It was just another ordinary day. The sky above Newark International airport was an ordinary blue. Pilots, staff and passengers entered United Airlines flight 93 bound for San Francisco. At 8.42am the plane took off. Orders for breakfast were taken. Passengers relaxed. Forty-three minutes later, four terrorists hijacked the plane, and the ordinary got its throat slit. At 10.03am, UA93 crashed into an empty field in Pennsylvania — and right into the headlines of history.

Paul Greengrass’s film is the story of the fourth plane hijacked on September 11, 2001. Its place in history has been secured not by sensational footage — like the two that crashed into the twin towers — but by the sudden burst of bravery by the passengers, which prevented the plane from hitting its intended target. Greengrass, director of Bloody Sunday, is not really interested in the whos and whys of that day, only what happened. (Or, when it comes to those army and aviation officials in charge on the ground, what didn’t happen.) United 93 has the verisimilitude of a true-life documentary shot in real time, along with the gut-wrenching drama of the most gripping disaster movie you’ve ever seen.

In making a docudrama, Greengrass gains a remarkable intimacy with the actual events, but not with the people. There are no introductions, no flashbacks. We don’t really know these people as individuals; they are simply passengers. We experience them the way we would if we were on board.

Watching this film is a disorientating experience. And not because of its wobbly, at times frantic, camera work. It’s like being a time traveller hurled into the past.

Everything is seen through the heightened prism of hindsight, where the most mundane conversations are the stuff of heartbreak:

“I like to be home with my babies,” says a stewardess at the start. As we watch the passengers settling in — reaching for magazines, asking for blankets — a small knot forms in our stomachs. We share with the sweaty, nervous terrorists the tension that comes from waiting for the moment when they will make their move. You feel a kind of relief when it happens.

Greengrass wants to take us back to that faraway world of pre-9/11 America. The world’s only superpower looks innocent, unprepared and ineffectual. Its familiar world has gone Awol. The action moves between events inside the cabin and the chaos in the control rooms of the aviation and army authorities. We watch men in power barking out orders for “information” and “answers now!” and getting only silence.

The dramatic power of United 93 can’t be denied. It’s one of those rare films that, when it’s over, fixes you to your seat. You don’t say anything. You leave quietly, as though departing not from a film but a funeral service. Yet there are questions we should be asking. For starters, just how accurate is it? The film creates the impression that here is what really happened on board that plane. But the truth — as Greengrass will admit — is that nobody knows what actually happened. The evidence from the flight recorder and phone calls from the passengers is relatively slight.

Then there is the awkward question of the much-celebrated bravery of the passengers. Were all of them heroic, or just the half-dozen we see charging the terrorists? It’s interesting that the most vocal passenger to advocate a policy of do-nothing is not an American but a German. Greengrass and his actors meticulously researched and created all the scenarios, but how did they establish that he was the leading advocate of appeasement? Surely one of the passengers didn’t phone home to point out there was a cowardly German on board who wanted to give in? The film doesn’t want to deal with the possibility that there were Americans who opted to stay silent and seated. Greengrass wants it both ways: he wants to pose both as the objective documentarist who just presents the facts as they unfolded, and as the dramatist who presents an upbeat portrait of American bravery that makes everybody look good. And he wants us to see the passengers as uncommonly wise as well. He has said they were the ones who first realised they were living in a post-9/11 world; and what’s more, they, unlike the bumbling army, unsure of the rules of engagement, knew what to do. I suspect they were simply people motivated by panic and a desire to survive.

It may sound flippant to say this, but United 93 is the ultimate date movie. Much has been made of its discreet celebration of heroism (and there are no Hollywood heroics here), but what it affirms is something other than bravery. We see passengers making farewell calls to friends and family, and what they want to talk about is not jobs or celebrities or any of the things we fill our lives with. Those about to die have only one message for the living: in the end, it’s love that really matters.

United 93, 15, 111 mins, Four stars