Jumping across time and space is tough, thankless business in “Predestination,” a slab of science-fiction speculation draped in old-fashioned detective story crepe. The story centers on a temporal agent, a futuristic enforcer (he tries to right wrongs before they happen) nicely played by Ethan Hawke with a hungry, hangdog look that suggests that his character has spent long nights howling in the wasteland, often without either a scrap or a prayer. Whether slinking through 1985 or another vintage year (usually while chasing down a bomber), the temporal agent looks like a classic lone wolf.

He is and isn’t, as the story’s multiple twists gradually, if not altogether too clearly, reveal. The movie opens with a misterioso figure whose face is obscured by a fedora and some clever camera angles and editing. There’s a boom, a mess of melting flesh and, shortly thereafter, the temporal agent is in bed with his face wrapped in bandages, much like Humphrey Bogart’s in the 1947 noir “Dark Passage.” In that film (based on a David Goodis novel), Bogart’s character, wrongly accused of murder, undergoes plastic surgery to avoid recapture. “Predestination” similarly plays around with enduring topics like fate and imprisonment, metaphysical and otherwise, and pins them on a character forced to change identities. But it also tosses in a whole lot of time travel.

The noir atmospherics seem to have been included largely because the story jumps in and out of 1945, or perhaps because the writer-director brothers Peter and Michael Spierig like tipping their fedoras to film history. Whatever the case, after the bandages come off in one decade, the newly mustachioed temporal agent turns up tending bar in another, pouring shots for a man curiously known only as the Unmarried Mother (Sarah Snook, wearing a sneer and a sack suit). The Unmarried Mother writes confession stories from the women’s angle, one he knows intimately. He has a story to tell, which begins with “When I was a little girl” and leaps across the years and yawning gaps in logic.