“Remember Me” is a tearjerker that won’t make you cry. It will, however, make you groan and squirm and possibly snore as it painstakingly details the lackluster love story of a bitter rich-kid-turned-rebel and a sunny social-worker-to-be brought together by police brutality. That may sound a bit peculiar but, as Al Jolson once said, you ain’t heard nothin’ yet.

“Remember” is the kind of pet project that gets the go-ahead when its star becomes a surprise sensation (and, in this case, an executive producer) with some new-found box office clout. In this case, that would be Robert Pattinson, who became a household name and an international idol as the dark-eyed, ivory-skinned Edward Cullen, the heroic vampire condemned to an eternity of teen angst in the “Twilight” films.

Pattinson is sharp enough to realize the sands are already running on the “Twilight” series — the third installment, “Eclipse,” opens June 30, and “Breaking Dawn,” based on the final book in Stephenie Meyer’s quadrilogy, goes before the cameras this fall — and, if he wants to extend his cinematic shelf life he knows he’s got to act fast. Apparently, he also thinks he’s got to act like a misconceived mash-up of James Dean, Marlon Brando, Robert DeNiro and Al Pacino, which is exactly what he attempts to do, with only spotty success, throughout “Remember.”

In the sizzling summer of 2001, Pattinson’s disaffected but dashing Tyler Hawkins has a temper that’s hotter than the New York sidewalks on which he mopes. But who wouldn’t be grimacing day in and day out if you were the son of an ultra-wealthy Irish lawyer (Pierce Brosnan) and a lovely Swedish mom (Lena Olin) who looks vaguely miserable even in her happiest moments? A little James Joyce and a little Ingmar Bergman makes for a whole lotta trouble.

Tyler parties joylessly with Aidan (Tate Ellington), his chatterbox of a roommate, and a revolving chorus of anonymous babes until a street brawl brings him into close physical contact with Sgt. Neil Craig (Chris Cooper). For reasons that make sense only to screenwriter Will Fetters, testy Tyler takes on the sergeant and receives an artfully roughed-up face for his trouble.

Hey, Aidan notes, that mean ol’ cop has a hot young daughter named Ally (Emilie de Ravin, best known as Claire from “Lost”). What if Tyler seduced and abandoned Ally? Aidan bets Tyler can’t pull it off; Tyler accepts the challenge.

Payback is a bitch — and bitch, thy name is Tyler Hawkins.

So “Remember” becomes one more of those “love on a dare” stories, as Tyler woos the oblivious Ally and discovers she’s a bit of a non-conformist, too: She insists on eating her mango ice cream before her dinner of lamb vindaloo because “I just don’t see the point in waiting.” After all, she notes, you never know when an asteroid could drop from the heavens and abruptly end everything, and after about 40 minutes of this movie, you may be praying for some sort of harsh astronomical intervention.

Past tragedies hang over Tyler and Ally like the Sword of Damocles. She witnessed her mom’s murder in a subway station; he lost his older brother to suicide. He disapproves of the way his dad ignores his ex-wife and 6-year-old daughter; she bristles at her father’s over-protectiveness. He smokes too much; she can’t handle her Jello shots. They must be made for each other.

“Remember” falls into the same trap as the second “Twilight” film, “New Moon,” believing that excessive brooding and surly skulking are endlessly fascinating to watch. But striking the same tortured note again and again does not create a solemn symphony. The movie lumbers along at a near-funereal pace on its way to the inevitable “I never meant to hurt you” confrontation/revelation, giving you plenty of time to ponder such weighty questions as whether Pattinson will ever play a character who’s not dating a cop’s daughter.

Then, in its final 10 minutes, “Remember” makes the leap from mere monotony to jaw-dropping ghastliness in a finale so staggeringly stupid it’s almost impossible not to laugh. “Twilight” flips over into “The Twilight Zone,” and the movie suddenly flies spectacularly off the rails, leaving you feeling simultaneously offended, bewildered and, perhaps, a little bit astonished that the filmmakers actually thought they might be able to get away with it.

Ultimately, “Remember Me” sells a sermon about the importance of family unity and the message comes through, although perhaps not in the way Pattinson and company intended: As the lights came up, my almost-15-year-old niece turned to me and said, “I don’t ever want to see that movie again” — and I couldn’t have agreed with her more.