Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality

by Manjit Kumar

  Werner Karl Heisenberg was born on 5 December 1901 in Würzburg, Germany. He was eight when his father was appointed to the country’s only professorship of Byzantine philology at Munich University and the family moved to the Bavarian capital. For Heisenberg and his brother Erwin, almost two years older, home became a spacious apartment in the fashionable suburb of Schwabing on the northern outskirts of the city. They attended the prestigious Maximilians Gymnasium, where Max Planck had been a student 40 years earlier. It was also the school where their grandfather was now in charge. If the staff were tempted to treat the headmaster’s grandsons more leniently than other pupils, then they quickly discovered there was no need. ‘He has an eye for what is essential, and never gets lost in details’, Werner’s first-year teacher reported.1 ‘His thought processes in grammar and mathematics operate rapidly and usually without mistakes.’

  August Heisenberg’s father, forever the teacher, devised all manner of intellectual games for Werner and Erwin. In particular he always encouraged mathematical games and problem-solving. Pitting one brother against the other as they raced to solve them, it was evident that Werner was the more mathematically talented. Around the age of twelve he started learning calculus and asked his father to get him maths books from the university library. Seeing this as an opportunity to improve his son’s grasp of languages, he started supplying him with books written in Greek and Latin. It was the beginning of Werner’s fascination with the work of the Greek philosophers. Then came the First World War and the end of Heisenberg’s comfortable and secure world.

  The end of the war brought in its wake political and economic chaos throughout Germany, but few places experienced this more intensely than Munich and Bavaria. On 7 April 1919, radical socialists declared Bavaria a ‘Soviet Republic’. As they waited for troops sent by Berlin to arrive and restore the deposed government, those opposed to the revolutionaries organised themselves into military-style companies. Heisenberg and some friends joined one of these. His duties were largely confined to writing reports and running errands. ‘Our adventures were over after a few weeks,’ Heisenberg recalled later, ‘then the shooting died down and military service became increasingly monotonous.’2 By the end of the first week in May the ‘Soviet Republic’ had been ruthlessly crushed, leaving over a thousand dead.

  The harsh post-war reality led young middle-class teenagers like Heisenberg to embrace the romantic ideals of an earlier age as they flocked to join youth organisations such as the Pathfinders, the German equivalent of the Boy Scouts. Others, wanting more independence, set up their own groups and clubs. Heisenberg led one such group formed by younger pupils at his school. Gruppe Heisenberg, as they styled themselves, went hiking and camping in the Bavarian countryside and discussed the new world their generation would create.

  In the summer of 1920, after graduating from the Gymnasium with such ease that he won a prestigious scholarship, Heisenberg wanted to study mathematics at Munich University. When a disastrous interview ended any chance of doing so, a despondent Heisenberg sought his father for advice. He made an appointment for his son to see an old friend, Arnold Sommerfeld. Although the ‘small squat man with his martial dark moustache looked rather austere’, Heisenberg did not feel intimidated.3 He sensed that despite his appearance, here was a man with a ‘genuine concern for young people’.4 August Heisenberg had already told Sommerfeld that his son was particularly interested in relativity and atomic physics. ‘You are much too demanding’, he told Werner.5 ‘You can’t possibly start with the most difficult part and hope that the rest will automatically fall into your lap.’ Always eager to encourage and recruit raw talent to mould, he softened: ‘It may be that you know something; it may be that you know nothing. We shall see.’6

  Sommerfeld allowed the eighteen-year-old to attend the research seminar intended for more advanced students. Heisenberg was lucky. Together with Bohr’s institute in Copenhagen and Born’s group in Göttingen, Sommerfeld’s institute would form the golden triangle of quantum research in the years to come. When Heisenberg attended his first seminar he ‘spotted a dark-haired student with a somewhat secretive face in the third row’.7 It was Wolfgang Pauli. Sommerfeld had already introduced him to the portly Viennese during a tour around the institute on his first visit. The professor had been quick to tell Heisenberg, once Pauli was out of ear-shot, that he considered the boy to be his most talented student. Recalling Sommerfeld’s advice that he could learn a great deal from him, Heisenberg sat down next to Pauli.

  ‘Doesn’t he look the typical Hussar officer?’ whispered Pauli as Sommerfeld entered.8 It was the beginning of a lifelong professional relationship that never quite blossomed into a closer personal friendship. They were simply too different. Heisenberg was quieter, friendlier, less outspoken and critical than Pauli. He romanticised nature and loved nothing more than hiking and camping with his friends. Pauli was drawn to cabarets, taverns and cafes. Heisenberg had done half a day’s work while Pauli still slept soundly in his bed. Yet Pauli exerted a strong influence on Heisenberg and never passed up a chance to tell him, with tongue in cheek: ‘You are a complete fool.’9

  In the middle of writing his dazzling review of relativity, it was Pauli who steered Heisenberg away from Einstein’s theory and towards the quantum atom as a more fertile area of research in which to make his name. ‘In atomic physics we still have a wealth of uninterpreted experimental results,’ he told Heisenberg; ‘nature’s evidence in one place seems to contradict that in another, and so far it has not been possible to draw an even halfway coherent picture of the relationship involved.’10 It was likely, thought Pauli, that everyone would still be ‘groping about in a thick mist’ for years to come.11 As Heisenberg listened, he was inexorably drawn into the realm of the quantum.

  Sommerfeld soon assigned Heisenberg a ‘little problem’ in atomic physics. He asked him to analyse some new data on the splitting of spectral lines in a magnetic field and to construct a formula that replicated the splitting. Pauli warned Heisenberg that Sommerfeld hoped that deciphering such data would lead to new laws. It was an attitude that for Pauli bordered on ‘a kind of number mysticism’, but then he admitted, ‘no one has been able to suggest anything better’.12 The exclusion principle and electron spin still lay in the future.

  Heisenberg’s ignorance of the accepted rules and regulations of quantum physics allowed him to tread where others, wedded to a more cautious and rational approach, feared to. It enabled him to construct a theory that appeared to explain the anomalous Zeeman effect. Having dismissed an earlier version, Heisenberg was relieved when Sommerfeld sanctioned the publication of his latest effort. Although it was later shown to be incorrect, his first scientific paper brought Heisenberg to the attention of Europe’s leading physicists. Bohr was one of those who sat up and took notice.

  They first met in Göttingen in June 1922 when Sommerfeld took some of his students to hear Bohr’s series of lectures on atomic physics. What struck Heisenberg was how precise Bohr was in his choice of words: ‘Each one of his carefully formulated sentences revealed a long chain of underlying thoughts, of philosophical reflections, hinted at but never fully expressed.’13 He was not alone in sensing that Bohr reached his conclusions more by intuition and inspiration than by detailed calculations. At the end of the third lecture, Heisenberg rose to point out some difficulties that remained in a published paper that Bohr had praised. As people began to mingle after the question-and-answer session, Bohr sought out Heisenberg and asked the twenty-year-old if he would like to accompany him on a walk later that day. Their hike to a nearby mountain lasted some three hours, and Heisenberg later wrote ‘that my real scientific career only started that afternoon’.14 For the first time, he saw ‘that one of the founders of quantum theory was deeply worried by its difficulties’.15 When Bohr invited him to Copenhagen for a term, Heisenberg suddenly saw his future as one ‘full of hope and new possibilities’.16

  Copenhagen would have to wait. Sommerfeld was due to go to
America and in his absence had arranged for Heisenberg to study with Max Born in Göttingen. Although he looked ‘like a simple farm boy, with short fair hair, clear bright eyes, and a charming expression’, Born quickly discovered that there was much more to him than met the eye.17 He was ‘easily as gifted as Pauli’, Born wrote to Einstein.18 When he returned to Munich, Heisenberg finished his doctoral thesis on turbulence. Sommerfeld had chosen the topic to broaden his knowledge and understanding of physics. During the oral examination his inability to answer simple questions, such as the resolving power of a telescope, almost cost him his doctorate. Wilhelm Wien, the head of experimental physics, was dismayed when Heisenberg struggled to explain how a battery worked. He wanted to fail the upstart theorist, but reached a compromise with Sommerfeld. Heisenberg would get his doctorate, but would be awarded the second-lowest mark – grade III. Pauli had passed with grade I.

  Feeling humiliated, that evening he packed his bags and caught the overnight train. He could not bear to stay in Munich a minute longer and fled to Göttingen. ‘I was astonished when, one morning long before the appointed time, he suddenly appeared before me with an expression of embarrassment on his face’, recalled Born later.19 Heisenberg anxiously recounted the tale of his oral exam, worried that his services would no longer be required as an assistant. Eager to cement Göttingen’s growing reputation for theoretical physics, Born was confident that Heisenberg would bounce back and told him so.

  Born was convinced that physics had to be rebuilt from the ground up. The mish-mash of quantum rules and classical physics that was at the heart of the Bohr-Sommerfeld quantum atom had to give way to a logically consistent new theory that Born called ‘quantum mechanics’. None of this was new for physicists trying to disentangle the problems of atomic theory. However, it signalled the awareness of a creeping sense of crisis in 1923 at the inability of physicists to cross the atomic Rubicon. Pauli was already loudly proclaiming to anyone who would listen that the failure to explain the anomalous Zeeman effect was evidence ‘that we must create something fundamentally new’.20 After meeting him, Heisenberg believed that Bohr was the one most likely to make the breakthrough.

  Pauli had been in Copenhagen as Bohr’s assistant since the autumn of 1922. He and Heisenberg kept each other informed about the latest developments at their respective institutes through a regular exchange of letters. Heisenberg, like Pauli, had also been working on the anomalous Zeeman effect. Just before Christmas 1923, he wrote to Bohr about his latest efforts and received an invitation to spend a few weeks in Copenhagen. On Saturday, 15 March 1924, Heisenberg stood in front of the three-storey neo-classical building with its red tiled roof at Blegdamsvej 17. Above the main entrance he saw the sign that greeted every visitor: ‘Universitetets Institut for Teoretisk Fysik’. Better known as the Bohr Institute.

  Heisenberg soon discovered that only half of the building, the basement and the ground floor, was used for physics. The rest was set aside for accommodation. Bohr and his growing family lived in an elegantly furnished flat that occupied the entire first floor. The family maid, the caretaker, and honoured guests were housed on the top floor. On the ground floor, besides the lecture hall with its six long rows of wooden benches, was a well-stocked library and offices for Bohr and his assistant. There was also a modest-sized workroom for visitors. Despite its name, the institute had two small laboratories on the first floor, with the main laboratory housed in the basement.

  The institute was struggling for space with a permanent staff of six and almost a dozen visitors. Bohr was already making plans to expand. Over the next two years the adjacent land was bought and two new buildings were added that doubled the capacity of the institute. Bohr and his family moved out of their flat into a large purpose-built house next door. The extension meant a substantial renovation of the old building that included more office space, a dining room, and a new self-contained three-room flat on the top floor. It was here that Pauli and Heisenberg often stayed in later years.

  There was one thing that no one at the institute wanted to miss: the arrival of the morning post. Letters from parents and friends were always welcome, but it was correspondence from far-flung colleagues and the journals that were seized upon for the latest breaking news from the frontiers of physics. However, not everything revolved around physics, even if much of the talking did. There were musical evenings, games of table tennis, hiking trips, and outings to watch the latest motion picture.

  Heisenberg had arrived with such high hopes, but his first few days at the institute left him feeling frustrated. Expecting to spend time with Bohr almost as he stepped through the front door, he had hardly seen him. Used to being the best, Heisenberg was suddenly faced with Bohr’s international posse of brilliant young physicists. He was intimidated. They all spoke several languages, while he sometimes struggled to express himself clearly in German. Enjoying nothing more than walks in the countryside with his friends, Heisenberg thought that everyone at the institute possessed a worldliness that he did not. However, nothing left him as despondent as the realisation that they understood much more of atomic physics than he did.

  As he tried to shake off the blows to his self-esteem, Heisenberg wondered if he would ever get the chance to work with Bohr. He had been sitting in his room when there was a knock on the door and in strode Bohr. After apologising for being so busy, he proposed that the two of them go on a short walking tour. There was little chance, Bohr explained, of him being left alone long enough at the institute for the pair of them to talk at any length. What better way of getting to know one another than a few days of walking and talking? It was Bohr’s favourite pastime.

  Early the following morning they caught the tram to the northern outskirts of the city and began their walk. Bohr asked Heisenberg about his childhood and what he remembered about the outbreak of war ten years earlier. As they headed north, instead of physics they talked about the pros and cons of war, Heisenberg’s involvement in the youth movement, and Germany. After spending the night at an inn, they walked to Bohr’s country cottage in Tisvilde, before heading back to the institute on the third day. The 100-mile walk had the effect that Bohr desired and Heisenberg craved. They got to know each other more quickly.

  They had talked about atomic physics, yet when they finally returned to Copenhagen, it was Bohr the man, rather than the physicist, that had captivated Heisenberg. ‘I am, of course, absolutely enchanted with the days I am spending here’, he wrote to Pauli.21 He had never before met a man like Bohr with whom he could discuss just about anything. Despite his genuine concern for the welfare of everyone at his institute, Sommerfeld upheld the traditional German role of professor, one step removed from his subordinates. In Göttingen, Heisenberg would not have dared to broach with Born the range of subjects he and Bohr had discussed so freely. Unknown to him, it was Pauli, in whose footsteps he always seemed to be following, who was behind Bohr’s warm reception.

  Pauli always took a keen interest in what Heisenberg was doing, as the pair kept each other informed about their latest ideas. Pauli had returned to Hamburg University when he learnt that Heisenberg was going to spend a few weeks in Copenhagen, and he wrote to Bohr. For a man already notorious for his scathing wit, the fact that he described Heisenberg as a ‘gifted genius’ who would ‘one day advance science greatly’ made a deep impression on Bohr.22 But before that day arrived, Pauli was sure that Heisenberg’s physics had to be underpinned by a more coherent philosophical approach.

  Pauli believed that to overcome the problems besetting atomic physics it was necessary to stop making arbitrary ad hoc assumptions whenever experiments yielded data in conflict with existing theory. Such an approach could only paper over the problems without ever leading to their solution. Given his deep understanding of relativity, Pauli was an ardent admirer of Einstein and the way in which he had constructed the theory using a few guiding principles and assumptions. Believing that it was the correct approach to adopt in atomic physics too, Pauli wanted to emu
late Einstein by setting up the underlying philosophical and physical principles before moving on to develop the necessary formal mathematical nuts and bolts that held the theory together. By 1923 it was an approach that had left Pauli in despair. Having avoided introducing assumptions that could not be justified, he nevertheless failed to find a consistent and logical account of the anomalous Zeeman effect.

  ‘Hopefully you will then take atomic theory forward in good measure and solve several of the problems with which I have tormented myself in vain and which are too difficult for me’, Pauli wrote to Bohr.23 ‘I hope also that Heisenberg will then bring back home a philosophical attitude in his thinking.’ By the time the young German arrived, Bohr had been well briefed. Throughout the two-week visit, the principles of physics rather than any particular problem was the focus of their discussions as Bohr and Heisenberg strolled through Faelledpark next to the institute or chatted over a bottle of wine in the evenings. Many years later, Heisenberg described his time in Copenhagen in March 1924 as a ‘gift from heaven’.24

  ‘I shall, of course, miss him (he is a charming, worthy, very bright man, who has become very dear to my heart), but his interest precedes mine, and your wish is decisive for me’, Born wrote to Bohr after Heisenberg received an invitation for an extended stay in Copenhagen.25 Due to spend the forthcoming winter semester teaching in America, Born would not need the services of his assistant until May the following year. At the end of July 1924, having successfully completed his habilitation thesis and gained the right to teach at German universities, Heisenberg left for a three-week hiking tour around Bavaria.