einstein

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 Jürgen Renn. 67
Thus he returned to the tensor analysis that he had used in Zurich, with its greater emphasis on the mathematical goal of finding equations that
were generally covariant. “Once every last bit of confidence in the earlier theories had given way,” he told a friend, “I saw clearly that it was only
through general covariance theory, i.e., with Riemann’s covariant, that a satisfactory solution could be found.” 68
The result was an exhausting, four-week frenzy during which Einstein wrestled with a succession of tensors, equations, corrections, and updates
that he rushed to the Prussian Academy in a flurry of four Thursday lectures. It climaxed, with the triumphant revision of Newton’s universe, at the
end of November 1915.
Every week, the fifty or so members of the Prussian Academy gathered in the grand hall of the Prussian State Library in the heart of Berlin to
address each other as “Your Excellency” and listen to fellow members pour forth their wisdom. Einstein’s series of four lectures had been
scheduled weeks earlier, but until they began—and even after they had begun—he was still working furiously on his revised theory.
The first was delivered on November 4. “For the last four years,” he began, “I have tried to establish a general theory of relativity on the
assumption of the relativity even of non-uniform motion.” Referring to his discarded Entwurf theory, he said he “actually believed I had discovered
the only law of gravitation” that conformed to physical realities.
But then, with great candor, he detailed all of the problems that theory had encountered. “For that reason, I completely lost trust in the field
equations” that he had been defending for more than two years. Instead, he said, he had now returned to the approach that he and his mathematical
caddy, Marcel Grossmann, had been using in 1912. “Thus I went back to the requirement of a more general covariance of the field equations, which
I had left only with a heavy heart when I worked together with my friend Grossmann. In fact, we had then already come quite close to the solution.”
Einstein reached back to the Riemann and Ricci tensors that Grossmann had introduced him to in 1912. “Hardly anyone who truly understands it
can resist the charm of this theory,” he lectured. “It signifies a real triumph of the method of the calculus founded by Gauss, Riemann, Christoffel,
Ricci, and Levi-Civita.” 69
This method got him much closer to the correct solution, but his equations on November 4 were still not generally covariant. That would take
another three weeks.
Einstein was in the throes of one of the most concentrated frenzies of scientific creativity in history. He was working, he said, “horrendously
intensely.” 70 In the midst of this ordeal, he was also still dealing with the personal crisis within his family. Letters arrived from both his wife and
Michele Besso, who was acting on her behalf, that pressed the issue of his financial obligations and discussed the guidelines for his contact with
his sons.
On the very day he turned in his first paper, November 4, he wrote an anguished—and painfully poignant—letter to Hans Albert, who was in
Switzerland:
I will try to be with you for a month every year so that you will have a father who is close to you and can love you. You can learn a lot of good
things from me that no one else can offer you. The things I have gained from so much strenuous work should be of value not only to strangers
but especially to my own boys. In the last few days I completed one of the finest papers of my life. When you are older, I will tell you about it.
He ended with a small apology for seeming so distracted: “I am often so engrossed in my work that I forget to eat lunch.” 71
Einstein also took time off from furiously revising his equations to engage in an awkward fandango with his erstwhile friend and competitor David
Hilbert, who was racing him to find the equations of general relativity. Einstein had been informed that the Göttingen mathematician had figured out
the flaws in the Entwurf equations. Worried about being scooped, he wrote Hilbert a letter saying that he himself had discovered the flaws four
weeks earlier, and he sent along a copy of his November 4 lecture. “I am curious whether you will take kindly to this new solution,” Einstein asked
with a touch of defensiveness. 72
Hilbert was not only a better pure mathematician than Einstein, he also had the advantage of not being as good a physicist. He did not get all
wrapped up, the way Einstein did, in making sure that any new theory conformed to Newton’s old one in a weak static field or that it obeyed the
laws of causality. Instead of a dual math-and-physics strategy, Hilbert pursued mainly a math strategy, focusing on finding the equations that were
covariant. “Hilbert liked to joke that physics was too complicated to be left to the physicists,” notes Dennis Overbye. 73
Einstein presented his second paper the following Thursday, November 11. In it, he used the Ricci tensor and imposed new coordinate
conditions that allowed the equations thus to be generally covariant. As it turned out, that did not greatly improve matters. Einstein was still close to
the final answer, but making little headway. 74
Once again, he sent the paper off to Hilbert. “If my present modification (which does not change the equations) is legitimate, then gravitation must
play a fundamental role in the composition of matter,” Einstein said. “My own curiosity is interfering with my work!” 75
The reply that Hilbert sent the next day must have unnerved Einstein. He said he was about ready to oblige with “an axiomatic solution to your
great problem.” He had planned to hold off discussing it until he explored the physical ramifications further. “But since you are so interested, I would
like to lay out my theory in very complete detail this coming Tuesday,” which was November 16.
He invited Einstein to come to Göttingen and have the dubious pleasure of personally hearing him lay out the answer. The meeting would begin
at 6 p.m., and Hilbert helpfully provided Einstein with the arrival times of the two afternoon trains from Berlin. “My wife and I would be very pleased if
you stayed with us.”
Then, after signing his name, Hilbert felt compelled to add what must surely have been a tantalizing and disconcerting postscript. “As far as I