The first rule of time travel movies is there are no plausible rules of time travel movies. Whether it’s “Slaughterhouse-Five” or “Back to the Future,” “Time After Time” or “Looper,” “Somewhere in Time” or “The Terminator,” it doesn’t matter how much exposition we get, or whether there’s some kind of geeky “flux capacitor” explanation. We just have to go with it and see where the story takes us. If we care enough about the characters and their journey, we buy into it.

So it goes with writer-director Ned Benson’s sun-dappled Los Angeles time-travel romance “The Greatest Hits,” which takes a big pretty swing in the genre with a sentimental premise that might have you rolling your eyes — but only if you’re a COLD-HEARTED CYNIC WHO DOESN’T BELIEVE IN LOVE. (Just kidding. As far as you know.)

When we meet Lucy Boynton’s Harriet in present day, she’s a troubled soul who is still in deep mourning two years after her movie-star handsome boyfriend Max (David Corenswet, star of next year’s “Superman”) was killed in a car accident. Thing is, Harriet can’t really move on, because every time she hears a song attached to a memory of Max, she’s rocketed back in time to that moment, and can stay there only as long as the duration of the tune. (Where’s the uncut version of “Autobahn” by Kraftwerk when you need it!)

Harriet’s apartment is filled with albums marked “Tested” and “Untested.” Sometimes she travels back in time by choice and tries to manipulate events; on other occasions, when she’s out in public and a time-triggering song plays on a car radio or in a coffee shop, well, that’s problematic, as it sends Harriet into spasms and causes her to pass out. Harriet wears noise-canceling headphones, and she works in a library to minimize the risk of an unplanned journey, but you can’t control the music everywhere you go.

With needle drops from an eclectic mix that includes Jamie xx, Roxy Music, Nelly Furtado and Technotronic setting the pace, “The Greatest Hits” introduces a number of familiar character tropes, including Austin Crute’s Morris, who is Harriet’s gay best friend and exists mainly to advise and support her and happens to be a DJ, which feels almost too on point, and Retta’s wise and caring group therapy leader, Dr. Evelyn Bartlett.

The sensitive and cutely awkward David (Justin H. Min), who recently lost both his parents and manages their charmingly dusty antiques store, develops a real crush on Harriet, though when she tells him about the Hunky Dead Boyfriend and the time-travel thing, he has his doubts. (Boynton infuses Harriet with such loveliness and charm that we believe David might stick around despite her crazy story.)

The script from writer-director Benson takes some interesting turns. We want Harriet to be reunited with Max, but dang it, what about David?

Just when you think “The Greatest Hits” has painted itself into a corner, the script finds a way and the story lands in just the right place. I could see myself going back and watching it again, even though I know exactly how it will all play out. Hey! Sort of like in a time travel movie.