Einstein: His Life and Universe

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What made the flurry of political and personal turmoil in the fall of 1915 so remarkable was that it highlighted Einstein’s ability to concentrate on, and compartmentalize, his scientific endeavors despite all distractions. During that period, with great effort and anxiety, he was engaged in a competitive rush to what he later called the greatest accomplishment of his life.⁵⁸

Back when Einstein had moved to Berlin in the spring of 1914, his colleagues had assumed that he would set up an institute and attract acolytes to work on the most pressing problem in physics: the implications of quantum theory. But Einstein was more of a lone wolf. Unlike Planck, he did not want a coterie of collaborators or proteges, and he preferred to focus on what again had become his personal passion: the generalization of his theory of relativity.⁵⁹

So after his wife and sons left him for Zurich, Einstein moved out of their old apartment and rented one that was nearer to Elsa and the center of Berlin. It was a sparsely furnished bachelor’s refuge, but still rather spacious: it had seven rooms on the third floor of a new five-story building.⁶⁰

Einstein’s study at home featured a large wooden writing table that was cluttered with piles of papers and journals. Padding around this hermitage, eating and working at whatever hours suited him, sleeping when he had to, he waged his solitary struggle.

Through the spring and summer of 1915, Einstein wrestled with his Entwurf theory, refining it and defending it against a variety of challenges. He began calling it “the general theory” rather than merely “a generalized theory” of relativity, but that did not mask its problems, which he kept trying to deflect.

He claimed that his equations had the greatest amount of covariance that was permissible given his hole argument and other strictures of physics, but he began to suspect that this was not correct. He also got into an exhausting debate with the Italian mathematician Tullio Levi-Civita, who pointed out problems with his handling of the tensor calculus. And there was still the puzzle of the incorrect result the theory gave for the shift in Mercury’s orbit.

At least his Entwurf theory still successfully explained—or so he thought through the summer of 1915—rotation as being a form of relative motion, that is, a motion that could be defined only relative to the positions and motions of other objects. His field equations, he thought, were invariant under the transformation to rotating coordinates.⁶¹

Einstein was confident enough in his theory to show it off at a weeklong series of two-hour lectures, starting at the end of June 1915, at the University of Gottingen, which had become the preeminent center for the mathematical side of theoretical physics. Foremost among the geniuses there was David Hilbert, and Einstein was particularly eager—too eager, it would turn out—to explain all the intricacies of relativity to him.

The visit to Gottingen was a triumph. Einstein exulted to Zangger that he had “the pleasurable experience of convincing the mathematicians there thoroughly.” Of Hilbert, a fellow pacifist, he added, “I met him and became quite fond of him.” A few weeks later, after again reporting, “I was able to convince Hilbert of the general theory of relativity,” Einstein called him “a man of astonishing energy and independence.” In a letter to another physicist, Einstein was even more effusive: “In Gottingen I had the great pleasure of seeing that everything was understood down to the details. I am quite enchanted with Hilbert!”⁶²

Hilbert was likewise enchanted with Einstein and his theory. So much so that he soon set out to see if he could beat Einstein to the goal of getting the field equations right. Within three months of his Gottingen lectures, Einstein was confronted with two distressing discoveries: that his Entwurf theory was indeed flawed, and that Hilbert was racing feverishly to come up with the correct formulations on his own.

Einstein’s realization that his Entwurf theory was unraveling came from an accumulation of problems. But it culminated with two major blows in early October 1915.

The first was that, upon rechecking, Einstein found that the Entwurf equations did not actually account for rotation as he had thought.⁶³ He hoped to prove that rotation could be conceived of as just another form of relative motion, but it turned out that the Entwurf didn’t actually prove this. The Entwurf equations were not, as he had believed, covariant under a transformation that uniformly rotated the coordinate axes.

Besso had warned him in a memo in 1913 that this seemed to be a problem. But Einstein had ignored him. Now, upon redoing his calculations, he was dismayed to see this pillar knocked away. “This is a blatant contradiction,” he lamented to the astronomer Freundlich.

He assumed that the same mistake also accounted for his theory’s inability to account fully for the shift in Mercury’s orbit. And he despaired that he would not be able to find the problem. “I do not believe I am able to find the mistake myself, for in this matter my mind is too set in a deep rut.”⁶⁴

In addition, he realized that he had made a mistake in what was called his “uniqueness” argument: that the sets of conditions required by energy-momentum conservation and other physical restrictions uniquely led to the field equations in the Entwurf. He wrote Lorentz explaining in detail his previous “erroneous assertions.”⁶⁵

Added to these problems were ones he already knew about: the Entwurf equations were not generally covariant, meaning that they did not really make all forms of accelerated and nonuniform motion relative, and they did not fully explain Mercury’s anomalous orbit. And now, as this edifice was crumbling, he could hear what seemed to be Hilbert’s footsteps gaining on him from Gottingen.

Part of Einstein’s genius was his tenacity. He could cling to a set of ideas, even in the face of “apparent contradiction” (as he put it in his 1905 relativity paper). He also had a deep faith in his intuitive feel for the physical world. Working in a more solitary manner than most other scientists, he held true to his own instincts, despite the qualms of others.

But although he was tenacious, he was not mindlessly stubborn. When he finally decided his Entwurf approach was untenable, he was willing to abandon it abruptly. That is what he did in October 1915.

To replace his doomed Entwurf theory, Einstein shifted his focus from the physical strategy, which emphasized his feel for basic principles of physics, and returned to a greater reliance on a mathematical strategy, which made use of the Riemann and Ricci tensors. It was an approach he had used in his Zurich notebooks and then abandoned, but on returning to it he found that it could provide a way to generate generally covariant gravitational field equations. “Einstein’s reversal,” writes John Norton, “parted the waters and led him from bondage into the promised land of general relativity.”⁶⁶

Of course, as always, his approach remained a mix of both strategies. To pursue a revitalized mathematical strategy, he had to revise the physical postulates that were the foundation for his Entwurf theory. “This was exactly the sort of convergence of physical and mathematical considerations that eluded Einstein in the Zurich notebook and in his work on the Entwurf theory,” write Michel Janssen and Jurgen Renn.⁶⁷