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The plot of the dreamy indie Another Earth sounds like something a grief chaser like Jodi Picoult might cook up: young woman with a bright future kills a man's wife and child while driving drunk and struggles to make it up to him, secretly. But this tragedy takes place within a science fiction scenario. A newly discovered planet advancing on Earth appears to be a mirror image of our world — complete with our population. There are no little green men and no special effects to speak of, but the looming presence of that planet and its possibilities turns Another Earth into a metaphysical treat, with influences that range from Krzysztof Kieslowski's The Double Life of Veronique and Blue to Andrei Tarkovsky's Solaris. It's the most soulful art movie of the summer.

Rhoda Williams (Brit Marling, who co-wrote the screenplay with her director, Mike Cahill) is about to head off to MIT to study astrophysics. She's 17, and she's been dancing and drinking and kissing someone. "I felt like anything was possible, and it was," she says in voiceover. But as she drives home, she's distracted, craning her neck to see the newly identified planet, then just a distant point of light. The movie telegraphs the coming crash, but it's still a shock.

Four years later, with the other Earth now hovering on the horizon like a bloated harvest moon, the judicial system is done punishing Rhoda, but she has just begun her own penance. When her parole officer suggests school or jobs that might match her intelligence, she demurs. She'd rather scrub toilets at her old high school. At night she retreats to a room stripped of all her old possessions, creating a bare cell within her parent's home and listening to music composed by John Burroughs (William Mapother), the Yale music professor whose family and life she destroyed. Inevitably, these two walking ghosts will meet.

Mapother, who's (somewhat) recognizable for playing Ethan on Lost, is the only veteran in the cast (unless you count 92-year-old Wes Anderson favorite Kumar Pallana, as a janitor who fears the new planet). If this were a European movie instead of an indie that just felt like one, it would be remade with Hollywood stars, except for Marling: this is one of those moments when someone comes out of nowhere and seems instantly a movie star. Though clad in shapeless navy coveralls and a wool hat for much of the film, she has the allure of Carolyn Bessette Kennedy. But her beauty is incidental to her grave and controlled performance. She's impeccably in tune with Rhoda; every action feels true. Cahill and Marling guide the character through the process of coming to terms with what she did, albeit with a secondary plot that could have come from a Star Trek episode. Or a dorm room filled with pot smoke and philosophy majors.

People who don't particularly like sci-fi shouldn't stay away from Another Earth. The second Earth adds an element of mystery and an undercurrent of fear, but it never overwhelms the central story of Rhoda and John in recovery. Most of what the audience learns about the other planet comes from radio broadcasts or voices on television; it's the background hum of the movie, representing the same kind of what-if theme of human connectivity explored in Kieslowski's films. At one point, someone asks Rhoda what if she met her double on the other Earth. What would she say to herself? "Better luck next time," she says — but the movie makes a case for a more profound conversation built on compassion and forgiveness.

• Mary Pols