It's highly probable that JJ Abrams had not seen The Dark Knight when he began work on his forthcoming Star Trek reboot. But he must have been chuckling to himself when he did finally check it out. While Abrams' movie is unlikely to top Christopher Nolan's film for moody brilliance, it is already ahead in at least one area.

Of the 20 minutes or so of footage screened for the press this morning at an event hosted by Abrams, the standout action scene was a bravura set piece featuring Kirk (Chris Pine) and Sulu (John Cho) landing on a platform in the Vulcan desert. In The Dark Knight, Nolan had his hero leap out of a moving plane and into a skyscraper. Abrams goes one better: he has his characters skydiving ... from space.

Abrams has said he sees Star Trek as the antidote to the fad for gritty reinventions of famous franchises. From what I saw this morning, it looks like he's successfully echoed the optimism of the original TV series: there's a definite feel of wide-eyed, Apollo-era innocence to the movie. And yet, despite the kitsch costumes - all figure-hugging, primary-coloured spandex, with miniskirts for the Enterprise's female crew - and the odd postmodern in-joke, Abrams knows how to push the right buttons to snap his audience back into the story.

As those who've been following this reboot since its announcement last year will know, the new Star Trek is an origins tale. From what I gathered this morning, it centres on an invasion of Spock's home planet, Vulcan, by perfidious Romulans. In Abrams' retelling, Kirk, far from being the captain of the Enterprise, fails to be picked from Starfleet Academy for the journey into space. He has to fake a medical condition just to get on board the ship. And even when the incumbent, Captain Pike, is forced to take his leave, it's Spock who's left in charge of the bridge, with Kirk as his second-in-command.

There seem to be some other changes too. I'm no Trekkie, but I don't remember Scotty inventing time travel in the original series. He does here, which is rather useful, as the writers were desperate to shoehorn the original Spock, Leonard Nimoy, into the plot. Simon Pegg, who said a few words at the screening ("Me geek. Love Star Trek. Dream come true, etc") looks excellent in the role. Breathe a sigh of relief, Pegg fans, the accent is absolutely spot on.

Abrams apparently allowed all his main cast members room for manoeuvre when it came to portraying such well-established characters, and I'm pleased to report that most have chosen not to go down the impersonation route. Pine does not really remind you much of William Shatner, Karl Urban's Bones is not a lot like DeForest Kelley's (although he does say "dammit Jim" a fair bit) and other than a loosely similar racial background - he's Korean-American, George Takei is Japanese-American - John Cho is not an obvious Sulu. Anton Yelchin is, sadly, a bit rubbish as Chekov, possibly because he's trying too hard to ape those famous Slavic vowels.

But there are some subtle nods to the original: wearing red is still likely to reduce your life expectancy by several decades, and the new Spock (Heroes' Zachary Quinto) is still bloody annoying. The Trekkies will no doubt be pleased with Nimoy's cameo, too, although the poor old fellow looks pretty wooden in comparison with his bright and breezy new crewmates.

So far so good then. A few minutes of footage do not a great movie make, and this is the sort of film that might easily be scuppered by an annoying plot hole, some disgustingly fake-looking CGI or a spot of crap alien makeup. But if it does avoid problems of that sort, Abrams' movie might well be the first Star Trek film worth watching by anyone who doesn't know how to correctly perform a Vulcan salute since 1982's The Wrath of Khan. I'm not a Star Trek fan, and I really wanted to give this one a good, hard kick in the dilithium crystals. But dammit, Jim, if it doesn't look like a half decent movie.