It is also brilliant theatre. The three characters - Bohr, Heisenberg and Bohr's wife Margrethe - are on stage nearly all of the time. Notionally, they are in the Bohrs' house, with three chairs as their only props. But they grip us continually with words, tones, gestures, movement and lights. The professional magic of the Royal National Theatre, embodied in David Burke [Bohr], Sara Kestelman [Margrethe] and Matthew Marsh [Heisenberg], is mediated by the refined direction of Michael Blakemore. But Frayn's sharp, spare script is the score for an intricate contrapuntal trio, played briskly back and forth in crisp sentences that merge into a sparkling stream of conversation, confrontation and debate among three old friends.

Historically, of course, Bohr was notoriously woolly in speech, and Margrethe was probably much gentler. Sometimes Heisenberg interpolates comments into a conversation about himself from which he is supposedly absent, or Margrethe plays Greek chorus to the other two. But this is not an exercise in factitious reconstruction. In any case, they are all ghosts, trying to work out in an after-life what really happened, re-enacting various versions of that brief encounter or recalling other times together. With unostentatious skill, these chunks of memory and afterthought are woven seamlessly into the fabric of the conversation. Nothing is unclear - except what was actually said between two people in a few fateful minutes.

And that uncertainty - the physics metaphor is much used throughout - is genuine. It was a very secret, undated conversation, of which the participants gave changing and conflicting accounts in later years. On stage, the actors are as much in the dark as the many historians who have studied the two physicists' lives and times. The actors must also infer the facts from the surrounding circumstances, with only the advantage of fallible emotional memories and empathic insights. Stepping out of that frame, we see how the author has built into his drama as much as he can find out about two highly complex individuals and about the extremely tense world in which they lived. Alas for the recent death of Charles Frank (Physics World June p43), who interrogated many German scientists at the end of the Second World War and edited the "Farm Hall" transcripts, in which Heisenberg unwittingly revealed some of his thoughts when he heard of Hiroshima. Not being an expert on this subject, I can only assume that Michael Frayn has pretty fairly represented what is now publicly known.

The question is: in which of many contexts should the visit be best interpreted? The political context is obvious. But it is deeply fissured and riddled with secret caverns. Heisenberg was involved in a German nuclear weapons project. He suspected that there was a parallel Anglo-American project, and might have been fishing for information about it from Bohr. Or was he trying to tell the Americans, through Bohr, that the German project was not likely to be fruitful? Or perhaps it was just a subtle move in Heisenberg's campaign to retain control of his project inside the Nazi bureaucratic jungle.

The patriotic context seems clearer, yet makes no sense. Heisenberg was a sentimental German. His country was his beloved home: its people were his people. It must continue to shine among nations for its science, he felt. In 1941 the ultimate national disaster was not obvious. Even though Hitler was a homicidal maniac, it would probably come out all right in the end, he possibly thought. In visiting the Bohrs, Heisenberg tries clumsily to play a card of potential protection for Bohr, who is half-Jewish. They love him, but are affronted by his disregard for their Danish patriotism. Could he really have expected to enlist Bohr in the Nazi cause?

Hindsight makes the immediate scientific context too credible. Was a Uranium-235 fission bomb feasible? Conveniently for his conscience, Heisenberg had grossly overestimated the required critical mass of such a bomb, and was only trying to build a power reactor. But even if Bohr would not help directly, his confirmation of the estimate would have been reassuring. Indeed, in retrospect, one can imagine a fearful alternative universe opening up, in which Bohr suggests to Heisenberg that he should check his calculation, the Germans make the bomb, and eventually London replaces Hiroshima as the first nuked city.

All physicists know of the communal context. Just fifteen years earlier, Bohr and Heisenberg had tirelessly walked and talked themselves into the "Copenhagen interpretation" of quantum mechanics. Advised by Balazs Gyorffy, formerly professor of theoretical physics at Bristol University, Frayn has made a witty attempt to present this in lay terms, although I cannot guess how successfully. The main point is that Bohr and Heisenberg were at the centre of a truly international "invisible college" in which the new theoretical physics was being created. Perhaps Heisenberg was moved by the fragmentation of that community under the hammers of anti-Semitism and war, and was seeking vaguely to regenerate it.

It could be, of course, that Heisenberg, who had worked as a brilliant young man with Bohr back in the 1920s, has returned years later to show himself off to his former patron as a power in the great world. I doubt it. Certainly, the intellectual rivalry with Schrödinger spilled into their professional careers, but that was all past. Much more likely was a deeper personal context, in which Bohr plays father figure to the clever but insecure younger man. Was Heisenberg desperately seeking moral reassurance? Was he asking for absolution for the sin of plunging pure physics into the pitchpot of war? But then, didn't he realize that there could be no forgiveness for putting the diabolic power of the atom into human hands, especially the hands of such demons as the Hitler gang? Did even Niels Bohr understand then what is now all too clear?

It is impossible to answer these questions, for nobody can know what happened that evening in Copenhagen. The contexts and dimensions are too complex and contradictory. But these are also the contexts and dimensions of the great world of physics. They can no more be reconciled or resolved in the large than in the small. Copenhagen rehearses in microcosm the indeterminacy of all our lives and works. It is a fable for our times, a Greek tragedy where fate itself is shrouded in mystery and uncertainty. Go and see it, for sure.

Copenhagen is on at the Royal National Theatre in London and at the Playhouse in Oxford at various dates until September. Further details are available from the RNT box office (tel. +44 (0)171 452 3000; http://www.nt-online.org)