Einstein's Masterwork

by John Gribbin

  Breaking free

  There is some confusion about how exactly Einstein engineered his escape from Munich, but this is the most likely pattern of events. He was certainly depressed and managed to persuade his doctor to provide a certificate stating that he should rejoin the family for health reasons. He also persuaded his maths teacher to provide a letter stating that Einstein had already mastered the syllabus, and there was nothing more he could teach the young man. Armed with these documents, Einstein approached the principal of the school and told him that he was leaving; the principal’s response, we are told, was that Einstein was being expelled anyway, for being a disruptive influence. The likelihood is that Einstein had carefully cultivated his role as a disruptive influence in order to ensure that he would not be asked – let alone ordered – to stay on. Whether he jumped or was pushed, there is no doubt that in the spring of 1895, just six months after being left in Munich to complete his education, Einstein turned up on the doorstep of his parents’ new home in Milan, in northern Italy.c He duly renounced his German citizenship (the declaration took effect in January 1896) and swore he would never go back to that country. By then, Einstein was living in Switzerland and set in motion the slow process of obtaining Swiss citizenship; but in those relatively free and easy days in Europe the lack of a passport did not prevent him travelling as he pleased, in particular between Switzerland and Italy. On official forms, under ‘nationality’ he simply described himself as ‘the son of German parents’.

  In the summer of 1895 Einstein was sixteen, in Italy, with no responsibilities (and no prospects). Although he did some work for the family business and had vague notions of becoming a teacher of philosophy, for several months he mostly just enjoyed himself, touring the art centres of Italy, visiting the Alps and falling in love with the culture. When pressed by his father to settle down and give some thought to the future, Einstein assured Hermann that in the autumn he would take the entrance examination for the Swiss Federal Polytechnic in Zurich (often known by the initials of its German name, as the ETH). The ETH was not a great university in the mould of Heidelberg or Berlin, but a new kind of institution devoted primarily to the education of would-be teachers and engineers. The cocksure Einstein was certain he would be able to walk into an establishment with such relatively modest academic standards, and it came as a rude shock when he failed the exam. (His later claim to have failed deliberately, in order to avoid being pushed into a profession by his father, should be taken with a large pinch of salt; if that were the case, why would he have gone back and embarked on the same course a year later?)

  In fact, Einstein was lucky to be allowed to take the exam. The normal age for this was eighteen, and applicants were expected to have a high school diploma; Einstein was still six months short of his seventeenth birthday and had left high school under a cloud. But the director of the ETH, Albin Herzog, recognised Einstein’s potential and offered him a lifeline. He suggested that Einstein should enrol in a Swiss secondary school in the town of Aarau, a little way outside of Zurich, to do some catching up before taking the entrance exam again in 1896. There, he could lodge in the home of Jost Winteler, a teacher at the school, and live as one of the family.

  The domestic arrangements suited Einstein down to the ground. As Winteler taught Latin and Greek he was not one of Einstein’s tutors, so school did not intrude too much on daily life. One of Einstein’s cousins, Robert Koch, was a student at the school and lodging next door. And there was plenty of family life – the Wintelers had three daughters and four sons, plus a couple of other paying guests, and Einstein was soon one of the family. A classmate during this year in Aarau later described the Einstein of 1895–6, to his biographer Carl Seelig, as ‘sure of himself, his grey felt hat pushed back on his thick, black hair [striding] energetically up and down … unhampered by convention, his attitude towards the world was that of the laughing philosopher, and his witty mockery pitilessly lashed any conceit or pose.’

  Mature beyond his years, Einstein clearly made a big impact on his companions – none more so than Marie Winteler, the eighteen-year-old daughter of the house, who had just completed her course as a trainee teacher and was living with her parents while waiting to start her first job. In spite of the age difference, an enormous gulf for most teenagers, the two fell in love. Both families seem to have been happy with the development, which blossomed into something like an unofficial engagement and persisted after Einstein returned to Pavia and then moved on to Zurich. But in the spring of 1897, as his own horizons broadened and he made new friends in the city, he broke off the relationship. It took some time to convince Marie that he meant it, but in the end everything was settled amicably, and the Einsteins and the Wintelers remained good friends – so much so that Einstein’s sister Maja later married Marie’s brother Paul. Anna, another of the Winteler siblings, married Michele Besso, Einstein’s best friend in Zurich and for long after his student days were over. In a letter written to Besso’s wife and son after he died in 1955, Einstein said ‘what I admired most about Michele was the fact that he was able to live so many years with one woman, not only in peace but also in constant unity, something I have lamentably failed at twice.’2

  Alongside his happy relationship with the Winteler family, an active social life, music and his first experience of love, Einstein did enough work at school (where he had been allowed to join the final year group, with classmates a year older than himself) to achieve high grades in all his subjects except French, which he always struggled with. In the Swiss system, examination papers were marked on a grading scale from 1 to 6, with 6 being the top mark. Einstein’s average of 5½ was the best in his year, from the youngest pupil in the class. Although this was brought down by his French paper, which was rather generously graded between 3–4, the essay he wrote (in French) for the examination is the most interesting of the papers (which survive and can be found in The Collected Papers of Albert Einstein) because the set subject of the essay was ‘Mes Projets d’Avenir’.d Ignoring the terrible French, the essay gives us a glimpse into Einstein’s personal ambitions at the time, which seem remarkably limited in the light of what he would achieve:

  If I am lucky enough to pass my examinations, I will attend the Polytechnic in Zurich. I will stay there four years to study mathematics and physics. My idea is to become a teacher in these fields of natural science and I will choose the theoretical part of these sciences.

  Einstein goes on to say that this ambition is partly based on the fact that he lacks any ‘practical talent’, but also because ‘there is a certain independence in the profession of science that greatly appeals to me’. That certainly chimes with the way his life would develop. But there was already a hint of what was to come in some of the ideas Einstein did not commit to paper in 1896. He later recalled that while still a schoolboy in Aarau, he puzzled over the idea that if you could run at the speed of light, you would see a light wave standing still alongside you, frozen in time, as it were; but the laws of physics said that such a ‘time-independent wave-field’ could not exist.3 It would be nine years before he found the solution to that puzzle.

  Einstein and the Poly

  After passing his entrance examination for the ETH early in the summer of 1896, Einstein spent some time with his family in Italy, where the electrical business was once again in crisis. Jakob left to work for another company and ended up living comfortably in Vienna as the manager of a firm of instrument makers; Hermann tried to make another fresh start in Milan. Albert was sufficiently concerned about the prospects for this latest venture that he tried unsuccessfully to dissuade his relations from pouring more money into the scheme; but in October he had to put these family difficulties behind him as he returned to Zurich to enrol for his course.

  In spite of the year spent in Aarau, Einstein was still six months short of the official age for admission, eighteen, and one of the youngest students ever admitted to the ETH. The ‘Poly’, as it was known locally, wasn’t that old itself, having
been founded in 1855 as the first university-level academic institution in Switzerland (the Swiss Confederation only came into being in 1848). Since then, three universities had been established in Switzerland – in Basel, Zurich and Geneva. Unlike the Poly, which was a Federal Swiss government establishment, the universities were run by their respective cantons. Unlike the universities, initially the Poly could not award doctoral degrees; but in 1911 it was given full university status including the right to award doctorates. That hasn’t stopped it being known as the Poly right down to the present day.

  At the end of the 19th century, there were just under a thousand students at the ETH. But, as its name implies, the ETH was primarily devoted to the education of engineers, not theoretical physicists, and there were just five students, including Einstein, taking the science course in his year. These included Marcel Grossmann, a model student who attended all the lectures and took detailed notes which he kept carefully for revision. Grossmann became a firm friend of Einstein, and in the long run those beautifully written notes would prove even more important to him than to Grossmann. The group also included a lone woman, Mileva Maric, a Serbian, from what was then part of the Hungarian Empire. Mileva had had to struggle with an unsympathetic family and unsupportive school system at home to make it to university in Switzerland, the only German-speaking country where women were admitted to university at that time. Indeed, Mileva was only the fifth woman to be admitted to study physics at the ETH. The other two members of the class were Jakob Ehrat, a hardworking but unspectacular student, and Louis Kollros; both, like Grossmann, were Swiss.

  Like many students, Einstein enjoyed the freedom of university life to the full and didn’t worry too much about the academic side until the examinations loomed. He didn’t reckon anyone could teach him mathematics better than he could learn on his own with the aid of books, and he seldom attended the lectures, leading one of his professors, Hermann Minkowski, later famously to describe the student Einstein as a ‘lazy dog’, who ‘never bothered about mathematics at all’. In fact, Minkowski was one of the few professors at the ETH that Einstein respected, and when he did attend a lecture given by Minkowski during his final semester at the ETH, Einstein remarked to Louis Kollros that ‘this is the first lecture on mathematical physics we have heard at the Poly’.4

  Cutting lectures gave Einstein plenty of time to indulge his passions for: coffee-house discussions with his friends setting the world to rights (including scientific discussions about the latest ideas in physics); the company of women (he always got on well with women, who were charmed by his manners, his music and his masculine good looks); sailing on the lake (where he always took a notebook in case the wind dropped, so that he could scribble down his ideas on physics); and music (combining this with his love of the company of women, Einstein often gave violin recitals in the homes of ladies of his acquaintance). He lived in lodgings in Zurich, getting by financially on an allowance of 100 Swiss francs a month, generously provided by one of his maternal aunts, and supplemented by a little private tuition. Out of this, he set aside 20 francs to save towards the fee he would have to pay when he was eventually awarded Swiss citizenship. On Sundays, he took lunch with the family of Michael Fleischmann, a Zurich businessman, echoing the way the Einsteins had looked after Max Talmey in Munich.

  It was music that brought Einstein and his lifelong friend Michele Besso together. Besso was six years older than Einstein and already working as a mechanical engineer. They met at a house where Einstein was among the musicians entertaining a group of students and other people, an important, if informal, social activity in those days before TV, radio or recorded music. It was Besso who introduced Einstein to the work of Ernst Mach, an Austrian philosopher-physicist who had made important contributions to the scientific debate raging at the end of the 19th century concerning the reality of atoms.

  From our modern perspective, it is hard to believe that only a little over a hundred years ago people were still arguing about whether or not atoms were real. But this was indeed an important debate, which would influence a great deal of Einstein’s early scientific work and become a significant feature of his annus mirabilis.

  Popular accounts of the history of science often tell you that the idea of atoms goes back to the time of the Ancient Greeks, but this is only true up to a point. What is true is that the Greek philosopher Democritus, who lived in the 5th century BC, did discuss the idea that everything is made of tiny, indestructible particles moving through a void (the vacuum) and interacting with one another. But this was never more than a minority view at the time and was dismissed by most of the Ancient Greek thinkers because they could not accept the idea of the void, a genuine nothingness between atoms. The idea was revived from time to time, notably by the Frenchman Pierre Gassendi in the 17th century, but was always dismissed, for the same reason. It was only in the 19th century that a large group of scientists really began to take the idea of atoms seriously, and even then others argued against the idea.

  The scientists who took the idea of atoms seriously found evidence supporting it in both chemistry and physics. In the early 1800s, John Dalton, in England, developed the idea that each element (such as hydrogen or oxygen) is made up of a different kind of atom (but with all the atoms of a particular element identical to one another), and that compound substances (such as water) are made up of molecules in which different kinds of atom join together (in this case, as H2O). As early as 1811, jumping off from these chemical discoveries, the Italian Amadeo Avogadro announced his famous hypothesis, that at a given temperature and pressure, equal volumes of gas contain the same number of particles (molecules or atoms), with the clear implication that there is nothing in the space between these particles. But his idea was ignored for decades, and there was no clear idea of the differences between atoms and molecules until the work of Avogadro’s compatriot, Stanislao Cannizaro, in the 1850s.

  By then, evidence supporting the idea of molecules was coming in from the physicists. One of the most important practical applications of science in the 19th century concerned the study of heat and motion (known as thermodynamics), which was directly relevant to the application of steam power during the industrial revolution. By studying the way in which heat could be generated and how it flowed from one object to another, scientists came up with laws of thermodynamics to describe the relationship between work and energy on the scale of the kind of machinery that powered the Industrial Revolution – sometimes referred to as the ‘macroscopic’ scale. Physicists such as the Scot James Clerk Maxwell, Hermann von Helmholtz in Germany and the Austrian Ludwig Boltzmann then developed models to describe these macroscopic phenomena in terms of the accumulated effect of huge numbers of atoms and molecules bouncing around and interacting with one another like tiny, hard spheres, obeying the basic laws of mechanics discovered by Isaac Newton 200 years earlier. This behaviour of atoms and molecules at a lower level is often referred to as ‘microscopic’ behaviour, but, crucially, atoms are actually far too small to be seen by any microscope available in the 19th century.

  The way the cumulative behaviour of vast numbers of atoms and molecules interacting on the microscopic scale combines to produce measurable effects on the macroscopic scale is called ‘statistical mechanics’. For the particular case of gas trapped in a box, this approach proved an excellent way to explain how the pressure and temperature of the gas change as the box is made smaller or larger and the speed of the molecules and atoms changes; this is known as the ‘kinetic theory’, since it is all about movement.

  All of these ideas were in the air in the 1890s and formed the subject of many conversations between Einstein, Grossmann, Besso and their friends, wreathed in tobacco smoke as they lingered over coffee in some Zurich café, or while striding through the countryside on extended walks. The problem was that although ideas like statistical mechanics and the kinetic theory worked at a practical level to provide a mathematical description of what was going on, nobody had seen atoms – more t
o the point, given the technology of the time it was physically impossible to see atoms. This left the door open for philosophers such as Mach to argue that the atomic hypothesis was no more than a hypothesis, what is known as a ‘heuristic device’, meaning that just because things in the macroscopic world behave as if they were made of atoms that doesn’t prove that they are made of atoms. Mach regarded atoms as no more than a convenient fiction, which provided a basis for physicists to make calculations; anything that could not be detected by the human senses, he argued, was not the proper subject of scientific debate.

  Einstein disagreed and argued the case for atoms with his friends. He became obsessed with the idea and determined that if no one else could prove that atoms were real, he would do it himself. As he wrote many years later in his Autobiographical Notes, he determined that as soon as he had graduated from the ETH he would search for evidence ‘which would guarantee as much as possible the existence of atoms of definite finite size’. He succeeded, as we shall see in the next chapter. Important as that success was, though, just as important as the fact that he succeeded is the fact that at the beginning of the 20th century Albert Einstein, widely regarded as the greatest genius of the 20th century, thought that the most important problem facing science was to prove the reality of atoms. That alone shows just how far we have come in the past hundred years.

  At first, Einstein did well at the ETH, his brilliance enabling him to shine in his intermediate examinations even though he had not been following the curriculum as diligently as his friend Grossmann. But alongside his studies and his discussions about the latest hot topics in science he developed another passion, one which meshed with his interest in physics but would eventually prove a distraction from his scientific work. It isn’t clear exactly how or when Einstein and Mileva Maric became more than just friends, but their discussions about physics seem to have developed a romantic side by the early summer of 1897. It may be no coincidence that Einstein broke off his relationship with Marie Winteler in the spring of that year, but Mileva seems to have been the first to be seriously affected by the new relationship.