For some reason, a lot of shows I've watched lately have involved Time Travel, and some of it heavily. Usually, time travel is handled so sloppily that I have to just not think too hard about it, because the writers rarely care about consistency. But one I've watched might be making an effort--Timeless. I'm not SURE yet; they've shown some really bad writing techniques pretty early on (one of my least favorite: characters being deliberately vague not because they're keeping secrets, but because the alternative is revealing things too early for the story) so I'm not sure I trust them. But then again, every time I go over every thing they've done, they might actually be remaining consistent in their time travel.
And then I watched Dirk Gently's Holistic Detective Agency, which is also consistent, but within a very small matrix. And it's a completely different kind of consistent, running with different rules. But that's okay, because the rules its using are obvious and it remains consistent within them.
And that got me thinking; what rule sets are there? And I've largely broken it down into three rule sets and then two variations that affect each rule set. I started thinking about things I've seen over the years that involve time travel: Continuum, Back to the Future, Terminator, Star Trek, Twelve Monkeys, Bill and Ted's Excellent Adventure...just to name a few.
First, I'll talk about the variations because they're universal, and the variations are about how the universe treats changes in the timestream and whether or not some unseen force reacts in opposition. I call one the "quiet lake" theory of time travel, or alternately the "butterfly" theory of time travel. In this one, time is a lake and if you throw a stone in the lake, waves of energy ripple out from the stone, eventually subsiding. The more stones you throw, the more violent it gets. The idea being that time is relatively fragile. Small changes can turn into big changes. i.e, the butterfly flapping its wings and affecting things elsewhere. In this theory, time is extremely malleable and even small, seemingly inconsequential things can have huge, possibly catastrophic effects. An example here is Back to the Future -- small actions ended up having major consequences on the timeline.
The other theory is the "river" theory of time; here, time is a river. If you throw a stone in the river, nothing really happens; the current of time is very powerful and simply keeps going. You have to do something large and build a dam to change time. In this theory, something keeps time on its course, and major changes are more difficult to do. Depending on the needs of the story, the river can be more or less powerful. Little changes to the timestream are corrected by having someone or something else do the actions necessary to lead to the same or at least similar result. In this theory, major changes are very difficult to do, though minor changes will likely still happen. The Feng Shui RPG operates this way, and the time travel in The Flash sometimes operates this way, though it's not a particularly powerful river.
Theory #1: The Closed Loop
In the Closed Loop theory, time is not linear but it is fixed and predictive. Which is to say, if someone travels back into the past from the future, they're not actually changing the timeline; instead, the non-linear nature of time predicted this would happen; if you go back in time and talk to your younger self, you'll always have had that conversation. There will never be a version of reality where you didn't. Dirk Gently's took this route, as did Bill and Ted's Excellent Adventure, and Babylon 5 used this one, I think.
This one can be very satisfying, because it's easy to write consistently. However, it can be difficult to explain why this consistency happens; sometimes, having foreknowledge of what's going to happen and trying to prevent it should cause actions that will do it. Sometimes making this happen will really feel or look like Deus Ex Machina. And sometimes, well, it IS, because the characters in a closed loop will learn that they cannot change anything, eventually.
It also requires limiting the availability of time travel. It must be rare and difficult to control for whatever reason, if for no other purpose than preventing people from changing the worst things about their own futures. Another issue is that introduction of items and information needs to be handled carefully. For example, someone who carries an item or information from the future to the past could inadvertently carry that same item back into the past, meaning that particular item has no actual origin or ending. This violates causality. Note that The Terminator kind of did this: in T2, we learn that Skynet was actually created from a leftover chip from the original Terminator. This violates causality, though Terminator was actually an Open Loop where this is more acceptable.
The lake/river variants of time travel don't really affect this one, since time is fixed, just not linear.
Theory #2: The Open Loop
In this theory, time is linear. If you go back in time and change something, then everything following that is changed, including the one who changed it. Sometimes these changes are immediate; sometimes it takes time for these changes to propagate. Back To The Future, for example, was (mostly) the Closed Loop, though it didn't do this completely consistently. For example, when Marty accidentally caused his mom not to fall in love with his dad, he started being erased from existence. This part is fine, as we assume the propagation of this effect takes some time (heh) to happen.
But where it failed on consistency is when he returned to a different future than he left, he should have (eventually) only remembered the new future, not the old one. But he was surprised that his family was now wealthy, well off and happy, whereas he only remembered the oppressed, unhappy family that he left. Ahh, consistency.
In the Closed Loop, you can make catastrophic changes to the timestream, and in theory create a paradox that will simply destroy the universe. Don't do that. The lake/river theory of time travel controls how fragile things really are. Back to the Future was a lake; if it had been a river, then Marty may have actually returned to the future to find Biff was his dad (ugh) instead of George, for example. In that version, attempts to change time would have been met with opposition from time itself, and the major events wouldn't have changed, though minor details might have.
Theory #3: Branching timelines
In the third theory, time is actually immutable, and instead travelling in time creates new branches of time which is now fully independent from the original.
In this theory, there is a single 'master' timeline, and in this timeline time travel doesn't (apparently) work and never will and never has. That's the timeline we (theoretically) live in. In that timeline, if someone travels through time, they disappear, never to return, thought dead. Possibly this happens a lot, and then eventually people give up trying to travel through time, because you can't.
However, what actually happened is that Time Traveler Jane went back in time, and in so doing immediately created a new time branch, which is subtly (or majorly) changed. Jane then returns to her original time -- she only remembers the master timeline, so any changes are new to her. But the people she returned to only remember the branched timeline. To those people, Jane had always traveled in time.
The more time travel happens, the more branches are created. In theory, it is impossible to return to an old branch.
When writing this one, the original perspective is often not the master timeline, but some branch where time travel has already happened, but the original time traveler (possibly a variant of the protagonist(s)) has already moved off into other branches and so can't be interacted with, except perhaps in the past.
This one is tricky to keep track of, especially since if you have several POV characters, if they don't travel as a group, they can all change. A person the audience has been tracking might suddenly be a new character because of changes in history.
Timeless and Continuum both used this theory. Timeless avoids the duplication of people problem by hand-waving and saying that you can't visit somewhere you've already been; Continuum does no such thing and in fact duplicated characters pretty regularly. By the time it was over, Continuum had rewritten reality several times; not entirely consistently, but reasonably satisfyingly.
This one can be made even more complicated if the time device can actually move to a different branch; at that point you also get what is effectively multi-dimensional travel as well as time travel.
When writing this one, there are some interesting artifacts: you don't actually have to worry about what someone (unknown) will do in the past, because that will affect some other timeline. The history of the timeline you're in at that moment is actually set. Of course, the characters may not actually realize this, thus leading to time wars. But as an author, you can ignore time travel that happens and doesn't concern your plot, because it goes off and happens elsewhere.
You also get an interesting recursion issue. Let's say Jane time travels 3 times, at points A, B and C, to some arbitrary point in the past. At time Travel C, she travels back before A and B. When the timeline branches, in the new branch, time travels A and B happen again now using new versions of Jane from the new timeline, each causing new branches...this can lead to theoretically infinite recursion. My "solution" for this is that if you return to the point in time where you left, you merge with/replace the new timeline version of you that would have been there. Otherwise you end up with endless universal echoes.
Or maybe the infinite echoes happen and the universe doesn't care. It's infinite, after all.
But let's go more complicated; let's say that time changes Jane made were significant enough that she no longer does time travel A, B or C. When she returns, the version of herself that didn't do time travel C is probably somewhere else. There are two possibilities, and I've seen them both happen in literature: in one version, she still replaces herself, which means she ends up somewhere unexpected (wherever the original version of her was at that point), and in the other version, she appears where she would expect but now there's another version of her, who didn't travel in time, running around.
So there's all that. There isn't, ultimately, a point to this, other than I've been thinking about this a lot and wanted to get this down.