The time loop story, in which characters repeatedly relive the same span of time, has become synonymous with the 1993 film Groundhog Day, but the idea has much older roots. In PD Ouspensky’s 1915 novel Strange Life of Ivan Osokin, the feckless Osokin is given the chance to live his life over again, only to find himself making all the same mistakes. Like Groundhog Day’s insufferable Phil Connors, Osokin can change nothing without changing himself.

Solvej Balle’s much-lauded series On the Calculation of Volume takes a very different approach. She first began working on the idea decades ago, several years before Groundhog Day was released. The film, she says, “helped me with research by trying out some of the roads I did not want to take”. The books, five so far with two more planned, have proved a literary sensation in her native Denmark, with the first three volumes together scooping the 2022 Nordic Council Literature prize, the highest literary honour in Scandinavia. This is the third to be published in English this year; the first was shortlisted for the 2025 International Booker prize.

Balle’s protagonist, Tara Selter, is an antiquarian book dealer from a small town in France who, on a buying trip to Paris, finds herself trapped in 18 November. For everyone else, as morning comes and the day resets, it is 18 November for the first time. They perform the same actions in the same order, unaware of any repetition. Only Tara remembers the November 18ths that have gone before. She counts the days and tries to grasp the bafflingly inconsistent rules of her new reality. Some possessions she acquires stay with her when the day repeats itself, while others return to wherever they came from. She herself can travel: she is trapped in time but not in space. She can interact with people, too, changing the events of their day. The problem is that, as 18 November loops round again, they remember nothing.

In Volume I, Tara returns home from Paris to her partner, Thomas. She tries to enlist his help but the ordeal of explaining anew every morning exhausts her and she moves into the spare room, haunting his day invisibly, like a ghost. In Volume II, hungry for seasons, she traverses Europe, north to south, seeking the ordinary shape of a year in a single repeated day. It is only at the start of Volume III that she finally detects a break in the pattern. “I have met someone who remembers,” she announces, giddy with grateful incredulity.

Henry Dale, a Norwegian sociologist, is also trapped in 18 November. For 1,143 days, Tara’s journals have been her “sole witness, [her] confidant”. Now she has Henry; not a friend exactly but a fellow traveller. Before long they meet another couple who share their predicament. The four find themselves suddenly defined by one another, and the different ways they have chosen to respond to their situation. Which is most reasonable, most ethical, most correct? They struggle to agree. Should they use their foreknowledge to prevent the accidents and disasters that repeatedly occur on 18 November? Or should they – could they – change the systems that make accidents inevitable? Is it enough to pay meticulous attention, to try to understand what repetition reveals about the world? How should they structure their shared lives now that they are four?

Volume III is more digressive than its predecessors, more freighted with history and philosophy. It is also looser, opening its sealed spaces to more air and light. For all her sensitivity and fierce intelligence, Balle’s Tara is a disconcertingly disembodied creation: indifferent to food and, after Thomas, untroubled by sexual appetite, she never once in three volumes alludes to her period, surely for a woman in her 30s a definitive marker of time. She is also dispiritingly disinclined to make jokes.

But as her focus widens, Balle introduces some welcome flashes of humour while sustaining the compulsively hypnotic effect of the first two books. And they are compulsive, there can be no doubt about that. Three volumes in, Balle’s piercing attentiveness and her forensic curiosity continue to render 18 November endlessly interesting. From a continuously looping span of 24 ordinary hours, she spins a profound meditation on love and loneliness, on grief and hope and longing, on the rapacity of human consumption and the ordinary, unthinking mundanity of everyday life, on how we understand the past and anticipate the future. Her sinuous sentences wrap themselves around us, her readers, binding us over and over to 18 November, drawing us deeper and deeper into its ungraspable possibilities. By this third volume, the day no longer belongs exclusively to Tara. It belongs to her three companions – and to us.

In Groundhog Day and indeed in Strange Life of Ivan Osokin, the story draws its propulsive momentum from the protagonist’s search for an escape. Somewhere, within them or without, is a key that will unlock time and set them free. Tara Selter no longer believes in freedom. She knows she will never escape. But what she learns from her November 18ths, and what other people teach her, adds up to its own lifetime.

• On the Calculation of Volume III by Solvej Balle, translated by Sophia Hersi Smith and Jennifer Russell, is published by Faber (£12.99). To support the Guardian, order your copy at guardianbookshop.com. Delivery charges may apply.