The E=mc2Coda, September 1905
Einstein had raised the curtain on his miracle year in his letter to his Olympia Academy mate Conrad Habicht, and he celebrated its climax with his one-sentence drunken postcard to him. In September, he wrote yet another letter to Habicht, this one trying to entice him to come work at the patent office. Einstein’s reputation as a lone wolf was somewhat artificial. “Perhaps it would be possible to smuggle you in among the patent slaves,” he said. “You probably would find it relatively pleasant. Would you actually be ready and willing to come? Keep in mind that besides the eight hours of work, each day also has eight hours for fooling around, and then there’s also Sunday. I would love to have you here.”
As with his letter six months earlier, Einstein went on to reveal quite casually a momentous scientific breakthrough, one that would be expressed by the most famous equation in all of science:
One more consequence of the electrodynamics paper has also crossed my mind. Namely, the relativity principle, together with Maxwell’s equations, requires that mass be a direct measure of the energy contained in a body. Light carries mass with it. With the case of radium there should be a noticeable reduction of mass. The thought is amusing and seductive; but for all I know, the good Lord might be laughing at the whole matter and might have been leading me up the garden path.81
Einstein developed the idea with a beautiful simplicity. The paper that the Annalen der Physik received from him on September 27, 1905, “Does the Inertia of a Body Depend on Its Energy Content?,” involved only three steps that filled merely three pages. Referring back to his special relativity paper, he declared, “The results of an electrodynamic investigation recently published by me in this journal lead to a very interesting conclusion, which will be derived here.”82
Once again, he was deducing a theory from principles and postulates, not trying to explain the empirical data that experimental physicists studying cathode rays had begun to gather about the relation of mass to the velocity of particles. Coupling Maxwell’s theory with the relativity theory, he began (not surprisingly) with a thought experiment. He calculated the properties of two light pulses emitted in opposite directions by a body at rest. He then calculated the properties of these light pulses when observed from a moving frame of reference. From this he came up with equations regarding the relationship between speed and mass.
The result was an elegant conclusion: mass and energy are different manifestations of the same thing. There is a fundamental interchangeability between the two. As he put it in his paper, “The mass of a body is a measure of its energy content.”
The formula he used to describe this relationship was also strikingly simple: “If a body emits the energy L in the form of radiation, its mass decreases by L/V 2.” Or, to express the same equation in a different manner:L=mV 2. Einstein used the letter L to represent energy until 1912, when he crossed it out in a manuscript and replaced it with the more common E. He also used V to represent the velocity of light, before changing to the more common c. So, using the letters that soon became standard, Einstein had come up with his memorable equation:
E=mc 2
Energy equals mass times the square of the speed of light. The speed of light, of course, is huge. Squared it is almost inconceivably bigger. That is why a tiny amount of matter, if converted completely into energy, has an enormous punch. A kilogram of mass would convert into approximately 25 billion kilowatt hours of electricity. More vividly: the energy in the mass of one raisin could supply most of New York City’s energy needs for a day.83
As usual, Einstein ended by proposing experimental ways to confirm the theory he had just derived. “Perhaps it will prove possible,” he wrote,“to test this theory using bodies whose energy content is variable to a high degree, e.g., salts of radium.”
CHAPTER SEVEN
THE HAPPIEST THOUGHT
1906–1909
Recognition
Einstein’s 1905 burst of creativity was astonishing. He had devised a revolutionary quantum theory of light, helped prove the existence of atoms, explained Brownian motion, upended the concept of space and time, and produced what would become science’s best known equation. But not many people seemed to notice at first. According to his sister, Einstein had hoped that his flurry of essays in a preeminent journal would lift him from the obscurity of a third-class patent examiner and provide some academic recognition, perhaps even an academic job. “But he was bitterly disappointed,” she noted. “Icy silence followed the publication.”1
That was not exactly true. A small but respectable handful of physicists soon took note of Einstein’s papers, and one of these turned out to be, as good fortune would have it, the most important possible admirer he could attract: Max Planck, Europe’s revered monarch of theoretical physics, whose mysterious mathematical constant explaining black-body radiation Einstein had transformed into a radical new reality of nature. As the editorial board member of Annalen der Physik responsible for theoretical submissions, Planck had vetted Einstein’s papers, and the one on relativity had “immediately aroused my lively attention,” he later recalled. As soon as it was published, Planck gave a lecture on relativity at the University of Berlin.2
Planck became the first physicist to build on Einstein’s theory. In an article published in the spring of 1906, he argued that relativity conformed to the principle of least action, a foundation of physics that holds that light or any object moving between two points should follow the easiest path.3
Planck’s paper not only contributed to the development of relativity theory; it also helped to legitimize it among other physicists. Whatever disappointment Maja Einstein had detected in her brother dissipated. “My papers are much appreciated and are giving rise to further investigations,” he exulted to Solovine. “Professor Planck has recently written to me about that.”4
The proud patent examiner was soon exchanging letters with the eminent professor. When another theorist challenged Planck’s contention that relativity theory conformed to the principle of least action, Einstein took Planck’s side and sent him a card saying so. Planck was pleased. “As long as the proponents of the principle of relativity constitute such a modest little band as is now the case,” he replied to Einstein, “it is doubly important that they agree among themselves.” He added that he hoped to visit Bern the following year and meet Einstein personally.5
Planck did not end up coming to Bern, but he did send his earnest assistant, Max Laue.* He and Einstein had already been corresponding about Einstein’s light quanta paper, with Laue saying that he agreed with “your heuristic view that radiation can be absorbed and emitted only in specific finite quanta.”
However, Laue insisted, just as Planck had, that Einstein was wrong to assume that these quanta were a characteristic of the radiation itself. Instead, Laue contended that the quanta were merely a description of the way that radiation was emitted or absorbed by a piece of matter. “This is not a characteristic of electromagnetic processes in a vacuum but rather of the emitting or absorbing matter,” Laue wrote, “and hence radiation does not consist of light quanta as it says in section six of your first paper.”6 (In that section, Einstein had said that the radiation “behaves thermodynamically as if it consisted of mutually independent energy quanta.”)
When Laue was preparing to visit in the summer of 1907, he was surprised to discover that Einstein was not at the University of Bern but was working at the patent office on the third floor of the Post and Telegraph Building. Meeting Einstein there did not lessen his wonder. “The young man who came to meet me made so unexpected an impression on me that I did not believe he could possibly be the father of the relativity theory,” Laue said, “so I let him pass.” After a while, Einstein came wandering through the reception area again, and Laue finally realized who he was.
They walked and talked for hours, with Einstein at one point offering a cigar that, Laue recalled, “was so unpleasant that I ‘accidentally’ dropped it into the river.” Ein
stein’s theories, on the other hand, made a pleasing impression. “During the first two hours of our conversation he overthrew the entire mechanics and electrodynamics,” Laue noted. Indeed, he was so enthralled that over the next four years he would publish eight papers on Einstein’s relativity theory and become a close friend.7
Some theorists found the amazing flurry of papers from the patent office to be uncomfortably abstract. Arnold Sommerfeld, later a friend, was among the first to suggest there was something Jewish about Einstein’s theoretical approach, a theme later picked up by anti-Semites. It lacked due respect for the notion of order and absolutes, and it did not seem solidly grounded. “As remarkable as Einstein’s papers are,” he wrote Lorentz in 1907, “it still seems to me that something almost unhealthy lies in this unconstruable and impossible to visualize dogma. An Englishman would hardly have given us this theory. It might be here too, as in the case of Cohn, the abstract conceptual character of the Semite expresses itself.”8
None of this interest made Einstein famous, nor did it get him any job offers. “I was surprised to read that you must sit in an office for eight hours a day,” wrote yet another young physicist who was planning to visit. “History is full of bad jokes.”9 But because he had finally earned his doctorate, he had at least gotten promoted from a third-class to a second-class technical expert at the patent office, which came with a hefty 1,000-franc raise to an annual salary of 4,500 francs.10
His productivity was startling. In addition to working six days a week at the patent office, he continued his torrent of papers and reviews: six in 1906 and ten more in 1907. At least once a week he played in a string quartet. And he was a good father to the 3-year-old son he proudly labeled “impertinent.” As Mari wrote to her friend Helene Savi, “My husband often spends his free time at home just playing with the boy.”11
Beginning in the summer of 1907, Einstein also found time to dabble in what might have become, if the fates had been more impish, a new career path: as an inventor and salesman of electrical devices like his uncle and father. Working with Olympia Academy member Conrad Habicht and his brother Paul, Einstein developed a machine to amplify tiny electrical charges so they could be measured and studied. It had more academic than practical purpose; the idea was to create a lab device that would permit the study of small electrical fluctuations.
The concept was simple. When two strips of metal move close to each other, an electric charge on one will induce an opposite charge on the other. Einstein’s idea was to use a series of strips that would induce the charge ten times and then transfer that to another disc. The process would be repeated until the original minuscule charge would be multiplied by a large number and thus be easily measurable. The trick was making the contraption actually work.12
Given his heritage, breeding, and years in the patent office, Einstein had the background to be an engineering genius. But as it turned out, he was better suited to theorizing. Fortunately, Paul Habicht was a good machinist, and by August 1907 he had a prototype of the Maschinchen, or little machine, ready to be unveiled. “I am astounded at the lightning speed with which you built the Maschinchen,” Einstein wrote. “I’ll show up on Sunday.” Unfortunately, it didn’t work. “I am driven by murderous curiosity as to what you’re up to,” Einstein wrote a month later as they tried to fix things.
Throughout 1908, letters flew back and forth between Einstein and the Habichts, filled with complex diagrams and a torrent of ideas for how to make the device work. Einstein published a description in a journal, which produced, for a while, a potential sponsor. Paul Habicht was able to build a better version by October, but it had trouble keeping a charge. He brought the machine to Bern, where Einstein commandeered a lab in one of the schools and dragooned a local mechanic. By November the machine seemed to be working. It took another year or so to get a patent and begin to make some versions for sale. But even then, it never truly caught hold or found a market, and Einstein eventually lost interest.13
These practical exploits may have been fun, but Einstein’s glorious isolation from the priesthood of academic physicists was starting to have more drawbacks than advantages. In a paper he wrote in the spring of 1907, he began by exuding a joyful self-assurance about having neither the library nor the inclination to know what other theorists had written on the topic. “Other authors might have already clarified part of what I am going to say,” he wrote. “I felt I could dispense with doing a literature search (which would have been very troublesome for me), especially since there is good reason to hope that others will fill this gap.” However, when he was commissioned to write a major year-book piece on relativity later that year, there was slightly less cockiness in his warning to the editor that he might not be aware of all the literature. “Unfortunately I am not in a position to acquaint myself about everything that has been published on this subject,” he wrote, “because the library is closed in my free time.”14
That year he applied for a position at the University of Bern as a privatdozent, a starter rung on the academic ladder, which involved giving lectures and collecting a small fee from anyone who felt like showing up. To become a professor at most European universities, it helped to serve such an apprenticeship. With his application Einstein enclosed seventeen papers he had published, including the ones on relativity and light quanta. He was also expected to include an unpublished paper known as a habilitation thesis, but he decided not to bother writing one, as this requirement was sometimes waived for those who had “other outstanding achievements.”
Only one professor on the faculty committee supported hiring him without requiring him to write a new thesis, “in view of the important scientific achievements of Herr Einstein.” The others disagreed, and the requirement was not waived. Not surprisingly, Einstein considered the matter “amusing.” He did not write the special habilitation or get the post.15
The Equivalence of Gravity and Acceleration
Einstein’s road to the general theory of relativity began in November 1907, when he was struggling against a deadline to finish an article for a science yearbook explaining his special theory of relativity. Two limitations of that theory still bothered him: it applied only to uniform constant-velocity motion (things felt and behaved differently if your speed or direction was changing), and it did not incorporate Newton’s theory of gravity.
“I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me,” he recalled. “If a person falls freely, he will not feel his own weight.”That realization, which “startled” him, launched him on an arduous eight-year effort to generalize his special theory of relativity and “impelled me toward a theory of gravitation.”16 Later, he would grandly call it “the happiest* thought in my life.”17
The tale of the falling man has become an iconic one, and in some accounts it actually involves a painter who fell from the roof of an apartment building near the patent office.18 In fact, probably like other great tales of gravitational discovery—Galileo dropping objects from the Tower of Pisa and the apple falling on Newton’s head19—it was embellished in popular lore and was more of a thought experiment than a real occurrence. Despite Einstein’s propensity to focus on science rather than the merely personal, even he was not likely to watch a real human plunging off a roof and think of gravitational theory, much less call it the happiest thought in his life.
Einstein refined his thought experiment so that the falling man was in an enclosed chamber, such as an elevator in free fall above the earth. In this falling chamber (at least until it crashed), the man would feel weightless. Any objects he emptied from his pocket and let loose would float alongside him.
Looking at it another way, Einstein imagined a man in an enclosed chamber floating in deep space “far removed from stars and other appreciable masses.” He would experience the same perceptions of weightlessness. “Gravitation naturally does not exist for this observer. He must fasten himself with strings to the floor, otherwise the slightest impact a
gainst the floor will cause him to rise slowly towards the ceiling.”
Then Einstein imagined that a rope was hooked onto the roof of the chamber and pulled up with a constant force. “The chamber together with the observer then begin to move ‘upwards’ with a uniformly accelerated motion.”The man inside will feel himself pressed to the floor. “He is then standing in the chest in exactly the same way as anyone stands in a room of a house on our earth.” If he pulls something from his pocket and lets go, it will fall to the floor “with an accelerated relative motion” that is the same no matter the weight of the object—just as Galileo discovered to be the case for gravity. “The man in the chamber will thus come to the conclusion that he and the chest are in a gravitational field. Of course he will be puzzled for a moment as to why the chest does not fall in this gravitational field. Just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chamber is suspended at rest in the gravitational field.”
“Ought we to smile at the man and say that he errs in his conclusion?” Einstein asked. Just as with special relativity, there was no right or wrong perception. “We must rather admit that his mode of grasping the situation violates neither reason nor known mechanical laws.”20
A related way that Einstein addressed this same issue was typical of his ingenuity: he examined a phenomenon that was so very well-known that scientists rarely puzzled about it. Every object has a “gravitational mass,” which determines its weight on the earth’s surface or, more generally, the tug between it and any other object. It also has an “inertial mass,” which determines how much force must be applied to it in order to make it accelerate. As Newton noted, the inertial mass of an object is always the same as its gravitational mass, even though they are defined differently. This was obviously more than a mere coincidence, but no one had fully explained why.
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