– W.E.B. DuBois
Schrödinger’s work was greeted with not just skepticism but hostility from Heisenberg and other supporters of matrix mechanics, who revealed what Mara Beller called ‘a dogmatic preference for older conceptions rather than a dispassionate objectivity’, and who were all the more annoyed because of the beauty and simplicity of Schrödinger’s approach compared to the ungainly and complex matrix methods.1 Schrödinger, meanwhile, made no secret of his scorn for matrix mechanics. The formation of quantum mechanics, indeed, was a remarkable episode in the history of science in the way hostile emotions flared in private, and even formal published papers are marked by an ‘unusually emotional undertone.’2 Envy, rivalry, anger, disbelief, conviction, stress, hope, despair, dejection – all can be found in the documents. Yet the existence of this emotional undercurrent to scientific research is omitted from most historical accounts.
Most histories of science run something like this: An unexpected discovery is made. Explanations are applied, but none work well. New equipment is built to make new measurements, but the explanation is still incomplete. The phenomenon is looked at from yet another side, with other instruments and measurements. And so on.
This is what might be called the ‘standard model’ of how science works. It emphasizes the collective and impersonal dimension, and downplays the experiences of specific individuals. The principal structural ingredients are discoveries, instruments, measurements, and theories. It is allied with a conception of science as a way of eradicating mysteries and controlling nature. Its familiarity often leads scientists to tell their own stories in ways that emphasize these ingredients, reinforcing the standard model. In this model, it’s as if the emotional life and experiences, personal successes and disappointments, and so forth, of the person comprised a train running down one track, and the scientific career – the research program, discoveries, events, and so forth – running down another track. And the two tracks are entirely separate, driven by different kinds of locomotives – two sides of one person.
But listen carefully to the scientists speaking about their work – as some popular biographies do – and you can hear another story as well, highlighting human experience. In it, motivating forces include excitement at the discovery, puzzlement at why the explanations do not work, curiosity about what might explain it, growing perplexity as more explanations do not work, imagination at devising new instruments, and wonder as the explanations shed a different kind of light than thought at the outset, even awe at learning something fundamental. As these more fully integrated pictures of science in process show, the standard model has limits, there is something beyond it, and it is ultimately destined to be superceded. It is due to be succeeded by a program of grand unification, in which these two tracks are seen to be merged, in which science is done by individuals, not dividuals, whose life and work are part and parcel of the same person.
To see what I mean, look at the collection of Richard Feynman’s letters published a few years ago. In them, you see Feynman’s character, poses and all, as inextricably intertwined with his craft. You see that his curiosity, presumption, haranguing, and desire to set people straight were seamlessly interwoven – that the physicist and educator and his character cannot be disentangled. The same force fueled both his scientific inquiries and his interactions with others. ‘The real fun of life’, he wrote, ‘is this perpetual testing to realize how far out you can go with any potentialities.’ And you see this testing in the way he dealt with cranks, editors, ordinary people, and with nature. This provides a taste, I think, of what lies beyond the standard model.
We can also see this grand unification in Einstein. Here science historian Gerald Holton has written a good article called ‘Einstein’s Third Paradise.’ Einstein’s ‘first paradise’ refers to the intensely religious phase Einstein went through in childhood – a period of ‘the religious paradise of youth’, he called it. This phase is well attested to by Einstein himself, and by his sister Maja. This paradise ended when he was about twelve, after reading popular science books that revealed to him that not all the biblical stories could be true. He also discovered the joys of Euclidean plane geometry after being given a little book on it – he called the book ‘holy’, and a ‘wonder.’ He became acquainted with other works of science that presented nature as ‘a great, eternal riddle’, contemplation of which could give him ‘inner freedom and security.’ He called this, too, a ‘Paradise.’ Breaking away from the first paradise to enter the second paradise, he wrote, was an attempt to ‘free myself from the chains of the ‘merely personal’, from an existence dominated by wishes, hopes, and primitive feelings.’
Biographers have tended to contrast these two paradises, deeming them two separate, disconnected phases of his life, from a religious to a nonreligious phase. But Holton disagrees. At the heart of Einstein’s mature identity Holton sees a fusion of the first and second paradises, ‘where the meaning of a life of brilliant scientific activity drew on the remnants of his fervent first feelings of youthful religiosity.’
In this third paradise, Einstein seems to exemplify someone who had feelings that we can call religious and that were essential to his work but who did not credit the existence of a Master Mechanic. As he says in one letter, he was a ‘deeply religious unbeliever.’ This third paradise, then, is the kind of thing that would be described in what I called the grand unification. Consider Einstein’s speech honoring the sixtieth birthday of Max Planck. In it, Einstein said the search for a simplified, lucid image of the world was not only a scientific goal, but corresponded to a deep psychological need. A scientist could make the effort to pursue this goal the ‘centre of gravity of his emotional life.’ And, Einstein added, pursuing the most difficult scientific problems requires ‘a state of feeling similar to that of a religious person or a lover.’ Holton then mentions instances by Einstein and others in which they were brought to great despair, or great joy, by developments in science, in which the psychological commitment of these people cannot be treated as separate from the tasks they set for themselves. The science and the personal commitment are bound up with each other. Holton treats Einstein’s drive to unify apparently different phenomena as an example of this interpenetration of emotional life and career. He points to a letter to Grossmann in 1901, referring to his very first paper, on capillarity, which unifies opposing behaviours of bodies. ‘It is a wonderful feeling’, Einstein wrote (echoing Kant), ‘to recognize the unity of a complex of appearances which, in direct sense experiences, appear to be quite separate things.’ And in another letter, 15 years later, Einstein says that he is ‘driven by my need to generalize.’ Holton points out that, practically, too, ‘Einstein lived under the compulsion to unify.’ He loathed nationalisms, and dreamed of a unified world government. Holton sums up: ‘No boundaries, no barriers: none in life, as there are none in nature. Einstein’s life and his work were so mutually resonant that we recognize both to have been carried on together in the service of one grand project – the fusion into one coherency.’ Likewise, Holton says, ‘there were no boundaries or barriers between Einstein’s scientific and religious feelings.’ In his writings on science and religion late in life, Einstein often uses the same phrases to refer to the aims of science and religion. ‘I maintain that the cosmic religious feeling is the strongest and noblest motive for scientific research… A contemporary has said not unjustly that in this materialistic age of ours the serious scientific workers are the only profoundly religious people.’ And again, ‘The most beautiful experience we can have is the mysterious. A knowledge of the existence of something we cannot penetrate, our perceptions of the profoundest reason and the most radiant beauty, which only in their most primitive forms are accessible to our minds – it is this knowledge and this emotion that constitute true religiosity; in this sense, and in this alone, I am a deeply religious man.’ Thus in Einstein, too, we can see glimpses of what lies beyond the standard model: an account of science in which character and perso
nal feeling are not marginal to the scientific process, not a prelude to a person’s scientific labours, but what sustains them and carries them forward.
10
Living with Uncertainty:
THE HEISENBERG UNCERTAINTY PRINCIPLE
DESCRIPTION: Establishing the position of a particle in a small region of space makes its momentum uncertain, and vice versa, and the overall uncertainty is greater than or equal to a certain amount.
DISCOVERER: Werner Heisenberg
DATE: 1927
Everyone understands uncertainty. Or thinks he does.
– Werner Heisenberg character, in
Michael Frayn’s play Copenhagen
We owe many a debt to Werner Heisenberg. As one of the founders of quantum mechanics, he left a huge legacy to physics. As the inventor of the uncertainty principle, he also left a huge legacy outside physics. Albert Einstein may be more widely recognized by the public – and his theory of relativity often crops up in popular culture – but Heisenberg has had a similar far-reaching impact on public discourse and popular culture.
While most nonscientists may recognize Einstein’s equation E = mc2, generally they are aware that its effects are noticeable only in certain restricted conditions, and that its meaning is truly clear only to physicists. The same is not true of Heisenberg’s equation Δ × Δ Ρ ≥ – h/2, the Heisenberg uncertainty principle, which seems to have a spiritual meaning to the public that is at once profound and transparent. Browse through any bookshop’s new-age section, for instance, and you’ll find wild claims confidently asserted about the uncertainty principle, such as that its implications are ‘psychedelic’ and that it heralds ‘cultural revolution.’ Strange interpretations turn up even in academic circles. Consider the following conversation, published in American Theatre, between the well-known theatre director Anne Bogart and Kristin Linklater, the noted vocal coach:1
Linklater: Some thinker has said that the greatest spiritual level is insecurity.
Bogart: Heisenberg proved that. Mathematically.
Linklater: There you are.
But where are we, exactly? And how did we get here? The uncertainty principle sprang from a purely mathematical approach to atomic physics, where it has a well-defined and highly restricted scope of applicability.
The Path to Helgoland
Werner Heisenberg, son of a professor of Greek at the University of Munich, had the character one often associates with poets: dashing good looks, a physical frailty including severe vulnerability to allergies, excellent musicianship, and a sensitive and often emotional responsiveness to the world around him.2 He also had a sharp but imaginative intellect and a willingness to risk unconventional but mathematically rigorous means to fit theories to experimental data. And he had the terrific fortune to be reared amid one of the sharpest and most ruthlessly demanding scientific communities ever, whose members included Niels Bohr, Max Born, Pascual Jordan, Hendrik Kramers, and Wolfgang Pauli.
These theorists were largely distributed among three centres of research: Munich, Göttingen, and Copenhagen. Each had a distinctive character. Munich was experimentally oriented, Göttingen was a world-renowned centre of formal mathematics, and Copenhagen had a rigorous philosophical approach to the quantum world stemming from its founder and leader, Bohr. The intense and often brutally frank exchanges of this community of physicists – carried on in personal conversations as well as in letters, drafts of work in progress, and copies of published papers – kept anyone who dared participate to a high standard. Many times a thought initiated by one person was completed by another. Heisenberg, a central player, circulated among the three centres, and his insights, too, often arose in conversation.
Werner Heisenberg (1901–1976)
In July 1923, Heisenberg completed his doctoral exam at Munich, and had arranged to work under Max Born in Göttingen that fall. But Heisenberg, a supposed wunderkind, had nearly failed thanks to his almost total ignorance of experimental physics – he could not even explain how a storage battery worked – and passed only after aggressive intervention by one of his examiners. The day after the humiliating exam he showed up at Born’s door in Göttingen, unannounced and despondent, to confess to Born the embarrassing news and ask if Born still wanted him. Born was supportive, and Heisenberg left, reassured, for a summer trip he regularly took with a youth group.
This was just the time in quantum theory that historian Max Jammer described as an unruly mess, when those problems that could be solved at all were first analysed classically, then restricted by quantum conditions to obtain a few ‘allowed’ states of motion. Heisenberg, still only 21 years old, was determined to make it all rational.
He knew that classical physics had to be the starting point. ‘The concepts for quantum mechanics can only be explained by already knowing the Newtonian concepts’, he remarked much later. ‘That is, quantum theory is based upon the existence of classical physics. This is the point that Bohr emphasized so strongly – that we cannot talk about quantum physics without already having classical physics.’3
In classical physics, all events take place inside a four-dimensional space-time stage or playing field. Everything is at a specific place at any and every time. When things move from one place to another, they do so in response to definite forces and take definite paths. Classical physics mainly concerns itself with what happens when things are disturbed, and tracks which forces produce which effects. The path of each thing can be followed – and predicted – like that of a smoothly flowing stream, with the thing moving continuously and smoothly from each point to the next. Physical properties, which can all be measured, propagate smoothly and continuously through space-time in a mechanical way. Classical physics thus provides a confident ontology, or vision of what the ultimate elements of the universe are and how they interact. This kind of event is therefore anschaulich.
But a quarter-century of attempts to devise classical models of quantum phenomena had failed. Stimulated by the debates swirling in his rich intellectual environment, young Heisenberg began to wonder if that were not the problem; if the effort to construct pictures of the world inside the atom – the positions and paths of electrons, and the dimensions and frequencies of their orbits – was doomed from the start. He had heard Pauli remark that models of atomic events had ‘only a symbolic sense’ and were classical ‘analogues’ of the quantum phenomena.4 Wasn’t the lesson of Maxwell’s path to his equations that sometimes one had to abandon mechanical explanations to capture reality? Wasn’t it likely, then, that when theorists construct models based on what experimenters measure, these models are only symbols of a reality that humans cannot picture?5 Progress in science usually involves sacrifice, Heisenberg once wrote, a sacrifice that is at the cost of our claim to understand nature. What had to go, this time, Heisenberg and his colleagues thought, might be visualizability.
Heisenberg therefore decided to make a virtue of necessity by junking the attempt to produce theories that picture how atomic events unfold on a space-time stage. Drawing on the appreciation for formal structures he had acquired at Göttingen, he would seek a purely mathematical description of what experimenters actually observed: the frequencies and amplitudes of the light emitted by electrons. These descriptions would need to respect only the correspondence principle – that large quantum numbers obeyed classical laws – and certain other constraints such as the conservation of energy. But there would be no need to have measurable properties or continuously propagating functions; indeed, discontinuity seemed to Heisenberg the principal distinctive feature of the quantum realm, and thus would characterize its theory.
This insight was momentous. It has been likened to Copernicus’s insight into the structure of the solar system. Both changed the viewpoint from which scientists had been used to regard the world, treating what had been naïvely assumed to be the image of objective reality as the more complex product of an interaction between the human observer and nature.
The step was revolutionary
, but the way had been prepared not entirely by Heisenberg. First, he was utilizing theoretical tools acquired from Bohr, Born, and others, and abandoning the space-time stage only because that seemed the price one had to pay to use them. Second, Heisenberg had a fine precedent in the strategy Einstein used in 1905 to give birth to special relativity. Einstein had abandoned the traditional meaning of ‘simultaneous’ as ‘happening at the same space-time instant’, and redefined it in terms of what an observer could see. Heisenberg hoped to achieve a similar breakthrough by abandoning the traditional conception of ‘position’ and ‘momentum’ inside the atom – which were unobserved but inferred quantities – and redefine these in terms of what experimenters saw from the outside: the frequencies and amplitudes of spectral lines. Finally, it was not such a radical step to give up trying to construct a theory that tried to picture what could not be observed given the utter failure of all the theories that had tried.
But like most revolutions, it had long-range consequences that would take years to become clear. If to be a ‘thing’ meant occupying a specific place at a specific time, this approach meant ‘eliminating the concept of a particle, or ‘thinghood’, from the atomic domain.’6 This approach essentially replaced the Newtonian ontology of nature, in which its most fundamental pieces are all objectively present in a particular place at a particular time, with a new ontology involving, as one philosopher of science put it much later, ‘a subtle subjectivity at the very heart of the scientific enterprise.’7 The subjectivity relates to the fact that our pictures of the atomic world are not an image of objective reality but are partly a function of the human mind constructing the pictures. The subtlety related to the fact that it was not yet clear what role the mind played.
A Brief Guide to the Great Equations Page 23