Tick.
Even Discworld has trouble with time. In Roundworld it's worse. There was a time (there we go) when space and time were considered to be totally different things. Space had, or was, extension - it sort of spread itself around, and you could move through it at will. Within reason, maybe 20 miles (30km) a day on a good horse if the tracks weren't too muddy and the highwaymen weren't too obtrusive.
Tick.
Time, in contrast, moved of its own volition and took you along with it. Time just passed, at a fixed speed of one hour per hour, always in the direction of the future. The past had already happened, the present was happening right now - oops, gone already - and the future had yet to happen, but by jingo, it would, you mark my words, when it was good and ready.
Tick.
You could choose where you went in space, but you couldn't choose when you went in time. You couldn't visit the past to find out what had really happened, or visit the future to find out what fate had in store for you; you just had to wait and find out. So time was completely different from space. Space was three-dimensional, with three independent directions: left/right, back/forward, up/down. Time just was.
Tick.
Then along came Einstein, and time started to get mixed up with space. Time-like directions were still different from space-like ones, in some ways, but you could mix them up a bit. You could borrow time here and pay it back somewhere else. Even so, you couldn't head off into the future and find yourself back in your own past. That would be time travel, which played no part in physics.
What science abhors, the arts crave. Time travel may be a physical impossibility, but it is a wonderful narrative device for writers, because it allows the story to move to past, present, or future, at will. Of course you don't need a time machine to do that - the flashback is a standard literary device. But it's fun (and respectful to narrativium) to have some kind of rationale that fits into the story itself. Victorian writers liked to use dreams; a good example is Charles Dickens's A Christmas Carol of 1843, with its ghosts of Christmas past, present, and yet-to-come. There is even a literary subgenre of 'timeslip romances', some of them really quite steamy. The French ones.
Time travel causes problems if you treat it as more than just a literary device. When allied to free will, it leads to paradoxes. The ultimate cliche here is the `grandfather paradox', which goes back to Rene Barjavel's story Le Voyageur Imprudent. You go back in time and kill your grandfather, but because your father is then not born, neither are you, so you can't go back to kill him ... Quite why it's always your grandfather isn't clear (except as a sign that it's a cliche, a low-bred form of narrativium). Killing your father or mother would have the same paradoxical consequences. And so might the slaughter of a Cretaceous butterfly, as in Ray Bradbury's 1952 short story `A Sound of Thunder', in which a butterfly's accidental demise at the hands [1] of an unwitting time traveller changes present-day politics for the worse.
Another celebrated time paradox is the cumulative audience paradox. Certain events, the standard one being the Crucifixion, are so endowed with narrativium that any self-respecting time tourist will insist on seeing them. The inevitable consequence is that anyone who visits the Crucifixion will find Christ surrounded by thousands, if not millions, of time travellers. A third is the perpetual investment paradox. Put your money in a bank account in 1955, take it out in 2005, with accumulated interest, then take it back to 1955 and put it in again ... Be careful to use something like gold, not notes - notes from 2005 won't be valid in 1955. Robert Silverberg's Up the Line is about the Time Service, a force of time police whose job is to prevent such paradoxes from getting out of hand. A similar theme occurs in Isaac Asimov's The End of Eternity.
An entire class of paradoxes arises from time loops, closed loops of causality in which events only get started because someone comes from the future to initiate them. For example, the easiest way for today's humanity to get hold of a time machine is if someone is presented with one by a time traveller from the far future, when such
[1] Actually, foot.
machines have already been invented. He or she then reverse engineers the machine to find out how it works, and these principles later form the basis for the future invention of the machine. Two classic stories of this type are Robert Heinlein's 'By His Bootstraps' and `All you Zombies', the second being noteworthy for a protagonist who becomes his own father and his own mother (via a sex change). David Gerrold took this idea to extremes in The Man Who Folded Himself.
Science-fiction authors are divided on whether time paradoxes always neatly unwrap themselves to produce consistent results, or whether it is genuinely possible, in their fictional setting, to change the past or the present. (No one worries much about changing the future, mind you, presumably because `free will' amounts to precisely that. We all change the future, from what it might have been to what it actually becomes, thousands of times every day. Or so we fondly imagine.) So some authors write of attempts to kill your grandfather that, by some neat twist, bring you into existence anyway. For example, your true father was not his son at all, but a man he killed. By mistakenly eliminating the wrong grandfather, you ensure that your true father survives to sire you. Others, like Asimov and Silverberg, set up entire organisations dedicated to making sure that the past, hence the present, remains intact. Which may or may not work.
The paradoxes associated with time travel are part of the subject's fascination, but they do rather point towards the conclusion that time travel is a logical impossibility, let alone a physical one. So we are happy to allow the wizards of Unseen University, whose world runs on magic, the facility to wander at will up and down the Roundworld timeline, switching history from one parallel universe to another, trying to get Charles Darwin - or somebody - to write That Book. The wizards live in Discworld, they operate outside Roundworld constraints. But we don't really imagine that Roundworld people could do the same, without external assistance, using only Roundworld science.
Strangely, many scientists at the frontiers of today's physics don't agree. To them, time travel has become an entirely respectable [1] research topic, paradoxes notwithstanding. It seems that there is nothing in the `laws' of physics, as we currently understand them, that forbids time travel. The paradoxes are apparent rather than real; they can be `resolved' without violating physical law, as we will see in Chapter 8. That may be a flaw in today's physics, as Stephen Hawking maintains; his `chronology protection conjecture' states that as yet unknown physical laws conspire to shut down any time machine just before it gets assembled - a built-in cosmological time cop.
On the other hand, the possibility of time travel may be a profound statement about the universe. We probably won't know for sure until we get to tackle the issue using tomorrow's physics. And it's worth remarking that we don't really understand time, let alone how to travel through it.
Although (apparently) the laws of physics do not forbid time travel, it turns out that they do make it very difficult. One theoretical scheme for achieving that goal, which involves towing black holes around very fast, requires rather more energy than is contained in the entire universe. This is a bit of a bummer, and it does seem to rule out the typical science fiction time machine, about the size of a car[2]
The most extensive descriptions of Discworld time are found in Thief of Time. The ingredients for this novel include a member of the Guild of Clockmakers, Jeremy Clockson, who is determined to make a completely accurate clock. However, he is up against a theoretical barrier, the paradoxes of the Ephebian philosopher Xeno, which are first Well, let's not exaggerate. You can publish papers on it without risking losing your job. It's certainly better than publishing nothing, which definitely will lose you your job.