Michael Haneke writes and directs movies about one thing: People with seemingly secure, orderly lives who are suddenly confronted by an outside force that shatters their calm. The danger may be home invaders (“Funny Games”), the presence of a concealed camera (“Caché”), the first stirrings of authoritarianism (“The White Ribbon”) or a sudden reappearance by a vengeful acquaintance (“The Piano Teacher”).

In “Amour,” the implacable interloper is Time itself. Octogenarians Georges and Anne (Jean-Louis Trintignant and Emmanuelle Riva) sit at breakfast, discussing the concert one of her former piano students gave the previous night. She freezes, stares into space, doesn’t respond to his questions or a damp towel on the back of her neck.

Minutes later, she unfreezes as if nothing had happened, but this small stroke will be the first step on the painful march toward death. (That’s no spoiler: The movie’s first scene shows her lying dead.)

Haneke chronicles every moment of decline along that road: Physical therapy, manual wheelchair, electric wheelchair, nurses helpful and unhelpful, sponge baths and diapers, assisted feeding, imprisonment behind a speechless tongue, the ceaseless vague moans of unending despair.

He shoots the movie in his usual clinical style: He favors long takes, often seen from a distance, interspersed with rare but effective close-ups. When Georges helps the stricken Anne shuffle up and down their hallway, we watch every plodding step, because Haneke wants us to see exactly how onerous simple movements have become for her.

At the same time, he and the actors capture emotions. We sense the shame Anne feels for needing help with every action and the shame Georges feels for being angry over her constant neediness.

Their daughter (Isabelle Huppert) offers well-meant advice, but Georges can’t accept it. He has promised Anne he will never take her back to the hospital, and his understanding of love – which is what “Amour” means, of course – consists of devoting himself to Anne’s well-being while keeping that promise. (The daughter’s presence shows how tightly these two old people have closed themselves off from the world, but her marital problems lengthen and dilute the story.)

The superb Trintignant and the Oscar-nominated Riva – who would win, in a just world – embody once-vigorous people in inevitable decline. Yet as another critic has said, the film is sad without being depressing: Their love is so firmly rooted that it inspires a wish to emulate them, should we ever be so unfortunate as to become them.

Haneke always pays unusual attention to detail, from the décor of their handsome but not opulent apartment to the cold light coming in through their balcony window. So I can’t help but think he wanted us to listen closely to the music played by Anne’s pupil and Anne in a flashback.

It’s mostly by Franz Schubert, who died at 31 and represents the greatest loss at a young age in classical music history. (Even Mozart had more fully explored his genius when he died at 35.)

Hearing Schubert’s impromptus, we may wonder which is better: To go relatively quickly, at the height of one’s powers, or slowly, with every vestige of our individuality wrenched away. Haneke doesn’t choose, but he shows us the only way the latter situation can be ameliorated: with deep, unshakeable love.