This curious little book is a coda to Michael Frayn's successful play Copenhagen, in which his current co-author David Burke played the Danish atomic physicist Niels Bohr. The play explored the mystery of the German physicist Werner Heisenberg's visit to Niels Bohr in Copenhagen in 1941, at a time when the two men's countries were at war. We know the visit marked the end of the friendship between Bohr and Heisenberg, but we do not know why, though Heisenberg's role in the Nazi attempt to make an atom bomb was a crucial factor. Copenhagen shows both the difficulties in filling lacunae in history, and the force of our compulsion to do so.

Celia's Secret reads like a fictional jeu d'esprit on similar themes—except that its authors tell us it is a true story which happened during the first West End run of the play. Celia Rhys-Evans, a woman who had just seen it, sent Frayn some scraps of dingy yellow paper which had once been hidden under the floorboards of Home Farm, the British farm where a group of physicists, including Heisenberg, was interned and monitored by British intelligence after the war. Though Frayn's patient efforts only seem to reveal fractured instructions in German for making a table-tennis table, he is instantly hooked on the possible light to be thrown on his play's protagonists, and begins a regular correspondence with Celia, who feeds him, a page or two at a time, more of the “German bumf” she claims her children found when the family lived at Home Farm. The more implausible the scraps seem, the more ingenious become the interpretations Frayn excitedly foists on anyone who will listen, particularly the cast of Copenhagen.

Eventually, Matthew Marsh, the actor who plays Heisenberg opposite David Burke's Niels Bohr, pitying Frayn's credulity, blows the gaff—“Celia Rhys-Evans” is in fact being impersonated by David Burke. Frayn feels “the hot burn of shame”.

The rest of the book is taken up by a return match, as Frayn, unable to confront Burke directly without implicating Marsh, tries to flush him out with various forgeries of his own, such as a frightening and very funny letter from the Ministry of Defence ordering Celia Rhys-Evans to surrender the “unauthorized” documents forthwith under threat of “a maximum of two years' imprisonment and/or an unlimited fine”. A “jokaholic”'s stalemate is reached, and Frayn nearly despairs: “Perhaps the rest of our lives was going to be spent like this.” At last, Burke throws in the towel.

What is really going on here? Frayn raises the possibility with the reader that the whole narrative is a spoof—“The joke was on you all the time”—only to dismiss it. “It's all fact! Honestly! Believe me!” I believe him. If the story is true, Celia's Secret is a better book, telling us chastening truths about the gullibility of clever men and demonstrating the extraordinary lengths to which practical jokers will go in what is at bottom an act of aggression—making a fool of someone else. (One can just about understand why an actor, forced to dance to the writer's tune every night for an arduous West End run, might want to take this kind of protracted revenge; Frayn airbrushes out any element of natural annoyance or tit-for-tat in his own response. Unlike Heisenberg and Bohr, the two men ended up still friends.)

Reviewers have speculated that the whole story is invented. Granted, the short sentences and flexible speech-rhythms of the two alternating narrators are worryingly similar; has Burke unconsciously assimilated the fluid intimacy of Frayn's style? As Heisenberg says in Copenhagen, “our minds shift endlessly back and forth between the two approaches”.

However, Michael Frayn was fastidious in his approach to historical truth in Copenhagen, and would surely not now waste what he has called “this most precious meanwhile” on hoaxing the public.