What would the world look like if men were afraid of women rather than women being afraid of men? Science fiction has long questioned the conventional exercise of power between the sexes, from the utopian dreams of Charlotte Perkins Gilman, through the wild speculations of Joanna Russ and subtle inner journeys of Ursula Le Guin, on to Margaret Atwood’s dystopias and out to the seamier shores of pulp. Through exaggeration and reversal, many books have set out to illuminate inequality or open up new vistas of possibility. But I don’t think I’ve ever seen the status quo inverted to such devastating effect as in Naomi Alderman’s fourth novel.

It starts with teenage girls. At 14 or 15, the age when in our present world girls are waking to an awareness of their own sexuality tangled up in all the ways society will seek to stifle or exploit it, Alderman has them come alive to the thrill of pure power: the ability to hurt or even kill by releasing electrical jolts from their fingertips. “Something’s happening. The blood is pounding in her ears. A prickling feeling is spreading along her back, over her shoulders, along her collarbone. It’s saying: you can do it. It’s saying: you’re strong.”

Footage of girls electrocuting men floods the internet; uncontrolled individual outbursts swell into the knowledge of collective power as more girls learn how to harness this strange new ability, and show older women how to awaken it too. Men start to give teenage girls a wide berth on the street; boys are segregated into single-sex schools for their own safety. The phenomenon is blamed on nerve gas, witchcraft, an anti-male conspiracy, a mystery virus; it’s assumed that an antidote will be found and the “normal” balance of power restored.

But every individual exercise of power contributes to power relations as a whole, and change is unstoppable. The victims of sex traffickers turn on their assailants. There are revolutions in Riyadh and Delhi. Oppressed women assume that divine intervention has saved them from the hell-on-earth of their previous existence, and a new religious leader is ready and waiting to feminise faith: “Jews: look to Miriam, not Moses ... Muslims: look to Fatimah, not Muhammad. Buddhists: remember Tara, the mother of liberation. Christians: pray to Mary for your salvation.” Armies become female, to harness and exploit girls’ natural aggression; sexual violence flows in the other direction now. Drugs are developed to heighten the power, and porn created to fetishise it.

Alderman conducts her thought experiment through the lives of four main characters. There’s Allie, an abused American foster kid who reinvents herself as faith leader Mother Eve, and is seeking to build a community away from men; she joins forces with Roxy, the daughter of a London crime boss, who revels in her new abilities. Tunde is a Nigerian journalist reporting on seismic global change and discovering what it’s like to be an attractive young man in a woman’s world; while Margot, an American politician on the rise, comes to see that power resides with strength rather than authority – and as an unscrupulous middle-aged woman, strength is what she suddenly has.

The novel is constructed as a big, brash, page-turning, drug-running, globetrotting thriller, one in which people say things such as: “It’s only you I’ve blimmin come to find, isn’t it?” and “You wanna stand with me? Or you wanna stand against me?” But it’s also endlessly nuanced and thought-provoking, combining elegantly efficient prose with beautiful meditations on the metaphysics of power, possibility and change. We’re counting down, throughout, to a global cataclysm, while the book itself is presented as a “historical novel” from thousands of years in the future, written by one “Neil Adam Armon” who dares to question how the natural dominance of women over men might have developed. Alderman has sly fun with the letters between Neil and “Naomi Alderman” that bookend the novel, as Neil shyly and submissively invites Naomi’s approval and advice on his manuscript: “Anyway, sorry, I’ll shut up now … Thank you so much for this.”

The novel is constructed as a big, brash, page-turning, drug-running, globetrotting thriller

High-concept novels can be reductive, but Alderman’s book is multivalent. You can read the girls’ power as a symbol of untapped or unthinkable possibility as well as an SF plot device. It’s not clear at first that society won’t cast the new development as just another aspect of dangerous femaleness that needs to be contained, and it’s no surprise that girls who won’t use their power get called names: gimp, flick, flat battery, pzit (“the sound of a woman trying to make a spark and failing”).

Alderman wrote brilliantly in her last novel, The Liars’ Gospel, about how the narrative of faith is constructed to suit different agendas. Here domination gets, as usual, a religious blessing: Mother Eve, whose mission is powered by a drolly laconic voice in her head, has a theological blueprint for the new world order. “They have said to you that man rules over woman as Jesus rules over the Church. But I say unto you that woman rules over man as Mary guided her infant son, with kindness and with love.”

One of the most impressive aspects of the book is how it uses a new schematics of sex and power to illuminate our reality, with Tunde’s experiences demonstrating what it’s like to come of age as the weaker sex. “Nothing worse has happened to him than to anyone. There’s no reason for him to be afraid, no more reason than any other man.” The passages of sexual violence are truly horrifying, with atrocity venturing into the realm of Greek tragedy.

Why do people abuse power? The novel can’t offer any answer beyond the one already found in our world: because they can. “That is the only answer there ever is.” This is a bleak truth, but not a bleak book – it’s far too smart, readable and joyously achieved for that. The Power is an instant classic of speculative fiction.

• The Power is published by Viking. To order a copy for £10.65 (RRP £12.99) go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.