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

by Manjit Kumar

  Had Ångström lived (he died in 1874 aged 59), he would have been astounded by Balmer’s use of his formula to predict the existence of other series of spectral lines for the hydrogen atom in the infrared and ultraviolet regions by simply setting n to 1, 3, 4 and 5 while letting m cycle through different numbers, as he had done with n set at 2 to generate the four original lines. For example, with n=3 and m=4 or 5 or 6 or 7…, Balmer predicted the series of lines in the infrared that were discovered in 1908 by Friedrich Paschen. Each of the series forecast by Balmer was later discovered, but no one had been able to explain what lay behind the success of his formula. What physical mechanism did the formula, arrived at through a process of trial and error, symbolise?

  ‘As soon as I saw Balmer’s formula,’ Bohr said later, ‘the whole thing was immediately clear to me.’22 It was electrons jumping between different allowed orbits that produced the spectral lines emitted by an atom. If a hydrogen atom in the ground state, n=1, absorbs enough energy, then the electron ‘jumps’ to a higher-energy orbit such as n=2. The atom is then in an unstable, excited state and quickly returns to the stable ground state when the electron jumps down from n=2 to n=1. It can do so only by emitting a quantum of energy that is equivalent to the difference in energy of the two levels, 10.2eV. The wavelength of the resulting spectral line can be calculated using the Planck-Einstein formula, E=h, where is the frequency of the emitted electromagnetic radiation.

  An electron jumping from a range of higher energy levels to the same lower energy level produced the four spectral lines of the Balmer series. The size of the quanta emitted depended only on the initial and final energy levels involved. This was why Balmer’s formula generated the correct wavelengths when n was set equal to 2 but m was 3, 4, 5 or 6 in turn. Bohr was able to derive the other spectral series predicted by Balmer by fixing the lowest energy level that the electron could jump to. For example, transitions ending with the electron jumping to n=3 produced the Paschen series in the infrared, while those that ended at n=1 generated the so-called Lyman series in the ultraviolet region of the spectrum.23

  Figure 7: Energy levels, line spectra and quantum jumps (not drawn to scale)

  There is, as Bohr discovered, a very strange feature associated with an electron’s quantum leap. It is impossible to say where an electron actually is during a jump. The transition between orbits, energy levels, has to occur instantaneously. Otherwise as the electron travelled from one orbit to another it would radiate energy continuously. In Bohr’s atom, an electron could not occupy the space between orbits. As if by magic, it disappeared while in one orbit and instantly reappeared in another.

  ‘I’m fully convinced that the problem of spectral lines is intimately tied to the question of the nature of the quantum.’ Remarkably, it was Planck, in February 1908, who wrote these words in a notebook.24 But in his ongoing struggle to minimise the impact of the quantum, and before the Rutherford atom, it was as far as Planck could go. Bohr embraced the idea that electromagnetic radiation was emitted and absorbed by atoms in quanta, but in 1913 he did not accept that electromagnetic radiation itself was quantised. Even six years later, in 1919, few believed in Einstein’s quantum of light when Planck declared in his Nobel Prize lecture that Bohr’s quantum atom was ‘the long-sought key to the entrance-gate into the wonderland’ of spectroscopy.25

  On 6 March 1913, Bohr sent Rutherford the first of a trilogy of papers and asked him to send it on to the Philosophical Magazine. At the time, and for many years to come, every junior scientist like Bohr needed someone of Rutherford’s seniority to ‘communicate’ a paper to a British journal to ensure swift publication. ‘I am very anxious to know what you may think of it all’, he wrote to Rutherford.26 He was particularly concerned about the reaction to his mixing of the quantum and classical physics. Bohr did not have to wait long for the answer: ‘Your ideas as to the mode of origin of spectra in hydrogen are very ingenious and seem to work out well; but the mixture of Planck’s ideas with the old mechanics make it very difficult to form a physical idea of what is the basis of it all.’27

  Rutherford, as others would, was having trouble picturing how the electron in the hydrogen atom ‘jumped’ between energy levels. The difficulty lay in the fact that Bohr had violated a cardinal rule of classical physics. An electron moving in a circle is an oscillating system, with one complete orbit being an oscillation and the number of orbits per second being the frequency of oscillation. An oscillating system radiates energy at the frequency of its oscillation, but since two energy levels are involved in an electron making a ‘quantum jump’, there are two frequencies of oscillation. Rutherford was complaining that there was no link between these frequencies, between the ‘old’ mechanics and the frequency of the radiation emitted as the electron jumps between energy levels.

  He also identified another more serious problem: ‘There appears to me one grave difficulty in your hypothesis, which I have no doubt you fully realize, namely, how does an electron decide what frequency it is going to vibrate at when it passes from one stationary state to the other? It seems to me that you would have to assume that the electron knows beforehand where it is going to stop.’28 An electron in the n=3 energy level can jump down to either the n=2 or the n=1 levels. In order to make the jump, the electron appears to ‘know’ to which energy level it is heading so that it can emit radiation of the correct frequency. These were weakness of the quantum atom to which Bohr had no answer.

  There was another, more minor criticism that concerned Bohr far more deeply. Rutherford thought the paper ‘really ought to be cut down’, since ‘long papers have a way of frightening readers, who feel that they have not time to dip into them’.29 After offering to correct Bohr’s English where necessary, Rutherford added a postscript: ‘I suppose you have no objection to my using my judgement to cut out any matter I may consider unnecessary in your paper? Please reply.’30

  When Bohr received the letter he was horrified. For a man who agonised over the choice of every word and went through endless drafts and revisions, the idea that someone else, even Rutherford, would make changes was appalling. Two weeks after posting the original paper, Bohr sent a longer revised manuscript containing alterations and additions. Rutherford agreed that the changes were ‘excellent and appear quite reasonable’, but he once again urged Bohr to cut the length. Even before he received this latest letter, he wrote to Rutherford telling him that he was coming to Manchester on holiday.31

  When Bohr knocked on the front door, Rutherford was busy entertaining his friend Arthur Eve. He later recalled that Rutherford immediately took the ‘slight-looking boy’ into his study, leaving Mrs Rutherford to explain that the visitor was a young Dane and her husband thought ‘very highly indeed of his work’.32 Through hour after hour of discussions over several long evenings during the days that followed, Bohr admitted that Rutherford ‘showed an almost angelic patience’ as he tried to defend every word in his paper.33

  An exhausted Rutherford finally gave in and afterwards began regaling his friends and colleagues with tales of the encounter: ‘I could see that he had weighed up every word in it, and it impressed me how determinedly he held on to every sentence, every expression, every quotation; everything had a definite reason, and although I first thought that many sentences could be omitted, it was clear, when he explained to me how closely knit the whole was, that it was impossible to change anything.’34 Ironically, Bohr admitted years later that Rutherford had been right ‘in objecting to the rather complicated presentation’.35

  Bohr’s trilogy was published virtually unchanged in the Philosophical Magazine as ‘On the Constitution of Atoms and Molecules’. The first, dated 5 April 1913, appeared in July. The second and third parts, published in September and November, were a presentation of ideas concerning the possible arrangements of electrons inside atoms that would preoccupy Bohr for the next decade as he used the quantum atom to explain the periodic table and the chemical properties of the elements.

  Bo
hr had built his atom using a heady cocktail of classical and quantum physics. In the process he had violated tenets of accepted physics by proposing that: electrons inside atoms can occupy only certain orbits, the stationary states; electrons cannot radiate energy while in those orbits; an atom can be in only one of a series of discrete energy states, the lowest being the ‘ground state’ electrons can ‘somehow’ jump from a stationary state of high energy to a stationary state of low energy and the difference in energy between the two is emitted in a quantum of energy. Yet his model correctly predicted various properties of the hydrogen atom such as its radius, and it provided a physical explanation for the production of spectral lines. The quantum atom, Rutherford said later, was ‘a triumph of mind over matter’ and until Bohr unveiled it, he believed that ‘it would require centuries’ to solve the mystery of the spectral lines.36

  A true measure of Bohr’s achievement was the initial reactions to the quantum atom. It was discussed publicly for the first time on 12 September 1913 at the 83rd annual meeting of the British Association for the Advancement of Science (BAAS), held that year in Birmingham. With Bohr in the audience, it received a muted and mixed reception. J.J. Thomson, Rutherford, Rayleigh and Jeans were all there, while the distinguished foreign contingent included Lorentz and Curie. ‘Men over seventy should not be hasty in expressing opinions on new theories’, was Rayleigh’s diplomatic response when pressed for his opinion about Bohr’s atom. In private, however, Rayleigh did not believe ‘that Nature behaved in that way’ and admitted that he had ‘difficulty in accepting it as a picture of what actually takes place’.37 Thomson objected to Bohr’s quantisation of the atom as totally unnecessary. James Jeans begged to differ. He pointed out in a report to the packed hall that the only justification that Bohr’s model required was ‘the very weighty one of success’.38

  In Europe, the quantum atom was greeted with disbelief. ‘This is all nonsense! Maxwell’s equations are valid under all circumstances’, said Max von Laue during one heated discussion. ‘An electron in a circular orbit must emit radiation.’39 While Paul Ehrenfest confessed to Lorentz that Bohr’s atom ‘has driven me to despair’.40 ‘If this is the way to reach the goal,’ he continued, ‘I must give up doing physics.’41 In Göttingen, Bohr’s brother Harald reported that there was great interest in his work, but that his assumptions were deemed too ‘bold’ and ‘fantastic’.42

  One early triumph for Bohr’s theory clinched the support of some, including Einstein. Bohr predicted that a series of lines found in the spectrum of light from the sun that had been attributed to hydrogen actually belonged to ionised helium, helium with one of its two electrons removed. This interpretation of the so-called ‘Pickering-Fowler lines’ was at odds with that of its discoverers. Who was right? The issue was settled by one of Rutherford’s team in Manchester after a detailed study of the spectral lines instigated at the behest of Bohr. Just in time for the BAAS meeting in Birmingham, it was found that the Dane had been correct in his assignment of the Pickering-Fowler lines to helium. Einstein heard the news during a conference in Vienna at the end of September from Bohr’s friend Georg von Hevesy. ‘The big eyes of Einstein,’ reported Hevesy in a letter to Rutherford, ‘looked still bigger and he told me: “Then it is one of the greatest discoveries”.’43

  By the time Part III of the trilogy was published in November 1913, another member of Rutherford’s group, Henry Moseley, had confirmed the idea that the nuclear charge of an atom, its atomic number, was a unique whole number for a given element and the key parameter that decided its position within the periodical table. It was only after Bohr visited Manchester in July that year and spoke to Moseley about the atom that the young Englishman began shooting beams of electrons at different elements and examined the resulting X-ray spectra.

  By then it was known that X-rays were a form of electromagnetic radiation with wavelengths thousands of times shorter than those of visible light, and that they were produced when electrons with sufficient energy struck a given metal. Bohr believed that X-rays were emitted because one of the innermost electrons was knocked out of an atom and an electron moved down from a higher energy level to fill the vacancy. The difference in the two energy levels was such that the quantum of energy emitted in the transition was an X-ray. Bohr realised that, using his atomic model, it was possible to determine the charge of the nucleus using the frequencies of the emitted X-rays. It was this intriguing fact that he had discussed with Moseley.

  With a prodigious capacity for work matched only by his stamina, while others slept Moseley stayed in the laboratory working through the night. Within a couple of months he had measured the frequencies of X-rays emitted by every element between calcium and zinc. He discovered that as the elements he bombarded got heavier, there was a corresponding increase of frequencies of the emitted X-rays. Moseley predicted the existence of missing elements with atomic numbers 42, 43, 72 and 75 on the basis that each element produced a characteristic set of X-ray spectral lines and those adjacent to each other in the periodic table had very similar ones.44 All four were later discovered, but by then Moseley was dead. When the First World War began he enlisted in the Royal Engineers and served as a signals officer. He died, shot through the head, in Gallipoli on 10 August 1915. His tragic death at the age of 27 robbed him of a certain Nobel Prize. Rutherford personally gave him the highest possible accolade: he hailed Moseley as ‘a born experimenter’.

  Bohr’s correct assignment of the ‘Pickering-Fowler lines’ and Moseley’s ground-breaking work on nuclear charge were beginning to win support for the quantum atom. A more significant turning point in its acceptance came in April 1914, when the young German physicists James Franck and Gustav Hertz bombarded mercury atoms with electrons and found that the electrons lost 4.9eV of energy during these collisions. Franck and Hertz believed they had succeeded in measuring the amount of energy required to rip an electron from a mercury atom. Not having read his paper, due to the initial widespread scepticism that greeted it in Germany, it was left to Bohr to provide the correct interpretation of their data.

  When the electrons fired at the mercury atoms had energies of less than 4.9eV, nothing happened. But when a bombarding electron with energy above 4.9eV scored a direct hit, it lost that amount of energy and the mercury atom emitted an ultraviolet light. Bohr pointed out that 4.9eV was the energy difference between the ground state of the mercury atom and its first excited state. It corresponded to an electron jumping between the first two energy levels in the mercury atom, and the energy difference between these levels was exactly as predicted by his atomic model. When the mercury atom returns to its ground state, as the electron jumps down to the first energy level, it emits a quantum of energy that produces an ultraviolet light of wavelength 253.7nm in the mercury line spectra. The Franck-Hertz results provided direct experimental evidence for Bohr’s quantised atom and the existence of atomic energy levels. Despite initially having misinterpreted their data, Franck and Hertz were awarded the 1925 Nobel Prize in physics.

  Just as Part I of the trilogy was published in July 1913, Bohr had finally been appointed to a lectureship at Copenhagen University. Before long he was unhappy, as his major responsibility was to teach elementary physics to medical students. At the beginning of 1914, with his reputation on the rise, Bohr set about trying to establish a new professorship in theoretical physics for himself. It would be difficult, as theoretical physics as a distinct discipline was still poorly recognised as such outside Germany. ‘In my opinion Dr Bohr is one of the most promising and able of the young Mathematical Physicists in Europe today’, wrote Rutherford in the testimonial to the Department of Religious and Educational Affairs in support of Bohr and his proposal.45 The immense interest that his work had attracted internationally ensured that Bohr received the backing of the faculty, but once again the university hierarchy chose to postpone any decision. It was then that a dejected Bohr received a letter from Rutherford offering an escape route.

  ‘I daresay
you know Darwin’s tenure of readership has expired, and we are now advertising for a successor at £200’, Rutherford wrote.46 ‘Preliminary inquiries show that not many men of promise are available. I should like to get a young fellow with some originality in him.’ Having already told the Dane that his work showed ‘great originality and merit’, Rutherford wanted Bohr without explicitly saying so.47

  In September 1914, having been granted a year’s leave of absence, as any decision on the professorship he wanted was unlikely before then, Niels and Margrethe Bohr arrived in Manchester to a warm welcome at their safe arrival after a stormy voyage around Scotland. The First World War had begun and much had changed. The wave of patriotism that swept the country had virtually emptied the laboratories as those eligible to fight signed up. The hope that the war would be short and sharp receded by the day as the Germans smashed through Belgium and into France. Men who had only recently been colleagues were now fighting on opposing sides. Marsden was soon at the western front. Geiger and Hevesy had joined the armies of the Central Powers.

  Rutherford was not in Manchester when Bohr arrived. He had left in June to attend the annual meeting of the British Association for the Advancement of Science, being held that year in Melbourne, Australia. Recently knighted, he visited his family in New Zealand before travelling on to America and Canada as planned. Once back in Manchester, Rutherford devoted much of his time to anti-submarine warfare. Since Denmark was neutral, Bohr was not allowed to take part in any war-related activities. He concentrated largely on teaching, and what research was possible was impeded by the lack of journals and the censorship of letters from and to Europe.

  Originally planning to spend just a year in Manchester, Bohr was still there when in May 1916 he was formally appointed to the newly created post of professor of theoretical physics in Copenhagen. The growing recognition of his work had secured the post, but despite its successes there were problems that the quantum atom could not solve. The answers it gave for atoms with more than one electron failed to tally with experiments. It could not even account for helium with just two electrons. Worse, Bohr’s atomic model predicted spectral lines that could not be found. In spite of the introduction of ad hoc ‘selection rules’ to explain why some lines were observed and others were not, all the central elements of Bohr’s atom were accepted by the end of 1914: the existence of discrete energy levels, the quantisation of angular momentum of the orbiting electrons, and the origin of spectral lines. However, if there existed a single spectral line that could not be explained, even with the imposition of some new rule, then the quantum atom was in trouble.