by John Gribbin
Einstein himself continued to publish, though not at the prodigious and unsustainable rate of 1905, and his first paper really to make waves in the scientific community appeared in 1907. In this work, Einstein used the idea of energy quanta, combined with his now familiar statistical approach, to explain the way the temperature of an object increases as it absorbs heat. The kinetic theory explains in a qualitative way that the rise in temperature of a solid body as it absorbs energy means that the atoms and molecules vibrate more strongly when the material is hotter. Einstein introduced the idea that the energy being absorbed by the individual atoms and molecules can only be accepted in quanta with energy h. He was able to explain otherwise puzzling features of the process and found a formula for the specific heat of a body, which is a measure of how much its temperature rises when a certain amount of heat is absorbed. Planck’s colleague in Berlin, the professor of Physical Chemistry Walther Nernst, took up the idea and incorporated it into his own work on thermodynamics and specific heat, which established over the next few years that it was essential to incorporate quantum ideas into any satisfactory understanding of the thermodynamic behaviour of solid objects.
The geometry of relativity
But the most important outside contribution, not only to popularising Einstein’s ideas but (eventually) to shaping the way Einstein’s own work would develop, came in September 1908, from Hermann Minkowski, formerly a professor of mathematics at the ETH who had been one of Einstein’s teachers, but was now based at the University of Göttingen. Minkowski had been fascinated by the Special Theory as soon as he saw Einstein’s paper, and astounded that a pupil he remembered as a ‘lazy dog’ should have come up with something so profound.2 He accepted Einstein’s ideas without question, and set about re-formulating them into a more elegant mathematical package. What he found was that everything contained in the Special Theory could be described in terms of geometry – provided that time was regarded as a fourth dimension, on a par with the three familiar dimensions of space.
The natural way to get a handle on this is to think of some everyday experiences in terms of geometrical coordinates. If you draw a triangle on a piece of graph paper, you can specify the triangle completely by giving the coordinates on the grid of the three corners of the triangle then drawing straight lines to join them up. Similarly, if you arrange to meet someone on the corner of, say, Fourth Street and Main, you are specifying a geometrical location in terms of similar coordinates in two dimensions. If you arrange to meet in the coffee shop on the second floor of the building at the corner of Fourth and Main, you are specifying the location in three dimensions, since the level in the building now comes in as an extra coordinate. And if you say you will meet in the coffee shop on the second floor of the building on the corner of Fourth and Main at three o’clock, you have introduced a fourth coordinate, the time.
Minkowski showed how the mathematics behind things like shrinking rulers and clocks that run slow could be incorporated into this kind of language, set in a framework of a four-dimensional entity, which became known as spacetime. Crucially, this means that there are properties of objects which always stay the same in spacetime, even if they look different to different inertial observers in three dimensions. A nice analogy is with the length of the shadow cast by a pencil on a wall. By twisting the pencil about in three dimensions you can make the two-dimensional shadow longer or shorter, but the pencil always stays the same length. In four dimensions, the equivalent property to length is called ‘extension’, and by twisting objects around in four dimensions you can change the length of the ‘shadow’ it casts in three dimensions. The fact that time stretches while space shrinks for a moving object reflects the fact that the four-dimensional extension in spacetime stays the same – in a sense, the two effects balance each other.
Minkowski presented his ideas in a lecture given in Cologne at the beginning of September 1908. Introducing his talk, he said:
The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.3
Minkowski never lived to see those words in print, since he died, from complications resulting from appendicitis, in January 1909, when he was just 44 years old. But it is no coincidence that widespread acceptance of Einstein’s ideas, broad recognition of his abilities and the opening up of doors into academic life, all followed after Minkowski’s re-formulation of the Special Theory.
At first, Einstein himself was slightly miffed about the way the mathematicians had picked up his ball and run off with it. Perhaps not entirely seriously, but with an undercurrent of irritation, he commented that ‘since the mathematicians have attacked the relativity theory, I myself no longer understand it,’ and said ‘the people in Göttingen sometimes strike me not as if they wanted to help one formulate something clearly, but as if they wanted only to show us physicists how much brighter they are than we.’4 But he soon changed his tune, when he discovered that Minkowski’s geometrisation of the Special Theory was one of two important steps that would eventually put him on the road to his greatest triumph, the General Theory of Relativity. The other key step was an insight that struck him in 1907, while sitting at his desk in the patent office.
At the time, still months before Minkowski’s geometrisation of the Special Theory, he was working on an article about the Special Theory for publication in an annual review of science. In a lecture he gave in Japan in 1922, Einstein said:
I was sitting in a chair in the patent office in Bern when all of a sudden a thought occurred to me: ‘If a person falls freely he will not feel his own weight.’ I was startled. This simple insight made a deep impression on me. It impelled me toward a theory of gravitation.
It was, he said, ‘the happiest thought of my life’.a But the theory derived from that happy thought would take Einstein almost another decade of intermittent but often intense struggle to achieve, even with the help of Minkowski’s geometrisation of the Special Theory.
The reason why the ‘sudden thought’ was so important is that as soon as he had completed the Special Theory Einstein began to attempt to find ways to make the theory more general (hence the name) by adapting it to deal with accelerated motion, not just motion at constant velocities. A freely-falling object is accelerating, and Einstein’s insight was the realization that this acceleration exactly cancels out the weight of the object. Turning this around (and remember, Einstein was working on this before the time of space rockets, or even high-speed elevators), if you were standing on a platform that was being accelerated in a straight line through space, you would feel as if you were standing still and held down by your own weight in a gravitational field. In 1907, Einstein realised that acceleration and gravity are exactly equivalent to one another, so that his General Theory, when he found it, would be a theory of gravity, not just a theory of motion. But the path from the insight to the theory was long and tortuous, and Einstein’s personal life underwent many changes along the way.
Moving on
The first significant change came when he moved on from the patent office in 1909, four years after the annus mirabilis. Until then, his home life hadn’t really changed much. On the strength of his doctorate, in 1906 he had been promoted to Technical Expert II Class, with an increased salary of 4,500 francs a year, but this made little difference to his frugal lifestyle. In 1908, he became a Privatdozent at the University of Bern – a kind of part-time, poorly paid lecturer. This was rather pointless in itself, but an essential step before he would be considered for a full university post. Curiously, though, before doing this Einstein seriously considered the idea of becoming a school teacher, rejecting the university system that had, so far, rejected him. He wrote to Marcel Grossmann that this idea stemmed from an ‘ardent wish to be able to continue my private scientific work u
nder easier conditions’,5 and actually applied for a post teaching mathematics at a Zurich high school, enclosing with his application copies of all his published scientific papers. The bemused school governors did not shortlist him for an interview, even though in his covering letter he pointed out that he would be able to teach physics as well. How different might the development of physics have been if they had had more imagination?
It was only after failing with this application that Einstein buckled down to writing the thesis that was required in order to be accepted as a Privatdozent at the University of Bern. This was simply an extension of his 1905 work on light quanta, and a pure formality. Einstein duly became a Privatdozent in February 1908, but the tiny remuneration associated with the position was not enough for him to give up the day job, so he now had more work to do and less time for science. His lectures took place on Tuesdays and Saturdays at 7am, and initially attracted an audience of three. By the summer of 1909, there was only one student attending, and the lectures were cancelled. No wonder the high school job had appealed to him.
The next step would be a professorship, which would enable him to give up the patent office job at last. Even before making that step, in July 1909 Einstein was awarded his first honorary degree (by the University of Geneva). Meanwhile, a long campaign waged by the physics professor at Zurich, Alfred Kleiner, had persuaded the university to establish a new post for a professor of theoretical physics – only a kind of junior professorship with a lower status than Kleiner’s chair, but still a long way up from being a Privatdozent. Kleiner had one person in mind for the new post, and it was not Einstein but a young man called Friedrich Adler, who had been a student contemporary of Einstein at the ETH. But Adler, the son of the leader of the Austrian Social Democratic Party and himself politically active, decided he was better suited to political philosophy than to physics. He told Kleiner of his decision in June 1908, and at that meeting the two of them decided that Einstein was the right man for the job.
Kleiner visited Einstein in Bern to discuss the possibilities, and at the end of June attended one of Einstein’s lectures. He was not impressed, and at first Einstein’s lack of skill at lecturing seemed to have ruled him out. But Kleiner relented sufficiently to allow Einstein to give what amounted to an audition in the form of a lecture in Zurich. For once, Einstein prepared properly and presented the lecture adequately. ‘Contrary to habit,’ he wrote to a friend, ‘I lectured well on that occasion.’ In spite of some objections to Einstein’s Jewishness, Kleiner got the appointment approved in March 1909, and the post was duly offered to Einstein – who calmly turned it down, since the salary offered was less than he was getting at the patent office. But the salary offered was increased, and he accepted. The pay was now exactly the same as that of a Technical Expert II Class at the patent office, but from taking up the appointment in the autumn of 1909 he could at last call himself Herr Professor Einstein. In the years that followed, Adler missed few opportunities to let people know that he had stood aside to make room for Einstein in Zurich.
Just before taking up the appointment, in July 1909 Einstein received his honorary doctorate from the University of Geneva, part of the celebrations of the anniversary of the founding in 1559, by John Calvin, of the Academy which evolved into the university. Einstein was greatly amused at the contrast between the teachings of Calvin and the lavish festivities laid on to mark the 350th anniversary. But though he remained as uninterested as ever in the trappings that society associated with success, he was now definitely part of the academic establishment.
A few weeks later, in September 1909, Einstein attended a conference in Salzburg, which focussed on the new developments in relativity theory and quantum physics. This gave him an opportunity to meet luminaries such as Max Planck, who he had previously known only through their publications and letters. To the surprise of the organisers, Einstein chose to provide a contribution on quantum theory, not relativity, having temporarily put aside his quest for what would become the General Theory to concentrate on what he regarded as the more pressing problem of reconciling the particle (quantum) and wave descriptions of light. The result was a lecture that became recognised as one of the landmarks of 20th-century science.
‘Light,’ Einstein told his audience, ‘has certain basic properties that can be understood more readily from the standpoint of the Newtonian emission theory than from the standpoint of the wave theory,’ and ‘I thus believe that the next phase of theoretical physics will bring us a theory of light that can be interpreted as a kind of fusion of the wave and the emission [particle] theories of light.’ This was the genesis of the idea of wave-particle duality. He warned that this would mean a profound change in physics, which could undermine the classical (that is, Newtonian) concept of determinism. He was right, but it took twenty years for physics to catch up with his insight, and some physicists are still arguing about the implications today. In 1909, it was all too much for Planck and many members of the audience, and Einstein, now aged 30, moved on to Zurich to take up his chair without having convinced many people. There, he turned his attention back to relativity theory, remarking to a friend: ‘The more successes the quantum theory enjoys, the sillier it looks.’
Rather than settling down in Zurich and working his way up the academic ladder there, Einstein’s move marked the beginning of his years as a peripatetic professor, hopping from university to university in search of security and (more importantly) the opportunity to work on what he wanted the way he wanted. It also marked the beginning of the end for his marriage; I will look briefly at the personal side before getting back to the physics.
In the shadow of a giant
Einstein’s marriage had already been showing signs of strain before 1909. It wasn’t easy for a woman who had once had scientific aspirations of her own, and had struggled so hard to get an education, to live in the shadow of Einstein’s growing success and fame, quite apart from the emotions associated with giving birth to and then giving away an illegitimate daughter. We now see Einstein as the iconic 20th-century scientist, an almost unique genius. But in the first decade of the 20th century, Mileva didn’t even have the comfort of knowing just how special he was. Not long before, they had been equals; now, he had flown far above her. She must have thought, at least occasionally, that if it had not been for the accident of her gender she could have achieved what he had done. As Einstein’s reputation grew, Mileva found herself increasingly left out of his life. When he wasn’t working, he was talking about physics with his new friends, many of them young men fired with enthusiasm for their subject who must have reminded her all too painfully of her own failed ambitions in science. Things hadn’t been so bad when Albert was an unknown scientist, but now he was being taken away from her. Mileva had never expected to become a housewife; there are also signs that she suffered from clinical depression, an illness even less sympathetically dealt with then than now.
Their return to Zurich, the city in which Albert and Mileva had met and fallen in love, seems to have provided a temporary revival of their relationship. Within a month of the move, Mileva was pregnant with their second son, Eduard, who would be born on 28 July 1910. But although at first the move to Zurich must have seemed like an opportunity to revisit the scene of their own youth, and perhaps make a fresh start, it didn’t work out as she had hoped. The birth of Eduard was difficult for Mileva, and Eduard turned out to be a sickly baby who needed a lot of attention, while six-year-old Hans Albert could hardly be ignored.
By chance, the Einsteins had rented an apartment in the same building where Friedrich Adler and his wife lived, providing the opportunity for a firm friendship to develop between the couples, and Einstein with a sounding board on which to try out his ideas. He also renewed acquaintance with Marcel Grossmann, now a professor of mathematics at the ETH, whose notes had helped Einstein to pass his examinations. Einstein’s ability as a lecturer improved a little, but what really endeared him to his students was his informality. He would all
ow his lectures to be interrupted by questions – almost unheard of in the German-speaking academic world at the time – and he invited any students who wanted to join him after the lectures at the Café Terasse to talk physics and set the world to rights. The birth of Eduard also brought out the fathering instinct in Einstein, after his own fashion. He was a loving – even doting – father who played with the boys and told them stories; but there are also, as we have mentioned, many accounts of occasions when he could be found rocking the crib with one hand while writing equations with the other, pushing a pram on which a notebook lay open on the blankets of the sleeping baby, or otherwise being lost in thought when he should have been paying close attention to the children.
Initially, everything had seemed fairly settled in Zurich. But in March 1910, just five months after taking up his post there and before Eduard was born, Einstein received an invitation to put himself forward for a full professorship in Prague. Things were complicated, because once again there were difficulties at home with the now-pregnant Mileva. We don’t know the details, but Einstein hinted darkly about these difficulties in letters to his mother, who had by now returned to Germany and was living in Berlin. A move to Prague – a move anywhere – would surely not appeal to Mileva, but her feelings were clearly of secondary importance, at best. The Prague post was superficially attractive as a career move – a full professorship with a larger salary in a German-speaking university (Prague was then, of course, part of the Austro-Hungarian Empire). But there were hurdles to jump. Under the notoriously bureaucratic Austro-Hungarian regime, Einstein could not simply be headhunted. The university had to present a shortlist of preferred candidates to the Ministry of Education in Vienna, which had the final say. Einstein was top of the list, with a strong recommendation from no less a physicist than Max Planck. But the ministry didn’t like the idea of appointing Einstein, not least because he was Jewish. They offered the post to the second candidate on the list, a non-Jewish Austrian, Gustav Jaumann.
