Einstein's War

by Matthew Stanley

  Eddington felt more and more out of place in British science. His solitude at the observatory was matched by his increasingly long solitary bicycle rides through the English countryside. While he composed Schwarzschild’s obituary he took a break for a ninety-mile trip from Sibford to Cambridge. Thanks to his obsessive record-keeping, we know this was one of his longest bike rides ever. This gave him plenty of time to think about the twin problems of the fracturing of international science and the enigmas of relativity.

  Eddington had hoped that his memorial of Schwarzschild would serve as a reminder to his colleagues that the Germans, too, were human and essential parts of the universal scientific quest. Yet Schwarzschild had been an enthusiastic German soldier, so was of limited value for this. The still-obscure Einstein and his mysterious theory might provide something better. World-changing science and a figure untainted by the German war machine. A symbol of how science could push beyond the pitfalls of nationalism. But Britain remained a hostile land; Eddington needed to plan relativity’s invasion.

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  EINSTEIN DID NOT know much about his new ally across the English Channel, and looked for help closer to home. He had been eagerly digging into his own theory to see what other mysteries might be hidden there, and corresponded actively with those who might help. Supporters were still somewhat rare. One of these was Hermann Weyl, a Göttingen-trained mathematician. In a letter thanking Weyl for his interest, Einstein commented that while not everyone agreed with the theory, its advocates always seemed to be smarter than its critics. “This is objective evidence, of a sort, for the naturalness and rationality of the theory.”

  David Hilbert, Einstein’s rival in the original formulation of the field equations, regularly reported his own progress. A late May 1916 letter from Hilbert commiserated about Schwarzschild’s death and invited Einstein to come visit Göttingen again. In a sign of the dire living conditions of wartime Germany, he casually assured Einstein that if they couldn’t find any food for their guest, they could go to a neighboring village that had better supplies.

  Hilbert’s research that spring had focused on the energy laws that emerged from the principles of general relativity. The law of conservation of energy was one of the cornerstones of physics, but it was not obvious whether it could be directly derived from relativity. Einstein had one solution to this; Hilbert had another. To help resolve the puzzle Hilbert brought in one of his students, Emmy Noether. Noether had overcome extensive sexism (both casual and structural) to attain her PhD in mathematics. Despite being one of the world’s experts in differential invariant theory, she was unpaid as a lecturer at Göttingen—statutes prevented women from becoming formal instructors. Hilbert tried to persuade the establishment that the sex of a scholar was irrelevant: “After all, we are a university, not a bathing establishment.” He recognized her genius and sought her assistance in a variety of projects. She was famous for speaking incredibly fast. One of her colleagues invited her for walks so she would become tired and speak more slowly.

  Her expertise was particularly relevant to developing the mathematics of general relativity. Einstein was grateful regardless of her gender and did what he could to support her work: “Upon receiving the new work by Miss Noether, I again feel it is a great injustice that she be denied the venia legendi [the right to lecture officially]. I would very much support our taking an energetic step at the Ministry [to overturn this].” Eventually she would formulate what is now known as Noether’s theorem. This established symmetry as a fundamental principle of modern physics, and is an indispensable tool for theoretical physics today. After the Nazis came to power she was expelled from her position at Göttingen, along with many others of Jewish descent. Like Einstein, she went to the United States as a refugee.

  But in 1916, Einstein was still hard at work in Berlin. While Noether and Hilbert considered the relationship between energy and relativity, Einstein tackled a crucial problem: how does gravity get from place to place? And how fast does it get there? Right now the sun’s gravity holds the Earth in its orbit. If the sun suddenly vanished, how long would it take for that disruption of gravity to be felt here? Instantaneously? The eight minutes it takes light to get here? Some speed unique to gravity? Newton never gave a satisfying answer for his theory of gravity, so if Einstein succeeded in this it would be a significant boost for his alternative.

  Einstein modeled his approach to this problem on the analogous issue in one of the other fundamental forces of nature: electromagnetism. Back in the nineteenth century James Clerk Maxwell (one of Einstein’s idols) had figured out that electromagnetic force traveled in waves. A wobbling electrical charge set up a jiggle in the surrounding electromagnetic field, which then traveled at the speed of light. Maxwell inferred that this meant light was itself an electromagnetic wave. This was confirmed in the laboratory by Heinrich Hertz, unifying light and electricity. Einstein hoped he could do the same for gravity.

  So his task was to inspect the field equations and see if they could be arranged in a way that could be interpreted as a moving jiggle in space-time—a gravitational wave. He wrote to Lorentz, de Sitter, and—a few months before his death—Schwarzschild for help. The differences between electromagnetism and gravity meant he couldn’t follow Maxwell’s recipe exactly, but he kept trying. He slid back and forth from certainty that gravitational waves couldn’t exist to certainty that they must, eventually settling on a lukewarm confidence. He found that his equations allowed for a mathematical entity that carried energy and moved at the speed of light—a pretty good candidate for a gravitational wave. But was it real? Unfortunately, gravitational waves make their presence known by absurdly small deformations in space-time as they travel. To see even the largest of these deformations a physicist would need to be able to measure a change in length of 1 in 1021—vastly beyond the ability of Einstein’s colleagues (they were not detected until September 14, 2015). Gravitational waves were not going to persuade anyone of the truth of general relativity.

  Einstein needed to talk—there was only so much that could be done by letter. He decided he could not wait for peacetime. That summer he renewed his efforts to make a trip to the Netherlands to see Ehrenfest, Lorentz, and de Sitter. In August he went to the Foreign Office in Berlin to get permission. They were reluctant. His frequent trips to Switzerland—the most common point of entry for spies into Germany—had raised suspicions. Many peace activists were having their travel curtailed as well. He quickly fired off a letter to Ehrenfest saying that an official invitation from a Dutch university would be helpful. Ehrenfest complied immediately. Among other hoops he had to jump through, Einstein still had to get the original of his Swiss citizenship certificate, perhaps to demonstrate his good reasons for travel there. He complained: “A long chain of other still obscure obstacles awaits me. So don’t be surprised if many more delays occur.” Finally, on September 27, he boarded a train for Leiden.

  Einstein arrived at the Ehrenfest home a grateful man. Once again he was with friends who understood both his physics and his politics. As he put it, he was pleased with “the concurrence in opinion on non-scientific matters.” In addition to views on the war, this meant music. Einstein brought his violin and played duets with Ehrenfest on the piano, as they did every time they met. Usually they played Beethoven, but Einstein made a daring new suggestion—Bach. Ehrenfest never cared much for the Baroque composer and was skeptical. Nonetheless, Einstein converted his friend and Ehrenfest spent more time on Bach than physics for the next few months. His wife, Tatyana, herself a distinguished physicist, was not happy about this change.

  There was plenty of science during the visit, though. Einstein bounced ideas off his friends, and they drowned him in questions. This personal interaction was particularly important for de Sitter, who had started learning general relativity well after Lorentz and Ehrenfest. Even though he and Einstein had a lively correspondence, when learning a theory there is no substitute for actually sitti
ng down with an expert and talking. It is not a coincidence that Leiden and Göttingen were the best places to learn relativity and were also where Einstein made regular trips. The spread of relativity followed the trenches closely—the only person in Belgium who made any progress in grasping relativity was the physicist Théophile de Donder, who happened to live in a German-occupied area. This need for personal contact emphasizes the challenge Eddington had in teaching himself relativity.

  Einstein was particularly pleased to be able to talk with Lorentz during his trip. The elder physicist often set the younger man up with difficult questions just for the joy of seeing him solve them. Ehrenfest described dinner at Lorentz’s house: Einstein was given the best easy chair and a fine cigar before being presented with a tough problem. Then, as Lorentz pushed harder: “Einstein began to puff less frequently on his cigar, and he sat up straighter and more intently in his armchair. . . . [Eventually] the cigar was out, and Einstein pensively twisted his finger in a lock of hair over his right ear.” While Lorentz sat smiling, as though at a “beloved son,” Einstein finally declared that he “had it”! The debate continued with “a bit of give and take, interrupting one another, a partial disagreement, very quick clarification and a complete mutual understanding, and then both men with beaming eyes skimming over the shining riches of the new theory.”

  Einstein reluctantly prepared to return to Berlin after two weeks. Elsa had asked him to buy some lard (a rare commodity in wartime Germany) while he was in the Netherlands. He had failed to find any and warned that she would “have to receive me lardless but with kindness all the same.” Upon his return he wrote a gushing letter to Ehrenfest to thank him for his hospitality: “The reinvigorating days spent with you have melted into a beautiful dream which I relive tirelessly in my imagination.” He even wrote to his friends in Switzerland to let them know how much he had enjoyed his time in the Netherlands. He reported that relativity had “already come very much alive there. Not only are Lorentz and the astronomer de Sitter working independently on the theory but a number of other young colleagues as well. The theory has also taken root in England.”

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  IN A SCENE familiar to many of us, Einstein had come home from vacation to piles of mail and work. One of his tasks was putting into motion a plan he had developed with Lorentz. The two of them had discussed creating a commission to investigate reported German atrocities in Belgium. Einstein tried to recruit Planck to this cause, but the senior scientist thought it would be impossible to get honest testimony from anyone involved. He decided that Planck was “skittish” about anything with “the faintest political flavor.” He went on to press Wilhelm von Waldeyer-Hartz, secretary of the Prussian Academy, on the idea. Reportedly the secretary received it “very warmly.” After his political overtures were made, Einstein returned to his normal routine. This included Elsa’s companionship as well as mundane irritations—on November 17 he had to stay home, as he once again couldn’t find his keys to the front door.

  As winter came to Germany, conditions degenerated. The season was even worse than the previous year—in February 1917 the average temperature was –1 Fahrenheit (–18 Celsius). Further, the British blockade was working. Before the war, Germany imported nearly a third of its food, and famine was now widespread. The potato crop failed and food riots erupted in thirty cities. This was the so-called turnip winter, when that former animal feed replaced potatoes, which had themselves been the replacement for wheat. It is estimated that some 120,000 Germans died of malnutrition in 1916 and 1917. Food prices doubled, and then quadrupled. Anti-Semitic conspiracy theories emerged that blamed Jewish refugees for the shortages. Mass food protests were a daily occurrence in Berlin, occasionally bursting into full-scale rioting. Many farmers stopped bringing their produce into the city because of the danger. After taking control of the economy in 1916, the military began seizing foodstuffs directly from farms and distributing it themselves. It was hoped that some military efficiency would be brought to food distribution. In reality, everything was made worse as the military took first pick of food and monopolized the railways.

  The combination of poor diet and concentrated work took its toll on Einstein. Soon after 1917 began, his stomach started bothering him more and more, and at Elsa’s insistence, “contrary to my most ingrained principles,” he went to the doctor. His doctor diagnosed him with inflammation of the stomach and recommended a special fat-rich diet that was essentially impossible to maintain in starving Berlin—milk was unknown and average meat consumption had dropped to one-eighth of prewar levels. Most sausage available there was of the ersatz (substitute) variety, of which there were officially 837 government-approved types. Ersatz sausage was often adulterated, and scams proliferated. Berlin teachers took students into the forest to gather materials for ersatz foodstuffs.

  Einstein asked his friends in Switzerland if they could send the ten pounds of rice, five pounds of semolina, five pounds of macaroni, and a “most substantial quantity” of zwieback (a type of cracker) that he needed every four to six weeks. His relatives in southern Germany could no longer send any of it—they no longer had any. The food parcels began arriving in February—Einstein thanked his friends for “the chicken feed.” He reported that one package never arrived, an unsurprising development given the unreliable state of the mail. Having food sent from elsewhere was a common practice in Berlin to get around food shortages, though the practice was soon made illegal. The situation in Berlin became so bad that German soldiers in occupied countries sent care packages home. Elsa came over to his apartment to prepare all Albert’s meals without salt—so as not to excite the “wrath of the evil spirits”—and ministered to his needs while he tried to work.

  Einstein’s sickness got worse, and he lost nearly fifty pounds in two months. He had a “sickly appearance” and his hands were always cold. His doctor shifted the diagnosis from stomach to liver. Maybe gallstones? He wanted Albert to take some time at the spa in Tarasp, Switzerland, as a treatment. The patient declined, agreeing only to two glasses of Mergentheimer mineral water per day. At least the pain was better under the diet.

  Bedridden, he still tried to push through the illness. He was finally making progress on problems that had been bedeviling him all year. These were, essentially, questions about the nature of the universe. Does the universe have a border? And if so, what is there? As Einstein described it, he was trying to uncover “the limiting conditions in the infinite.” In technical terms, Einstein was exploring something called boundary conditions. Often scientists will have a differential equation with many possible solutions, and choosing the right ones is made much easier if you know a little bit about the state of the whole thing you are trying to understand. To use Einstein’s own metaphor, imagine a piece of cloth suspended in the air. The possible twists and turns of the cloth are limited by the material it is made of, whether it is moving, and what is happening to the edges—is the cloth free to move around? Is it being held securely? If so, how tightly? These states of the edges are called the boundary conditions of the cloth, and help determine how it can behave. In this analogy, the cloth is like the space-time fabric of the universe. What, Einstein wondered, were the boundary conditions of the universe? Was space-time fixed in place? Could it move around? Was there a limit at all?

  Einstein actually came to these questions indirectly. He was still trying to establish the validity of what he saw as one of the foundations of general relativity: Mach’s principle. Even though the principle had led him astray in the hole argument, he still thought of it as essential to his ideas. As Einstein presented it, the principle suggested that inertia (that is, resistance to being pushed or pulled) was not an intrinsic property of mass but rather was generated only through gravitational interactions with other matter. This made mass and inertia relative, much like the other fundamental categories of space and time that were warped by relativity. If the principle was correct, then the iner
tia of a coffee mug would be due to the gravity of huge amounts of unseen, diffuse matter far away in the universe. Your coffee is hard to pick up in the morning because at vast, essentially infinite distances, matter was hiding and gently tugging on it. These implications stimulated Einstein to think about what was happening at the very edges of the universe. Einstein saw these investigations as a test of general relativity—could his theory handle being extended to infinity? Was there a limit to the domain of relativity?

  He was thinking about these problems as early as May 1916, but it was not until that fall that he began focusing on them in earnest. An exchange of letters with de Sitter brought them into sharper focus. It was fine for Einstein the theoretical physicist to speculate on matter spread conveniently throughout the universe in just the right way that Mach’s principle would apply. But de Sitter was an astronomer. To him, the structure of the universe was an astronomical problem—something you could see in a telescope—about which he and his colleagues knew a great deal. Einstein couldn’t just imagine gigantic masses because it rescued his explanation for inertia! De Sitter wrote: “If I am to believe all of this, your theory will have lost much of its classical beauty for me. . . . I would prefer having no explanation for inertia to this one.” He assured Einstein that he spoke so frankly only because he knew Einstein would not take it amiss.