Basically, you can only travel forwards in time because going backwards violates causality
However
Because of the possible 4th dimensional geometry of the universe and what that means for how it behaves over deep time intervals, it could theoretically be possible to go so far forward you end up back in time.
This possibility relies on the accuracy of the theory of the bang and crunch cycle, which basically states that the universe is a bubble of infiniteness and that if you figure out how to ride out a big crunch and following big bang, you can just keep fast forwarding infinitely until random happenstance takes you far enough forward in time to a universe that is identical to ours except you’re arriving to a point that is identical to one that was “back in time” from where you started.
It’s probably one of the more depressing takes on time travel since it’s impossible to ever go “home” but then again in that sense you’ve never returned to the home you left from in the morning, because the one you return to exists forward in time from where you left.
There’s a hard sci-fi novel (1970s or 1980s) called “Tau Zero” that features this idea.
Book summary (spoils all of it)
A colony ship with a Bussard Ramjet on each end (debunked theoretical spaceship drive that uses interstellar hydrogen for propulsion, i.e. the faster you go, the more medium you hit and the harder you accelerate) suffers an accident that destroys the deceleration engine. They keep accelerating because they need the engine’s magnetic field to protect them from interstellar dust. First they try reach the void between galaxies to safely repair the ship, when the interstellar medium is still too “dense,” they go for the void between galaxy clusters, then superclusters, then they just stay on the throttle until the big crunch, at which point, in the nothingness after the universe collapsed in on itself, they can finally fix their ship and begin decelerating into the bounce-back big bang of the forming next universe and colonize a planet.
I prefer the theory of “OMLY FORWARD!”
Basically, you can only travel forwards in time because going backwards violates causality
However
Because of the possible 4th dimensional geometry of the universe and what that means for how it behaves over deep time intervals, it could theoretically be possible to go so far forward you end up back in time.
This possibility relies on the accuracy of the theory of the bang and crunch cycle, which basically states that the universe is a bubble of infiniteness and that if you figure out how to ride out a big crunch and following big bang, you can just keep fast forwarding infinitely until random happenstance takes you far enough forward in time to a universe that is identical to ours except you’re arriving to a point that is identical to one that was “back in time” from where you started.
It’s probably one of the more depressing takes on time travel since it’s impossible to ever go “home” but then again in that sense you’ve never returned to the home you left from in the morning, because the one you return to exists forward in time from where you left.
There is a great Futurama episode that visualises this. The Late Philip J. Fry - Futurama S06E07
There’s a hard sci-fi novel (1970s or 1980s) called “Tau Zero” that features this idea.
Book summary (spoils all of it)
A colony ship with a Bussard Ramjet on each end (debunked theoretical spaceship drive that uses interstellar hydrogen for propulsion, i.e. the faster you go, the more medium you hit and the harder you accelerate) suffers an accident that destroys the deceleration engine. They keep accelerating because they need the engine’s magnetic field to protect them from interstellar dust. First they try reach the void between galaxies to safely repair the ship, when the interstellar medium is still too “dense,” they go for the void between galaxy clusters, then superclusters, then they just stay on the throttle until the big crunch, at which point, in the nothingness after the universe collapsed in on itself, they can finally fix their ship and begin decelerating into the bounce-back big bang of the forming next universe and colonize a planet.