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

by Manjit Kumar

  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.’25 Soon 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 tra
nsition 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

  REVOLUTION IN SCIENCE

  NEW THEORY OF THE UNIVERSE

  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 paym
ents.

  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 1919.52 Soon 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.