"How did it come to this?" asks Kamila Shamsie's new novel of one man's arrival, shackled and terrified, at what he guesses are the interrogation cells of Guantánamo Bay. In answering that question, Burnt Shadows distils much of the most notorious history of the past 65 years into its pages. It moves in space from Nagasaki to Delhi, Karachi, the Pakistani-Afghan frontier, New York, Canada and Cuba, and in time from the 1945 bombing of Nagasaki to Indian independence and partition, the Soviet invasion of Afghanistan, the 9/11 attacks, the overthrow of the Taliban and America's subsequent extra-legal round-up of "enemy combatants". For once, the standard publisher's hyperbole - "sweeping in its scope" - is no more than the truth.

These tangled historical strands are bound together by Hiroko Tanaka, a Nagasaki-born polyglot who belongs everywhere and nowhere. When her German fiance is killed by the atom bomb, she flees to the home of his sister, Ilse Weiss, and her English husband, James Burton, in Delhi. She falls in love with Burton's Muslim employee Sajjad Ashraf and they leave India to raise their son Raza in the new country of Pakistan, where their lives become fatally entangled with anti-Soviet mujahideen, the Taliban and the CIA, in the shape of the Burtons' Americanised son Harry. Through it all, Hiroko, branded by the bird-shaped scars - the "burnt shadows" - the bomb seared into her back, survives through her skill with new languages, her willingness to assume new identities and her refusal to judge others on their own origins.

Burnt Shadows is an argument for the fluidity of identity: "History had blown them all off course, no one ending - or even middling, where they had begun," Shamsie writes. The novel is pessimistic about the possibility of rootedness. Beloved places prove as ephemeral as relationships; even America, where Hiroko is delighted to hear "Urdu, English, Japanese, German all in the space of a few minutes", ultimately betrays her.

The redeeming counterpoint to all this turmoil, the novel hints, is a loyalty that goes beyond less elevated ties to home and family. The Tanaka-Ashrafs and the Weiss-Burtons "are each other's spiders," says Harry, a reference to the Muslim legend of a spider spinning a web across the mouth of a cave where the Prophet was hiding, throwing his pursuers off his trail. But Hiroko's commitment to this ideal has its own brutality. Days after Harry's death at the hands of an Afghan gunman, she manipulates his reluctant daughter Kim into smuggling an Afghan mujahid across the Canadian border and berates her for judging the man "on five minutes of conversation". As an argument for the merits of freewheeling cultural exchange, it is not convincing.

Burnt Shadows is dense with history and principle, often at the expense of lightness of touch. Shamsie's prose is highly stylised - "Optimism. That was Sajjad's gift. She opened her mouth to breathe it in" - and her minor characters in particular can appear little more than ciphers. Oddly, in a novel so intent on the evils of national stereotyping, the Raj official James Burton lives in a colonial villa named "Bungle Oh!" and expresses his deepest feelings through cricketing metaphors.

When the novel shakes off its didactic tendencies, the results are moving snapshots of its characters' lost worlds. Sajjad recalls his father's story of the Emperor Shah Jehan cutting the Delhi sky with scissors to reveal the beautiful Jama Masjid mosque; Harry visits Karachi's chaotic ice- and fish-strewn harbour; Raza is overcome with excitement at running away to a mujahideen camp in the "vast, thrilling playground" of northern Pakistan. It is these vivid glimpses of particular corners of the world, rather than Hiroko's attempts to free herself from attachment to them, that are Burnt Shadows' best achievement.

The huge ambition of Kamila Shamsie's fifth novel is announced in the prologue. As an unnamed captive is unshackled and stripped naked in readiness for the anonymity of an orange jumpsuit, he wonders: "How did it come to this?" The vastness of the question as applied to a prisoner in Guantánamo is a challenge to which this epic yet skilfully controlled novel rises in oblique and unexpected ways.

Unfolding in four sections, the novel traces the shared histories of two families, from the final days of the second world war in Japan, and India on the brink of partition in 1947, to Pakistan in the early 1980s, New York in the aftermath of 11 September and Afghanistan in the wake of the ensuing US bombing campaign. At its heart is the beautifully drawn Hiroko Tanaka, first seen in Nagasaki in August 1945 as a young schoolteacher turned munitions factory worker whose artist father is branded a traitor for his outbursts against the emperor and kamikaze militarism. She falls in love with a lanky, russet-haired idealist from Berlin, Konrad Weiss, with whom she shares - along with other key characters - a love of languages. But their romance is curtailed by the flash of light that renders Konrad a shadow on stone and burns the birds on Hiroko's kimono into her back, a fusion of "charred silk, seared flesh".

Hiroko finds refuge in Old Delhi, in the twilight of the raj, with her dead fiancé's sister Ilse and her English husband James Burton. Befriended by the unhappy Ilse, Hiroko is more drawn to Sajjad Ali Ashraf, a dashing Muslim employee who agrees to teach her Urdu. Her hosts discourage their romance ("His world is so alien to yours"), even misinterpreting a moment of tenderness as one of predation by Sajjad. Yet the couple grow closer as partition sunders Sajjad from Delhi as shockingly as Nagasaki was lost to Hiroko.

In Karachi, the saga of the Weiss-Burtons and Tanaka-Ashrafs shifts to Hiroko and Sajjad's son Raza, a linguist given to impersonating Afghan refugees from the Soviet invasion of 1979, and James and Ilse's son Henry, a Kipling-like figure mourning a lost Indian childhood (his daughter is named Kim). As Harry Burton, Henry has transferred his idealistic allegiance to his adoptive US, becoming a covert CIA operative in cold-war Pakistan. Raza's naive bid for a kind of gap year in Afghanistan's training camps with his Afghan friend Abdullah brings adventures with gunrunners and poppy growers, but also sobering loss for the family and enduring guilt for Raza.

After Hiroko decamps to New York, disgusted by nuclear posturing between India and Pakistan, and encounters Abdullah as a taxi driver, the final section alternates between an apartment she shares with Kim, overlooking the smouldering fires of Ground Zero, and Afghanistan, where Harry and his interpreter Raza have joined forces in a private security firm. CIA backing for the mujahideen's resistance war, and abandonment of them once the Soviet army withdrew, is seen as a grim policy failure whose legacy is being reaped in "Jihadi blowback". But pivotal to the novel's final betrayals, guilt and loss is a conversation fraught with suspicion and misunderstanding between Kim and Abdullah. As Abdullah says in exasperation, "everyone just wants to tell you what they know about Islam, how they know so much more than you do, what do you know, you've just been a Muslim all your life".

Through its succession of seemingly disparate, acutely observed worlds, Burnt Shadows reveals the impact of shared histories, hinting at larger tragedies through individual loss. The two families, while watching each other's back, can also prove instrumental in each other's destruction. There are minor flaws in plotting, and occasional excesses - gorilla suits as modes of escape, or soft toys sentimentalised as road kill to make a point. But the subtlety lies in repeated patterns of allegiance and estrangement, betrayal and atonement, in the echoes between kamikaze pilots and suicide bombers, or between Ilse's alacrity in branding Sajjad as a rapist in the novel's Forsterian vignette and Kim's suspicion of Muslims after 9/11.

The final section's title, "The Speed Necessary to Replace Loss", is taken from The English Patient, a guiding spirit, though this novel begins where Michael Ondaatje's ends, with a mushroom cloud over Asia. Anita Desai's influence is also palpable, in a pre-partition Old Delhi steeped in Urdu poetry. Yet Shamsie's voice is clear and compelling, with a welcome spareness, free of the sometimes cloying archness of earlier books.

The historical threads between Nagasaki and Guantánamo are implicit, though crucial. The atomic age marked the start of the cold war, fought hot in proxy wars from Vietnam to Afghanistan, with blood spilt by the superpowers' hi-tech weaponry. As Abdullah says bitterly, "My brother died winning their Cold War." In Hiroko's view, all it takes to wipe people out without scruple is to "put them in a little corner of the big picture" - whatever the "war" in the frame. A similar logic informs a chilling conversation about interrogation techniques. "What wouldn't I do if I thought it was effective?" Harry muses. "Almost nothing. Children are out of bounds. Rape is out of bounds. But otherwise ... what works, works." Tellingly, he asks not to be quoted to his daughter.

The identity of the Guantánamo captive remains unclear till the powerful denouement, as events unfold with a malign logic whereby even a man's stooping for a cricket ball can be fatally misconstrued. Any reader anticipating a predictable yarn about the radicalisation of Islamist youth may feel cheated. Far more, I suspect, will feel challenged and enlightened, possibly provoked, and undoubtedly enriched.

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