WHEN EINSTEIN MET BOHR - THE QUANTUM - Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar

Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar (2009)



'Those are the madmen who do not occupy themselves with quantum theory', Einstein told a colleague as they looked out of the window of his office in the Institute of Theoretical Physics at the German University in Prague.1 After his arrival from Zurich in April 1911, he had been puzzled as to why only women used the grounds in the mornings and only men in the afternoons. As he struggled with his own demon he discovered that the beautiful garden next door belonged to a lunatic asylum. Einstein was finding it difficult to live with the quantum and the dual nature of light. 'I wish to assure you in advance that I am not the orthodox light-quantizer for whom you take me', he told Hendrik Lorentz.2 It was a faulty impression that arose, he claimed, 'from my imprecise way of expressing myself in my papers'.3 Soon he gave up even asking if 'quanta really exist'.4 By the time he returned from the first Solvay conference in November 1911 on 'The Theory of Radiation and the Quanta', Einstein had decided that enough was enough and pushed the lunacy of the quantum to one side. Over the next four years, as Bohr and his atom took centre stage, Einstein effectively abandoned the quantum to concentrate on extending his theory of relativity to encompass gravity.

Founded in the mid-fourteenth century, Prague University was divided in 1882 along lines of nationality and language into two separate universities, one Czech and the other German. It was a division that reflected a society where Czechs and Germans harboured a deep-seated suspicion and mistrust of each other. After the easy-going, tolerant atmosphere of Switzerland and the cosmopolitan mix of Zurich, Einstein was ill at ease in spite of the full professorship and the salary that enabled him to live in some comfort. It provided just a quantum of solace against the creeping sense of isolation.

By the end of 1911, as Bohr contemplated his move from Cambridge to Manchester, Einstein desperately wanted to return to Switzerland, and it was then that an old friend came to his rescue. Recently appointed as the dean of the mathematics and physics section of the Swiss Federal Technical University (ETH), Marcel Grossmann offered Einstein a professorship in Zurich at the renamed former Polytechnic. Although the job was his, there were formalities that Grossmann had to observe. High on the list was seeking the advice of eminent physicists about Einstein's possible appointment. One of those asked was France's premier theorist, Henri Poincaré, who described Einstein as 'one of the most original minds' he knew.5 The Frenchman admired the ease with which he adapted to new concepts, his ability to see beyond classical principles, and when 'faced with a physics problem, [he] promptly envisages all possibilities'.6 Where Einstein had once failed to get a job as an assistant, in July 1912 he returned as a master physicist.

It was inevitable that sooner rather than later Einstein would become a prime target for the men in Berlin. In July 1913 Max Planck and Walther Nernst boarded the train to Zurich. They knew that it would not be easy to persuade Einstein to return to a country he had left almost twenty years ago, but they were prepared to make him an offer he simply could not refuse.

As Einstein met them off the train, he knew why Planck and Nernst had come, but not the details of the proposal they were about to make. Having just been elected a member of the prestigious Prussian Academy of Sciences, he was being offered one of its two salaried positions. This alone was a great honour, but the two emissaries of German science also offered a unique research professorship without any teaching duties and the directorship of the Kaiser Wilhelm Institute of Theoretical Physics once it was established.

He needed time to mull over the unprecedented package of three jobs. Planck and Nernst went on a short sightseeing train ride as he considered whether or not to accept. Einstein told them they would have his answer when they returned by the colour of the rose he carried. If red, he would go to Berlin; if white, he would stay in Zurich. As they got off the train, Planck and Nernst knew they had got their man when they saw Einstein clutching a red rose.

Part of the lure of Berlin for Einstein was the freedom to 'give myself over completely to rumination' with no obligations to teach.7 But with it came the pressure of having to deliver the sort of physics that made him the hottest property in science. 'The Berliners are speculating with me as with a prize-winning laying hen,' he told a colleague after his farewell dinner, 'but I don't know if I can still lay eggs.'8 After celebrating his 35th birthday in Zurich, Einstein moved to Berlin at the end of March 1914. Whatever reservations he might have had about returning to Germany, he was soon enthusing: 'Intellectual stimulation abounds here, there is just too much of it.'9 The likes of Planck, Nernst and Rubens were all within easy reach, but there was another reason why he found 'odious' Berlin exciting - his cousin Elsa Löwenthal.10

Two years earlier, in March 1912, Einstein had begun an affair with the 36-year-old divorcee with two young daughters - Ilse, aged thirteen, and Margot, eleven. 'I treat my wife like an employee whom I cannot fire', he told Elsa.11 Once in Berlin, Einstein would often disappear for days without a word of explanation. Soon he moved out of the family home altogether and drew up a remarkable list of conditions under which he was willing to return. If Mileva accepted his terms she would indeed become an employee, and one her husband was determined to fire.

Einstein demanded: '1. that my clothes and laundry are kept in good order and repair; 2. that I receive my three meals regularly in my room; 3. that my bedroom and my office are always kept neat, in particular, that the desk is available to me alone.' Further, she was to 'renounce all personal relations' and refrain from criticising him 'either in word or deed in front of my children'. Finally he insisted that Mileva adhere to 'the following points: 1. You are neither to expect intimacy from me nor reproach me in any way. 2. You must desist immediately from addressing me if I request it. 3. You must leave my bedroom or office immediately without protest if I so request.'12

Mileva agreed to his demands and Einstein returned. But it could not last. At the end of July, after just three months in Berlin, Mileva and the boys went back to Zurich. As he stood on the platform waving goodbye, Einstein wept, if not for Mileva and the memories of what had been, then for his two departing sons. But within a matter of weeks he was happily enjoying living alone 'in my large apartment in undiminished tranquillity'.13 It was a tranquillity that few would enjoy as Europe descended into war.

'One day the great European war will come out of some damned foolish thing in the Balkans', Bismarck was once reported as saying.14 That day was Sunday, 28 June 1914, and it was the assassination in Sarajevo of Archduke Franz Ferdinand, the heir to the crowns of Austria and Hungary. Austria, supported by Germany, declared war on Serbia. Germany declared war on Serbia's ally Russia on 1 August and on France two days later. Britain, who guaranteed Belgian independence, declared war on Germany on 4 August after it had violated Belgium's neutrality.15 'Europe in its madness has now embarked on something incredibly preposterous', Einstein wrote on 14 August to his friend Paul Ehrenfest.16

While Einstein felt 'only a mixture of pity and disgust', Nernst at 50 volunteered as an ambulance driver.17 Planck, unable to contain his patriotism, declared: 'It is a great feeling to be able to call oneself a German.'18 Believing that it was a glorious time to be alive, as rector of Berlin University, Planck sent his students to the trenches in the name of a 'just war'. Einstein could hardly believe it when he discovered that Planck, Nernst, Röntgen and Wien were among the 93 luminaries who signed the Appeal to the Cultured World.

This manifesto was published on 4 October 1914 in leading German newspapers and in others abroad, its signatories protesting against 'the lies and defamations with which our enemies are trying to besmirch Germany's pure cause in the hard life-and-death struggle forced upon it'.19 They asserted that Germany bore no responsibility for the war, had not violated Belgian neutrality, and had committed no atrocities. Germany was 'a cultured nation to whom the legacy of Goethe, Beethoven and Kant is fully as sacred as its hearths and plots of land'.20

Planck quickly regretted having signed, and in private began apologising to his friends among foreign scientists. Of all those that lent their names to the falsehoods and half-truths of the Manifesto of the Ninety-Three, as it became known, Einstein had expected better from Planck. Even the German chancellor had publicly admitted that Belgium's neutral status had been violated: 'The wrong that we are committing, we will endeavour to make good as soon as our military goal is reached.'21

As a Swiss citizen, Einstein was not asked to add his signature. However, he was deeply concerned at the long-term effect of the unbridled national chauvinism of the manifesto and was involved in producing a counter-manifesto entitled an Appeal to Europeans. It called on 'educated men of all states' to ensure that 'the conditions of peace did not become the source of future wars'.22 It challenged the attitude expressed by the Manifesto of the Ninety-Three as 'unworthy of what until now the whole world has understood by the term culture, and it would be a disaster if it were to become the common property of educated people'.23 It castigated German intellectuals for behaving 'almost to a man, as though they had relinquished any further desire for the continuance of international relations'.24 However, including Einstein, there were only four signatories.

By the spring of 1915 the attitudes of his colleagues at home and abroad had left Einstein feeling deeply disheartened: 'Even scholars of the various nations behave as if their cerebrums had been amputated eight months ago.'25Soon all hope that the war would be short-lived evaporated, leaving him by 1917 'constantly very depressed about the endless tragedy we must witness'.26 'Even the habitual flight into physics does not always help', he confessed to Lorentz.27 Yet the four years of war proved to be among his most productive and creative, as Einstein published a book and some 50 scientific papers, and in 1915 completed his masterpiece - general relativity.

Even before Newton, it had been assumed that time and space were fixed and distinct, the stage on which the never-ending drama of the cosmos was played out. It was an arena where mass, length and time were absolute and unvarying. It was a theatre in which spatial distances and time intervals between events were identical for all observers. Einstein, however, discovered that mass, length and time were not absolute and unchanging. Spatial distances and time intervals depended on the relative motion of observers. Compared to his earth-bound twin, for an astronaut travelling at near light-speed, time slows down (the hands on a moving clock are slower), space contracts (the length of a moving object shrinks), and a moving object gains mass. These were the consequences of 'special' relativity, and each would be confirmed by experiments in the twentieth century, but the theory did not incorporate acceleration. 'General' relativity did. In the midst of his struggle to construct it, Einstein said that it made special relativity look like 'child's play'.28 Just as the quantum was challenging the accepted view of reality in the atomic realm, Einstein took humanity closer to understanding the true nature of space and time. General relativity was his theory of gravity, and it would lead others to the big bang origin of the universe.

In Newton's theory of gravity, the force of attraction between two objects, such as the sun and the earth, is proportional to the product of their respective masses and inversely proportional to the square of the distance separating their centres of mass. With no contact between the masses, in Newtonian physics gravity is a mysterious 'action-at-a-distance' force. In general relativity, however, gravity is due to the warping of space caused by the presence of a large mass. The earth moves around the sun not because some mysterious invisible force pulls it, but because of the warping of space due to the sun's enormous mass. In short, matter warps space and warped space tells matter how to move.

In November 1915, Einstein tested general relativity by applying it to a feature of Mercury's orbit that could not be explained using Newton's gravitational theory. In its journey around the sun, Mercury does not trace out exactly the same path every orbit. Astronomers had precise measurements that revealed that the planet's orbit rotated slightly. Einstein used general relativity to calculate this orbital shift. When he saw that the number matched the data within the margins of error, he had palpitations of the heart and felt as if something had snapped inside. 'The theory is beautiful beyond comparison', he wrote.29 With his boldest dreams fulfilled, Einstein was content but the Herculean effort left him worn out. When he recovered he turned to the quantum.

Even as he worked on the general theory, in May 1914, Einstein was among the first to grasp that the Franck-Hertz experiment was a confirmation of the existence of energy levels in atoms and 'a striking verification of the quantum hypothesis'.30 By the summer of 1916, Einstein had 'a brilliant idea' of his own about an atom's emission and absorption of light.31 It led him to an 'astonishingly simple derivation, I should say, the derivation of Planck's formula'.32 Soon Einstein was convinced that 'light-quanta are as good as established'.33 However, it came at a price. He had to abandon the strict causality of classical physics and introduce probability into the atomic domain.

Einstein had offered alternatives before, but this time he could derive Planck's law from Bohr's quantum atom. Starting with a simplified Bohr atom with only two energy levels, he identified three ways in which an electron could jump from one level to the other. When an electron jumps from a higher to a lower energy level and emits a quantum of light, Einstein called this 'spontaneous emission'. It occurs only when an atom is in an excited state. The second type of quantum leap happens when an atom becomes excited as an electron absorbs a light-quantum and jumps from a lower to a higher energy level. Bohr had invoked both types of quantum leap to explain the origin of atomic emission and absorption spectra, but Einstein now revealed a third: 'stimulated emission'. It occurs when a light-quantum strikes an electron in an atom that is already in an excited state. Instead of absorbing the incoming light-quantum, the electron is 'stimulated', nudged, to leap to a lower energy, emitting a light-quantum. Four decades later, stimulated emission formed the basis of the laser, an acronym for 'light amplification by stimulated emission of radiation'.

Einstein also discovered that light-quanta had momentum, which, unlike energy, is a vector quantity; it has direction as well as magnitude. However, his equations clearly showed that the exact time of spontaneous transition from one energy level to another and the direction in which an atom emits a light-quantum was entirely random. Spontaneous emission was like the half-life of a radioactive sample. Half the atoms will decay in a certain amount of time, the half-life, but there was no way of knowing when any given atom would decay. Likewise, the probability that a spontaneous transition will take place could be calculated but the exact details were entirely left to chance, with no connection between cause and effect. This concept of a transition probability that left the time and direction of the emission of a light-quantum down to pure 'chance' was for Einstein a 'weakness' of his theory. It was something he was prepared to tolerate for the moment in the hope that it would be removed with the further development of quantum physics.34

Einstein was uneasy with this discovery of chance and probability at work in the heart of the quantum atom. Causality appeared to be at risk even though he no longer doubted the reality of quanta.35 'That business about causality causes me a lot of trouble, too', he wrote to Max Born three years later in January 1920.36 'Can the quantum absorption and emission of light ever be understood in the sense of the complete causality requirement, or would a statistical residue remain? I must admit that there I lack the courage of my convictions. But I would be very unhappy to renounce complete causality.'

What troubled Einstein was a situation akin to an apple being held above the ground, that when let go did not fall. Once the apple is let go, it is in an unstable state with respect to the state of lying on the ground, so gravity acts immediately on the apple, causing it to fall. If the apple behaved like an electron in an excited atom, then instead of falling back as soon as it was let go, it would hover above the ground, falling at some unpredictable time that can be calculated only in terms of probability. There may be a high probability that the apple will fall within a very short time, but there is a small probability that the apple will just hover above the ground for hours. An electron in an excited atom will fall to a lower energy level, resulting in the more stable ground state of the atom, but the exact moment of the transition is left to chance.37 In 1924, Einstein was still struggling to accept what he had unearthed: 'I find the idea quite intolerable that an electron exposed to radiation should choose of its own free will, not only its moment to jump off, but also its direction. In that case, I would rather be a cobbler, or even an employee in a gaming-house, than a physicist.'38

It was inevitable that the years of intense intellectual effort coupled with his bachelor lifestyle would take their toll. In February 1917, aged only 38, Einstein collapsed with intense stomach pains and the diagnosis was a liver complaint. Within two months he lost 56 pounds as his health deteriorated. It was the beginning of a series of illnesses, including gallstones, a duodenal ulcer and jaundice, that dogged him over the next few years. Plenty of rest and a strict diet were the prescribed cure. It was easier said than done, as life was transformed beyond recognition by the trials and tribulations of war. Even potatoes were a rarity by then in Berlin, and most Germans went hungry. Few actually starved to death, but malnutrition claimed lives - an estimated 88,000 in 1915. The following year it rose to more than 120,000 as riots erupted in more than 30 German cities. It was hardly surprising, as people were forced to eat bread made from ground straw instead of wheat.

There was an ever-growing list of such ersatz foods. Plant husks mixed with animal hides replaced meat, and dried turnips were used to make 'coffee'. Ash masqueraded as pepper, and people spread a mixture of soda and starch on their bread, pretending it was butter. Constant hunger made cats, rats and horses appear tasty alternatives for Berliners. If a horse dropped dead in the street it was swiftly butchered. 'They fought each other for the best pieces, their faces and clothing covered in blood', reported an eyewitness to one such incident.39

Real food was scarce, but still available to those who could afford to pay. Einstein was luckier than most, as he received food parcels from relatives in the south and from friends in Switzerland. Amid all the suffering, Einstein felt 'like a drop of oil on water, isolated by mentality and outlook on life'.40 Yet he could not look after himself and reluctantly moved into a vacant apartment next door to Elsa's. With Mileva still unwilling to grant a divorce, Elsa finally had Einstein as near to her as propriety would allow. Nursing Albert slowly back to health gave Elsa the perfect opportunity to pressurise him into doing whatever it took to get a divorce. Einstein initially had no intention of rushing into marriage a second time, as the first felt like 'ten years of prison', but eventually he relented.41 Mileva agreed after Einstein proposed to increase his existing payments, make her the recipient of his widow's pension, and offer her the money when he won the Nobel Prize. By 1918, having been nominated in six of the previous eight years, he was a dead certainty to be awarded the prize some time soon.

Einstein and Elsa married in June 1919. He was 40, she three years older. What happened next was beyond anything that Elsa could have imagined. Before the end of the year, the lives of the newlyweds were transformed as Einstein became world-famous. He was hailed as the 'new Copernicus' by some, derided by others.

In February 1919, just as Einstein and Mileva were finally divorced, two expeditions set off from Britain. One headed to the island of Principe off the coast of West Africa, the other to Sobral in the north-west of Brazil. Each destination had been carefully chosen by astronomers as a perfect site from which to observe the solar eclipse on 29 May. Their aim was to test a central prediction of Einstein's general theory of relativity, the bending of light by gravity. The plan was to photograph stars in close proximity to the sun that would be visible only during the few minutes of blackout of a total solar eclipse. In reality, of course, these stars were nowhere near the sun, but their light passed very close to it before reaching the earth.

The photographs would be compared with those taken at night six months earlier when the earth's position in relation to the sun ensured that the light from these same stars passed nowhere near the neighbourhood of the sun. The bending of light due to the presence of the sun warping the space-time in its vicinity would be revealed by small changes in the position of the stars in the two sets of photographs. Einstein's theory predicted the exact amount of displacement due to the bending or deflection of light that should be observed. At a rare joint meeting of the Royal Society and the Royal Astronomical Society on 6 November in London, the cream of British science gathered to hear whether Einstein was right or not.42

Newtonian Ideas Overthrown

… were the headlines on page twelve of the London Times the following morning. Three days later, on 10 November, the New York Times carried an article with six headings: 'Lights all askew in the heavens/Men of science more or less agog over results of eclipse observation/Einstein theory triumphs/Stars not where they seem or were calculated to be, but nobody need worry/A book for 12 wise men/ No more in all world could comprehend it, said Einstein, when his daring publishers accepted it.'43 Einstein had never said any such thing, but it made good copy as the press latched onto the mathematical sophistication of the theory and the idea of warped space.

One of those who unwittingly contributed to the mystique surrounding general relativity was Sir J.J. Thomson, the president of the Royal Society. 'Perhaps Einstein has made the greatest achievement in human thought,' he told a journalist afterwards, 'but no one has yet succeeded in stating in clear language what the theory of Einstein's really is.'44 In fact, by the end of 1916 Einstein had already published the first popular book on both the special and general theories.45

'The general theory of relativity is being received with downright enthusiasm among my colleagues', Einstein reported to his friend Heinrich Zangger in December 1917.46 However, in the days and weeks that followed the first press reports, there were many who came forth to pour scorn on 'the suddenly famous Dr Einstein' and his theory.47 One critic described relativity as 'voodoo nonsense' and 'the moronic brainchild of mental colic'.48 With supporters like Planck and Lorentz, Einstein did the only sensible thing; he ignored his detractors.

In Germany, Einstein was already a well-known public figure when the Berliner Illustrirte Zeitung gave over its entire front page to a photograph of him. 'A new figure in world history whose investigations signify a complete revision of nature, and are on a par with insights of Copernicus, Kepler, and Newton', read the accompanying caption. Just as he refused to be riled by his critics, Einstein kept a sense of perspective about being anointed the successor of three of history's great scientists. 'Since the light deflection result became public, such a cult has been made out of me that I feel like a pagan idol', he wrote after the Berliner Illustrirte Zeitung hit the newsstands. 'But this, too, God willing, will pass.'49 It never did.

Part of the widespread public fascination with Einstein and his work lay in a world still coming to terms with the upheavals in the aftermath of the First World War, which ended at 11am on 11 November 1918. Two days earlier, on 9 November, Einstein had cancelled his relativity course lecture 'because of revolution'.50 Later that day, Kaiser Wilhelm II abdicated and fled to Holland as a republic was proclaimed from a balcony of the Reichstag. Germany's economic problems were among the most difficult challenges facing the new Weimar Republic. Inflation was quickly on the rise, as Germans lost confidence in the mark and were busy either selling it or buying anything they could before it fell further.

It was a vicious circle that war reparations sent spiralling out of control, and the economy went into meltdown as Germany defaulted on its payments of wood and coal towards the end of 1922, and 7,000 marks bought one US dollar. However, that was nothing to the hyperinflation that occurred throughout 1923. In November that year, one dollar was worth 4,210,500,000,000 marks, a glass of beer cost 150 billion marks and a loaf of bread 80 billion. With the country in danger of imploding, the situation was brought under control only with the help of American loans and a reduction in reparation payments.

Amid the suffering, talk of warped space, bending light beams, and shifting stars that only '12 wise men' could comprehend fired the public imagination. However, everyone thought they had an intuitive grasp of concepts like space and time. As a result, the world appeared to Einstein to be a 'curious madhouse' as 'every coachman and every waiter argues about whether or not relativity theory is correct'.51

Einstein's international celebrity and his well-known anti-war stance made him an easy target for a campaign of hate. 'Anti-semitism is strong here and political reaction is violent', Einstein wrote to Ehrenfest in December 1919.52Soon he began receiving threatening mail and on occasions suffered verbal abuse as he left his apartment or office. In February 1920, a group of students disrupted his lecture at the university, one of them shouting, 'I'm going to cut the throat of that dirty Jew.'53 But the political leaders of the Weimar Republic knew what an asset Einstein was, as its scientists faced exclusion from international conferences after the war. The minister of culture wrote to reassure him that Germany, 'was, and will forever be, proud to count you, highly honoured Herr Professor, among the finest ornaments of our science'.54

Niels Bohr did as much as anyone to ensure that personal relations between scientists on opposing sides were restored as quickly as possible after the war. As a citizen of a neutral country, Bohr felt no resentment towards his German colleagues. He was among the first to extend an invitation to a German scientist when he asked Arnold Sommerfeld to lecture in Copenhagen. 'We had long discussions on the general principle of the quantum theory and the application of all kinds of detailed atomic problems', Bohr said after Sommerfeld's visit.55 Excluded for the foreseeable future from international meetings, German scientists and their hosts knew the value of these personal invitations. So when he received one from Max Planck to give a lecture on the quantum atom and the theory of atomic spectra in Berlin, Bohr gladly accepted. When the date was fixed as Tuesday, 27 April 1920, he was excited at the prospect of meeting Planck and Einstein for the first time.

'His must be a first-rate mind, extremely critical and far-seeing, which never loses track of the grand design', was Einstein's assessment of the young Dane, six years his junior.56 It was October 1919 and such an appraisal was a spur for Planck to get Bohr to Berlin. Einstein had long been an admirer. In the summer of 1905 as the creative storm that had broken loose in his mind began to subside, Einstein found nothing that was 'really exciting' to tackle next.57 'There would of course be the topic of spectral lines,' he told his friend Conrad Habicht, 'but I believe that a simple relationship between these phenomena and those already investigated does not exist at all, so that for the moment, the thing looks rather unpromising to me.'58

Einstein's nose for a physics problem ripe for attack was second to none. Having passed on the mystery of spectral lines, he came up with E=mc2, which said that mass and energy were interconvertible. But for all he knew, God Almighty was having a laugh at his expense by leading him 'around by the nose'.59 So when in 1913 Bohr showed how his quantised atom solved the mystery of atomic spectra, it appeared to Einstein 'like a miracle'.60

The uneasy mixture of excitement and apprehension that had taken hold of his stomach as Bohr made his way from the station to the university vanished as soon as he met Planck and Einstein. They put him at his ease by moving quickly from pleasantries to talk of physics. The two men could not have been more dissimilar. Planck was the epitome of Prussian formality and rectitude, while Einstein with his big eyes, unruly hair and trousers that were just a little too short gave the impression of a man at ease with himself, if not the troubled world in which he lived. Bohr accepted Planck's invitation to stay at his home during the visit.

His days in Berlin, Bohr said later, were spent 'discussing theoretical physics from morning to night'.61 It was the perfect break for the man who just loved to talk physics. He particularly enjoyed the lunch that the younger university physicists had thrown for him, from which they excluded all the 'bigwigs'. It was a chance for them to quiz Bohr after his lecture had left them 'somewhat depressed because we had the feeling that we had understood very little'.62 Einstein, however, understood perfectly well what Bohr was arguing and he did not like it.

Like virtually everyone else, Bohr did not believe in the existence of Einstein's light-quanta. He accepted, like Planck, that radiation was emitted and absorbed in quanta, but not that radiation itself was quantised. For him there was just too much evidence in favour of the wave theory of light, but with Einstein in the audience, Bohr told the assembled physicists: 'I shall not consider the problem of the nature of radiation.'63 However, he had been deeply impressed by Einstein's work of 1916 on spontaneous and stimulated emission of radiation and electron transitions between energy levels. Einstein had succeeded where he had failed by showing that it was all a matter of chance and probability.

Einstein continued to be troubled by the fact that his theory could not predict either the time or the direction in which the light-quantum emitted as an electron jumps from one energy level to a lower one. 'Nevertheless,' he had written in 1916, 'I fully trust in the reliability of the road taken.'64 He believed it was a road that would eventually lead to a restoration of causality. In his lecture, Bohr argued that no exact determination of time and direction was ever possible. The two men found themselves on opposite sides. In the days that followed, each tried to convert the other to his point of view as they walked the streets of Berlin together or dined at Einstein's home.

'Seldom in my life has a person given me such pleasure by his mere presence as you have', Einstein wrote to Bohr soon after he returned to Copenhagen. 'I am now studying your great publications and - unless I happen to get stuck somewhere - have the pleasure of seeing before me your cheerful boyish face, smiling and explaining.'65 The Dane had made a deep and lasting impression. 'Bohr was here, and I am just as enamoured of him as you are', Einstein told Paul Ehrenfest a few days later. 'He is like a sensitive child and walks about this world in a kind of hypnosis.'66 Bohr was equally intent in trying to convey, in his less than polished German, what it meant to him to have met Einstein: 'It was to me one of my greatest experiences to have met you and to talk to you. You cannot imagine what a great inspiration it was for me to hear your views from you in person.'67 Bohr did so again quite soon, as Einstein made a fleeting visit as he stopped off in Copenhagen in August on his way back from a trip to Norway.

'He is a highly gifted and excellent man', Einstein wrote to Lorentz after seeing Bohr.68 'It is a good omen for physics that prominent physicists are mostly also splendid people.' Einstein had become the target of two men who were not. Philipp Lenard, whose experimental work on the photoelectric effect Einstein had used in 1905 in support of his light-quanta, and Johannes Stark, the discoverer of the splitting of spectral lines by an electric field, had become rabid anti-Semites. The two Nobel laureates were behind an organisation calling itself the Working Group of German Scientists for the Preservation of Pure Science, whose prime aim was to denounce Einstein and relativity.69 On 24 August 1920 the group held a meeting at Berlin's Philharmonic Hall and attacked relativity as 'Jewish physics' and its creator as both a plagiarist and a charlatan. Not to be intimidated, Einstein went along with Walther Nernst and watched the proceedings from a private box as he was vilified. Refusing to rise to the bait, he said nothing.

Nernst, Heinrich Rubens and Max von Laue wrote to the newspapers defending Einstein against the outrageous charges levelled at him. Many of his friends and colleagues were therefore dismayed when Einstein wrote an article for the Berliner Tageblatt entitled 'My Reply'. He pointed out that had he not been Jewish and an internationalist he would not have been denounced, nor his work attacked. Einstein immediately regretted having been riled into writing the article. 'Everyone has to sacrifice at the altar of stupidity from time to time, to please the Deity and the human race', he wrote to the physicist Max Born and his wife.70 He was well aware that his celebrity status meant that 'like a man in the fairy tale who turned everything into gold - so with me everything turns into a fuss in the newspapers'.71 Soon there were rumours that Einstein might leave the country, but he chose to stay in Berlin, 'the place to which I am most closely tied by human and scientific connections'.72

In the two years after their meetings in Berlin and Copenhagen, Einstein and Bohr continued their individual struggles with the quantum. Both were beginning to feel the strain. 'I suppose it's a good thing that I have so much to distract me,' Einstein wrote to Ehrenfest in March 1922, 'else the quantum problem would have got me into a lunatic asylum.'73 A month later, Bohr confessed to Sommerfeld: 'In the last few years, I have often felt myself scientifically very lonesome, under the impression that my effort to develop the principles of the quantum theory systematically to the best of my ability has been received with very little understanding.'74 His feelings of isolation were about to end. In June 1922, he travelled to Germany and gave a celebrated series of seven lectures spread over eleven days at Göttingen University that became known as the 'Bohr Festspiele'.

More than a hundred physicists, old and young, came from all over the country to hear Bohr explain his electron shell model of the atom. It was his new theory about the arrangement of electrons inside atoms that explained the placing and grouping of elements within the periodic table. He proposed that orbital shells, like layers of an onion, surrounded an atomic nucleus. Each such shell was actually made up of a set or subset of electron orbits and was able to accommodate only a certain maximum number of electrons.75 Elements that shared the same chemical properties, Bohr argued, did so because they had the same numbers of electrons in their outermost shell.

According to Bohr's model, sodium's eleven electrons are arranged 2, 8 and 1. Caesium's 55 electrons are arranged in a 2, 8, 18, 18, 8, 1 configuration. It is because the outer shell of each element has a single electron that sodium and caesium share similar chemical properties. During the lectures Bohr used his theory to make a prediction. The unknown element with atomic number 72 would be chemically similar to zirconium, atomic number 40, and titanium, atomic number 22, the two elements in the same column of the periodic table. It would not, Bohr said, belong to the 'rare earth' group of elements that were on either side of it in the table, as predicted by others.

Einstein did not attend Bohr's Göttingen lectures, as he feared for his life following the murder of Germany's Jewish foreign minister. Walther Rathenau, a leading industrialist, had been in office only a few short months when he was gunned down in broad daylight on 24 June 1922 to become the 354th political assassination by the right since the end of the war. Einstein was one of those who had urged Rathenau not to take such a high-profile post within government. When he did, it was deemed 'an absolutely unheard of provocation of the people!' by the right-wing press.76

'Here our daily lives have been nerve-racking since the shameful assassination of Rathenau', Einstein wrote to Maurice Solovine.77 'I am always on the alert; I have stopped my lectures and am officially absent, though I am actually here all the time.' Warned by reliable sources that he was a prime target for assassination, Einstein confided to Marie Curie that he was thinking about giving up his post at the Prussian Academy to find a quiet place to settle down as a private citizen.78 For the man who in his youth had hated authority had now become a figure of authority. He was no longer simply a physicist, but was a symbol of German science and of Jewish identity.

Despite the turmoil, Einstein read Bohr's published papers, including 'The Structure of the Atoms and the Physical and Chemical Properties of the Elements', which appeared in the Zeitschrift für Physik in March 1922. He recalled nearly half a century later how Bohr's 'electron-shells of the atoms together with their significance for chemistry appeared to me like a miracle - and appears to me as a miracle even today'.79 It was, Einstein said, 'the highest form of musicality in the sphere of thought'. What Bohr had done was indeed as much art as science. Using evidence gathered from a variety of different sources such as atomic spectra and chemistry, Bohr had built up a particular atom, one electron shell at a time, layer by onion layer, until he had reconstructed every element in the entire periodic table.

At the heart of his approach lay Bohr's belief that quantum rules apply on the atomic scale, but any conclusion drawn from them must not conflict with observations made on the macroscopic scale where classical physics rules. Calling it the 'correspondence principle' allowed him to eliminate ideas on the atomic scale that when extrapolated did not correspond to results that were known to be correct in classical physics. Since 1913 the correspondence principle had helped Bohr bridge the divide between quantum and classical. Some viewed it as a 'magic wand, which did not act outside Copenhagen', recalled Bohr's assistant Hendrik Kramers.80 Others might have struggled to wave it, but Einstein recognised a fellow sorcerer at work.

Whatever reservations there might have been at the lack of hard mathematics to underpin Bohr's theory of the periodic table, everyone had been impressed by the Dane's latest ideas and gained a greater appreciation of the problems that remained. 'My entire stay in Göttingen was a wonderful and instructive experience for me,' Bohr wrote on his return to Copenhagen, 'and I cannot say how happy I was for all the friendship shown me by everybody.'81He was no longer feeling under-appreciated and isolated. Later that year there was further confirmation, if he needed it.

As the telegrams of congratulation landed on Bohr's desk in Copenhagen, none meant more to him than the one from Cambridge. 'We are delighted that you have been awarded the Nobel Prize', Rutherford wrote. 'I knew it was merely a question of time, but there is nothing like the accomplished fact. It is well merited recognition of your great work and everybody here is delighted in the news.'82 In the days that followed the announcement, Rutherford had never been far from Bohr's thoughts. 'I have felt so strongly how much I owe you,' he told his old mentor, 'not only for your direct influence on my work and your inspiration, but also for your friendship in these twelve years since I had the great fortune of meeting you for the first time in Manchester.'83

The other person Bohr could not help thinking about was Einstein. He was delighted and relieved that the day he received the 1922 prize, Einstein had been awarded the Nobel Prize for 1921 that had been deferred for a year. 'I know how little I have deserved it,' he wrote to Einstein, 'but I should like to say that I consider it a good fortune that your fundamental contribution in the special area in which I work as well as contributions by Rutherford and Planck should be recognized before I was considered for such an honour.'84

Einstein was on a ship bound for the other side of the world when the Nobel Prize winners were announced. On 8 October, still fearing for his safety, Einstein and Elsa had left for a lecture tour of Japan. He 'welcomed the opportunity of a long absence from Germany, which took me away from temporarily increased danger'.85 He did not return to Berlin until February 1923. The original six-week itinerary turned into a grand tour lasting five months, during which he had received Bohr's letter. He replied during the voyage home: 'I can say without exaggeration that [your letter] pleased me as much as the Nobel Prize. I find especially charming your fear that you might have received the award before me - that is typically Bohr-like.'86

A blanket of snow covered the Swedish capital on 10 December 1922 as the invited guests assembled in the Great Hall of the Academy of Music in Stockholm to watch the presentation of the Nobel Prizes. The ceremony began at five o'clock in the presence of King Gustav V. The German ambassador to Sweden received the prize on behalf of the absent Einstein, but only after winning a diplomatic argument with the Swiss over the physicist's nationality. The Swiss were claiming Einstein as one of their own, until the Germans discovered that by accepting the appointment at the Prussian Academy in 1914 Einstein had automatically become a German citizen, even though he had not given up his Swiss nationality.

Having renounced his German citizenship in 1896 and taken Swiss citizenship five years later, Einstein was surprised to learn that he was a German after all. Whether he liked it or not, the needs of the Weimar Republic meant that Einstein officially had dual nationality. 'By an application of the theory of relativity to the taste of readers,' Einstein had written in November 1919 in an article for the London Times, 'today in Germany I am called a German man of science and in England I am represented as a Swiss Jew. If I come to be regarded as a bête noire, the descriptions will be reversed and I shall become a Swiss Jew for the Germans and a German man of science for the English!'87Einstein might have recalled these words had he been at the Nobel banquet and heard the German ambassador propose a toast that expressed the 'joy of my people that once again one of them has been able to achieve something for all of mankind'.88

Bohr rose after the German ambassador and gave a short speech as tradition demanded. After paying tribute to J.J. Thomson, Rutherford, Planck and Einstein, Bohr proposed a toast to the international cooperation for the advancement of science, 'which is, I may say, in these so manifoldly depressing times, one of the bright spots visible in human existence'.89 Given the occasion, it is understandable that he chose to forget the continuing exclusion of German scientists from international conferences. The next day Bohr was on firmer ground as he gave his Nobel lecture on 'The structure of the atom'. 'The present state of atomic theory is characterized by the fact that we not only believe the existence of atoms to be proved beyond a doubt,' he began, 'but we even believe that we have an intimate knowledge of the constituents of the individual atoms.'90 Having given a survey of the developments in atomic physics of which he had been such a central figure in the past decade, Bohr conclude his lecture with a dramatic announcement.

In his Göttingen lectures, Bohr had predicted the properties that the missing element with an atomic number of 72 should possess, based upon his theory of the arrangement of electrons in atoms. At exactly that time a paper was published outlining an experiment performed in Paris that confirmed a long-standing rival French claim that element 72 was a member of the 'rare earth' family of elements that occupied slots 57 to 71 in the periodic table. After the initial shock, Bohr began having serious doubts about the validity of the French results. Fortunately his old friend Georg von Hevesy, who was now in Copenhagen, and Dirk Coster devised an experiment to settle the dispute about element 72.

Bohr had already left for Stockholm by the time Hevesy and Coster completed their investigation. Coster telephoned Bohr shortly before his lecture and he was able to announce that 'appreciable quantities' of element 72 had been isolated, 'the chemical properties of which show a great similarity to those of zirconium and a decided difference from those of the rare earths'.91 Later called hafnium after the ancient name for Copenhagen, it was a fitting conclusion to Bohr's work on the configuration of electrons within atoms that he had begun in Manchester a decade earlier.92

In July 1923, Einstein gave his Nobel lecture on the theory of relativity as part of the 300th anniversary celebrations of the founding of the Swedish city of Göteborg. He broke with tradition by choosing relativity, when he had been awarded the prize 'for his attainments in mathematical physics and especially for his discovery of the law of the photoelectric effect'.93 By limiting the award of the prize for the 'law', the mathematical formula that accounted for the photoelectric effect, the committee deftly sidestepped endorsing Einstein's controversial underlying physical explanation - the light-quantum. 'In spite of its heuristic value, however, the hypothesis of light-quanta, which is quite irreconcilable with so-called interference phenomena, is not able to throw light on the nature of radiation', Bohr had said during his own Nobel lecture.94 It was a familiar refrain echoed by every self-respecting physicist. But as Einstein went to meet Bohr for the first time in nearly three years, he knew that an experiment performed by a young American meant that he no longer stood alone in defence of the quantum of light. Bohr had heard the dreaded news before Einstein.

In February 1923 Bohr received a letter dated 21 January, from Arnold Sommerfeld, alerting him to the 'most interesting thing that I have experienced scientifically in America'.95 He had swapped Munich, Bavaria for Madison, Wisconsin for a year and managed to escape the worst of the hyperinflation about to engulf Germany. It had been a shrewd financial move for Sommerfeld. To get an early glimpse of the work of Arthur Holly Compton before his European colleagues was an unexpected bonus.

Compton had made a discovery that challenged the validity of the wave theory of X-rays. Since X-rays were electromagnetic waves, a form of short-wavelength invisible light, Sommerfeld was saying that the wave nature of light, contrary to all the evidence in its favour, was in serious trouble. 'I do not know if I should mention his results', wrote Sommerfeld somewhat coyly, since Compton's paper had not yet been published. 'I want to call your attention to the fact that eventually we may expect a completely fundamental and new lesson.'96 It was a lesson that Einstein had been trying to teach with varying degrees of enthusiasm since 1905. Light was quantised.

Compton was one of America's leading young experimenters. He had been appointed professor and head of physics at the University of Washington in St Louis, Missouri in 1920 at just 27. His investigations into the scattering of X-rays conducted two years later would be described as 'the turning point in twentieth-century physics'.97 What Compton did was fire a beam of X-rays at a variety of elements such as carbon (in the form of graphite) and measure the 'secondary radiation'. When the X-rays slammed into the target most of them passed straight through, but some were scattered at a variety of angles. It was these 'secondary' or scattered X-rays that interested Compton. He wanted to find out if there was any change in their wavelength compared to the X-rays that had struck the target.

He found that the wavelengths of the scattered X-rays were always slightly longer than those of the 'primary' or incident X-rays. According to the wave theory they should have been exactly the same. Compton understood that the difference in wavelength (and therefore frequency) meant the secondary X-rays were not the same as the ones that had been fired at the target. It was as strange as shining a beam of red light at a metal surface and finding blue light being reflected.98 Unable to make his scattering data tally with the predictions of a wavelike theory of X-rays, Compton turned to Einstein's light-quanta. Almost at once he found 'that the wavelength and the intensity of the scattered rays are what they should be if a quantum of radiation bounced from an electron, just as one billiard ball bounces from another'.99

If X-rays came in quanta, then a beam of X-rays would be similar to a collection of microscopic billiard balls slamming into the target. Although some would pass through without hitting anything, others would collide with electrons inside atoms of the target. During such a collision an X-ray quantum would lose energy as it was scattered and the electron sent recoiling from the impact. Since the energy of an X-ray quantum is given by E=hv, where h is Planck's constant and v its frequency, then any loss of energy must result in a drop in frequency. Given that frequency is inversely proportional to wavelength, the wavelength associated with a scattered X-ray quantum increases. Compton constructed a detailed mathematical analysis of how the energy lost by the incoming X-ray and the resulting change in the wavelength (frequency) of the scattered X-ray was dependent upon the angle of scattering.

No one had ever observed the recoiling electrons that Compton believed should accompany the scattered X-rays. But then no one had been looking for them. When he did, Compton soon found them. 'The obvious conclusion,' he said, 'would be that X-rays, and so also light, consist of discrete units, proceeding in definite directions, each unit possessing the energy hv and the corresponding momentum h.'100 The 'Compton effect', the increase in wavelength of X-rays when they are scattered by electrons, was irrefutable evidence for the existence of light-quanta, which until then many had dismissed at best as science fiction. It was by assuming that energy and momentum are conserved in the collision between an X-ray quantum and an electron that Compton was able to explain his data. It was Einstein, in 1916, who had been the first to suggest that light-quanta possessed momentum, a particle-like property.

In November 1922 Compton announced his discovery at a conference in Chicago.101 However, although he sent his paper to the Physical Review just before Christmas, it was not published until May 1923 as the editors failed to understand the significance of its content. The avoidable delay meant that the Dutch physicist Pieter Debye beat Compton into print with the first complete analysis of the discovery. A former Sommerfeld assistant, Debye had submitted his paper to a German journal in March. Unlike their American counterparts, the German editors recognised the importance of the work and published it the following month. However, Debye and everyone else gave the talented young American the credit and recognition he deserved. It was sealed when Compton was awarded the Nobel Prize in 1927. By then, Einstein's light-quantum had been rechristened the photon.102

There had been 2,000 at his Nobel lecture in July 1923, but Einstein knew that most of them had come to see rather than to listen to him. Sitting on the train as he made his way from Göteborg to Copenhagen, Einstein was looking forward to meeting a man who would listen to his every word and probably disagree. When he got off the train, Bohr was there to greet him. 'We took the streetcar and talked so animatedly that we went much too far', Bohr recalled almost 40 years later.103 Speaking in German, they were oblivious to the curious stares of fellow passengers. Whatever was discussed, as they rode back and forth missing their stop, it was sure to include the Compton effect, soon to be described by Sommerfeld as 'probably the most important discovery that could have been made in the current state of physics'.104 Bohr was unconvinced and refused to accept that light was made up of quanta. It was he, not Einstein, who was now in the minority. Sommerfeld was in no doubt that 'the death-knell of the wave theory of radiation' had been sounded by Compton.105

Like the doomed hero in the westerns that he later liked to watch, Bohr was outnumbered as he made one last stand against the quantum of light. In collaboration with his assistant Hendrik Kramers and a visiting young American theorist, John Slater, Bohr proposed sacrificing the law of conservation of energy. It was a vital component in the analysis leading to the Compton effect. If the law was not strictly enforced on the atomic scale as it was in the everyday world of classical physics, then Compton's effect was no longer incontrovertible evidence for Einstein's light-quanta. The BKS proposal, as it became known (after Bohr, Kramers and Slater), appeared to be a radical suggestion but was in truth an act of desperation that showed how much Bohr abhorred the quantum theory of light.

The law had never been experimentally tested at the atomic level and Bohr believed that the extent of its validity remained an open question in processes such as the spontaneous emission of light-quanta. Einstein believed that energy and momentum were conserved in every single collision between a photon and an electron, while Bohr believed they were valid only as a statistical average. It was 1925 before experiments by Compton, then at Chicago University, and by Hans Geiger and Walther Bothe at the Physikalische-Technische Reichsanstalt, confirmed that energy and momentum were conserved in collisions between a photon and an electron. Einstein had been right and Bohr wrong.

Confident as ever, on 20 April 1924, more than a year before experiments silenced the doubters, Einstein eloquently summed up the situation for the readers of the Berliner Tageblatt: 'There are therefore now two theories of light, both indispensable and - as one must admit today despite twenty years of tremendous effort on the part of theoretical physicists - without any logical connection.'106 Einstein meant that both the wave theory of light and quantum theory of light were in some way valid. Light-quanta could not be invoked to explain the wave phenomena associated with light, such as interference and diffraction. Conversely, a full explanation of Compton's experiment and the photoelectric effect could not be provided without recourse to the quantum theory of light. Light had a dual, wave-particle character, which physicists just had to accept.

One morning, not long after the article appeared, Einstein received a parcel with a Paris postmark. Opening it, he discovered a note from an old friend seeking his opinion of the accompanying doctoral thesis written by a French prince on the nature of matter.