The flight to the future is explained by scientific gibberish that contains a high concentration of mumbo jumbo, but the gist of it is that the speed of Allison’s plane (around 10,000 mph) added to the rotational speed of the Earth plus the speed of the Earth’s orbit around the sun plus the speed of the Solar System around the center of the galaxy plus maybe another speed or two, managed to bring his total speed close to that of light, which brought him to the future. Apparently, reversing his plane’s path is all that’s needed to return him to the past (ideally with Trirene beside him).
A self-defeating act paradox is set up nicely (if Alison stops the plague, then the citadel in the, future won’t be there to send him back to stop the plague), but the issue is never explicitly discussed and the ending of the film is inconclusive on the matter. Nevertheless, I commend the film for being the first to raise the issue of time travel paradoxes, albeit in the background.
I saw this in the theater with Deb Baker and Jon Shultis during a winter trip to Pittsburgh for a small computer science education conference.
The story continues in a 1990 sequel, Times Change.
If he dug it up now and carried it back to his ship, it would not be there for him to find on that high summer day in the twenty-third century. And if that was true, how could he be here, in this time, to dig it up at all?
Joe: Wait—the what, now?
Barry: If you travel back in time to change something, then you end up being the causal factor of that event.
Cisco: Like . . . Terminator.
Joe: Ah!
Wells: Or is time plastic? Is it mutable, whereby any changes in the continuum could create an alternate timeline?
Cisco: Back to the Future.
Joe: Ah, saw that one, too.
Suffice it to say that when all the Librarians up in the Citadel woke from their sleeps and returned from their treks, we had a celebration that was strident enough to raise Lazurus Long himself from the dead (if he is dead, that is).