Einstein's Masterwork

by John Gribbin

  The circumstantial evidence suggests that at about this time Mileva began to fall in love with Einstein and became confused about her future prospects. She had made a huge effort, as a woman, to get a place at the ETH – a foothold on a professional career in science – and seems to have become concerned at the possibility that it might all be wasted if she were to marry, settle down and (as would have been almost inevitable in those days) have children. In the summer of 1897, she went home to her family as normal and kept up a correspondence with Einstein; but at the end of the summer, instead of returning to Zurich she went, without explanation, to Heidelberg. Although this was the home of one of the great German universities, it wasn’t so good for women, who were patronisingly allowed to attend lectures by special permission of individual professors but were not allowed to take a degree. Whatever her motives for this diversion, by April 1898 Mileva was back in Zurich, where Einstein promised to help her catch up with her coursework (using Grossmann’s notes); but, as we shall see, academically she never did make up for this lost time.

  Einstein himself sailed through the ‘intermediate diploma examination’, held in October 1898, coming top of his small class with a grade average of 5.7; Grossmann came second with 5.6, and Mileva had to postpone the exam because of the time she had spent in Heidelberg. Einstein’s promised help with her catching up proved to be more of a hindrance than a help, in more ways than one.

  In his third year at the ETH, Einstein developed his interest in electromagnetism, and in particular the behaviour of light. Mileva was roped in and used as a sounding board for his ideas – much more exciting than the course-work – when she should have been concentrating on the curriculum. Maxwell (who, as it happens, died in the year Einstein was born, 1879) had discovered a set of equations which describe, among other things, the way electromagnetic waves move. The equations predicted that the speed of those waves would be 300,000 kilometres per second.e Since the speed of light was being measured accurately at around the same time that Maxwell came up with this number (in the 1860s), and the speed of light exactly matches the predicted speed of electromagnetic waves, this was seen as proof that light is a form of electromagnetic vibration.

  But what was vibrating? By analogy with the way sound waves propagate as vibrations in the air, or in other substances, in the 19th century physicists thought that light (and other forms of electromagnetic wave) must propagate in the form of vibrations in a tenuous substance they called ‘the ether’. The ether was assumed to fill all of space, and even somehow to fill the atmosphere of the Earth, mingling with the air, to enable light to propagate. It would, though, have to be very tenuous, since planets, and even people, seemed to be able to move through it as if it did not exist. And yet, since the speed with which waves travel depends on the stiffness of the substance they propagate in (so that sound travels faster in steel than in air), it would have to be incredibly stiff – far stiffer than steel.

  By the end of the 19th century, unsuccessful attempts were being made to measure the speed of the Earth through the ether, by measuring the speed of light in directions along the line of the Earth’s motion through space and at right angles to its motion; but the speed of light always seemed to be the same, whichever way the experimental apparatus was pointed. Einstein seems to have either been unaware of these experiments or unim-pressed by them, but he was fascinated by Maxwell’s equations and their prediction of a specific speed for light. He now had another ‘thought experiment’ to highlight the mysterious nature of these waves. If you could run at the speed of light while holding a mirror in front of your face, would you be able to see your reflection? Presumably not, since the light leaving your face to bounce off the mirror and come back into your eyes as a reflection would never be able to catch up with the mirror!

  But there was something else about Maxwell’s achievement that appealed to Einstein. Maxwell had worked his ideas out entirely theoretically. He had produced his equations and predicted the speed of light without doing an experiment. He had also predicted that there must be other forms of electromagnetic waves, what we now call ‘radio waves’, and these had duly been discovered by the German Heinrich Hertz in 1888. Or rather, Hertz had not discovered radio waves; he had merely detected what Maxwell, the theorist, had ‘discovered’. Instead of experimenters making observations which the theorists then had to try to explain, the theorist had worked it all out on his own. This was what appealed to Einstein: the idea that the power of the human mind and mathematics was alone enough to conjure up deep truths about the world, echoing the way the Greeks had conjured up deep truths about geometry.

  As early as the summer of 1899, Einstein wrote to Mileva that:

  I’m more and more convinced that the electro-dynamics of moving bodies as it is presented today doesn’t correspond to reality, and that it will be possible to present it in a simpler way.5

  And he said in the same letter that it was not possible ‘to ascribe physical meaning’ to the concept of the ether. But he seems to have been unable to take his ideas further at that time, and the discussion of electrodynamics lapsed during his fourth and final year at the ETH. Getting ahead of our story only slightly, the idea of the ether was indeed soon made redundant, and physicists now think of light and other forms of radiation in terms of ‘fields’, rather like the pattern of lines of force that you can see when a bar magnet is placed under a sheet of paper and iron filings are gently sprinkled on top of the paper. Once they are given a push, waves propagate through these fields until they interact with something else.

  Einstein’s own interaction with Mileva clearly intensified during their fourth year at the ETH, and it was probably sometime during that year that they decided to get married. They had spent the summer of 1899 apart, with Einstein on holiday with his mother and sister, and Mileva at home revising for her postponed intermediate examination. But although they still had separate lodgings in Zurich on their return, Einstein seems to have spent as much time at hers as in his own, and in a letter written in October 1899 refers to his ‘household’ with Mileva.6 Soon, he was addressing her as ‘Doxerl’ (‘Dolly’, as in ‘little doll’) and she was calling him ‘Johonzel’ (‘Johnny’). In spite of the deepening of their relationship and his neglect of the formal lectures throughout his time at the ETH, by cramming hard using Grossmann’s notes Einstein was able to pass his final examinations. Not gloriously. He came fourth out of the five students sitting the exam, with a grade average of 4.9. But Mileva, who lacked his genius, was unable to make up adequately for lost time; she scored only 4.0 and failed. She did spectacularly badly at maths, in particular, scoring only 2.5 out of the possible 6 marks.

  By now of course, Einstein’s parents knew all (or perhaps, not quite all) about his relationship with Mileva. In spite of his rebellious nature and lack of obedience to authority, their Albert had made it through the educational system to earn a diploma which ensured him a respectable job. But when he told them, in the summer of 1900, that he intended to marry ‘Dolly’, they were aghast. In their view he was far too young (only just 21), they weren’t sure about the girl (who was in any case four years older than him), and they believed that a man ought to achieve security (not least, a job) before he even contemplated marriage. Even Einstein’s friends in Zurich seem to have been surprised that a man who was so attractive to women should have chosen this one for his permanent partner. But part of the attraction to him seems to have been the thought of sharing his life with someone he could share everything with, including science. He fantasised in his letters to Mileva about them both getting PhDs and working together on scientific papers that would take the world by storm. But first, she had to retake her examinations at the ETH, and he had to get a job in Zurich at the Poly itself or at the University, so that they could be together.

  Rejection

  It was at this point that reality began to intrude on the dream. Einstein’s diploma from the ETH qualified him to work as a teacher of mathematics and science in
secondary schools. What he wanted was to get a job as an assistant to one of the professors and work for a PhD. Although the ETH did not at that time award doctorates, there was an arrangement whereby any graduate from the ETH could write a dissertation for submission to the University of Zurich and be considered for the award of a PhD; so this was by no means an impossible dream, at least for the top students. But Einstein was not, on paper at least, one of the top students. He seems to have been convinced that in spite of obtaining the worst pass in his year and still having a reputation as a cocky, know-it-all troublemaker, his innate ability (of which he at least was in no doubt) would be recognised and be sufficient to obtain the post he wanted. But that was not the way the system worked. Hardly surprisingly, the men who had done best in the exams received priority in consideration for what limited opportunities were available, and in any case the authorities at the ETH were happy to see the back of Einstein, who had been far from a model student. They may well, also, have known about his relationship with Mileva, which went beyond the bounds of what was regarded as ‘decent’ in that time and place.

  The couple again spent the summer apart, each with their respective families, and in the face of parental opposition talk of marriage ceased. Mileva studied for her resits, while Einstein applied unsuccessfully for assistantships, took a little holiday and tried to forget his troubles by studying Boltzmann’s work on thermodynamics. In the autumn, both returned to Zurich where, in spite of the lack of any job for Einstein at the ETH, they both paid the appropriate fees and registered to work in the lab there on problems involving heat and electricity (the electron itself had only been discovered in 1897, after Einstein had begun his course at the ETH), with a view to obtaining a pair of PhDs. Einstein’s allowance from his aunt had stopped when he graduated, and he had to make ends meet by private tutoring; Mileva still had a small allowance from her father. In these less than promising circumstances, Einstein completed his first scientific paper, on capillary action, which was duly published in the prestigious Annalen der Physik. The paper concerned the nature of the forces between molecules, and this led Einstein in a direction that would, eventually, result in the award of a doctorate. But Mileva’s hopes of obtaining a PhD gradually faded away.

  Apart from Einstein’s first scientific paper, the other highlight of what must have been a far from happy few months in Zurich came in February 1901, when Einstein at last became a Swiss citizen. Somewhat ironically, in view of his reasons for renouncing German citizenship, he then had to take a medical examination prior to a spell of compulsory military service – but failed on the grounds of flat feet and varicose veins. So he probably would not have been forced to serve in the German army even if he had stayed in Munich.

  Just a month after becoming a Swiss citizen, though, Einstein had to admit defeat in his efforts to find suitable employment in Zurich. Under pressure from his parents to get a real job (any job!), he abandoned the increasingly faint prospect of a dissertation on thermoelectricity and returned to Italy, leaving Mileva to work towards her second sitting of the final examinations (while also trying to keep her own studies of heat conduction going), and facing an uncertain future.

  In Milan, Albert at least had Michele Besso, who now lived in that city with his wife and young daughter, to talk to about physics. He also came across the new work of Max Planck, a German physicist who had just discovered that some of the properties of light and other forms of radiation could best be explained if the radiation is only emitted or absorbed by objects in the form of discrete packets of energy, which became known as ‘quanta’. His key paper, laying the foundations of what became quantum physics, had only been published in 1900, but as usual Einstein was keeping up with cutting-edge research in physics.

  He was also keeping up his older interests, including his interest in light and motion. His letters to Mileva are full of the usual endearments expressed by separated lovers, but they also include references to his scientific work, and one of those references in particular has led some people to see Mileva as a more important scientific influence on him than she really was. In a letter written in April 1901 he writes: ‘I’ll be so happy and proud when we are together and can bring our work on relative motion to a successful conclusion.’7 Taken out of context, you might see that as indicating that Mileva made a significant contribution to the theory of relativity. But the proper context is that she failed her exams (not least because she spent too much time discussing esoteric ideas with Einstein instead of concentrating on her proper coursework), and she was by far the weakest mathematician in her year. She was alone in Zurich, struggling (in the end, unsuccessfully) to prepare for her resits, and Einstein was trying to cheer her up by assuring her how important she was to him. In the same letter, he writes: ‘you are and will remain a shrine for me to which no one has access; I also know that of all people, you love me the most and understand me the best.’ He was clearly besotted with her and saw the work on what became relativity theory as ‘ours’ in the sense that ‘what’s mine is yours’. But there is not one shred of evidence that Mileva contributed anything more to the development of Einstein’s great theory than her role as a scientifically literate listener on whom he could try out his ideas.

  Soon after that letter was written, things began to look up for Einstein. The first good news came in a letter from his old friend Marcel Grossmann. Grossmann had mentioned Einstein’s increasingly desperate search for a job to his father, who happened to be a friend of the director of the Swiss Patent Office, Friedrich Haller. Haller had told the elder Grossmann that there would shortly be a vacancy at the patent office in Bern, and that Einstein should certainly apply for the post when it was advertised. Just when the post was likely to be advertised was not clear, but the very next day Einstein received another letter offering him some temporary work. Jakob Rebstein, who had formerly been an assistant at the ETH and knew both Einstein and Mileva, now had a job as a mathematics teacher in Winterthur, near Zurich, but was about to go on his spell of compulsory military service for a couple of months. Would Einstein like to act as his locum?

  The job would not only help to fill the gap while waiting for the patent office post to be advertised, but meant that he would be near Mileva. To celebrate the good news, the couple met up at Lake Como for a short holiday before he took over from Rebstein. In a letter to a friend, Mileva described how they rode through the snow-covered countryside in a horse-drawn sleigh:

  We drove one moment through long galleries and the next on the open road, where, all the way to the remotest distance, our eyes could see nothing but snow and more snow, so that at times I shuddered at this cold white infinity and firmly kept my arm round my sweetheart under the coats and blankets which covered us … I was so happy to have my lover for myself again for a while, the more so as I saw that he was just as happy.8

  Soon after this trip Mileva must have told Einstein that she was pregnant, since towards the end of May 1901 his letters to her start referring obliquely to the happy event, assuring her that he would stand by her and all would be well. Typically, though, those letters are much more excited about a wonderful new piece of physics Einstein has heard of. The German physicist Philipp Lenard had discovered that electrons could be knocked out of the surface of a metal by shining ultraviolet light onto it. Strangely, he had also discovered that the energy of the electrons ejected from the metal surface did not depend on how bright the light was. Whether it was faint or dim the electrons always came out with the same energy (essentially, the same speed). How could this be? Just four years later, Einstein would explain the phenomenon, and in 1922, he would receive the Nobel Prize for his explanation, with profound effects on the lives of himself and Mileva. But in 1901, the promise of the spring soon faded once again into uncertainty about their futures.

  Einstein quite liked his brief time as a teacher, and was especially pleased to discover that after five or six hours spent at the task (schools started early in Switzerland) he was still fresh enoug
h to work in the library or on interesting problems at home, so that he could continue his scientific work even if he didn’t have any official connection with a university. And on Sundays he could take the train in to Zurich to see Mileva. But when the temporary job ended, and the reality of the implications of Mileva’s pregnancy began to sink in, the future once again looked less promising, with no sign yet of the promised vacancy at the Bern Patent Office. In July, Mileva failed her exams again, almost as badly as she had done the year before. Abandoning all hope of a PhD, pregnant and depressed, she went home alone to see her parents and break the unwelcome news. Einstein took on an unsatisfactory job as a private tutor just to make ends meet and devoted all the time he could to writing a new dissertation, developing his ideas concerning the forces between molecules. He hoped to use this to obtain a PhD, which he now regarded as his best chance of getting an academic job.

  In the autumn, Mileva retuned to Switzerland but couldn’t stay with Einstein, or be seen with him, since her now visible pregnancy would have compromised his position as a respectable teacher. She stayed in a nearby town, while he made a succession of excuses that he could not find time to get away to see her. They had little contact, and once again she went back to her parents. In November, Einstein completed his dissertation and submitted it to the University of Zurich, scraping up the fee of 230 francs required for it to be considered. Professor Alfred Kleiner read the dissertation, but infuriated Einstein first by taking until well into the new year to comment on it, then advising the young man to withdraw it before it went any further. A furious Einstein did so (which at least meant he got his 230 francs back), and ranted to his friends about the incompetence of all professors, especially Kleiner. But the professor probably did Einstein a favour. No copy of the dissertation survives, and we cannot know what was wrong with it, but judging from the papers in Annalen der Physik on which it is supposed to have been based, Kleiner probably had a point. Einstein himself later described the paper as ‘worthless’.9