“… that final core of uncertainty at the heart of things” are the concluding words of Michael Frayan’s play, Copenhagen. by reflecting on the play and on the implications of Heisenberg’s uncertainty principle we consider the notion of uncertainty as product of enlightenment rationality in particular and of modern society in general. Or is Frayn saying that uncertainty lies at the centre of all human existence?
‘MARGRETHE Some questions remain long after their owners have died. Lingering like ghosts. Looking for the answer they never found in life.
BOHR Some questions have no answers to find.’
This statement is so true… How many times have we found ourselves asking questions for which no answer could be found? Questions like ‘where does the Universe end’? And how frustrating it can be when we realize that most likely we will never find an answer. Some questions go beyond our reason. Then again, is not a question something that we can find an answer for? If it is so, then, ‘where does the Universe end’ is not even a question… it is just a words-game, some silly game, maybe, that humans, superior to animals in that they can articulate their thoughts and make choices that go beyond instinct, are able to play… language, philosophy of language…
“HEISENBERG …I came to Copenhagen simply because I did think of it. A million things we might do or might not do every day. A million decisions that make themselves.” (p. 77) Everything is then put into doubt; we discover our limits, that things can go beyond our power, and everything becomes uncertain… “HEISENBERG …the Universe exists only as a series of approximations. Only within the limits determined by our relationship with it. Only through the understanding lodged inside the human head.” (p. 72) Michael Frayn’s Copenhagen is a play that deals with all this, with uncertainty: in ethics, in the way we make choices, in our regrets, in our relationships, in science… ‘Once upon a time’, there was Galileo, who believed in empirical evidence, in what we can see and demonstrate that it is there, abandoning the Church and morality. It was the sunrise of Modernity. The power of reason grew stronger and stronger, and science with it (Newton!)… it was Enlightenment.
In the 19th Century, after the French Revolution, things started changing. The belief in science was still strong, but different voices started speaking out against certain systems. Shelley warned of possible outcomes of science (Frankenstein…), Marx criticized firmly the capitalist society, a society based on the production of capital, Nietzsche claimed that society was becoming more and more decadent, and people were forgetting what the true inner forces of life were. The beginning of the 20th Century saw amazing technological development, in a world that was taking huge steps towards globalization. But where did this ‘enlightened’ development take us? The first half of the 20th Century has been one of the worst periods in human history: the imposition of certain ideologies caused the death of millions and millions of people all across the world, and mainly in the so-called ‘West’. Why? How was this possible? Were we not the sons of ‘Enlightenment’? Uncertainty… Heisenberg was one of those people who had to deal with this issue, with what Shelley warned us about.
The atomic bomb became one of the main scientific expressions of how far atrocity can go, in the name of development, peace (how ironic is that…), and civilazation. Heisenberg was a physicist. The main discoveries in this field that took place in the first half of the 19th Century regard the structure of atoms. Scientists had to hypothesize that as far as the study of atoms is concerned, the Newtonian and classical physics’ laws are not good enough anymore, in that it is not possible anymore through them to reach a satisfactory description of atoms’ motus and their components.
Two ‘theories’ followed these considerations: Quantum Theory and Heisenberg’s Uncertainty Principle. The revolutionary idea here is that energy is not something continuos and indefinitely divisible, but it exists in nature uniquely in a minimum ‘package’, or in multiples of it. More specifically: “Classically, i.e., in our macroscopic world, I can measure these two quantities to infinite precision (more or less). There is really no question where something is and what its momentum is. In the Quantum Mechanical world, the idea that we can measure things exactly breaks down. Let me state this notion more precisely. Suppose a particle has momentum p and a position x. In a Quantum Mechanical world, I would not be able to measure p and x precisely.
There is an uncertainty associated with each measurement, e.g., there is some dp and dx, which I can never get rid of even in a perfect experiment!!!. This is due to the fact that whenever I make a measurement, I must disturb the system. (In order for me to know something is there, I must bump into it.) This uncertainty leads to many strange things. For example, in a Quantum Mechanical world, I cannot predict where a particle will be with 100 % certainty. I can only speak in terms of probabilities. For example, I can say that an atom will be at some location with a 99 % probability, but there will be a 1 % probability it will be somewhere else (in fact, there will be a small but finite probability that it will be found across the Universe). This is strange. We do not know if this indeterminism is actually the way the Universe works because the theory of Quantum Mechanics is probably incomplete. That is, we do not know if the Universe actually behaves in a probabilistic manner (there are many possible paths a particle can follow and the observed path is chosen probabilistically) or if the Universe is deterministic in the sense that I can predict the path a particle will follow with 100 % certainty.”
Quantum physics confirms the existence of harmonies that are independent of us. They lie on the noumenal side of the map. This is a new great insight on the Universe: “HEISENBERG …I show him the strangest truth about the Universe that any of us has stumbled on since relativity- that you can never know everything about the whereabouts of a particle, or anything else, even Bohr now, as he prowls up and down the room in that maddening way of his, because we can’t observe it without introducing some new element into the situation, a molecule of water vapour for it to hit, or a piece of light…” (p. 67) Another useful example to understand uncertainty is the one of Shrodinger’s cat: a cat is put in a box, subject to radiations. Is the cat dead or alive? Both, dead and alive, or dead, or alive, or neither dead nor alive. Until we open the box. The implications of this have been huge. In his beautifully written play, Frayn is able to do so that all throughout it a general sense of uncertainty dominates.
The characters of the play (Heisenberg, Bohr and Margrethe) never seem to be really sure of anything. Why did Heisenberg go to Copenhagen? Who is responsible for the atomic bomb? Was that ‘good’ or ‘bad’? The closest we get to the answer to why Heisenberg went to Copenhagen is: “HEISENBERG Bohr, I have to know! I am the one who has to decide. If the Allies are building a bomb, what am I choosing for my country? ” (p. 42) Heisenberg found himself in a position where none of us would probably want to find themselves: on which side of the fence to stand. A big dilemma: Germany, the people’s good, or science? The ideal situation for him would probably be the one of ‘complementarity’, another important factor in physics, and something that very well describes Heisenberg’s condition at the time. And the condition of most of us, if not all of us…are we not ‘one, none, 100.000’ (to use Pirandello’s brilliant sentence)? “HEISENBERG Most interesting. So interesting that it never even occurred to you. Complementarity, once again. I’m your enemy; I’m also your friend. I’m a danger to mankind; I’m also your guest. I’m a particle; I’m also a wave. We have one set of obligations to the world in general, and we have other sets, never to be reconciled, to our fellow-countrymen, to our neighbours, to our friends, to our family, to our children. We have to go through not two slits at the same time, but twenty-two. All we can do is to look afterwards, and see what happened.” (p. 78)
It seems that we have only one certainty left: that everything is uncertain. “Whether something is “to be or not to be” is in part up to us.” Only in part. In a way, therefore, uncertainty does seem to lie at the centre of things, and of human existence. “The Periodic Table of Elements is grounded on an a priori ontological realm of pre-established harmonies. Here is what Max Planck had to say about this quantum business in 1933: ‘sensory perceptions do not of themselves create the physical world around us they bring news of another world which lies outside of ours and is entirely independent of us. . . . the external world forces itself upon our recognition with its own elemental power . . . measurements . . . give no direct information about external reality. They are only a register or representation of reactions to physical phenomena. As such they contain no explicit information and have to be interpreted.
As Helmholtz said, measurements furnish the physicist with a sign which he must interpret . . .’ Just as Shakespeare does not appear in his scenes, quanta are not directly visible in phenomena, yet are responsible for them. Between Shakespeare’s lines one can imagine him winking, laughing and sighing. Behind the scenes of our daily life there is an unseeable realm (a Dirac Sea) ruled in part by quantum physics. ‘The whole body like a chaos capable of any form that the next daring spirit shall brood upon it.’ The classical observables reign and show off, while the quantum physics does the actual governing.”
I would now want to go through some of the ‘uncertainties’ represented in the book. We talked about it when we studied the ‘Terror’ of the French Revolution: is that where the ‘liberating’ Enlightenment thoughts and ideas were supposed to take humanity? And we can ask this question again, in regard to the atomic bomb. Reality or dream? “HEISENBERG … I refused to believe it, when I first heard the news of Hiroshima. I though that it was just one of the strange dreams we were living in at that time.” (p. 45) Un-imaginable the effects those news must have had on that Manhattan Project Team and, in general, the people who worked on nuclear fission… “HEISENBERG Otto Hahn wants to kill himself, because it was he who discovered fission, and he can see the blood on his hands.” (p. 46) On the role of Heisenberg in the matter, Frayn (in the postscript to his play) says: “Some of the evidence undoubtedly appears to support Powers’s thesis in its stronger form, that Heisenberg deliberately sabotaged the project.” (p. 112)
Also, there is great uncertainty in personal relationships. “BOHR We must try to go on behaving like human beings.” (p. 13) But what is that like? Can Heisenberg count on anyone? Uncertainty…people love, and hate, and love, and hate… “MARGRETHE Silence again. Those first brief sparks have disappeared, and the ashes have become very cold indeed. So now of course I’m starting to feel almost sorry for him. Sitting here all on his own in the midst of people who hate him, all on his own against the two of us.” (p. 16) All of them were suffering of perhaps the worst uncertainty people could have: the one that lies between life and death. “HEISENBERG Perhaps, when this war is over… If we’re all spared… Goodbye.” (p. 32)
To support my earlier argument that in the end, for the way things ‘are’ and we learn about them, language plays a main role, in the postscript to the play Frayn writes (referring to the authenticity of the dialogues): “…he hopes ‘to demonstrate that science is rooted in conversations’. But, as he [Heisenberg] explains, conversations, even real conversations, cannot be reconstructed literally several decades later. So he freely reinvents them, and appeals in his turn to Thucydides. […] Thucydides explain in his preface to the History of the Peloponnesian War that, although he had avoided all ‘storytelling’, when it came to the speeches, ‘I have found it impossible to remember their exact wording. Hence I have made each orator speak as, in my opinion, he would have done in the circumstances, but keeping as close as I could to the train of thought that guided his actual speech.’ […] the only way into the protagonists’ head is through the imagination.
This indeed is the substance of the play.” (p. 97) Having said that, let us consider some manifestations of uncertainty in the ‘arts’ of the 20th Century, the general background that influenced and was influenced by, in some sort of dialectical way, the Uncertainty Principle. The general scenario that I would draw on is the following. From the second half of the 19th Century, the study of natural phenomena took the direction of the study of the ‘micro’, e.g., Pasteur in biology defined the existence of micro-organisms as pathogenic agents for diseases. In Physics, particular attention is given to the concept of thermodynamics. Sociology and Anthropology start becoming well-grounded ‘sciences’, exploring also remote and unknown cultures of, for example, the Pacific Ocean. To the eyes of our ‘ancestors’, the situation transformed from one in which they dealt with ‘macroscopic’ objects whose relations were represented by precise mechanical laws (from Newton to Laplace, etc.) into one where every single object slowly starts to un-structure and take up the characteristic of an interlacement of probabilities. We got to the atom, and we looked at particles not in a traditional way anymore, but as probabilistic waves. Philosophy ceases to deal with its traditional concepts and becomes Analysis of Language. Music is un-structured and takes up the forms of Dodecaphony.
In literature, the ‘falling apart’ starts off with the ‘stream of consciousness’ to then take the form of the Nouveau Roman. In painting and sculpture, Cubism, Dadaism and Futurism can also be seen as expressing a revolutionary idea of ‘movement’, so that the artists tries to represent the movement, because everything is constantly moving…is this not what Heisenberg was saying? It is not possible to say with total precision where something is. The result is, once more: uncertainty. “MARGRETHE That was the last and greatest demand that Heisenberg on his friendship with you. To be understood when he couldn’t understand himself. And that was the last and greatest act of friendship for Heisenberg that you performed in return. To leave him misunderstood.” (p. 89) Is sometimes better not to know? “If, if, if… The line of ifs is a long one. It remains just possible, though. The effects of real enthusiasm and real determination are incalculable. In the realm of the just possible they are sometimes decisive.” (p. 129)
 Frayn, M. (1998) Copenhagen. London, Methuen Drama, p. 3. From now on, the page reference will appear in brackets after the quote.
 www.britannica.com on Heisenberg’s Uncertainty Principle.
 www.britannica.com on Heisenberg.