einstein

indistinguishable from a case where the observer is at rest and the rest of the universe is rotating around him?
The most famous thought experiment along these lines was that described by Newton in the third book of his Principia. Imagine a bucket that
begins to rotate as it hangs from a rope. At first the water in the bucket stays rather still and flat. But soon the friction from the bucket causes the
water to spin around with it, and it assumes a concave shape. Why? Because inertia causes the spinning water to push outward, and therefore it
pushes up the side of the bucket.
Yes, but if we suspect that all motion is relative, we ask: What is the water spinning relative to? Not the bucket, because the water is concave
when it is spinning along with the bucket, and also when the bucket stops and the water keeps spinning inside for a while. Perhaps the water is
spinning relative to nearby bodies such as the earth that exert gravitational force.
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. 26 If 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,” 29 that 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. 31 Einstein 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,