Göteborg, in Sweden, waltzes with surprises. Expecting ski trails or high-walled fjords, strangers find meandering water instead. A river lazes its way across a Scandinavian steppe flat enough to be in Holland or somespace east of the Urals where Mongols thunder through. The slow moving river opens at Göteborg into a bay, Sweden’s busiest port. The terrain that Einstein found in July 1923 when he arrived to give his delayed Nobel lecture was as flat as Berlin. During the previous two years, while Germans were nursing hatreds and ruination, Sweden had been happily preparing for a tercentenary jubilee exposition to celebrate Göteborg’s founding in 1621. New plazas, streets, and buildings were erected to house a festival that lasted from May through September.
Einstein arrived at the height of the celebration to speak before an audience of 2,000 souls, including Sweden’s King Gustav V, in the new Memorial Hall. The event was an odd combination of the lost and the new. The Nobel Prize ceremony was a vestige of the lost civilization where borders mattered less than imagination. Meanwhile, the Göteborg jubilee honored the new—the secure frontier and the boasting about what had been accomplished behind it.
The city’s buildings were low and ordinary with nothing like the grand monuments that had been scattered across Berlin during the
half century before the Great War. Göteborg’s soil was to blame. It crunches like strips of dried pasta and cannot support tall structures. The most impressive buildings to greet Einstein had been constructed for the exposition. A new central plaza adorned the festival grounds and led to the exposition’s buildings. The plaza boasted a fountain with Poseidon wearing a conch cap above a Scandinavian face. Water splashed merrily about him as he clutched a shark in one hand and held a basin high with the other.
Einstein arrived in his accustomed role of reason’s champion, but the text he carried in his pocket was unusually dense. Typically, the difficulty of his lectures came from the unfamiliarity of his mathematics, or the listener’s unwillingness to surrender some complicating idea, or perhaps the novelty of Einstein’s concerns, but this time his density sounded like a parody of Bohr’s style. He used five words where one would do, added mathematical jargon he could easily have avoided, and he provided no signposts pointing toward where he was headed or how his thoughts moved. Even the lecture’s climactic finish was filled with obscure mathematical references that hid the talk’s surprisingly troubled emotions. The crowd that cheered Einstein as he strode past the Poseidon fountain probably did not know how unfairly challenging the lecture would be. Nonetheless, the handful among the audience able to follow the presentation would hear an account of what Einstein looked for in physics and where he wanted to go.
Surrounding the plaza, besides the hall where Einstein headed, rose two other exposition centers, Göteborg’s new art museum and a huge wooden building called Machinery Hall. The latter’s gothic roof was said to be the largest vaulted roof ever constructed. Its vast display floor overflowed with products ranging from the very old to the most up-to-date. It showed, for example, a history of cutting tools that ran from a stone age “ax” to a modern surgical scalpel made of the finest Swedish steel. Einstein’s hosts led him straight into Memorial Hall, past the many portraits of Göteborg’s leading citizens, and into the auditorium where he was richly applauded as he came into view.
The Nobel Prize statement had specifically mentioned the success of the photoelectric law and during the eight months since the prize’s announcement, Compton’s bullet had struck home. Einstein might,
therefore, have seized the opportunity to rebut Bohr’s own Nobel lecture and assert the validity of the light quanta. Instead, he said nothing at all about the photoelectric effect. He simply laid out his own agenda along with a description of how he could satisfy his ambitions.
His chief tasks were same ones that had consumed him when the World War ended: understand quantum radiation and unify his theory of relativity with the facts of electromagnetism. In the final words of his lecture he reported that he was ready to abandon many ideas to grasp the “most profound physical problem of the present time,” quantum theory. Relativity, he admitted, had so far been “ineffectual” at providing insights into the quantum’s nature and he could even imagine that some day the “solution of the quantum problem” would lead to “a complete change” in the understanding of space and time. If that happened, his great laws of relativity would be reduced to “limiting” equations that were valuable in solving many practical problems but do not describe nature’s foundations.
With his closing, Einstein had arrived at a radical level that Bohr would not reach for two more years. Only in 1925, after BKS’s failure forced acceptance of the Compton effect and light quanta, would Bohr concede that this result meant revolution. Einstein had sensed the revolution’s coming for years, and any uncertainty was settled after the Compton discovery. Light quanta—not just the mathematical abstraction hυ—but the light quanta themselves had become so important that they were soon given a sleeker, less clumsy name—photons—and as photons they will be known through the rest of our history. This new fact of nature that Einstein had called “revolutionary” back in 1905 would finally trigger the quantum revolution that was to begin in 1925.
Photons had already brought a technical revolution, changing the lives of millions of unscientific people, as could be seen plainly at Göteborg’s festival of progress. Electric lights illuminated the festival’s auditorium with trillions of photons. Introduced by Edison only 44 years earlier, they used a current that somehow stimulated a hair-thin filament to emit a steady blaze of light. Meanwhile, hospitals were using X-ray photons to study patients and their broken bones. Broadcasting, too, had come of age with towers emitting photons to send
wireless messages, permit ship-to-shore communications, and entertain and inform the public through radio programs. The age of the photon tool had arrived and anybody visiting Göteborg’s Machinery Hall could see that once something becomes a tool—be it made from stone, bronze, or steel—innovators find more and more uses for it. So the coming era of television, lasers, X-ray telescopes, compact disks, CAT scans, and a thousand other photon-based devices was implicitly promised in Göteborg on the day Einstein spoke there.
With the photon already established as a fact of technology, of nature, and of daily living, the question Einstein addressed in his lecture—What now?—was one faced in one way or another by many members of his audience. For the practical people who were inspired by the displays in Machinery Hall, new facts of nature call for new inventions. For them, understanding was never the point behind learning; using was the point. You could see that in the story of the compass. Vikings had transformed a mystery into an invaluable arrow that pointed their way across the featureless ocean. The compass served for centuries without its users ever gaining a clue as to how it worked. Even in 1923 magnetism was still not deeply understood.
Novelties can make the artistically inclined want to capture exactly how a new wonder changes the look of things. Each of the paintings in the Memorial Hall’s portrait gallery was the residue of that imaginative wonder and reflected an hour when an artist peered as attentively as possible at the facts of a single face. No less than experimentalists, artists wanted to know exactly what it was before them. “Nature for us men is more depth than surface,” Paul Cézanne had written, and Einstein would have agreed completely, but then the artist went on to advise introducing “into our light vibrations, represented by reds and yellows, a sufficient amount of blue to give the impression of air.” For artists the point of getting the facts right is to express what they see there. For them a compass was a detail to be seen exactly and portrayed precisely. Is there a clear piece of glass above the needle? And does it betray its presence by slightly altering the look of what’s behind it? Good, then get that subtle difference on the canvas.
Einstein’s reaction, a confident effort to understand nature’s power,
defined scientific wonder. For Einstein, something like a compass was a clue, a witness to be brought before the bar and cross-questioned as to its meaning. Einstein’s father had in fact shown him a compass when he was a small boy: “I can still remember—at least I believe I can remember—that this experience made a deep and lasting impression on me. Something deeply hidden had to be behind things.” At age five he might have not yet felt that anybody could discover the deep mystery behind this wonder, but somehow in the years since he saw his first compass Einstein had grown as confident as Sherlock Holmes that he could follow clues to their solution. He was no optimist about human affairs, but when it came to his own abilities he looked only for the heaviest lifting. The wondrous fact of the compass was that it moved without being touched. There must be something hidden but real, lying invisibly in empty space, something ready to spring into action whenever a compass goes by. He could have reverenced that mystery, or enfolded it into an art, or made practical use of it, but because he was a scientist by nature, Einstein sought simply to understand it, and in his Nobel lecture he told his audience exactly what was involved in that understanding.
It might have been entertaining to ask King Gustav what Einstein had said. Perhaps he would have been as quick-witted as Count Kessler and remarked that he caught the significance more than the meaning. Too bad, for the lecture was unusually detailed about how Einstein approached a mystery and struggled to take the step necessary to approach understanding.
Once Einstein had entered the auditorium and been applauded so roundly that the audience finally lost its need to clap further, the celebrated hero began to lay out what underlies “bona fide scientific knowledge.”
Facts of nature, he told the audience determine what concepts and distinctions will be allowed into a theory. Facts are a theory’s gatekeeper. It is not that scientists look harder than artists, or explore more fully than artisans and engineers. The secret behind Einstein’s scientific imagining was that he was always looking for meaning, which he defined as “the extent to which observable facts can be assigned to” concepts and other abstract forms “without ambiguity.” Facts without
concepts, Einstein once complained, produced “a catalogue and not a system.” On the other hand, a system without facts was not science. From his earliest days as an unemployed graduate in Switzerland, Einstein insisted that physics rested on concrete facts and that mathematical conceptualizing was only a means for expressing the laws governing these facts.
Logically, Einstein conceded, the problem of understanding was badly tangled. First, facts authorize concepts and give them meaning, but then concepts justify and explain the facts. A scientific theory becomes a self-supporting arch in which the factual pillar supports the concepts and the concept pillar supports the facts. The “step” that Einstein kept seeking was the discovery of an arch’s keystone that would allow facts and concepts to stand together by themselves.
Einstein saw the logical risks of this approach. It lacked the grace of Euclid’s enviable geometry, which pulled an entire system of knowledge out from a few self-evident truths, and he apologized for this gracelessness to his listeners, commenting, “We are … not sufficiently advanced in our knowledge of Nature’s elementary laws to adopt [a logically] more perfect method without going out of our depth.” Did King Gustav mutter to himself I’m glad he cleared that up?
The imaginative steps that Einstein took always managed to snap both pillars of a logical arch together. Snap, the fact tells us this about the concept and, pretty much simultaneously, snap, the concept tells us that about the fact. Compton’s discovery had shown the process. It is a fact that X-rays change frequency when they lose energy; Einstein’s concept of light particles says a photon’s energy changes as its frequency changes. So, snap, Einstein’s concept explains the change in X-ray frequency, while, snap, the fact of a change in frequency justifies Einstein’s concept. This snap-snap process lay behind much of Einstein’s success. He would struggle for years thinking about some paradoxical fact of nature and then, snap, realize that the fact implied something quite unexpected about a concept previously taken for granted and, snap, he would recognize too that the revised concept implied many things about the fact. Suddenly, in a tsunami of understanding, the years of puzzlement would be followed by a few weeks of intense labor that transformed the paradox into a coherent theory.
In his Nobel lecture, Einstein described the union of facts and concepts that led in 1905 to his creation of the special theory of relativity and then, 10 years later, to his generalizing of the theory. He concluded by telling his audience something of his interests in taking general relativity another step and uniting it with electromagnetism.
“The mind striving after the unification of the theory …,” he told the audience, generalizing again from himself. The whole phrase could have been replaced by the lone word “I.” If he had said that, more of the audience might have realized that he had shifted into a personal account of what interested him in science. Einstein told the room that he “cannot be satisfied that two fields should exist”—the gravitational field and the electromagnetic one—“which by their nature are quite independent.” He was seeking “a mathematically unified field theory … in which the gravitational … and the electromagnetic field are interpreted only as different” elements of the same thing.
This unification would be like the unity Einstein had already found when he showed that matter and energy are different forms of the same thing. It was also the kind of solution he wanted in the problem of photons. The Compton effect had shown that light is just as much a particle as it is a wave. He needed to adjust his concept of a wave so that the facts of light’s nature would become coherent. With that step, light’s wave-particle duality would change from being a paradoxical fact to being an intelligible one.
A problem for the unification of gravity and electromagnetism was, as Einstein told his audience in Göteborg, that gravity and electromagnetism do not contradict one another. They ignore one another. Once they had been contradictory, but with relativity Einstein himself had exorcised those paradoxes from physics. Now gravity and electromagnetism sat together like two strangers on a bus seat, paired and yet having nothing to do with each other. Einstein’s gravitational equations worked fine; so did the established equations defining an electromagnetic field. With neither contradictions nor harmonies to suggest a point where the two might arch together, Einstein told the people of Göteborg, “We are restricted to the criterion of mathematical simplicity.”
Did anyone among the 2,000 listeners come to attention here? Possibly not, but it is more agreeable to suppose that somewhere among all those heads was a brain alert enough to ask if Einstein was bidding farewell to the scientific quest. He had been saying throughout the lecture that scientific knowledge demands meaningful concepts. Mechanics before relativity, he said, had not always been meaningful. The mathematics had seemed clear enough, but on close examination it turned out to rest on rules and assumptions rather than facts of nature. When it came to postwar theories of gravity and electromagnetic fields, however, the philosophizing had been squeezed out of the equations. Everything rested on facts. But, Einstein said, there were no facts linking nature’s controlling fields. Simplicity as a goal, Einstein warned, “is not free from arbitrariness.”
There now, that one alert head could relax a bit after all.
Einstein was not abandoning science by trying to get away from the facts. He realized full well that he could not introduce any new concepts into his work. There could be no redefining time or proposing novelties like photons. He was still trying to explain nature in nature’s own terms. Einstein had returned to his familiar post as lone observer high in a crow’s nest looking at storm clouds while everybody on deck sees only open skies. As usual his cry of “Storm ho” was greeted by the officers on deck with skepticism and even a bit of gleeful contempt. There had been something satisfying in laughing at the great physicist’s talk of photons, but then the Compton effect wiped away the grins. Now Einstein was back on his lone perch, insisting there was a problem, and none took it seriously.
Of course, few, if any, members of the Göteborg audience realized how much thought lay beneath Einstein’s dense jungle of prose. They cheered anyway, possibly even applauding all the more loudly the less they understood. The point of sitting there was to be present when the prophet spoke. Nobody understood the Oracle of Delphi either, but that did not mean that nobody came to listen. So they applauded and no doubt decades later were still telling people they had heard the great Einstein give his Nobel lecture.
—Oh, and did you understand it?
—Not one word, laughs the boaster, still proud of having heard it and quite unembarrassed about having understood none of it.
It had not always been like that. A generation earlier physicists like Mach, Helmholtz, and Maxwell had given great popular lectures to ordinary working people who had understood the talks and been interested. Helmholtz, missionizing for science, preached, “There is a kind, I might almost say, of artistic satisfaction, when we are able to survey the enormous wealth of Nature as a regularly-ordered whole—a kosmos, an image of the logical thought in our own mind.” And Mach assured his audiences that a popular expression of the time—ignorabimus, we can never know—was a falsehood and that everything about the world could be learned “entirely by accurate observation and searching thought.”
Something had happened since those days of public optimism. Maybe the science had gotten harder, but mostly it was the great folly of the war and the increasing professionalization of science. It is telling that Thomas Mann chose that year (1923) to write that although he knew and understood “very little about the famous Mr. Einstein,” he had the clear impression that the boundary between physics and metaphysics had become more tenuous. Actually, the opposite was happening. Einstein had chased metaphysics out of the story of motion and gravity, but he had retained and reinforced the Helmholtz view of “Nature as a regularly-ordered whole.” Yet, the general public no longer expected to be able to follow the explanations and did not realize that Einstein was clarifying, not muddying. People were good humored about it, laughing at their own incomprehension, and thanking heaven that there was a hero like Einstein who did understand it. But they missed Einstein’s larger sermon that no matter what your vantage point, the cosmos follows the same natural laws.
The hero made his way out of the auditorium and moved back past the portraits of distinguished Göteborgians. Sunlight lasted 18 hours that day, providing ample time to do any sightseeing and socializing. Eventually he boarded a train for the south and followed the coast toward Malmö. On a ferry he put Sweden behind him as he steamed toward Denmark. It was not long before Copenhagen appeared as a smoky cloud, and then as factory chimneys poking above the horizon. Beneath the smoking chimneys as Copenhagen’s green-copper domes and red roofs rose into view, Niels Bohr was waiting for Einstein to land.