Walter Isaacson - Einstein - His Life and Universe

But imagine the bucket spinning in deep space with no gravity and no reference points. Or imagine it spinning alone in an otherwise empty universe. Would there still be inertia? Newton believed so, and said it was because the bucket was spinning relative to absolute space.

When Einstein’s early hero Ernst Mach came along in the mid-nineteenth century, he debunked this notion of absolute space and argued that the inertia existed because the water was spinning relative to the rest of the matter in the universe. Indeed, the same effects would be observed if the bucket was still and the rest of the universe was rotating around it, he said. 25

The general theory of relativity, Einstein hoped, would have what he dubbed “Mach’s Principle” as one of its touchstones. Happily, when he analyzed the equations in his Entwurf theory, he concluded that they did seem to predict that the effects would be the same whether a bucket was spinning or was motionless while the rest of the universe spun around it.

Or so Einstein thought. He and Besso made a series of very clever calculations designed to see if indeed this was the case. In their notebook, Einstein wrote a joyous little exclamation at what appeared to be the successful conclusion of these calculations: “Is correct.”

Unfortunately, he and Besso had made some mistakes in this work. Einstein would eventually discover those errors two years later and realize, unhappily, that the Entwurf did not in fact satisfy Mach’s principle. In all likelihood, Besso had already warned him that this might be the case. In a memo that he apparently wrote in August 1913, Besso suggested that a “rotation metric” was not in fact a solution permitted by the field equations in the Entwurf.

But Einstein dismissed these doubts, in letters to Besso as well as to Mach and others, at least for the time being. 26If experiments upheld the theory, “your brilliant investigations on the foundations of mechanics will have received a splendid confirmation,” Einstein wrote to Mach days after the Entwurf was published. “For it shows that inertia has its origin in some kind of interaction of the bodies, exactly in accordance with your argument about Newton’s bucket experiment.” 27

What worried Einstein most about the Entwurf, justifiably, was that its mathematical equations did not prove to be generally covariant, thus deflating his goal of assuring that the laws of nature were the same for an observer in accelerated or arbitrary motion as they were for an observer moving at a constant velocity. “Regrettably, the whole business is still so very tricky that my confidence in the theory is still rather hesitant,” he wrote in reply to a warm letter of congratulations from Lorentz.“The gravitational equations themselves unfortunately do not have the property of general covariance.” 28

He was soon able to convince himself, at least for a while, that this was inevitable. In part he did so through a thought experiment, which became known as the “hole argument,” 29that seemed to suggest that the holy grail of making the gravitational field equations generally covariant was impossible to reach, or at least physically uninteresting. “The fact that the gravitational equations are not generally covariant, something that quite disturbed me for a while, is unavoidable,” he wrote a friend. “It can easily be shown that a theory with generally covariant equations cannot exist if the demand is made that the field is mathematically completely determined by matter.” 30

For the time being, very few physicists embraced Einstein’s new theory, and many came forth to denounce it. 31Einstein professed pleasure that the issue of relativity “has at least been taken up with the requisite vigor,” as he put it to his friend Zangger. “I enjoy controversies. In the manner of Figaro: ‘Would my noble Lord venture a little dance? He should tell me! I will strike up the tune for him.’ ” 32

Through it all, Einstein continued to try to salvage his Entwurf approach. He was able to find ways, or so he thought, to achieve enough covariance to satisfy most aspects of his principle about the equivalence of gravity and acceleration. “I succeeded in proving that the gravitational equations hold for arbitrarily moving reference systems, and thus that the hypothesis of the equivalence of acceleration and gravitational field is absolutely correct,” he wrote Zangger in early 1914. “Nature shows us only the tail of the lion. But I have no doubt that the lion belongs with it even if he cannot reveal himself all at once. We see him only the way a louse that sits upon him would.” 33

Freundlich and the 1914 Eclipse

There was, Einstein knew, one way to quell doubts. He often concluded his papers with suggestions for how future experiments could confirm whatever he had just propounded. In the case of general relativity, this process had begun in 1911, when he specified with some precision how much he thought light from a star would be deflected by the gravity of the sun.

This was something that could, he hoped, be measured by photographing stars whose light passed close to the sun and determining whether there appeared to be a tiny shift in their position compared to when their light did not have to pass right by the sun. But this was an experiment that had to be done during an eclipse, when the starlight would be visible.

So it was not surprising that, with his theory arousing noisy attacks from colleagues and quiet doubts in his own mind, Einstein became keenly interested in what could be discovered during the next suitable total eclipse of the sun, which was due to occur on August 21, 1914. That would require an expedition to the Crimea, in Russia, where the path of the eclipse would fall.

Einstein was so eager to have his theory tested during the eclipse that, when it seemed there might be no money for such an expedition, he offered to pay part of the costs himself. Erwin Freundlich, the young Berlin astronomer who had read the light-bending predictions in Einstein’s 1911 paper and become eager to prove him correct, was ready to take the lead. “I am extremely pleased that you have taken up the question of the bending of light with so much zeal,” Einstein wrote him in early 1912. In August 1913, he was still bombarding the astronomer with encouragement.“Nothing more can be done by the theorists,” he wrote. “In this matter it is only you, the astronomers, who can next year perform a simply invaluable service to theoretical physics.” 34

Freundlich got married in August 1913 and decided to take his honeymoon in the mountains near Zurich, in the hope that he could meet Einstein. It worked. When Freundlich described his honeymoon schedule in a letter, Einstein invited him over for a visit. “This is wonderful because it fits in with our plans,” Freundlich wrote his fiancée, whose reaction to the prospect of spending part of her honeymoon with a theoretical physicist she had never met is lost to history.

When the newlyweds pulled into the Zurich train station, there was a disheveled Einstein wearing, as Freundlich’s wife recalled, a large straw hat, with the plump chemist Fritz Haber at his side. Einstein brought the group to a nearby town where he was giving a lecture, after which he took them to lunch. Not surprisingly, he had forgotten to bring any money, and an assistant who had come along slipped him a 100 franc note under the table. For most of the day, Freundlich discussed gravity and the bending of light with Einstein, even when the group went on a nature hike, leaving his new wife to admire the scenery in peace. 35

At his speech that day, which was on general relativity, Einstein pointed out Freundlich to the audience and called him “the man who will be testing the theory next year.”The problem, however, was raising the money. At the time, Planck and others were trying to lure Einstein from Zurich to Berlin to become a member of the Prussian Academy, and Einstein used the courtship to write Planck and urge him to provide Freundlich the money to undertake the task.