**DISCLAIMER: NO SCIENCE. FUCK SCIENCE. NOT PHYSICIST SCUM.**
Also: Wrote this assuming the 4th dimension spans time, and isn't just some extra space. idk why. Replace any mention of it with your own pet theory about how we'd transfer matter in leaps through time.
Taking the "wanton list of every concept I've ever encountered in science fiction" approach...
0.
DON'T FUCK UP DON'T FUCK UP
The rare universe where you might actually destroy the human race via butterfly effect, stop Hitler, invent popsicles six decades in advance, or otherwise drastically change the future as you know it.
Here, the universe is a potentially malleable thing, that wobbles and morphs when matter is displaced in it. Perhaps it stabilizes when no travel is happening, or perhaps it's constantly oscillating, constantly altering reality in ways that are invisible to a being in the system. I like to imagine it as a block of spacetimejello, and all human memories as faulty and everchanging products of shifting chains of causality.
Note: This option requires that timetravel somehow involves exiting the jello briefly, IE exiting spacetime completely.
1.
EVERYTHING IN ITS PLACE
The universe is pretty much a static block. The past has happened, the future has happened, all instances of timetravel have been accounted for. You won't change anything, no matter how hard you try. Everything is tragically prophetic. Fuck your free will, have some consolation beautiful clockwork.
Seeing as your timetravel is a predictable component of the universe, this must mean events in the 4th dimension or wherever you zoom through are also deterministic and fixed. Which opens up the possibility of a kind of mega-timetravel where you exit the 4th dimensional structure into the 5th dimension and proceed to actually alter it from the outside?? Weird.
2.
MULTIVERSES LIKE RABBITS
Timetravel causes the universe to branch. The previous state is preserved somewhere in the future/past as its own timeline, and instead you generate a new world.
Seemingly gets complicated if you believe multiverse theory is already in action, all possible worlds unfolding simultaneously, but really it'll just grow new branches since your unexpected presence in the past/future will engender very new possibilities.
Again, I guess you'd be traveling through a 4th dimension.
3.
LIKE A GHOST?
See "A Christmas Carol". You're on drugs or guided by some supernatural being and can view the future and past, but you're not physically present and you can't alter them in any way. Possibly a kind of cosmos in which consciousness operates on its own plane, and is not as tethered to a strict temporal progression as matter is. Oracles slot in here, somewhere.
3.1
NOT A GHOST, A MACHINE
A less paranormal interpretation where information can be transmitted across time by certain kinds of devices. Kind of a cop out unless you explain how, so... antennae into the 4th dimension? It's so nice how expanding space can explain anything away.
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Still, doesn't address how timelines would/wouldn't be changed by the information which would SURELY EFFECT PEOPLE'S ACTIONS.
4.
NOT ACTUAL TIMETRAVEL
Deterministic universe, supercomputer can recreate the past/predict the future in perfect resolution. You may wander through these pre/postdictions rendered as virtual reality type spaces. A lot of the time travel is restricted by a certain time frame because of the massive computation involved.
4.1
OKAY THIS IS JUST COOL BEAR WITH ME
I like the idea of generating endless virtual reality pasts/futures that people then play in and alter, creating a massive database of these many semi-possible universes and allowing for the easy illusion of timetravel. Just sounds fun.
5.
LIKE, THE OPPOSITE OF CHAOS THEORY?
So you can timetravel (somehow, probably through our friend the 4th dimension) and you can change a few things, but the dreadful march of history reasserts itself very quickly after your actions. Time is a current that tiny material blips cannot redirect for more than a moment. Perhaps some key events are set in stone. Perhaps spacetime is just a shitty medium that kills the propagation of any deviance. I dunno man.
6.
CREEPY BRAIN TRANSFER
Kind of an offshoot of "information/your consciousness can timetravel, but not matter", this is the bizarre scenario where you're sent back to inhabit your childhood body. Who knows how it works! Fucking crazy but I see it everywhere. Presumably limits travel to sometime during your lifespan, starting whenever you grow a noggin. Not sure where your actual childmind goes, did you kill it? Do you switch places? Does it exist consciously in parallel with no control of its body??
Other versions where you can go beyond your own lifetime by cannibalizing the existence of your ancestors, or possibly total strangers.
7.
THIS JUST SOUNDED REALLY COOL
I remember reading about an
ageless jellyfish that can revert to an earlier biological stage to regenerate and prolong its life. I suppose backwards time travel could be possible if the structure of space-time could be recorded somehow and rebuilt like genetic evolution, at the least I know the information about past events in space-time already exists because it takes light from other galaxies a long time to reach Earth.
Summarizing:
Most versions of timetravel involve some combination of a couple of factors:
Is timetravel even possible in this cosmos? Y/N
Can you actually change anything? Y/N
Travel is: Material/Mental/Illusory