Among the potentially unifying concepts that were mesmerizing Einstein, and much of the physics world, were those that sprang from kinetic theory, which had been developed in the late nineteenth century by applying the principles of mechanics to phenomena such as heat transfer and the behavior of gases. This involved regarding a gas, for example, as a collection of a huge number of tiny particles—in this case, molecules made up of one or more atoms—that careen around freely and occasionally collide with one another.
Kinetic theory spurred the growth of statistical mechanics, which describes the behavior of a large number of particles using statistical calculations. It was, of course, impossible to trace each molecule and each collision in a gas, but knowing the statistical behavior gave a workable theory of how billions of molecules behaved under varying conditions.
Scientists proceeded to apply these concepts not only to the behavior of gases, but also to phenomena that occurred in liquids and solids, including electrical conductivity and radiation. “The opportunity arose to apply the methods of the kinetic theory of gases to completely different branches of physics,” Einstein’s close friend Paul Ehrenfest, himself an expert in the field, later wrote.“Above all, the theory was applied to the motion of electrons in metals, to the Brownian motion of microscopically small particles in suspensions, and to the theory of blackbody radiation.”41
Although many scientists were using atomism to explore their own specialties, for Einstein it was a way to make connections, and develop unifying theories, between a variety of disciplines. In April 1901, for example, he adapted the molecular theories he had used to explain the capillary effect in liquids and applied them to the diffusion of gas molecules. “I’ve got an extremely lucky idea, which will make it possible to apply our theory of molecular forces to gases as well,” he wrote Mari. To Grossmann he noted, “I am now convinced that my theory of atomic attractive forces can also be extended to gases.”42
Next he became interested in the conduction of heat and electricity, which led him to study Paul Drude’s electron theory of metals. As the Einstein scholar Jürgen Renn notes, “Drude’s electron theory and Boltzmann’s kinetic theory of gas do not just happen to be two arbitrary subjects of interest to Einstein, but rather they share an important common property with several other of his early research topics: they are two examples of the application of atomistic ideas to physical and chemical problems.”43
Drude’s electron theory posited that there are particles in metal that move freely, as molecules of gas do, and thereby conduct both heat and electricity. When Einstein looked into it, he was pleased with it in parts. “I have a study in my hands by Paul Drude on the electron theory, which is written to my heart’s desire, even though it contains some very sloppy things,” he told Mari. A month later, with his usual lack of deference to authority, he declared, “Perhaps I’ll write to Drude privately to point out his mistakes.”
And so he did. In a letter to Drude in June,Einstein pointed out what he thought were two mistakes.“He will hardly have anything sensible to refute me with,” Einstein gloated to Mari, “because my objections are very straightforward.” Perhaps under the charming illusion that showing an eminent scientist his purported lapses is a good method for getting a job, Einstein included a request for one in his letter.44
Surprisingly, Drude replied. Not surprisingly, he dismissed Einstein’s objections. Einstein was outraged. “It is such manifest proof of the wretchedness of its author that no further comment by me is necessary,” Einstein said when forwarding Drude’s reply to Mari. “From now on I’ll no longer turn to such people, and will instead attack them mercilessly in the journals, as they deserve. It is no wonder that little by little one becomes a misanthrope.”
Einstein also vented his frustration to Jost Winteler, his father figure from Aarau, in a letter that included his declaration about a blind respect for authority being the greatest enemy of truth. “He responds by pointing out that another ‘infallible’ colleague of his shares his opinion. I’ll soon make it hot for the man with a masterly publication.”45
The published papers of Einstein do not identify this “infallible” colleague cited by Drude, but some sleuthing by Renn has turned up a letter from Mari that declares it to be Ludwig Boltzmann.46 That explains why Einstein proceeded to immerse himself in Boltzmann’s writings. “I have been engrossed in Boltzmann’s works on the kinetic theory of gases,” he wrote Grossmann in September, “and these last few days I wrote a short paper myself that provides the missing key-stone in the chain of proofs that he started.”47
Boltzmann, then at the University of Leipzig, was Europe’s master of statistical physics. He had helped to develop the kinetic theory and defend the faith that atoms and molecules actually exist. In doing so, he found it necessary to reconceive the great Second Law of Thermodynamics. This law has many equivalent formulations. It says that heat flows naturally from hot to cold, but not the reverse. Another way to describe the Second Law is in terms of entropy, the degree of disorder and randomness in a system. Any spontaneous process tends to increase the entropy of a system. For example, perfume molecules drift out of an open bottle and into a room but don’t, at least in our common experience, spontaneously gather themselves together and all drift back into the bottle.
The problem for Boltzmann was that mechanical processes, such as molecules bumping around, could each be reversed, according to Newton. So a spontaneous decrease in entropy would, at least in theory, be possible. The absurdity of positing that diffused perfume molecules could gather back into a bottle, or that heat could flow from a cold body to a hot one spontaneously, was flung against Boltzmann by opponents, such as Wilhelm Ostwald, who did not believe in the reality of atoms and molecules. “The proposition that all natural phenomena can ultimately be reduced to mechanical ones cannot even be taken as a useful working hypothesis: it is simply a mistake,” Ostwald declared. “The irreversibility of natural phenomena proves the existence of processes that cannot be described by mechanical equations.”
Boltzmann responded by revising the Second Law so that it was not absolute but merely a statistical near-certainty. It was theoretically possible that millions of perfume molecules could randomly bounce around in a way that they all put themselves back into a bottle at a certain moment, but that was exceedingly unlikely, perhaps trillions of times less likely than that a new deck of cards shuffled a hundred times would end up back in its pristine rank-and-suit precise order.48
When Einstein rather immodestly declared in September 1901 that he was filling in a “keystone” that was missing in Boltzmann’s chain of proofs, he said he planned to publish it soon. But first, he sent a paper to the Annalen der Physik that involved an electrical method for investigating molecular forces, which used calculations derived from experiments others had done using salt solutions and an electrode.49
Then he published his critique of Boltzmann’s theories. He noted that they worked well in explaining heat transfer in gases but had not yet been properly generalized for other realms. “Great as the achievements of the kinetic theory of heat have been in the domain of gas theory,” he wrote, “the science of mechanics has not yet been able to produce an adequate foundation for the general theory of heat.” His aim was “to close this gap.”50
This was all quite presumptuous for an undistinguished Polytechnic student who had not been able to get either a doctorate or a job. Einstein himself later admitted that these papers added little to the body of physics wisdom. But they do indicate what was at the heart of his 1901 challenges to Drude and Boltzmann. Their theories, he felt, did not live up to the maxim he had proclaimed to Grossmann earlier that year about how glorious it was to discover an underlying unity in a set of phenomena that seem completely separate.
In the meantime, in November 1901, Einstein had submitted an attempt at a doctoral dissertation to Professor Alfred Kleiner at the University of Zurich. The dissertation has not survived, but Mari told a friend that “it deal
s with research into the molecular forces in gases using various known phenomena.” Einstein was confident. “He won’t dare reject my dissertation,” he said of Kleiner, “otherwise the shortsighted man is of little use to me.”51
By December Kleiner had not even responded, and Einstein started worrying that perhaps the professor’s “fragile dignity” might make him uncomfortable accepting a dissertation that denigrated the work of such masters as Drude and Boltzmann. “If he dares to reject my dissertation, then I’ll publish his rejection along with my paper and make a fool of him,” Einstein said. “But if he accepts it, then we’ll see what good old Herr Drude has to say.”
Eager for a resolution, he decided to go see Kleiner personally. Rather surprisingly, the meeting went well. Kleiner admitted he had not yet read the dissertation, and Einstein told him to take his time. They then proceeded to discuss various ideas that Einstein was developing, some of which would eventually bear fruit in his relativity theory. Kleiner promised Einstein that he could count on him for a recommendation the next time a teaching job came up. “He’s not quite as stupid as I’d thought,” was Einstein’s verdict.“Moreover, he’s a good fellow.”52
Kleiner may have been a good fellow, but he did not like Einstein’s dissertation when he finally got around to reading it. In particular, he was unhappy about Einstein’s attack on the scientific establishment. So he rejected it; more precisely, he told Einstein to withdraw it voluntarily, which permitted him to get back his 230 franc fee. According to a book written by Einstein’s stepson-in-law, Kleiner’s action was “out of consideration to his colleague Ludwig Boltzmann, whose train of reasoning Einstein had sharply criticized.” Einstein, lacking such sensitivity, was persuaded by a friend to send the attack directly to Boltzmann.53
Lieserl
Marcel Grossmann had mentioned to Einstein that there was likely to be a job at the patent office for him, but it had not yet materialized. So five months later, he gently reminded Grossmann that he still needed help. Noticing in the newspaper that Grossmann had won a job teaching at a Swiss high school, Einstein expressed his “great joy” and then plaintively added, “I, too, applied for that position, but I did it only so that I wouldn’t have to tell myself that I was too faint-hearted to apply.”54
In the fall of 1901, Einstein took an even humbler job as a tutor at a little private academy in Schaffhausen, a village on the Rhine twenty miles north of Zurich. The work consisted solely of tutoring a rich English schoolboy who was there. To be taught by Einstein would someday seem a bargain at any price. But at the time, the proprietor of the school, Jacob Nüesch, was getting the bargain. He was charging the child’s family 4,000 francs a year, while paying Einstein only 150 francs a month, plus providing room and board.
Einstein continued to promise Mari that she would “get a good husband as soon as this becomes feasible,” but he was now despairing about the patent job. “The position in Bern has not yet been advertised so that I am really giving up hope for it.”55
Mari was eager to be with him, but her pregnancy made it impossible for them to be together in public. So she spent most of November at a small hotel in a neighboring village. Their relationship was becoming strained. Despite her pleas, Einstein came only infrequently to visit her, often claiming that he did not have the spare money. “You’ll surely surprise me, right?” she begged after getting yet another note canceling a visit. Her pleadings and anger alternated, often in the same letter:
If you only knew how terribly homesick I am, you would surely come. Are you really out of money? That’s nice! The man earns 150 francs, has room and board provided, and at the end of the month doesn’t have a cent to his name! ... Don’t use that as an excuse for Sunday, please. If you don’t get any money by then, I will send you some . . . If you only knew how much I want to see you again! I think about you all day long, and even more at night.56
Einstein’s impatience with authority soon pitted him against the proprietor of the academy. He tried to cajole his tutee to move to Bern with him and pay him directly, but the boy’s mother balked. Then Einstein asked Nüesch to give him his meal money in cash so that he would not have to eat with his family. “You know what our conditions are,” Nüesch replied. “There is no reason to deviate from them.”
A surly Einstein threatened to find new arrangements, and Nüesch backed down in a rage. In a line that could be considered yet another maxim for his life, Einstein recounted the scene to Mari and exulted, “Long live impudence! It is my guardian angel in this world.”
That night, as he sat down for his last meal at the Nüesch household, he found a letter for him next to his soup plate. It was from his real-life guardian angel, Marcel Grossmann. The position at the patent office, Grossmann wrote, was about to be advertised, and Einstein was sure to get it. Their lives were soon to be “brilliantly changed for the better,” an excited Einstein wrote Mari. “I’m dizzy with joy when I think about it,” he said. “I’m even happier for you than for myself. Together we’d surely be the happiest people on the earth.”
That still left the issue of what to do about their baby, who was due to be born in less than two months, by early February 1902. “The only problem that would remain to be solved would be how to keep our Lieserl with us,” Einstein (who had begun referring to their unborn child as a girl) wrote to Mari, who had returned home to have the baby at her parents’ house in Novi Sad. “I wouldn’t want to have to give her up.” It was a noble intention on his part, yet he knew that it would be difficult for him to show up for work in Bern with an illegitimate child. “Ask your Papa; he’s an experienced man, and knows the world better than your overworked, impractical Johnnie.” For good measure, he declared that the baby, when born, “shouldn’t be stuffed with cow milk, because it might make her stupid.” Mari’s milk would be more nourishing, he said.57
Although he was willing to consult Mari’s family, Einstein had no intention of letting his own family know that his mother’s worst fears about his relationship—a pregnancy and possible marriage—were materializing. His sister seemed to realize that he and Mari were secretly planning to be married, and she told this to members of the Winteler family in Aarau. But none of them showed any sign of suspecting that a child was involved. Einstein’s mother learned about the purported engagement from Mrs. Winteler. “We are resolutely against Albert’s relationship with Fraulein Mari, and we don’t ever wish to have anything to do with her,” Pauline Einstein lamented.58
Einstein’s mother even took the extraordinary step of writing a nasty letter, signed also by her husband, to Mari’s parents. “This lady,” Mari lamented to a friend about Einstein’s mother, “seems to have set as her life’s goal to embitter as much as possible not only my life but also that of her son. I could not have thought it possible that there could exist such heartless and outright wicked people! They felt no compunctions about writing a letter to my parents in which they reviled me in a manner that was a disgrace.”59
The official advertisement announcing the patent office opportunity finally appeared in December 1901. The director, Friedrich Haller, apparently tailored the specifications so that Einstein would get the job. Candidates did not need a doctorate, but they must have mechanical training and also know physics. “Haller put this in for my sake,” Einstein told Mari.
Haller wrote Einstein a friendly letter making it clear that he was the prime candidate, and Grossmann called to congratulate him. “There’s no doubt anymore,” Einstein exulted to Mari. “Soon you’ll be my happy little wife, just watch. Now our troubles are over. Only now that this terrible weight is off my shoulders do I realize how much I love you... Soon I’ll be able to take my Dollie in my arms and call her my own in front of the whole world.”60
He made her promise, however, that marriage would not turn them into a comfortable bourgeois couple: “We’ll diligently work on science together so we don’t become old philistines, right?” Even his sister, he felt, was becoming “so crass” in her appr
oach to creature comforts. “You’d better not get that way,” he told Mari. “It would be terrible. You must always be my witch and street urchin. Everyone but you seems foreign to me, as if they were separated from me by an invisible wall.”
In anticipation of getting the patent-office job, Einstein abandoned the student he had been tutoring in Schaffhausen and moved to Bern in late January 1902. He would be forever grateful to Grossmann, whose aid would continue in different ways over the next few years. “Grossmann is doing his dissertation on a subject that is related to non-Euclidean geometry,” Einstein noted to Mari. “I don’t know exactly what it is.”61
A few days after Einstein arrived in Bern, Mileva Mari, staying at her parents’ home in Novi Sad, gave birth to their baby, a girl whom they called Lieserl. Because the childbirth was so difficult, Mari was unable to write to him. Her father sent Einstein the news.
“Is she healthy, and does she cry properly?” Einstein wrote Mari. “What are her eyes like? Which one of us does she more resemble? Who is giving her milk? Is she hungry? She must be completely bald. I love her so much and don’t even know her yet!” Yet his love for their new baby seemed to exist mainly in the abstract, for it was not quite enough to induce him to make the train trip to Novi Sad.62
Einstein did not tell his mother, sister, or any of his friends about the birth of Lieserl. In fact, there is no indication that he ever told them about her. Never once did he publicly speak of her or acknowledge that she even existed. No mention of her survives in any correspondence, except for a few letters between Einstein and Mari, and these were suppressed and hidden until 1986, when scholars and the editors of his papers were completely surprised to learn of Lieserl’s existence.*
But in his letter to Mari right after Lieserl’s birth, the baby brought out Einstein’s wry side. “She’s certainly able to cry already, but won’t know how to laugh until much later,” he said. “Therein lies a profound truth.”
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