Einstein's Masterwork

by John Gribbin

  Meanwhile, in another twist, the students in Zurich had got wind of the possible move, and organised a petition calling on the authorities ‘to do your utmost to keep this outstanding researcher and teacher at our university’. The response of those authorities was to increase Einstein’s salary from 4,500 Swiss francs to 5,500 SF. This was where things stood in August 1910. But Jaumann now learned that he was the second choice of the Prague faculty for the professorship and turned the offer down, declaring: ‘I will have nothing to do with a university that chases after modernity and does not appreciate merit.’ The job was now very nearly Einstein’s – except for a final twist. Previously rejected for being Jewish, he was now on the brink of being rejected for not being Jewish enough. The Austro-Hungarian bureaucracy required all its employees to be members of a religion. Any religion would do. But Einstein, a non-believer, had stated on his application that he had no religion. When the difficulty was pointed out to him, he pragmatically filled in his religion as ‘Mosaic’ on the forms. He was also required to accept Austro-Hungarian citizenship, while retaining his Swiss citizenship, and was then officially appointed to the chair in January 1911, to take up his duties in March that year. The salary was the equivalent of 9,000 SF, enough for the family to rent a large apartment (with that new innovation, electric light) and employ a live-in maid.

  On the move

  Before taking up his post in Prague, Einstein (with Mileva) had visited Lorentz in Leiden. This was the first meeting between Einstein and the man who Abraham Pais has described as ‘the one father figure in Einstein’s life’. In an essay written in 1953 to mark the centenary of Lorentz’s birth, Einstein wrote ‘he meant more to me personally than anybody else I have met’.6 Once in Prague, he continued to make new scientific friends, most notably Paul Ehrenfest, a Viennese physicist who shared Einstein’s ‘Jewish atheism’ but unlike Einstein refused to compromise by pretending to a religious affiliation. At the time, he had been based in St Petersburg, where they were less scrupulous about such things, but visited Prague and met Einstein on a trip round the academic centres of Europe looking for a more congenial post. Ehrenfest soon succeeded Lorentz as professor in Leiden, much to Einstein’s delight. Lorentz stayed on in a part-time post, giving Einstein a double reason for future visits to the Dutch city, which he did almost every year when he was based in Berlin, where he completed the General Theory. But the road from Prague to Berlin still had another turn to take.

  Prague was far from being a quiet place to settle down to research in 1911. Although only about 5 per cent of the population of the city were German-speaking, they dominated cultural and political life, which inevitably caused friction with the bulk of the Czech population. In a further complication, about half of the Germans were Jewish and subject to other kinds of spoken and unspoken prejudice. In the last years of the Austro-Hungarian Empire Prague was a city where the German minority regarded themselves as socially superior to the Czech majority, the Czechs hated the Germans, and both communities disliked the Jews. Strange gypsy-like women from the Balkans were almost beneath contempt, but might just be tolerated if married to a respectable professor. In a letter to Besso, written soon after he arrived in Prague, Einstein said: ‘My position and my institute give me much joy, only the people are so alien to me.’7

  Like the rest of the Austro-Hungarian Empire, in the years after 1910 Prague was an accident waiting to happen. It didn’t help that the city was filthy, and the water unfit to drink, which was not good for the baby. Einstein was to an extent insulated from all this by his absorption in his work, but it cannot have been comfortable for Mileva. She loathed Prague, resented being left out of the scientific discussions between Einstein and his colleagues, and was left to brood on her own when Einstein embarked on a series of scientific travels around Europe.

  The most important of these was to attend a scientific conference, known as a Solvay Congress, in Brussels at the end of October 1911. This was the first of what became a long series of such events, sponsored by a wealthy Belgian chemist, Ernest Solvay. The theme of the first Solvay Conference (or Congress) was ‘the quantum problem’, and Einstein presented a paper on the application of quantum physics to the theory of specific heat. The details do not matter here, but his conclusion is as dramatic now as it was then: ‘These discontinuities, which we find so distasteful in Planck’s theory, seem really to exist in nature.’ In other words, quanta are real. As Lorentz pointed out at the time, this ‘seems in fact to be totally incompatible with Maxwell’s equations’. Einstein insisted that there had to be a way to reconcile the wave and particle theories of light: ‘In addition to Maxwell’s electrodynamics … we must also admit a hypothesis such as that of quanta.’

  As well as attending major conferences such as this, Einstein was often invited to give talks at universities around Europe. He also seems to have regarded the Prague post from the outset as merely a stepping stone in his career, and these visits provided a useful shop window for him to display his scientific wares. Mileva, increasingly suffering from depression, stayed in Prague with the children, and Einstein seems to have been glad to get away from her, as much as to spread the word about his ideas. It was against this background that on a visit to Berlin in Easter 1912 Einstein renewed acquaintance with a cousin, Elsa, who was three years older than Albert.

  Elsa Einstein, as she was originally and would become again, was even more closely related to Albert than the term ‘cousin’ suggests. She was indeed the daughter of the sister of Albert’s mother, but in addition her father Rudolf Einstein was the first cousin of Albert’s father. She had been married, briefly, had two daughters and, although now divorced, was known by her married name of Löwenthal. Elsa and Albert had sometimes played together as children and once went to the opera together when a little older, but had not seen each other in years. Elsa was in many ways the opposite of Mileva – a homely woman who enjoyed cooking and homemaking, and wanted nothing more than a comfortable life with a man who was a good provider. As for Albert, by now he was not looking for passion (though he never seems to have been averse to a dalliance) but craved a quiet domestic home life where he could be looked after and left to get on with his work.

  Whatever the details, some kind of spark was struck between the two of them that spring. On his return to Prague, Einstein initially kept up a flow of correspondence with Elsa. In one letter he wrote: ‘I have to have someone to love, otherwise life is miserable,’ adding ‘and this someone is you.’ But then he had qualms. In May 1912 he wrote again to Elsa, this time saying that: ‘It will not be good for the two of us, as well as for the others, if we form a closer attachment. So, I am writing to you today for the last time.’

  As so often with Einstein’s personal life, there was a professional reason associated with this change of heart. His attempts to find somewhere more congenial than Prague to work seemed to be bearing fruit, offering another ‘last chance’ to save his marriage. For some time, the University of Utrecht had been trying to recruit him, but Einstein had kept them on hold since he had an even better iron in the fire. In June 1911, the status of his alma mater, the ETH in Zurich, had been upgraded, and new professorships created. Even before he had left for Prague, Einstein had promised that he would not accept an offer from another institution without giving the ETH a chance to find a niche for him. But the bureaucratic wheels in Zurich were turning painfully slowly, with doubts once again being expressed in some quarters about his ability as a teacher. Einstein kept the pot boiling in Utrecht in a deliberate attempt to stir the ETH into action, even asking the Dutch to delay announcing the fact that they had already found another candidate, Peter Debye. But eventually, aided by letters of recommendation from Marie Curie and Henri Poincaré, Einstein got the job. He would return to Zurich, and the ETH, in July 1912, at the end of the academic year in Prague. Einstein wrote to a friend with the news: ‘Great joy about it among us old folks and the two bear cubs.’ There was less joy at the University of Prague, but n
othing they could do about it.

  The post at the ETH could, perhaps should, have been a job for life. The family were able to afford a six-roomed apartment in a good part of town, they had friends and they fitted in. But Mileva, who should have been the chief beneficiary, developed rheumatism, which made it painfully difficult for her to go out during the winter, and became increasingly depressed in spite of the efforts of her friends to cheer her up. Einstein was never good at understanding the difficulties of others, let alone making a real effort to help them overcome such problems. And then Elsa came back into the reckoning.

  In spite of breaking off his correspondence with her, Einstein had thoughtfully given Elsa his new address in Zurich, and she sent him a present for his 34th birthday in March 1913, adding a request for a photograph of him and disingenuously asking advice on a good book on relativity theory. The correspondence was renewed, on much the same terms as before. At which point, in July 1913, two of the pillars of the German scientific establishment, Max Planck and Walther Nernst, arrived in Zurich with the proverbial offer that could not be refused.

  The package put together by Planck and Nernst included a specially created professorship at the University of Berlin that need involve no teaching at all, if Einstein so wished it, together with membership of the prestigious Prussian Academy of Sciences (the youngest member of that august body), an enhanced salary and no administrative duties. It was a glorious offer, except for the impact such a move would surely have on Mileva. Einstein told Lorentz that: ‘I could not resist the temptation to accept a position in which I am relieved of all responsibilities so that I can give myself over completely to rumination.’ But that wasn’t the whole story. In a letter to Heinrich Zangger, only released to the world in 2006, Einstein said that Elsa ‘was the main reason for my going to Berlin’. If so, she has a lot to answer for, both good and bad.

  Having just escaped from Prague back to a country and a city she felt comfortable in, it is easy to imagine Mileva’s reaction when Albert told her about the job in Berlin. It was to prove the last straw, and although in the spring of 1914 Mileva did travel to Berlin with the children to join her husband, who had gone on ahead (not least to spend time with Elsa), it wasn’t long before she returned to Switzerland, taking her sons with her. The final break came on 29 July 1914, when Einstein came to see off Mileva and the boys – who had already left his apartment and had been staying with friends in Berlin for several weeks – on the morning train to Zurich. Einstein cried like a child, particularly distressed at the loss of his children.

  So Einstein was living alone in a large apartment in Berlin, but with Elsa and his own mother not far away, starting a new life when the First World War broke out. Even before the end of 1913, partly as a retreat from his domestic troubles, he had put the problems of quantum theory to one side and returned with full force to the attempt to generalise his theory of relativity. He now did so with an intensity which led to the breakthrough of 1915, while Elsa, hoping for the day when he would actually divorce Mileva and marry her, bided her time and kept his domestic affairs under control.

  Einstein worked obsessively, slept only when he was exhausted, forgot to eat and neglected personal hygiene. The result was that by 1915 he completed his General Theory and presented it to the Prussian Academy. It would also, as we shall see, lead to a breakdown in his health in 1917, when his life was probably only saved by Elsa’s attention.

  First steps

  For four years after his realization that ‘if a person falls freely he will not feel his own weight’, Einstein made no real effort to develop his ideas about non-uniform motion and gravity, even though he was convinced that this insight would enable him ‘to extend or generalize the concept of relativity to apply to accelerated systems … and in so doing, I expected that I would be able to resolve the problem of gravitation at the same time’.8 The puzzles of quantum physics seemed more urgent and required his full attention. But in 1911, he told his friend Michael Besso that he was tired of quantum physics and was going to concentrate on developing his general theory of motion and gravity. Before we look at how he did so, though, it’s worth spelling out just why a theory of accelerated objects is also a theory of gravity. The explanation is disarmingly simple, although nobody before Einstein spotted it.

  Einstein used to describe things in terms of a falling lift, appropriate for the technology of his day. But these days it makes more sense to talk about the behaviour of objects inside a windowless spaceship. If the rockets are turned off and the spaceship is moving through space at a constant velocity, everything floats around inside the cabin, weightless. Under these conditions, if a beam of light is shone across the cabin from one wall to the other, it will travel in a straight line and make a spot on the opposite wall the same height above the floor as the height of the light source. The obvious light source to use would be a laser, and it is worth mentioning that the physics underlying lasers was one of the things Einstein also worked out, just after completing the General Theory.

  What happens if the rockets are turned on and the spaceship is accelerating?b Everything falls to the floor, and it feels to any occupants exactly the same as having weight. But what happens to the light beam? During the time the beam takes crossing the cabin, the speed of the spaceship has increased, moving the spaceship a tiny bit ahead of the light beam, so the spot made on the wall is a little lower than when there is no acceleration. It will look to any occupants of the spacecraft as if the light beam has been bent. Einstein realised (without ever having seen a spaceship) that in order for gravity and acceleration to be equivalent to one another – his insight from the patent office days – exactly the same thing must happen if the spaceship is sitting on the launch pad on Earth. With no windows, the occupants would not be able to tell if their weight was caused by acceleration or by gravity. But they would be able to tell if the light beam went in a straight line across the cabin when it was sitting on the ground. So, Einstein reasoned (from his equivalent thinking about falling lifts, rather than spaceships), gravity must bend light by just the right amount to make acceleration and gravity precisely equivalent. This was his jumping off point when he returned to intense concentration on the search for a General Theory in 1911, during his time in Prague.

  The first fruits of this effort came in a paper published in the Annalen der Physik in 1911, in which he calculated that ‘a ray of light going past the sun would undergo a deflection of 0.83 seconds of arc’.c The exciting thing about this calculation was that it offered the prospect of testing the theory. Usually, we cannot see light passing close by the Sun, because of the glare of the Sun’s own light. But during a solar eclipse, when the light from the Sun is blocked by the Moon, it is possible to see distant stars, far beyond the Sun, by light which skims past the edge of the Sun on its way to us. (It also skims past the Moon, but the Moon is far too small to produce a measurable effect on the light; the Sun is 27 million times more massive than the Moon.) If the light rays were deflected as Einstein predicted, these stars would appear in a slightly different place on photographic plates taken during an eclipse to their positions in photographs taken when the Sun was not in the line of sight. As Einstein put it: ‘It would be a most desirable thing if astronomers would take up the question.’

  The challenge was taken up by Erwin Freundlich, an astronomer at the Berlin University Observatory, who knew that there would be a solar eclipse visible from the Crimea on 21 August 1914. Einstein was so enthusiastic that he offered to help to fund an expedition to make the necessary observation, although in the end the money came from the Krupp Foundation. But the timing was disastrous. Freundlich and two colleagues left for the Crimea on 19 July 1914. On 1 August, as part of the complicated political web that led to the First World War, Germany declared war on Russia. Freundlich and his colleagues were taken prisoner by the Russians, and their equipment confiscated. Hardly surprisingly, as Germans carrying cameras and surveying equipment they were suspected of spying and were luc
ky to be returned to Germany a few weeks later as part of a prisoner exchange. But there was a silver lining, at least as far as the General Theory was concerned. Einstein’s calculation from 1911 was wrong. If the expedition had been a success, it would have found a different deflection of light, providing a blow to Einstein’s prestige (not that he would have cared) and perhaps discrediting the theory. But by the summer of 1914, amid the turmoil of his move to Berlin, the final breakup of his marriage and the outbreak of war, Einstein was already thinking along new lines.

  ‘Everybody knows’ that light travels in straight lines, so how could a light ray be bent? One possible answer lay in the application of a different kind of geometry to the problem, a geometry in which straight lines are not straight in the everyday sense, where parallel lines can cross or diverge, and where the angles of a triangle do not add up to 180 degrees. The familiar geometry in which parallel lines never meet or diverge, the angles of a triangle add up to 180 degrees, and so on is known as Euclidean geometry, after the Greek mathematician who spelled out the ground rules; it describes the geometry of a flat surface, in the everyday sense of the word ‘flat’. This is the kind of geometry Minkowski used in his geometrisation of the Special Theory. Alternative geometries are therefore known as non-Euclidian geometries, and in the 19th century there had been a great deal of work on non-Euclidean geometries, largely as an abstract exercise in mathematics (although, as it happens, the geometry of the curved surface of the Earth is non-Euclidean). But Einstein did not know much about them, in spite of his earlier dilettante dabbling with Poincaré’s work, and he knew even less about how to work with the corresponding equations. Indeed, it is a fact which still has the power to surprise that although Einstein had great insight into the physical nature of the world, he was always, by the standards of top-flight physics, rather weak at maths. But he knew a man who was a whizz at maths – his old friend Marcel Grossmann. One of Einstein’s first actions on returning to Zurich in 1912 was to call on Grossmann for help in developing a set of mathematical equations – what physicists call a ‘field theory’ – that would enable him to write down the laws which describe the workings of gravity, or the gravitational field, in the way that Maxwell’s equations describe the workings of the electromagnetic field. Grossmann, who did indeed know the history of non-Euclidean geometry, was only too pleased to help.