'Space … the final frontier." When James Kirk first uttered those words in Star Trek in the 1960s, the phrase had a romance that was undercut by cardboard sets more evocative of amateur dramatics than "strange new worlds".

Forty years later, the rebooted Star Trek films have a different problem: everything is so shiny bright and glib that intergalactic travel seems no more difficult than a stroll to the corner shop.

In the hands of British director Christopher Nolan, however, the final frontier is made to feel truly interstellar. Nolan's new film conveys the wondrousness and vastness of the universe, as well as the sacrifices - physical, psychological, emotional - of attempting to step into it.

The science-fiction film that really informs Interstellar is Stanley Kubrick's 2001: A Space Odyssey, whose majesty and mystery Nolan is trying to capture. The director of Memento, the Batman trilogy and Inception is renowned for his narrative trickery and cinematic showmanship; but this is a giant leap.

In the near future, mankind's environmental misdeeds have come home to roost: the world has become a dustbowl, food is scarce, the atmosphere will soon be inhabitable. Farming has become the most valued skill, which is why we find former test pilot Cooper (Matthew McConaughey) redeployed in the cornfields around his home, which he shares with his father (John Lithgow) and two young children.

For a time the film is rooted to terra firma, where Cooper struggles with parenthood - especially with his feisty and inquisitive daughter Murph - and his personal frustrations. "We used to be explorers, pioneers, not caretakers," he laments, gazing at the stars.

But "Coop" will get his chance to be a space pioneer. A wormhole has appeared in the galaxy, which a NASA professor (Michael Caine) believes will enable a spaceship to travel to an otherwise too-distant part of the universe - and a choice of habitable worlds. Cooper is asked to fly the mission.

Nolan's preamble has been with the purpose of posing his hero's dilemma: the space-time conditions of relativity are such that if he flies off to save the world, the chances are that when he returns he will be younger than his children, if they are alive at all. As Cooper, the professor's own daughter (Anne Hathaway) and two others depart in the rotating spaceship Endurance, their expedition is a race against time.

Interstellar is in many ways a remarkable film, not least for the scale of its ambition, its story alternating between space and Earth, emotional dilemmas and scientific ones, action and introspection, and some far-out weirdness that represents the biggest nod to 2001. The IMAX images are glorious, recreating wormholes, black holes and a variety of different planets, and its action sequences are incredibly thrilling, the stand-out being a seat-of-pants attempt to dock with an out-of-control space ship. McConaughey, on a roll after his performances in Dallas Buyers Club and True Detective, perfectly embodies the cowboy space hero-cum-Everyman dad.

That said, the film itself is not perfect, with problems that can be firmly located in the script by Nolan and his brother Jonathan. Though their science can probably be trusted (the theoretical physicist Kip Thorne was an advisor), the manner in which the Nolans dispense it is often garbled and unconvincing; sometimes, as when Hathaway declares that love is "a new dimension" it's plain hokey.

But if the script would have benefited from some gravitational pull, one can't fault the film's ambition, so rare in commercial cinema, and the spirit with which Nolan imbues it, which combines Kubrick's intellectual daring with Spielberg's sense of wonder.