This sappy romantic fantasy proves that a movie doesn’t have to be a CGI extravaganza based on a video game, comic book or toy line to be inordinately dumb. “The Time Traveler’s Wife” is in the tradition of pictures like “Somewhere in Time” and “The Lake House,” in which true love can’t be deterred by a little problem like chronological imbalance. But it takes the absurdity of the premise further than any of its predecessors, simply dispensing with any logic whatever. No narrative rules and a deliberately muddled plotline make for a schmaltzy mess.

Adapted from a bestselling book by Bruce Joel Rubin and directed with a leaden touch by Robert Schwentke, the movie centers on Henry DeTamble (Eric Bana), a Chicago reference librarian with a “genetic anomaly” that’s affected him unpredictably since he was six, when he temporally transported out of the car he and his mother were careening toward their death in. Since then he’s periodically been swept unwillingly to some other date and place; whatever he’s wearing simply drops to the floor and he finds himself elsewhere—and naked (a circumstance obviously designed to appeal to the giddy females who will make up most of the audience).

In addition to the unpredictability—and nudity—of the experience, there are other drawbacks to Henry’s condition. Supposedly he can’t control where and when he goes (though this rule is shattered at the very start, when he appears as a thirty-year old to tell his six-year old self—played by Alex Ferris—that he’ll be all right). And apparently the switches are limited to various points in his own lifetime, which is kind of a drag—it means that he can’t ever hope to shake hands with Napoleon or Winston Churchill, clothed or no, or even to visit himself as Hector at the gates of Troy. With all the limitations and embarrassments, though, it’s still probably preferable to the experience of abruptly transforming into a big green behemoth from time to time, as poor Bana once did.

But Henry’s time-tripping does have one major reward: he meets his soulmate Clare (Rachel McAdams). Precisely when it’s impossible to say—their encounters are shuffled around much too incessantly to tell—but they’ve had a relationship of sorts from the time Clare was six, when he visited her (played by Brooklynn Proulx) repeatedly in a meadow near her rich father’s (Philip Craig) estate, where she regularly picnicked alone. (Yet another indication that he does have some degree of control over where he travels.) But it’s not until the grown-up Clare encounters him at his library job (at a time when he doesn’t know her “yet”) that their romance per se can begin. Soon they marry and try to have a child. But his periodic disappearances and reappearances put a strain on their life together, as does his fear that a son or daughter might inherit his condition. All of which sends him to geneticist Dr. Kendrick for help, who diagnoses him with a condition that has some similarities to epilepsy. (Kendrick is played by Stephen Tobolowsky, who’s had some prior experience with this sort of malarkey from his turns in both “Groundhog Day” and “Heroes.”) But the good doctor’s ministrations seem to have little effect.

“The Time Traveler’s Wife” has some moderately amusing bits based on Henry’s penchant for doing his invisible routine at inconvenient moments and suddenly showing up again at a somewhat different age; the best example is his and Clare’s wedding ceremony. But mostly the makers opt for mawkishness and sentimentality of the crassest kind. Among the actors Bana fares worst; though he has the occasional scene when he can smile, he’s called upon largely to look stricken and morose, suffering like a male version of Camille. McAdams fares better, especially after the first reel, when she encounters the grown-up Henry for the first time and is required to spend ten minutes or so grinning maniacally until she settles into vaguely human mode again. Of the supporting players, Ron Livingston has a few nice moments as a family friend and Arliss Howard is appropriately gloomy as Henry’s depression-prone father.

Like most pictures of this ilk, this one is spiffily appointed, with cinematography by Florian Ballhaus that sometimes looks as though it were shot through gauze-covered lenses (a few exterior scenes were filmed in Chicago, where the story is ostensibly set). Presumably Thom Nobe’s editing follows directorial instruction in prizing affect over coherence, and Michael Danna’s score lays on the syrup thick in an attempt to aid in bringing a tear to the eye of the easily touched.

And perhaps the movie will; it certainly works hard enough to do just that. But if you’re looking for a film that really brings a sense of magic to a tale of a romance that a difference in time can’t derail, the one to go for is still Joseph Mankiewicz’s “The Ghost and Mrs.Muir.” It’s more than sixty years old, but still has the power to enchant, unlike this garbled mixture of curdled whimsy and brutal heart-tugging.