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

by Manjit Kumar

  Back in Cambridge, the intellectual rapport that Bohr sought with Thomson never happened. Years later, Bohr identified one possible reason for the failure: ‘I had no great knowledge of English and therefore I did not know how to express myself. And I could say only that this is incorrect. And he was not interested in the accusation that it was not correct.’57 Infamous for neglecting papers and letters from students and colleagues alike, Thomson was also no longer actively engaged in electron physics.

  Increasingly disenchanted, Bohr met Rutherford again at the Cavendish research students’ annual dinner. Held in early December, it was a rowdy, informal affair with toasts, songs and limericks following a ten-course meal. Once again struck by the personality of the man, Bohr seriously began thinking about swapping Cambridge and Thomson for Manchester and Rutherford. Later that month he went to Manchester and discussed the possibility with Rutherford. A young man separated from his fiancée, Bohr desperately wanted something tangible to show for their year apart. Telling Thomson that he wanted ‘to know something about radioactivity’, Bohr was granted permission to leave at the end of the new term.58 ‘The whole thing was very interesting in Cambridge,’ he admitted many years later, ‘but it was absolutely useless.’59

  With only four months left in England, Bohr arrived in Manchester in the middle of March 1912 to begin a seven-week course in the experimental techniques of radioactive research. With no time to lose, Bohr spent his evenings working on the application of electron physics to provide a better understanding of the physical properties of metals. With Geiger and Marsden among the instructors, he successfully completed the course and was given a small research project by Rutherford.

  ‘Rutherford is a man whom one cannot be mistaken about,’ Bohr wrote to Harald, ‘he comes regularly to hear how things are going and talk about every little thing.’60 Unlike Thomson, who seemed to him unconcerned about the progress of his students, Rutherford was ‘really interested in the work of all people who are around him’. He had an uncanny ability to recognise scientific promise. Eleven of his students, along with several close collaborators, would win the Nobel Prize. As soon as Bohr arrived in Manchester, Rutherford wrote to a friend: ‘Bohr, a Dane, has pulled out of Cambridge and turned up here to get some experience in radioactive work.’61 Yet there was nothing in what Bohr had done to date to suggest that he was any different from the other eager young men in his laboratory, except the fact that he was a theorist.

  Rutherford held a generally low opinion of theorists and never lost an opportunity to air it. ‘They play games with their symbols,’ he once told a colleague, ‘but we turn out the real solid facts of Nature.’62 On another occasion when invited to deliver a lecture on the trends of modern physics, he replied: ‘I can’t give a paper on that. It would only take two minutes. All I could say would be that the theoretical physicists have got their tails up and it is time that we experimentalists pulled them down again!’63 Yet he had immediately liked the 26-year-old Dane. ‘Bohr’s different’, he would say. ‘He’s a football player!’64

  Late every afternoon, work in the laboratory stopped as the research students and staff gathered to chat over tea, cakes and slices of bread and butter. Rutherford would be there, sitting on a stool with plenty to say, whatever the subject. But most of the time the talk was simply of physics, particularly of the atom and radioactivity. Rutherford had succeeded in creating a culture where there was an almost tangible sense of discovery in the air, where ideas were openly exchanged and discussed in the spirit of co-operation, with no one afraid to speak – even a newcomer. At its centre was Rutherford, who Bohr knew was always prepared ‘to listen to every young man, when he felt he had any idea, however modest, on his mind’.65 The only thing Rutherford could not stand was ‘pompous talk’. Bohr loved to talk.

  Unlike Einstein who spoke and wrote fluently, Bohr frequently paused as he struggled to find the right words to express himself, whether in Danish, English or German. When Bohr spoke, he was often only thinking aloud in search of clarity. It was during the tea breaks that he got to know the Hungarian Georg von Hevesy, who would win the 1943 Nobel Prize for chemistry for developing the technique of radioactive tracing that was to become a powerful diagnostic tool in medicine, with widespread applications in chemical and biological research.

  Strangers in a strange country, speaking a language that both had yet to master, the pair formed an easy friendship that lasted a lifetime. ‘He knew how to be helpful to a foreigner’, Bohr said as he recalled how Hevesy, only a few months older, helped him ease into the life of the laboratory.66 It was during their conversations that Bohr first began to focus on the atom, as Hevesy explained that so many radioactive elements had been discovered that there was not enough room to accommodate them all in the periodic table. The very names given to these ‘radioelements’, spawned in the process of radioactive disintegration of one atom into another, captured the sense of uncertainty and confusion surrounding their true place within the atomic realm: uranium-X, actinium-B, thorium-C. But there was, Hevesy told Bohr, a possible solution proposed by Rutherford’s former Montreal collaborator, Frederick Soddy.

  In 1907 it was discovered that two elements produced during radioactive decay, thorium and radiothorium, were physically different but chemically identical. Every chemical test they were subjected to failed to tell them apart. During the next few years, other such sets of chemically inseparable elements were discovered. Soddy, now based at Glasgow University, suggested that the only difference between these new radioelements and those with which they shared ‘complete chemical identity’ was their atomic weight.67 They were like identical twins whose only distinguishing feature was a slight difference in weight.

  Soddy proposed in 1910 that chemically inseparable radioelements, ‘isotopes’ as he later called them, were just different forms of the same element and should therefore share its slot in the periodic table.68 It was an idea at odds with the existing organisation of elements within the periodic table, which listed them in order of increasing atomic weight, with hydrogen first and uranium last. Yet the fact that radiothorium, radioactinium, ionium, and uranium-X were all chemically identical to thorium was strong evidence in favour of Soddy’s isotopes.69

  Figure 5: The periodic table

  Until his chats with Hevesy, Bohr had shown no interest in Rutherford’s atomic model. But he now had an idea: it was not enough to distinguish between the physical and chemical properties of an atom; one had to differentiate between nuclear and atomic phenomena. Ignoring the problem of its inevitable collapse, Bohr took Rutherford’s nuclear atom seriously as he tried to reconcile isotopes with the use of atomic weights to order the periodic table. ‘Everything,’ he said later, ‘then fell into line.’70

  Bohr understood that it was the charge of the nucleus in Rutherford’s atom that fixed the number of electrons it contained. Since an atom was neutral, possessing no overall charge, he knew that the positive charge of the nucleus had to be balanced by the combined negative charge of all its electrons. Therefore the Rutherford model of the hydrogen atom must consist of a nuclear charge of plus one and a single electron with a charge of minus one. Helium with a nuclear charge of plus two must have two electrons. This increase in nuclear charge coupled to a corresponding number of electrons led all the way up to the then heaviest-known element, uranium, with a nuclear charge of 92.

  For Bohr the conclusion was unmistakable: it was nuclear charge and not atomic weight that determined the position of an element within the periodic table. From here he took the short step to the concept of isotopes. It was Bohr, not Soddy, who recognised nuclear charge as being the fundamental property that tied together different radioelements that were chemically identical but physically different. The periodic table could accommodate all the radioelements; they just had to be housed according to nuclear charge.

  At a stroke, Bohr was able to explain why Hevesy had been unable to separate lead and radium-D. If the electrons determined the che
mical properties of an element, then any two with the same number and arrangement of electrons would be identical twins, chemically inseparable. Lead and radium-D had the same nuclear charge, 82, and therefore the same number of electrons, 82, resulting in ‘complete chemical identity’. Physically they were distinct because of their different nuclear masses: approximately 207 for lead and 210 for radium-D. Bohr had worked out that radium-D was an isotope of lead and as a result it was impossible to separate the two by any chemical means. Later, all isotopes were labelled with the name of the element of which they were an isotope and their atomic weight. Radium-D was lead-210.

  Bohr had grasped the essential fact that radioactivity was a nuclear and not an atomic phenomenon. It allowed him to explain the process of radioactive disintegration in which one radioelement decayed into another with the emission of alpha, beta or gamma radiation as a nuclear event. Bohr realised that if radioactivity originated in the nucleus, then a uranium nucleus with a charge of plus 92 transmuting into uranium-X by emitting an alpha particle lost two units of positive charge, leaving behind a nucleus with a charge of plus 90. This new nucleus could not hold on to all of the original 92 atomic electrons, quickly losing two to form a new neutral atom. Every new atom formed as the product of radioactive decay immediately either acquires or loses electrons so as regain its neutrality. Uranium-X with a positive nuclear charge of 90 is an isotope of thorium. They both ‘possessed the same nuclear charge and differed only in the mass and intrinsic structure of the nucleus’, explained Bohr.71 It was the reason why those who tried, failed to separate thorium, with an atomic weight of 232, and ‘uranium-X’, thorium-234.

  His theory of what was happening at the nuclear level in radioactive disintegration implied, Bohr said later, ‘that by radioactive decay the element, quite independently of any change in its atomic weight, would shift its place in the periodic table by two steps down or one step up, corresponding to the decrease or increase in the nuclear charge accompanying the emission of alpha or beta rays, respectively’.72 Uranium decaying with the emission of an alpha particle into thorium-234 ended up two places further back in the periodic table.

  Beta particles, being fast-moving electrons, have a negative charge of minus one. If a nucleus emits a beta particle, its positive charge increases by one – as if two particles, one positive and the other negative, that existed in harmony as a neutral pair had been ripped apart with the ejection of the electron, leaving behind its positive partner. The new atom produced by beta decay has a nuclear charge that is one greater than the disintegrating atom, moving it one place to the right in the periodic table.

  When Bohr took his ideas to Rutherford he was warned about the danger of ‘extrapolating from comparatively meagre experimental evidence’.73 Surprised by this muted reception, he attempted to convince Rutherford ‘that it would be the final proof of his atom’.74 He failed. Part of the problem lay in Bohr’s inability to express his ideas clearly. Rutherford, preoccupied with writing a book, did not make the time to fully grasp the significance of what Bohr had done. Rutherford believed that although alpha particles were emitted from the nucleus, beta particles were just atomic electrons somehow ejected from a radioactive atom. Despite Bohr’s trying on five separate occasions to persuade him, Rutherford hesitated in following his logic all the way to its conclusion.75 Sensing that Rutherford was by now becoming ‘a bit impatient’ with him and his ideas, Bohr decided to let the matter rest.76 Others did not.

  Frederick Soddy soon spotted the same ‘displacement laws’ as Bohr, but unlike the young Dane, he was able to publish his research without first having to seek approval of a superior. Nobody was surprised that Soddy was at the forefront of these breakthroughs. But no one could have guessed that an eccentric 42-year-old Dutch lawyer would introduce an idea of fundamental importance. In July 1911, in a short letter to the journal Nature, Antonius Johannes van den Broek speculated that the nuclear charge of a particular element is determined by its place in the periodic table, its atomic number, not its atomic weight. Inspired by Rutherford’s atomic model, van den Broek’s idea was based upon various assumptions that turned out to be wrong, such as nuclear charge being equal to half the atomic weight of the element. Rutherford was suitably annoyed that a lawyer should publish ‘a lot of guesses for fun without sufficient foundation ’.77

  Having failed to gain any support, on 27 November 1913 in another letter to Nature, van den Broek dropped the assumption that the nuclear charge was equal to half the atomic weight. He did so after the publication of the extensive study by Geiger and Marsden into alpha particle scattering. A week later, Soddy wrote to Nature explaining that van den Broek’s idea made clear the meaning of the displacement laws. Then came an endorsement from Rutherford: ‘The original suggestion of van den Broek that the charge on the nucleus is equal to the atomic number and not to half the atomic weight seems to me very promising.’ He was writing in praise of van den Broek’s proposal a little more than eighteen months after advising Bohr against pursuing similar ideas.

  Bohr never complained that he had missed out on being the first to publish the concept of atomic number, or those ideas that won Soddy the Nobel Prize for chemistry in 1921, due to Rutherford’s lack of enthusiasm.78 ‘The confidence in his judgement,’ Bohr fondly remembered, ‘and our admiration for his powerful personality was the basis for the inspiration felt by all in his laboratory, and made us all try our best to deserve the kind and untiring interest he took in the work of everyone.’79 In fact, Bohr continued to regard an approving word from Rutherford as ‘the greatest encouragement for which any of us could wish’.80 The reason why he could afford to be so generous, when others would have been left feeling disappointed and bitter, was what happened next.

  After Rutherford dissuaded him from publishing his innovative ideas, by chance Bohr came across a recently published paper that grabbed his attention.81 It was the work of the only theoretical physicist on Rutherford’s staff, Charles Galton Darwin, the grandson of the great naturalist. The paper concerned the energy lost by alpha particles as they passed through matter rather than being scattered by atomic nuclei. It was a problem that J.J. Thomson had originally investigated using his own atomic model, but which Darwin now re-examined on the basis of Rutherford’s atom.

  Rutherford had developed his atomic model using the large-angle alpha particle scattering data gathered by Geiger and Marsden. He knew that atomic electrons could not be responsible for such large-angle scattering and so ignored them. In formulating his scattering law that predicted the fraction of scattered alpha particles to be found at any angle of deflection, Rutherford had treated the atom as a naked nucleus. Afterwards he simply placed the nucleus at the centre of the atom and surrounded it with electrons without saying anything about their possible arrangement. In his paper, Darwin adopted a similar approach when he ignored any influence that the nucleus may have exerted on the passing alpha particles and concentrated solely on the atomic electrons. He pointed out that the energy lost by an alpha particle as it passed through matter was due almost entirely to collisions between it and atomic electrons.

  Darwin was unsure how electrons were arranged inside Rutherford’s atom. His best guess was that they were evenly distributed either throughout the atom’s volume or over its surface. His results depended only on the size of the nuclear charge and the atom’s radius. Darwin found that his values for various atomic radii were in disagreement with existing estimates. As he read this paper, Bohr quickly identified where Darwin had gone wrong. He had mistakenly treated the negatively-charged electrons as if they were free, instead of being bound to the positively-charged nucleus.

  Bohr’s greatest asset was his ability to identify and exploit failures in existing theory. It was a skill that served him well throughout his career, as he started much of his own work from spotting errors and inconsistencies in that of others. On this occasion, Darwin’s mistake was Bohr’s point of departure. While Rutherford and Darwin had considered the nu
cleus and the atomic electrons separately, each ignoring the other component of the atom, Bohr realised that a theory that succeeded in explaining how alpha particles interacted with atomic electrons might reveal the true structure of the atom.82 Any lingering disappointment over Rutherford’s reaction to his earlier ideas was forgotten as he set about trying to rectify Darwin’s mistake.

  Bohr abandoned his usual practice of drafting letters even to his brother. ‘I am not getting along badly at the moment,’ Bohr reassured Harald, ‘a couple of days ago I had a little idea with regard to understanding the absorption of alpha-rays (it happened in this way: a young mathematician here, C.G. Darwin (grandson of the real Darwin), has just published a theory about this problem, and I felt that it not only wasn’t quite right mathematically (however, only slightly wrong) but very unsatisfactory in the basic conception, and I have worked out a little theory about it, which, even if it isn’t much, perhaps may throw some light on certain things connected with the structure of atoms). I am planning to publish a little paper about it very soon.’83 Not having to go to the laboratory ‘has been wonderfully convenient for working out my little theory’, he admitted.84

  Until he had put flesh onto the bare bones of his emerging ideas, the only person in Manchester whom Bohr was willing to confide in was Rutherford. Though surprised by the direction the Dane had taken, Rutherford listened and this time encouraged him to continue. With his approval, Bohr stopped going to the laboratory. He was under pressure, since his time in Manchester was almost up. ‘I believe I have found out a few things; but it is certainly taking more time to work them out than I was foolish enough to believe at first’, he wrote to Harald on 17 July, a month after first sharing his secret. ‘I hope to have a little paper ready to show Rutherford before I leave, so I’m busy, so busy; but the unbelievable heat here in Manchester doesn’t exactly help my diligence. How I look forward to talking to you!’85 He wanted to tell his brother that he hoped to fix Rutherford’s flawed nuclear atom by turning it into the quantum atom.