Romantic fantasies about lovers supernaturally separated by time and/or space have a long pedigree on screen–just think of “The Ghost and Mrs. Muir” (the gold standard) or “The Portrait of Jennie” from the 1940s, or “Somewhere in Time” (1980) and “Kate & Leopold” from 2001, or the even more recent “Just Like Heaven.” But to work they need a couple of basic qualities. One is, of course, a bit of finesse in the telling: a sense of discretion, knowing when to hold back–some subtlety, in other words. And the other is narrative rigor within the admittedly unrealistic world that’s being created. “The Lake House,” the latest entry in the genre (an adaptation of a Korean original), fails on both counts. Directed by Alejandro Agresti in a lugubrious, swooning style that accentuates the absurdities rather than glossing them over, it couldn’t be more heavy-handed and schmaltzy: the supposed magic dust is poured on with a trowel rather than a teaspoon. (There’s a bit of business, for instance, regarding the flag on an outdoor mailbox that goes mysteriously up and down to indicate that messages have been transmitted across the years. It’s a cute device, but is milked to such an extent that eventually its implausibility becomes crushing–and it gets tiring, too, like a joke too often repeated.)

The premise is that Dr. Kate Forester (Sandra Bullock) is forced to abandon her beloved suburban Chicago glass house, apparently on the northern coast of Lake Michigan, when she takes a job in the city. She leaves behind a note for the incoming occupant Alex Wyler (Keanu Reeves), a nice-guy cookie-cutter condo builder, whose estranged father, renowned architect Simon (Christopher Plummer, who seems to be in every second movie made nowadays), had built the place. But their subsequent correspondence, conducted via that magical mailbox, not only grows more and more personal and passionate over time, but reveals that he’s living his life exactly two years earlier than she is. How could such a thing be happening? And will it prevent their meeting and what seems an apparently destined romance?

This idea isn’t exactly brilliant, but if treated with delicacy and taste it might have been the foundation of a genuinely touching piece. (“Muir,” after all, wasn’t the most credible of stories, but Joseph L. Mankiewicz, Gene Tierney and Rex Harrison handled the material so deftly that–aided by Bernard Herrmann’s unfailingly lovely score–they made it soar.) No such luck here. David Auburn’s script is cluttered with subplots that bring things to a halt far too frequently: Alex’s strained relationships with his father and younger brother Henry (colorless Ebon Moss-Bachrach) and Kate’s on-again, off-again romance with stuffy lawyer Morgan (Dylan Walsh), as well as her conversations with her widowed mother (Willeke Van Ammelrooy) and her boss (Shohreh Aghdashloo), have some nice touches (though Plummer and Walsh overplay their hands), but even at their best (as in Van Ammelrooy’s lighthearted lines, or Aghdashloo’s more vivacious moments) these interludes tend to stop the proceedings dead in their tracks.

But even apart from that, the central love story is clumsy and episodic, largely composed of discrete episodes that shift back and forth between the principals, usually ending with a simple black-out that acts like an unfortunate narrative hiccup; there’s not much pulse or pace to the transitions in the editing by Lynzee Klingman and Alejandro Brodersohn. And while it’s pleasant to see Agresti employing old-fashioned cinematic devices–from the elegantly-dissolving credits to pans and visual dissolves (an especially nice one involves passersby changing as Kate and Alex sit on adjacent park benches at separate times)–to give the movie a nostalgic feel, too often they come across as affectations rather than choices that deepen the emotional content. The characters played by both Bullock and Reeves, moreover, are so gloomy and sullen throughout (especially her) that they cast a pall over the whole picture. Matters don’t appreciably improve on those rare occasions when the two stars share the screen, either; not only do they generate surprisingly little chemistry–certainly less than they did in “Speed”–but the storytelling contortions required to get them into a single scene are so off-the-wall (and often confusing) that one’s ability to suspend disbelief is pretty much shattered. (One of those joint moments is an obvious early telescoping of the movie’s tears-and-joy finale. I won’t reveal it here–though even the least discerning viewer will catch the significance at once–but will note that with this movie and “The Matrix,” Reeves is surely becoming the most resurrected actor in modern film.) Of course, even the best actors would have a lot of trouble dealing with what’s doubtlessly Auburn’s worst device–having them share one of those ultra-cute dogs so prevalent in pictures. Who could pull off a sequence in which Kate is supposed to be playing chess against the mutt, or referring to how the dog “sleeps like a person” (cutaway to the canine snoozing in a pile on the floor)? Agresti does what most directors at a loss will resort to under circumstances like these: he employs innumerable reaction shots of the animal, supposedly to break the monotony of the solemn proceedings with some easy laughs. (It doesn’t work.)

Add to the mix a production design by Nathan Crowley that’s at best pedestrian (his rendering of the title structure is especially uninteresting), cinematography by Alar Kivilo that goes in too persistently for mushy, gauzy-lensed atmosphere, and a remarkably unaffecting score by Rachel Portman, and you have a picture that never achieves the romantic mood it so desperately aims for. There is some visual solace in the Chicago setting, which allows for montages saluting the city’s magnificent architecture. But better to take the walk-around Alex prepares long-distance for Kate in person rather than accompany these two vicariously.

The final, most devastating blunder made by Auburn and Agresti is to draw a direct comparison in the dialogue between the supposedly impossible romance they’re depicting and the one in Jane Austen’s “Persuasion.” Simply put, the mere mention of that classic of nineteenth-century literature reveals “The Lake House” as the hopeless second-rater it is, a cheap knock-off of the authentic article. You’d be much better off reading Austen’s book than seeing this movie. Or watching the sublime film that Roger Michell made of it back in 1995. Now there’s a picture that rewards the viewer’s patience with love long unfulfilled. This one, with a finale that seems almost like a throw-away afterthought (and makes absolutely no sense), certainly doesn’t.