The installation is the work of a team of designers led by the museum’s director, Alice M. Greenwald, formerly an official at the United States Holocaust Museum in Washington. It is culled from over 10,000 artifacts in the museum’s collection, and some of them are devastating: recordings of last phone calls; photographs of doomed firefighters heading into action; surveillance videos of hijackers passing — no problem — undetected through airport security. Certain material, like video stills of people leaping from the towers, are set in alcoves with advisory notices, but even things not usually considered shocking can leave you dumbstruck. For some reason, the largest objects — an intact fire truck with carefully folded hoses but a burned-out cab; a steel column plastered with prayer cards; a storefront jeans display still covered with World Trade Center ashes — are the easiest to take, maybe because of their public identity, or even their resemblance to contemporary sculpture. The hundreds of small, battered personal items, many donated by families of the victims, are another story. Their natural realm is the purse, the pocket, the bedside drawer at home; they feel too ordinary and intimate to have ended up under plexiglass. Infused with lost life, they make the experience of moving through this museum at once theatrical, voyeuristic and devotional.

Its nearest equivalent I can think of is the dynamic of religious pilgrimage sites, whether Christian churches, Buddhist temples or Sufi shrines. There, the mortal remains of saints, and objects sanctified by their touch, are the focus of attention. Here, you also walk a long, sanctified route, stopping at the equivalent of side chapels and altars, contemplating icons, talismans and embodied miracles: a pair of crossed steel ground zero girders that to some eyes formed a crucifix, a Bible found fused to a hunk of steel and opened to a passage that warns against repaying violence with violence.

The prevailing story in the museum, as in a church, is framed in moral terms, as a story of angels and devils. In this telling, the angels are many and heroic, the devils few and vile, a band of Islamist radicals, as they are identified in a cut-and-dried, contextless and unnuanced film called “The Rise of Al Qaeda,” seen at the end of the exhibition.

The narrative is not so much wrong as drastically incomplete. It is useful history, not deep history; news, not analysis. This approach is probably inevitable in a museum that is, to an unusual degree, still living the history it is documenting; still working through the bereavement it is memorializing; still attached to the idea that, for better and worse, Sept. 11 “changed everything,” though there is plenty of evidence that, for better and worse, this is not so. The amped-up patriotism set off by the attacks has largely subsided. So has the tender, in-this-together generosity that Americans extended to one another at the time.

Still, within its narrow perspective, maybe because of it, the museum has done something powerful. And, fortunately, it seems to regard itself as a work in progress, involved in investigation, not summation. I hope so. If it stops growing and freezes its narrative, it will become, however affecting, just another Sept. 11 artifact. If it tackles the reality that its story is as much about global politics as about architecture, about a bellicose epoch as much as about a violent event, it could deepen all our thinking about politics, morality and devotion.