Einstein became a closer friend, and a walking partner, of another iconic figure at the Institute, the intensely introverted Kurt Gödel, a German-speaking mathematical logician from Brno and Vienna. Gödel was famous for his “incompleteness theory,” a pair of logical proofs that purport to show that any useful mathematical system will have some propositions that cannot be proven true or false based on the postulates of that system.
Out of the supercharged German-speaking intellectual world, in which physics and mathematics and philosophy intertwined, three jarring theories of the twentieth century emerged: Einstein’s relativity, Heisenberg’s uncertainty, and Gödel’s incompleteness. The surface similarity of the three words, all of which conjure up a cosmos that is tentative and subjective, oversimplifies the theories and the connections between them. Nevertheless, they all seemed to have philosophical resonance, and this became the topic of discussion when Gödel and Einstein walked to work together.6
They were very different personalities. Einstein was filled with good humor and sagacity, both qualities lacking in Gödel, whose intense logic sometimes overwhelmed common sense. This was on glorious display when Gödel decided to become a U.S. citizen in 1947. He took his preparation for the exam very seriously, studied the Constitution carefully, and (as might be expected by the formulator of the incompleteness theory) found what he believed was a logical flaw. There was an internal inconsistency, he insisted, that could allow the entire government to degenerate into tyranny.
Concerned, Einstein decided to accompany—or chaperone—Gödel on his visit to Trenton to take the citizenship test, which was to be administered by the same judge who had done so for Einstein. On the drive, he and a third friend tried to distract Gödel and dissuade him from mentioning this perceived flaw, but to no avail. When the judge asked him about the Constitution, Gödel launched into his proof that its internal inconsistency made a dictatorship possible. Fortunately, the judge, who by now cherished his connection to Einstein, cut Gödel off. “You needn’t go into all that,” he said, and Gödel’s citizenship was saved.7
During their walks, Gödel explored some of the implications of relativity theory, and he came up with an analysis that called into question whether time, rather than merely being relative, could be said to exist at all. Einstein’s equations, he figured, could describe a universe that was rotating rather than (or in addition to) expanding. In such a case, the relationship between space and time could become, mathematically, mixed up. “The existence of an objective lapse of time,” he wrote, “means that reality consists of an infinity of layers of ‘now’ which come into existence successively. But if simultaneity is something relative, each observer has his own set of ‘nows,’ and none of these various layers can claim the prerogative of representing the objective lapse of time.”8
As a result, Gödel argued, time travel would be possible. “By making a round trip on a rocket ship in a sufficiently wide curve, it is possible in these worlds to travel into any region of the past, present and future, and back again.” That would be absurd, he noted, because then we could go back and chat with a younger version of ourselves (or, even more discomforting, our older version could come back and chat with us). “Gödel had achieved an amazing demonstration that time travel, strictly understood, was consistent with the theory of relativity,” writes Boston University philosophy professor Palle Yourgrau in his book on Gödel’s relationship with Einstein, World Without Time. “The primary result was a powerful argument that if time travel is possible, time itself is not.”9
Einstein responded to Gödel’s essay along with a variety of others that had been collected in a book, and he seemed to be mildly impressed but also not totally engaged by the argument. In his brief assessment, Einstein called Gödel’s “an important contribution” but noted that he had thought of the issue long ago and “the problem here involved disturbed me already.” He implied that although time travel may be true as a mathematical conceivability, it might not be possible in reality.“It will be interesting to weigh whether these are not to be excluded on physical grounds,” Einstein concluded.10
For his part, Einstein remained focused on his own white whale, which he pursued not with the demonic drive of Ahab but the dutiful serenity of Ishmael. In his quest for a unified field theory, he still had no compelling physical insight—such as the equivalence of gravity and acceleration, or the relativity of simultaneity—to guide his way, so his endeavors remained a groping through clouds of abstract mathematical equations with no ground lights to orient him. “It’s like being in an airship in which one can cruise around in the clouds but cannot see clearly how one can return to reality, i.e., earth,” he lamented to a friend.11
His goal, as it had been for decades, was to come up with a theory that encompassed both the electromagnetic and the gravitational fields, but he had no compelling reason to believe that they in fact had to be part of the same unified structure, other than his intuition that nature liked the beauty of simplicity.
Likewise, he was still hoping to explain the existence of particles in terms of a field theory by finding permissible pointlike solutions to his field equations. “He argued that if one believed wholeheartedly in the basic idea of a field theory, matter should enter not as an interloper but as an honest part of the field itself,” recalled one of his Princeton collaborators, Banesh Hoffmann. “Indeed, one might say that he wanted to build matter out of nothing but convolutions of spacetime.” In the process he used all sorts of mathematical devices, but constantly searched for others. “I need more mathematics,” he lamented at one point to Hoffmann.12
Why did he persist? Deep inside, such disjunctures and dualities—different field theories for gravity and electromagnetism, distinctions between particles and fields—had always discomforted him. Simplicity and unity, he intuitively believed, were hallmarks of the Old One’s handiwork. “A theory is more impressive the greater the simplicity of its premises, the more different things it relates, and the more expanded its area of applicability,” he wrote.13
In the early 1940s, Einstein returned for a while to the five-dimensional mathematical approach that he had adopted from Theodor Kaluza two decades earlier. He even worked on it with Wolfgang Pauli, the quantum mechanics pioneer, who had spent some of the war years in Princeton. But he could not get his equations to describe particles.14
So he moved on to a strategy dubbed “bivector fields.” Einstein seemed to be getting a little desperate. This new approach, he admitted, might require surrendering the principle of locality that he had sanctified in some of his thought-experiments assaulting quantum mechanics.15 In any event, it was soon abandoned as well.
Einstein’s final strategy, which he pursued for the final decade of his life, was a resurrection of one he had tried during the 1920s. It used a Riemannian metric that was not assumed to be symmetric, which opened the way for sixteen quantities. Ten combinations of them were used for gravity, and the remaining ones for electromagnetism.
Einstein sent early versions of this work to his old comrade Schrödinger. “I am sending them to nobody else, because you are the only person known to me who is not wearing blinders in regard to the fundamental questions in our science,” Einstein wrote. “The attempt depends on an idea that at first seems antiquated and unprofitable, the introduction of a non-symmetrical tensor ... Pauli stuck his tongue out at me when I told him about it.”16
Schrödinger spent three days poring over Einstein’s work and wrote back to say how impressed he was. “You are after big game,” he said.
Einstein was thrilled with such support. “This correspondence gives me great joy,” he replied, “because you are my closest brother and your brain runs so similarly to mine.” But he soon began to realize that the gossamer theories he was spinning were mathematically elegant but never seemed to relate to anything physical. “Inwardly I am not so certain as I previously asserted,” he confessed to Schrödinger a few months later. “We have squandered a lot of time on th
is, and the result looks like a gift from the devil’s grandmother.”17
And yet he soldiered on, churning out papers and producing the occasional headline. When a new edition of his book, The Meaning of Relativity, was being prepared in 1949, he added the latest version of the paper he had shown Schrödinger as an appendix. The New York Times reprinted an entire page of complex equations from the manuscript, along with a front-page story headlined “New Einstein Theory Gives a Master Key to Universe: Scientist, after 30 Years’ Work, Evolves Concept That Promises to Bridge Gap between the Star and the Atom.”18
But Einstein soon realized that it still wasn’t right. During the six weeks between when he submitted the chapter and when it went to the printers, he had second thoughts and revised it yet again.
In fact, he continued to revise the theory repeatedly, but to no avail. His growing pessimism was visible in the lamentations he sent to his old friend from the Olympia Academy days, Maurice Solovine, then Einstein’s publisher in Paris. “I shall never ever solve it,” he wrote in 1948. “It will be forgotten and must later be rediscovered again.”Then, the following year: “I am uncertain as to whether I was even on the right track. The current generation sees in me both a heretic and a reactionary who has, so to speak, outlived himself.” And, with some resignation, in 1951: “The unified field theory has been put into retirement. It is so difficult to employ mathematically that I have not been able to verify it. This state of affairs will last for many more years, mainly because physicists have no understanding of logical and philosophical arguments.”19
Einstein’s quest for a unified theory was destined to produce no tangible results that added to the framework of physics. He was able to come up with no great insights or thought experiments, no intuitions about underlying principles, to help him visualize his goal. “No pictures came to our aid,” his collaborator Hoffmann lamented. “It is intensely mathematical, and over the years, with helpers and alone, Einstein surmounted difficulty after difficulty, only to find new ones awaiting him.”20
Perhaps the search was futile. And if it turns out a century from now that there is indeed no unified theory to be found, it will also look misconceived. But Einstein never regretted his dedication to it. When a colleague asked him one day why he was spending—perhaps squandering—his time in this lonely endeavor, he replied that even if the chance of finding a unified theory was small, the attempt was worthy. He had already made his name, he noted. His position was secure, and he could afford to take the risk and expend the time. A younger theorist, however, could not take such a risk, for he might thus sacrifice a promising career. So, Einstein said, it was his duty to do it.21
Einstein’s repeated failures in seeking a unified theory did not soften his skepticism about quantum mechanics. Niels Bohr, his frequent sparring partner, came to the Institute for a stay in 1948 and spent part of his time writing an essay on their debates at the Solvay Conferences before the war.22 Struggling with the article in his office one floor above Einstein’s, he developed writer’s block and called in Abraham Pais to help him. As Bohr paced furiously around an oblong table, Pais coaxed him and took notes.
When he got frustrated, Bohr sometimes would simply sputter the same word over and over. Soon he was doing so with Einstein’s name. He walked to the window and kept muttering, over and over, “Einstein . . . Einstein . . .”
At one such moment, Einstein softly opened the door, tiptoed in, and signaled to Pais not to say anything. He had come to steal a bit of tobacco, which his doctor had ordered him not to buy. Bohr kept muttering, finally spurting out one last loud “Einstein” and then turning around to find himself staring at the cause of his anxieties. “It is an understatement to say that for a moment Bohr was speechless,” Pais recalled. Then, after an instant, they all burst into laughter.23
Another colleague who tried and failed to convert Einstein was John Wheeler, Princeton University’s renowned theoretical physicist. One afternoon he came by Mercer Street to explain a new approach to quantum theory (known as the sum-over-histories approach) that he was developing with his graduate student, Richard Feynman. “I had gone to Einstein with the hope to persuade him of the naturalness of the quantum theory when seen in this new light,” Wheeler recalled. Einstein listened patiently for twenty minutes, but when it was over repeated his very familiar refrain: “I still cannot believe that the good Lord plays dice.”
Wheeler showed his disappointment, and Einstein softened his pronouncement slightly. “Of course, I may be wrong,” he said in a slow and humorous cadence. Pause. “But perhaps I have earned the right to make my mistakes.” Einstein later confided to a woman friend, “I don’t think I’ll live to find out who is correct.”
Wheeler kept coming back, sometimes bringing his students, and Einstein admitted that he found many of his arguments “sensible.” But he was never converted. Near the end of his life, Einstein regaled a small group of Wheeler’s students. When the talk turned to quantum mechanics, he once again tried to poke holes in the idea that our observations can affect and determine realities. “When a mouse observes,” Einstein asked them, “does that change the state of the universe?”24
The Lion in Winter
Mileva Mari, her health deteriorating due to a succession of minor strokes, was still living in Zurich and trying to take care of their institutionalized son, Eduard, whose behavior had become increasingly erratic and violent. Financial problems again plagued her and revived the tension with her former husband. The portion of the money that he had put into trust for her in America from the Nobel Prize had slipped away during the Depression, and two of her three apartment houses had been sold to help pay for Eduard’s care. By late 1946, Einstein was pushing to sell the remaining house and give control of the money to a legal guardian who would be appointed for Eduard. But Mari had the usufruct of the house and its proceeds, as well as power of attorney over it, and she was terrified of surrendering any control.25
One cold day later that winter, she slipped on the ice on the way to see Eduard and ended up lying unconscious until strangers found her. She knew she was going to die soon, and she had recurring nightmares about struggling through the snow, unable to reach Eduard. She was panicked about what would happen to him, and wrote heart-wrenching letters to Hans Albert.26
Einstein succeeded in selling her house by early 1948, but with her power of attorney she blocked the proceeds from being sent to him. He wrote to Hans Albert, giving him all the details and promising him that, whatever happened, he would take care of Eduard “even if it costs me all my savings.”27 That May, Mari had a stroke and lapsed into a trance in which she repeatedly muttered only “No, no!” until she died three months later. The money from the sale of her apartment, 85,000 Swiss francs, was found under her mattress.
Eduard lapsed into a daze and never spoke of his mother again. Carl Seelig, a friend of Einstein’s who lived nearby, visited him frequently and sent back regular reports to Einstein. Seelig hoped to get him to make contact with his son, but he never did. “There is something blocking me that I am unable to analyze fully,” Einstein told Seelig. “I believe I would be arousing painful feelings of various kinds in him if I made an appearance in whatever form.”28
Einstein’s own health began to decline in 1948 as well. For years he had been plagued by stomach ailments and anemia, and late that year, after an attack of sharp pains and vomiting, he checked into the Jewish Hospital in Brooklyn. Exploratory surgery revealed an aneurysm in the abdominal aorta,* but doctors decided there was not much they could do about it. It was assumed, correctly, that it was likely to kill him one day, but in the meantime he could live on borrowed time and a healthy diet.29
To recuperate, he went on the longest trip he would make during his twenty-two years as a Princeton resident: down to Sarasota, Florida. For once, he successfully avoided publicity. “Einstein Elusive Sarasota Visitor,” the local paper lamented.
Helen Dukas accompanied him. After Elsa’s death, she had b
ecome even more of a loyal guardian, and she even shielded Einstein from letters written by Hans Albert’s daughter, Evelyn. Hans Albert suspected that Dukas may have had an affair with his father, and said so to others. “On many occasions, Hans Albert told me of his long-held suspicion,” family friend Peter Bucky later recalled. But others who knew Dukas found the suggestion to be implausible.30
By then, Einstein had become much friendlier with his son, now a respected engineering professor at Berkeley. “Whenever we met,” Hans Albert later recalled of his trips east to see his father, “we mutually reported on all the interesting developments in our field and in our work.” Einstein particularly loved learning about new inventions and solutions to puzzles. “Maybe both, inventions and puzzles, reminded him of the happy, carefree, and successful days at the patent office in Bern,” said Hans Albert.31
Einstein’s beloved sister, Maja, the closest intimate of his life, was also in declining health. She had come to Princeton when Mussolini enacted anti-Jewish laws, but her husband, Paul Winteler, from whom she had been drifting apart for many years,32 moved to Switzerland to be with his own sister and her husband, Michele Besso. They corresponded often, but never rejoined one another.
Maja began, as Elsa had, to look more like Einstein, with radiating silver hair and a devilish smile. The inflection of her voice and the slightly skeptical wry tone she used when asking questions were similar to his. Although she was a vegetarian, she loved hot dogs, so Einstein decreed that they were a vegetable, and that satisfied her.33
Maja had suffered a stroke and, by 1948, was confined to bed most of the time. Einstein doted on her as he did no other person. Every evening he read aloud to her. Sometimes the fare was heavy, such as the arguments of Ptolemy against Aristarchus’s opinion that the world rotates around the sun. “I could not help thinking of certain arguments of present-day physicists: learned and subtle, but without insight,” he wrote Solovine about that evening. Other times, the readings were lighter but perhaps just as revealing, such as the evenings he read from Don Quixote; he sometimes compared his own quixotic parries against the prevailing windmills of science with that of the old knight with a ready lance.34
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