The equivalence principle. The experimenter inside the room cannot distinguish between the two cases.
ORIGINAL ILLUSTRATION BY JACOB FORD
Einstein decided that the equivalence principle would have to be a core principle of any further elaboration of relativity. It not only suggested avenues for solving the problem of gravity, it also hinted at how to fill the other great gap in his theory so far. That was the problem of acceleration. Recall that the “special” part of special relativity is a warning that it only applies in certain situations—when observers are at rest or coasting steadily. Most movement is not like that, though. Usually there are accelerations—changes of speed. Your train has to slowly get up to speed, and has to put on the brakes to stop. When those things happen, you feel it. It’s the nudge that spills your coffee or knocks someone into your newspaper. That nudge means special relativity can’t apply. Thus, if Einstein wanted his ideas to apply to the world as a whole, he had to move beyond his special theory and make a general theory of relativity. The equivalence principle was his first window into how to do so.
Even the basic thought experiment for the equivalence principle could yield important further insights. Consider our imprisoned scientist once more. She now notices a small hole in the wall, at about her shoulder level. A beam of light comes in through the hole. If the box is at rest or coasting in deep space (that is, no rocket acceleration and no gravity), the light beam shoots straight across and hits the far wall at shoulder level. Now put the rocket on the bottom and turn it on. This time, as the light beam moves across the box, the box accelerates upward. In the time it takes for the beam to move across the box, the floor has moved upward, and the beam hits the far wall lower than shoulder height. From the scientist’s point of view, the beam has curved downward due to the acceleration. She then invokes the equivalence principle. If acceleration bends light, gravity must do so as well. A sufficiently powerful gravitational field should produce a noticeable effect on the path of light.
Another possible test came out of the equivalence principle. The mathematics suggested that acceleration would cause time dilation much as inertial motion would. Einstein realized that this time dilation would cause another observable effect: a distortion of the light coming off of an accelerated source. The color of light is determined by the frequency with which the electromagnetic waves wiggle, and time dilation would slow that wiggle down. That slowing would be perceived by our eyes as the light becoming redder than it should be. And again, the equivalence principle suggests that whatever happens with acceleration must also be true of gravity. Gravity, then, should make light appear ever so slightly redder, a phenomenon called the gravitational redshift. Einstein now had two possible, albeit crude, predictions of his theory.
Acceleration bends light, and if the equivalence principle is correct, so must gravity.
ORIGINAL ILLUSTRATION BY JACOB FORD
Finally, there was a third possibility. Astronomers had spent two centuries applying Newton’s laws to the motion of the planets with fantastic accuracy. Every discrepancy had been accounted for with that Englishman’s theory—save one. The orbit of Mercury had a tiny wobble (technically known as the precession of the perihelion). It had been known for decades and resisted easy explanation. Astronomers assumed it was the result of the gravitational pull of an as-yet-undiscovered planet inside Mercury’s orbit, referred to as Vulcan. A successful explanation for that anomaly had been the holy grail of anyone proposing an alternative theory to Newton’s. Einstein now realized he was in that fantastical place of competing with the greatest mind his civilization had ever produced.
Within a few months of beginning to ponder the relationship of gravity and relativity, he had found three consequences of an extended version of relativity that, at least in principle, could be tested. If he could successfully make relativity into a more general and powerful theory, he could move it from the realm of speculation to that of confirmed science. Abstract ideas could be made tangible—measured and real.
ALL OF THESE were largely background thoughts for Einstein. Most of his work at the time, as encouraged by other physicists, examined molecules and quantum theory. To those distant colleagues, this was work worth supporting, not strange tales of physicists locked in rooms in deep space. And he followed that encouragement, grateful for the first time to have his ideas supported by real, professional physicists. So when a professorship of theoretical physics opened up at the University of Zurich in 1909, Einstein finally had people who would write him letters of recommendation. It was by no means an easy victory, though. One of his primary competitors was an old college friend, Friedrich Adler—ironically, one of the few full converts to relativity. In the end he received the position only because the top candidate suffered an attack of tuberculosis and had to withdraw from the competition. Even when the job was offered, Einstein had to hold firm until they matched his patent office salary. They did, and Einstein finally became a professor of physics. He had mixed feelings about becoming the sort of authority he used to antagonize. To a friend he wrote, “So now I am an official of the guild of whores.”
The Einstein family moved to Zurich to take on the more bourgeois lifestyle of a professor. They actually rented an apartment in the same building as the Adlers, and Einstein was happy to have friends nearby with whom he could talk physics and play the violin. Einstein loved playing with his son, building him toys out of string and matchboxes. Despite his father’s efforts, though, Hans Albert never took to music. Zurich was a more intellectually exciting place than Bern, and Einstein was expected to move in higher social circles (he ran into Carl Jung once or twice). His grooming habits had not improved and colleagues still remarked on his “somewhat shabby clothes” and “too short trousers.”
The end of his first year at Zurich brought two surprises. Another son, Eduard, called “Tete,” arrived in July, and the German University in Prague offered Albert a well-paid position as a full professor. The offer was an enticing one, but there were significant obstacles. Prague was part of the Austro-Hungarian Empire, a sprawling state that ruled eleven different major ethnic groups, from Germans to Serbs to Ukrainians. It was the largest political body on the Continent. Austria-Hungary was massively complicated to govern, and its reputation for bureaucracy was well earned. A peculiar moment happened when Einstein had to take an oath of allegiance. In order to swear the oath, he needed to declare a religious denomination. He tried to say “none.” That was not an acceptable answer, and for the first time in his life he had to formally identify as a Jew. He liked to joke that it was the emperor that had made him Jewish.
Einstein enjoyed the salon culture in Prague, and this was a critical year for Einstein’s professional development. He hosted the physicist Paul Ehrenfest, with whom he formed an immediate, intense friendship. Ehrenfest was an Austrian expat whose clear eyes peered out from wire-framed glasses that seemed to float between his unkempt hair and bushy mustache. He made major contributions to quantum physics, and his frequent smile concealed his severe, and eventually fatal, depression. His manic diary from his Prague trip recorded endless cordial arguments for days straight. With him Einstein found the perfect balance of physics insight, sharp-tongued debating, and musical appreciation.
Einstein made a number of trips around central Europe at that time, including his first visit to Berlin. He met Fritz Haber, the chemist whose nitrogen-fixing process made possible the large-scale production of artificial fertilizer and thus the feeding of billions. Haber, scarred from dueling and fond of wearing military garb, made a strange match for the internationalist Einstein dressed in coats full of holes. But they, too, became fast friends. Their political differences were concealed by deep respect for each other’s scientific work. One unusual but crucial encounter was with an obscure Berlin astronomer named Erwin Finlay Freundlich, who had taken an interest in relativity. He and Einstein had been corresponding for a while before meetin
g in person. Freundlich was interested in the predictions made by Einstein’s extensions to relativity: the gravitational deflection of light and the gravitational redshift. These were tasks better suited to an astronomer than a physicist, and Einstein was intrigued by the possibility of testing his new ideas.
The trip to Berlin also brought Einstein together with his cousin Elsa for the first time in their adult lives (she was both his first and second cousin, through both parents). Albert was enchanted upon seeing her again. Three years older than him and recently divorced with two children, Elsa was a lively and intriguing companion. Einstein’s marriage with Mileva had become increasingly tense, especially after moving to Prague, where she was almost completely isolated. Mileva resented the way his growing professional success took him away from the family; Elsa was deeply impressed with the young professor’s achievements. Elsa and Albert began corresponding regularly and passionately. In one of his first letters to her he declared, “I consider myself a full-fledged male. Perhaps I will sometime have the opportunity to prove it to you.”
One of Einstein’s journeys took him to the first Solvay Conference, a gathering of two dozen top physicists and chemists. The conference was funded by the Belgian industrialist Ernest Solvay to grapple with the mysteries of quantum theory and what light it might shed on the problems of radiation. It was held in Brussels at a time when hosting a scholarly conference was a mark of a country’s development and sophistication. Participation in international intellectual life was crucial for the status of a modern nation and its citizens.
Einstein was the second youngest in attendance, along with luminaries such as Marie Curie, Ernest Rutherford, and—most important to Einstein—Lorentz. Einstein was giddy at the chance to work with his idol. He praised Lorentz, stately and charming with his thinning white hair, as the mentor who “meant more than all the others I have met on my life’s journey.” He wrote to a friend, “Lorentz is a marvel of intelligence and tact. A living work of art! In my opinion he was the most intelligent among the theoreticians present.” To Lorentz himself he wrote a fawning letter, thanking the elder physicist for his “fatherly kindness.”
It was quite a coup for Einstein, still fairly new on the European physics scene, to be invited along with this stellar group. His contributions to quantum theory were seen as epochal, even if they were “the strangest thing ever thought up.” Curie was quite impressed with him, declaring, “One has every right to build the greatest hopes on him and to see in him one of the leading theoreticians of the future.” This was the first chance many of these distinguished scientists had to encounter Einstein in person and not merely through his papers. He earned significant respect at that meeting, even if some dignitaries were taken aback by the discovery that his laughter was like “the barking of a seal.”
His increasing status among physicists led to job offers from the University of Utrecht and, again, from Zurich. He returned to Switzerland once the salary was right and tried to focus more on his research. Specifically, he wanted to return to relativity. He hoped to extend the equivalence principle and other insights he had been toying with since 1907. While relativity was still a fairly obscure subject, others had been thinking about it during this time. Planck wrote a few modest papers. More important was the wholesale reconceptualization of relativity from Einstein’s old teacher Hermann Minkowski. Minkowski ran a seminar on electrodynamics that included the special relativity papers of 1905. He was a mathematician and focused primarily on the mathematical structures implicit in the theory, rather than its physical meaning.
Minkowski, like Planck, was interested in the less relative parts of relativity. He noticed that while two observers could disagree about their measurements of time and their measurements of space, there were some that they would always agree on. These were measurements of space-time, a new mathematical amalgam of three dimensions of space and one of time. While time and space were relative, the combination of them was absolute. This is similar to how people facing in opposite directions will give different directions for turning left or right but can both agree about whether you should turn north or south. Minkowski had found a new kind of measurement hidden under the equations of special relativity that would be independent of movement or point of view.
Minkowski was able to write down a new, elegant mathematical formalism based on this idea. For him the foundations of the universe were no longer three dimensions of space plus time, but rather a four-dimensional continuum in which time and space were woven together. Our perceptions of time and space as separate were fundamentally mistaken. We could take different trajectories through these four dimensions, which result in the different experiences of space and time called for in special relativity. He called this new concept “radical” and was not shy about describing the implications: “Henceforward space by itself and time by itself will totally decline into shadows, and only a kind of union of the two shall preserve independence.” Like the prisoners in Plato’s cave, we see merely the shadows of reality. Only mathematics could reveal the true nature of things. Minkowski had created a new four-dimensional geometry that was supposedly more real than our everyday perceptions of the world.
Einstein was not impressed. The notion of a four-dimensional space-time was exactly the kind of fuzzy-headed metaphysics he had been hoping relativity would dispose of. In fact, he dismissed Minkowski’s theory with the same disparagement he brought against the ether. It was “superfluous.” The elegant mathematics were no more exciting than were Minkowski’s lectures back at the ETH. Einstein reportedly complained, “Since the mathematicians pounced on the relativity theory I no longer understand it myself.” Minkowski had reduced Einstein’s subtle and powerful theory to mere geometry.
He had not produced much himself, though. In the three years since the happiest thought of his life, he published nothing on relativity or gravity. While in Prague he finally wrote a paper on those. It was a manifesto, a statement of intent to create a general theory of relativity that encompassed gravity. He presented the equivalence principle and its consequences along with some approximate numerical predictions for the gravitational deflection of light and the gravitational redshift. The redshift was absurdly small and seemed well beyond the possibility of measurement.
The deflection of light, however, might be within reach. If an observer on Earth looked at a star that appeared just at the edge of the sun, she would see the sun’s gravity bend the light from the star very slightly. This bending would cause the star’s image to be slightly pushed away from its true location, like looking through a thick sheet of glass. Of course, seeing a star next to the blazing sun was impossible, so one would have to wait until an eclipse covered the solar disk. Only in that rare moment could one test Einstein’s radical idea. He predicted that during an eclipse such a star would appear to be 0.83 arc-seconds away from its real position. This is a tiny amount—about how large a coin appears from a couple miles away. But astronomers regularly measured effects smaller than this. It could be done. Einstein had high hopes but he needed an astronomer to take on the project. He worried that practical-minded astronomers would be uninterested in his theory (with good reason). In recruiting allies he tried to simultaneously assuage those worries and generate excitement: “It is greatly to be desired that astronomers take up the question broached here, even if the considerations here presented may appear insufficiently substantiated or even adventurous.”
His only lead was the enthusiastic but somewhat hapless Freundlich. In September 1911, Einstein said he was “extremely pleased” to have him on board. In an impassioned letter, Einstein explained the importance of this measurement. This was the point on which the theory of relativity would live or die: “One thing can, nevertheless, be stated with certainty: If such a deflection does not exist, then the assumptions of the theory are not correct.”
Unfortunately total solar eclipses were rare events and Freundlich hardly had the resources necessary to mo
unt an expedition to observe one. Instead, he examined old photographic plates (precision astronomical pictures needed glass plates) taken at eclipses, looking carefully for any stars showing a deflection. Photographs of eclipses were usually intended to capture the corona or spectacular solar prominences, though, which required a setup precisely the opposite of what Freundlich needed. He saw no deflection. Freundlich began contacting astronomers around the world to see if anyone could help in their quest.
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BY THIS TIME Eddington had become an expert in maneuvering through exactly those international networks. In 1912 he became secretary of the Royal Astronomical Society as well as section president of the British Association for the Advancement of Science, and he sat comfortably in the upper echelons of British science. When William Christie had fallen ill, Eddington took over many of the Astronomer Royal’s duties at Greenwich. After Christie retired, the post was taken over by Frank Dyson. Dyson had once held Eddington’s position of chief assistant and the two became good friends. Beyond their shared passion for precise measurement, Eddington praised Dyson’s “complete unselfishness, his sincerity, his sociability.” They worked together closely at the observatory, forging bonds that would soon be sorely tried.
How the sun’s gravity changes the perceived position of a star
Einstein's War Page 6