electrons and probably nonsense for cats. See Greebo’s cameo appearance in The Science of Discworld .
    5 See Ian Stewart,