Copenhagen

by Michael Frayn

  Cassidy does not explore the parallel further. Powers even appends a footnote to his comment: ‘Forgive me.’ The apology seems to me unnecessary. It’s true that the concept of uncertainty is one of those scientific notions that has become common coinage, and generalised to the point of losing much of its original meaning. The idea as introduced by Heisenberg into quantum mechanics was precise and technical. It didn’t suggest that everything about the behaviour of particles was unknowable, or hazy. What it limited was the simultaneous measurement of ‘canonically conjugate variables’, such as position and momentum, or energy and time. The more precisely you measure one variable, it said, the less precise your measurement of the related variable can be; and this ratio, the uncertainty relationship, is itself precisely formulable.

  None of this, plainly, applies directly to our observations of thought and intention. Thoughts are not locatable by pairs of conjugate variables, so there can be no question of a ratio of precision. Powers seems to imply that in Heisenberg’s case the uncertainty arises purely because ‘questions of motive and intention cannot be established more clearly than he was willing to state them.’ It’s true that Heisenberg was under contradictory pressures after the war which made it particularly difficult for him to explain what he had been trying to do. He wanted to distance himself from the Nazis, but he didn’t want to suggest that he had been a traitor. He was reluctant to claim to his fellow-Germans that he had deliberately lost them the war, but he was no less reluctant to suggest that he had failed them simply out of incompetence.

  But the uncertainty surely begins long before the point where Heisenberg might have offered an explanation. He was under at least as many contradictory pressures at the time to shape the actions he later failed to explain, and the uncertainty would still have existed, for us and for him, even if he had been as open, honest, and helpful as it is humanly possible to be. What people say about their own motives and intentions, even when they are not caught in the traps that entangled Heisenberg, is always subject to question—as subject to question as what anybody else says about them. Thoughts and intentions, even one’s own—perhaps one’s own most of all—remain shifting and elusive. There is not one single thought or intention of any sort that can ever be precisely established.

  What the uncertainty of thoughts does have in common with the uncertainty of particles is that the difficulty is not just a practical one, but a systematic limitation which cannot even in theory be circumvented. It is patently not resolved by the efforts of psychologists and psycho-analysts, and it will not be resolved by neurologists, either, even when everything is known about the structure and workings of the brain, any more than semantic questions can be resolved by looking at the machine code of a computer. And since, according to the so-called ‘Copenhagen Interpretation’ of quantum mechanics—the interconnected set of theories that was developed by Heisenberg, Bohr, and others in the twenties—the whole possibility of saying or thinking anything about the world, even the most apparently objective, abstract aspects of it studied by the natural sciences, depends upon human observation, and is subject to the limitations which the human mind imposes, this uncertainty in our thinking is also fundamental to the nature of the world.

  ‘Uncertainty’ is not a very satisfactory word to come at this. It sits awkwardly even in its original context. You can be uncertain about things which are themselves entirely definite, and about which you could be entirely certain if you were simply better informed. Indeed, the very idea of uncertainty seems to imply the possibility of certainty. Heisenberg and Bohr used several different German words in different contexts. Bohr (who spoke more or less perfect German) sometimes referred to Unsicherheit, which means quite simply unsureness. In Heisenberg’s original paper he talks about Ungenauigkeit—inexactness—and the most usual term now in German seems to be Unschärfe—blurredness or fuzziness. But the word he adopts in his general conclusion, and which he uses when he refers back to the period later in his memoirs, is Unbestimmtheit, for which it’s harder to find a satisfactory English equivalent. Although it means uncertainty in the sense of vagueness, it’s plainly derived from bestimmen, to determine or to ascertain. This is reflected better in the other English translation which is sometimes used, but which seems to be less familiar: indeterminacy. ‘Undeterminedness’ would be closer still, though clumsy. Less close to the German, but even closer to the reality of the situation, would be ‘indeterminability’.

  Questions of translation apart, Heisenberg’s choice of word suggests that, at the time he wrote his paper, he had not fully grasped the metaphysical implications of what he was saying. Indeed, he concludes that the experiments concerned are affected by Unbestimmtheit ‘purely empirically.’ He was not, as Bohr complained, at that time greatly interested in the philosophical fallout from physics and mathematics (though he became much more so later on in life), and he was publishing in a hurry, as Bohr also complained, before he had had a chance to discuss the work with either Bohr or anyone else. His paper seems to imply that electrons have definite orbits, even if these are unknowable; he talks about a quantum of light completely throwing the electron out of its ‘orbit’, even though he puts the word into inverted commas, and says that it has no rational sense here. The tide of the paper itself reinforces this impression: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Again there are translation problems. ‘Anschaulich’ means graphic, concrete, ‘look-at-able’; the tide is usually translated as referring to the ‘perceptual’ content of the disciplines concerned, which again seems to suggest a contrast with their unperceived aspects—as if Heisenberg were concerned merely about our difficulties in visualising abstractions, not about the physical implications of this.

  *

  The Copenhagen Interpretation of quantum mechanics has been scientific orthodoxy for most of this century, and is the theoretical basis (for better or worse) on which the century’s dramatic physical demonstrations of nuclear forces have been constructed. But it has not gone unchallenged. Einstein never accepted it, though he could never find a way round it. The mathematician Roger Penrose regards the present state of quantum theory as ‘provisional’, and quotes Schrödinger, de Broglie, and Dirac as forerunners in this view.

  An alternative to the Copenhagen Interpretation, explaining the apparent superimposition of different states that appears at the quantum level in terms of a multiplicity of parallel worlds, was developed after the Second World War by Hugh Everett III, who had been a graduate student of John Wheeler, Bohr’s associate in the famous paper which opened the way to an understanding of uranium fission. David Deutsch, who proposes an extreme version of Everett’s ideas in his book The Fabric of Reality, claims that ‘hardly anyone’ still believes in the Copenhagen Interpretation. I have put this view to a number of physicists. They all seemed greatly surprised by it; but maybe I have hit upon precisely the supposed handful who remain in the faith.

  Another follower of Everett (though he seems to differ quite sharply from Deutsch) is Murray Gell-Mann, who with Yuval Ne’eman revolutionised elementary particle theory in the sixties with the introduction of the quark, in its three different ‘colours’ and six different ‘flavours’, as the fundamental unit of the material world. Gell-Mann believes that quantum mechanics is the fundamental tool for understanding the universe, but he sees the Copenhagen Interpretation, with its dependence upon an observer and the human act of measurement, as anthropocentric, and as characterizing merely a special case that he calls ‘the approximate quantum mechanics of measured systems.’ I hesitate to express any reservations about something I understand so little, particularly when it comes from such an authority, but it seems to me that the view which Gell-Mann favours, and which involves what he calls alternative ‘histories’ or ‘narratives’, is precisely as anthropocentric as Bohr’s, since histories and narratives are not freestanding elements of the universe, but human constructs as subjective and as restricted in their viewpoint as the act of
observation.

  The relevance of indeterminacy to quantum mechanics has also been challenged. A version of the famous thought experiment involving two slits has now actually been carried out in the laboratory (at the University of Konstanz). It confirms, as Bohr hypothesised, that while an unobserved particle seems to pass through both slits, so that it forms a characteristic interference pattern on a screen beyond them, any act of observation that attempts to determine which of the two paths the particle actually follows necessarily destroys the phenomenon, so that the interference pattern vanishes. But the experiment appears to suggest that, although the uncertainty principle is true, it accounts for discrepancies far too small to explain the loss of interference. The observation in the laboratory experiment, moreover, was carried out not, as in the old thought experiment, by hitting the particle involved with a photon, which transfers part of its energy to the particle and so alters its path, but by a way of marking with microwaves which has almost no effect on the particle’s momentum.

  Some physicists now accept that the loss of interference is caused by a much stranger and less quasi-classical aspect of the quantum world—entanglement. The notion was introduced by Schrödinger in 1935, and suggests that where quantum-mechanical entities become involved with each other (as with the particle and the photon), they form states of affairs which continue to have a collective identity and behaviour, even though their components have physically separated again. The difficulties in this are obvious, but there is no interpretation of quantum-mechanical phenomena that does not involve breathtaking challenges to the logic of our everyday experience.

  For the references to all these developments see the bibliography at the end of this Postscript.

  *

  What about my characters? Are they anything like their originals?

  It’s impossible to catch the exact tone of voice of people one never knew, with only the written record to go on, especially when most of what their contemporaries recall them as saying was originally said in other languages. There are also more particular problems with all three of my protagonists.

  Bohr, for a start, was as notorious for his inarticulacy and inaudibility as he was famous for his goodness and lovability. He was fluent in various languages, but I have heard it said that the problem was to know which language he was being fluent in. Schrödinger, after his epic confrontation with Bohr in 1926, described him as often talking ‘for minutes almost in a dreamlike, visionary and really quite unclear manner, partly because he is so full of consideration and constantly hesitates—fearing that the other might take a statement of his [Bohr’s] point of view as an insufficient appreciation of the other’s …’ My Bohr is necessarily a little more coherent than this—and I have been told by various correspondents who knew him that in private, if not in public, he could be much more cogent and incisive than Schrödinger evidently found him.

  The problem with Margrethe is that there is relatively little biographical material to go on. She and Niels were plainly mutually devoted, and everything suggests that she was as generally loved as he was. She had no scientific training, but Bohr constantly discussed his work with her, presumably avoiding technical language—though she must have become fairly familiar with even that since she typed out each draft of his papers. I suspect she was more gracious and reserved than she appears here, but she plainly had great firmness of character—in later life she was known as Dronning (Queen) Margrethe. She was always cooler about Heisenberg than Bohr was, and she was openly angry about his visit in 1941. According to Bohr she objected strongly to his being invited to the house, and relented only when Bohr promised to avoid politics and restrict the conversation to physics. Bohr himself always refused to be drawn about Heisenberg’s trip in 1941, but she insisted, even after the war, even after all Heisenberg’s attempts to explain, ‘No matter what anyone says, that was a hostile visit.’

  The problem with Heisenberg is his elusiveness and ambiguity, which is of course what the play is attempting to elucidate. The one thing about him that everyone agreed upon was what Max Born, his mentor in Göttingen, called ‘his unbelievable quickness and precision of understanding.’ The contrast with Bohr is almost comic. ‘Probably [Bohr’s] most characteristic property,’ according to George Gamow, ‘was the slowness of his thinking and comprehension.’

  As a young man Heisenberg seems to have had an appealing eagerness and directness. Born described him as looking like a simple farm boy, with clear bright eyes, and a radiant expression on his face. Somebody else thought he looked ‘like a bright carpenter’s apprentice just returned from technical school.’ Victor Weisskopf says that he made friends easily, and that everyone liked him. Bohr, after their first meeting in 1922, was delighted by Heisenberg’s ‘nice shy nature, his good temper, his eagerness and his enthusiasm.’ There was something about him of the prize-winning student, who is good at everything required of him, and Bohr was not the only father-figure to whom he appealed. He had a somewhat similar relationship to Sommerfeld, his first professor in Munich, and in his difficulties with the Nazis he turned to two elders of German physics for counsel, Max Planck and Max von Laue. His closest friend and colleague was probably Carl Friedrich von Weizsäcker, who was younger than him, but it is striking that during his internment the person he chose to confide his explanation of the Hiroshima bomb to was not Weizsäcker, who was interned with him (although he may well have discussed it with him already), but the 66-year-old Otto Hahn.

  The American physicist Jeremy Bernstein says that ‘he had the first truly quantum-mechanical mind—the ability to take the leap beyond the classical visualizing pictures into the abstract, all-but-impossible-to-vizualise world of the subatomic …’ Cassidy believes that a great part of his genius was his ‘ability to adopt a serviceable solution regardless of accepted wisdom.’ Rudolf Peierls stresses his intuition. He would ‘almost always intuitively know the answer to a problem, then look for a mathematical solution to give it to him.’ The obverse of this, according to Peierls, is that ‘he was always very casual about numbers’—a weakness that seems to have contributed to his downfall—or his salvation—in the atomic bomb programme.

  Margrethe always found him difficult, closed, and oversensitive, and this propensity to be withdrawn and inturned was exacerbated as life went on—first by his political problems in the thirties, and then by his efforts to reconcile the moral irreconcilables of his wartime work. His autobiographical writing is rather stiff and formal, and his letters to Bohr, even during the twenties and thirties, are correct rather than intimate. Throughout the period of their closest friendship they addressed each other with the formal Sie, and switched to du only when Heisenberg also had a chair.

  The conversations that Heisenberg claimed such freedom to recreate in his memoirs are stately. Much more plausibly colloquial is the transcript of David living’s long interview with him for The Virus House, living’s history of the German bomb programme, though he is still (naturally) watchful. In the transcripts of the relatively unguarded conversations that the German atomic team had among themselves during their internment, where Heisenberg emerges as the dominant figure, both morally and practically, a certain hard-headed worldliness can be detected. He is much concerned with professional prospects, and with how they might make some money out of their wartime researches. When one of the others says that if they agree to work on atomic matters under Allied control they will be looked down upon as traitors ‘in the eyes of the masses’, Heisenberg replies: ‘No. One must do that cleverly. As far as the masses are concerned it will look as though we unfortunately have to continue our scientific work under the wicked Anglo-Saxon control, and that we can do nothing about it. We will have to appear to accept this control with fury and gnashing of teeth.’

  There was always something a little sharp and harsh about him, something that at its best inspired respect rather than love, and that after the war occasioned really quite astonishing hostility and contempt. Even Samuel Goudsmit turned again
st him. Goudsmit was an old friend and colleague; when the investigators of the Alsos mission, the Allied agency for gathering intelligence on German atomic research, for which he was working, finally broke into Heisenberg’s office in 1945, one of the first things they saw was a picture of the two of them together that Heisenberg had kept there as a memento of happier days. But when Goudsmit subsequently interrogated Heisenberg he found him arrogant and self-involved. Goudsmit had understandably bitter feelings at the time—he had just discovered the record of his parents’ death in Auschwitz. Heisenberg was also caught in a false position. Confident that his team had been far ahead of the Americans, he offered Goudsmit his services in initiating them into the secrets of uranium fission. (Goudsmit did nothing to correct his misapprehension, which gave Heisenberg, when the truth finally came out, grounds for returning Goudsmit’s bitterness.) In his superficial and strangely unimpressive book on Alsos, Goudsmit wrote about Heisenberg and his team with contemptuous dismissal, and in the year-long correspondence in the American press that followed its publication, accused him of self-importance and dishonesty.