Einstein's War

by Matthew Stanley

  The Brazil team had the slightly easier task. Because they were able to take check plates on-site, they could just directly compare them to the eclipse photographs. Since both were taken in the same place with the same telescope, they could just measure how far the image of a certain star appeared to move when the sun’s gravity was present. This was not a matter of slapping down a ruler and lining up by eye, though. Small measurements were made with a complicated device called a micrometer that could assess much tinier distances than the human hand. These measurements required a great deal of training and patience, but were a standard part of an astronomer’s toolkit.

  Eddington needed an extra step. He had been unable to take check plates from Principe, so he could not make a direct measurement. He had to compare the image of the Hyades he took during the eclipse with the image of the Hyades taken in Oxford with the same telescope. But he had to account for the possibility that there was some subtle difference between Oxford and Principe that changed the image. So he had taken an image of a different star field in both locations, and by comparing those two photographs he could see what differences there were. Armed with that information, he could then account for that in his final measurements. It is very rare that a measurement in science has no interference or error. Rather, the trick is to understand those problems and correct for them.

  The Principe observations produced sixteen photographs, though thanks to the cloud only seven had useful images of stars. Fortunately all seven had the two stars with the highest predicted deflection. A reliable measurement required five stars for cross-reference, though, and only two of the plates had that many. Those two were consistent, at least, and gave an average deflection of 1.61 arc-seconds, ±0.30. That uncertainty was not superb, but it was adequate. Einstein’s predicted deflection was 1.75. For the first measurement of a completely unknown physical phenomenon, Eddington thought that was pretty good.

  There were two sets of photos from Sobral, one for the astrographic telescope and one for the four-inch. The astrographic images had looked discouraging even in the field, apparently due to the heating of the coelostat mirror. It was clear to everyone involved that these would not give trustworthy information. Nonetheless, Davidson and Turner analyzed them thoroughly and they showed a deflection of 0.93 arc-seconds (the poor image quality made it difficult to estimate error). This was much closer to the Newtonian half-deflection than the full Einstein value.

  Dyson was unsure how to handle this. The pattern of the image distortions suggested a systematic effect that could be accounted for mathematically. If they fixed the measurements with that systematic effect in mind, the numbers became 1.52 arc-seconds, much closer to the Einstein prediction. It was hard to be sure about the systematic effect, though. Dyson decided to leave the results uncorrected at 0.93.

  The four-inch telescope, only brought along as a backup at the last moment, saved the day. Seven of the eight plates taken with it had excellent images of all seven hoped-for stars. Measuring those provided much better results than those from Principe: 1.98 arc-seconds, ±0.12. Significantly more precise, and still supporting Einstein.

  By October, Eddington and Dyson had sent their results to each other by mail. Dyson sent the astrographic results first, causing Eddington a great deal of worry—they were simply not compatible with his own results. When the four-inch data arrived, he wrote back in relief: “I am glad the [4-inch] plates give the full deflection not only because of theory, but because I had been worrying over the Principe plates and could not see any possible way of reconciling them with the half-deflection.” He was also pleased that the four-inch plates had enough stars to graph how the deflection changed with distance from the edge of the sun (stars farther away were deflected less). This more detailed, internal consistency of the data made it even more persuasive: “It seemed to me rather interesting and deals with a point that ought not to be overlooked and brings out the really remarkable agreement of individual stars at Sobral.”

  So they had three results: 1.61, 1.98, and 0.93. The standard thing to do would be to average the three (according to arcane rules for weighting some of the numbers). This gave a mean measurement of 1.64 arc-seconds, arguably a solid confirmation for Einstein. As they began writing the report, though, Eddington had second thoughts:

  I do not like the combination of the astrographic with the other Sobral results—particularly because it makes the mean come so near the truth. I do not think it can be justified; the probable errors of both are I think below 0.1” so they are manifestly discordant. . . . It seems arbitrary to combine a result which definitely disagrees with a result which agrees and so obtain still better agreement.

  It was true that this standard mathematical approach gave a number close to the prediction. But two of the numbers agreed, and one did not. Averaging them hid that. That might look suspicious, and it also gave an incorrect sense of the results. It would be like coming upon two whole pies and one half pie. On average, you still had something like four-fifths of a pie, and that’s not bad. You might want to know, however, that two of the pies were pristine and one had already been half eaten. Sometimes quality is as important as quantity. Eddington and Dyson decided to present all three results separately, letting each stand on its own.

  While Eddington and Dyson were furiously measuring and calculating, they somehow still made time to set the stage for the eventual presentation of the results. Dyson was interviewed by a Times reporter about the measuring process. When asked what the data revealed, he cagily responded, “They disclose something, but what it is I am not prepared to state yet. It is a very curious position—but only one thing among many other things.”

  About the same time, Eddington ventured to the annual meeting of the BA in Bournemouth. This was his first public appearance since he left for the expedition in March, and the audience was eager. He described the theoretical background and how the observations had actually fared in the field. He declined to give any results, saying that the calculations were ongoing. Oliver Lodge commented that he hoped the results would support the Newtonian deflection. Other scientists proposed alternative explanations for the deflection, should it be found.

  Almost immediately after he and Dyson agreed on the results in late October, Eddington decided it was time for a test run. As a site he chose the ∇2 V Club (pronounced “del-squared vee”) in Cambridge, an informal organization of students and professors interested in physics and astronomy. This was the first meeting of the club in three and a half years, surely organized by Eddington for just this purpose. The president of the club was Ebenezer Cunningham, a fellow conscientious objector and relativity enthusiast. Fifteen other people were there, most of whom were highly skilled in both experimental and theoretical physics. So Eddington had chosen an audience that was extremely qualified to judge the results and still somewhat sympathetic. Perhaps most important was that it was a private meeting. If they shot everything down, it would not be a public disaster.

  It seems his conclusion was accepted, if not without contest—conversation went until midnight. But it went well enough that Eddington was ready to go public. The day after the meeting Dyson asked the Royal Society Council to schedule a special meeting on November 6, at which the results would be formally presented. There was no turning back now.

  * * *

  WE DON’T KNOW who leaked the news. Balthasar van der Pol, a colleague of H. A. Lorentz in Leiden, was at the Bournemouth meeting where Eddington spoke about the expeditions. He reported back to Lorentz that the results were in favor of Einstein. But Eddington did not formally announce that at the meeting. Perhaps he spoke personally to van der Pol and whispered the news? This would not be a particular surprise, even if it bent some rules. He was concerned about making sure the news crossed the wartime borders. In the wake of the formation of the IRC, perhaps he wanted to take any victory for scientific internationalism that he could. It was still impossible to send a message directly to
Berlin, so this was the next best thing.

  Lorentz immediately sent a telegram on to Einstein, urgent and brief: “Eddington found stellar shift at solar limb, tentative value between nine-tenths of a second [of a degree] and twice that.” Unfortunately we have no eyewitness account of Einstein first receiving the news. Fortunately, he then showed the telegram to anyone who came into his apartment, so we can see it through other eyes.

  Ilse Rosenthal-Schneider, a young physics student, was sitting with Einstein at his desk going through a book full of objections to relativity. Einstein suddenly interrupted their reading to reach for a document on the windowsill. He coolly remarked, “This may interest you,” and handed her Lorentz’s telegram. There are a few different versions of the story from this point. The most complete goes:

  Full of enthusiasm, I exclaimed, “How wonderful! This is almost the value you calculated!” Quite unperturbed, he remarked, “I knew that the theory is correct. Did you doubt it?” I answered, “No, of course not. But what would you have said if there had been no confirmation like this?” He replied, “I would have to pity our dear God. The theory is correct all the same.”

  Around the same time, two friends were visiting while he was ill in bed. In his pajamas, with his socks showing, he presented the telegram, saying, “I knew I was right.” In another version of the story he went to sleep even knowing that the results were on their way, confident in the outcome, while Planck waited up anxiously. This is a complete fabrication—he did not know the results were on their way.

  Einstein’s confident manner in these stories makes for great anecdotes, though it certainly does not mesh with his years of efforts trying to get precisely this confirmation. We can see more of his relief in a letter to his mother (“Today some happy news. H. A. Lorentz telegraphed me that the English expeditions have really verified the deflection of light by the Sun.”) and another to Planck:

  I cannot postpone telling you . . . how deeply and how heartily pleased I was about the news contained in Lorentz’s telegram. Thus the intimate union between the beautiful, the true, and the real has once again proved operative. You have already said many times that you personally never doubted the result; but it is beneficial, nonetheless, if now this fact is indubitably established for others as well.

  He had been hoping for precisely this for years. And he was in no mood to be shy about spreading the word.

  His friends in the Netherlands were overjoyed, particularly at their role in making it happen. De Sitter wrote to Einstein to “congratulate you heartily on the fine success of the English eclipse expeditions. The agreement is really very good, much better than I had expected, and the whole thing is very convincing.” Lorentz was baffled that no British journal had published the results yet: “This is certainly one of the finest results that science has ever accomplished, and we may be very pleased about it.” Ehrenfest hoped to get Einstein and Eddington both in Leiden at the same time so they could finally meet.

  Einstein immediately sent a note reporting the results to Arnold Berliner at Naturwissenschaften, who published it on October 10. He also wrote to his friends in Switzerland. The physics group in Zurich sent Einstein a poem:

  All doubts have now been spent

  At last it has been found:

  Light naturally is bent

  To Einstein’s great renown!

  Einstein’s responding verse was less mellifluous. One friend wrote, “So all is going better for you, even light has been bending a few million years to please you.” He wondered if Einstein could get the stars to do any other tricks.

  On October 23, Einstein was in the Netherlands for a physics colloquium. Ehrenfest had arranged for a visiting professorship so he would have an excuse to be there a few weeks each year (and to provide some hard currency—the German mark continued to plummet and Einstein was having trouble paying alimony). Eddington, busy with the final stages of data analysis, could not be there, but he did have time to write a letter to the astronomer Ejnar Hertzsprung reporting the state of the results. Given the timing, Eddington must have sent the letter right before his test presentation to the ∇2 V Club—essentially as soon as he had results from both expeditions. Einstein was delighted to see the more detailed version of the news:

  This evening at the colloquium Hertzsprung showed me a letter by Eddington, according to which the precise measurement of the plates has furnished the exact theoretical value for the light deflection. It was gracious destiny that I was allowed to witness this.

  As always, Einstein had a fabulous time with his Dutch friends, going on long walks and playing music in the evenings. He thanked Ehrenfest for “keeping this rickety trunk in good spirits” and for the gift of a thermos of soup to make the unheated train ride home bearable. He rhapsodized about his joy in spending two weeks deep in thinking about physics: “How hard this magnificent creation of ours seems to have to struggle just for that little bit of live awareness of its beauty! This beauty is so subtle and strange that one can’t quite shake off religious notions.” But the news from the eclipse dominated all his thoughts and he rushed to share it. Writing to his mother: “The result is now definite and signifies a perfect verification of my theory.” And to Elsa: “My theory has been verified exactly with the greatest precision conceivable. Eddington reported it here. Now no rational person can doubt the validity of my theory anymore.”

  * * *

  THAT WAS THE attitude Eddington was hoping to instill in his British colleagues. Dyson had requested that a joint meeting of the Royal Astronomical Society and the Royal Society take place November 6. JPEC regulations stipulated that such a meeting should be held as soon as practical after an expedition, though this one attracted attention like none before. On that Thursday the meeting was held at the Royal Society’s rooms at Burlington House in Piccadilly. The audience was seated in pews, with an overflow crowd standing among the columns lining the sides. Alistair Sponsel estimates that between 100 and 150 people crammed into the room that day.

  One of the attendees was Alfred North Whitehead, the distinguished philosopher-mathematician. He reported the excitement in the air:

  The whole atmosphere of tense interest was exactly like that of the Greek drama. . . . There was a dramatic quality in the very staging:– the traditional ceremonial, and in the background the picture of Newton to remind us that the greatest of scientific generalizations was now, after more than two centuries, to receive its first modification. Nor was the personal interest wanting: a great adventure in thought had at length come safe to shore.

  Dyson was scheduled to present the overall results, Crommelin to speak for the Brazil observers, and Eddington for Principe. Dyson carefully described the methods used, perhaps trying to emphasize their caution, perhaps to heighten the tension, before announcing, “After a careful study of the plates I am prepared to say that there can be no doubt that they confirm Einstein’s prediction. A very definite result has been obtained that light is deflected in accordance with Einstein’s law of gravitation.”

  There was no doubt a stir in the room as Dyson then sat to allow Crommelin to describe the Sobral results in detail. He was effusive in thanking the various locals who supported the work there. He explained the problems with the results from the astrographic and how they concluded that the coelostat mirror was the source. He presented those results even though everyone involved accepted that they were not reliable and should not be given much credence. The excellent data from the four-inch telescope took up most of his time.

  Eddington took the final part of the presentation so he could both describe the Principe expedition and place all the results in the wider scientific context of relativity. Eddington emphasized that, as Dyson said, the deflection was real and it was close to Einstein’s prediction. He acknowledged an important gap, though—the other remaining test of general relativity, the gravitational redshift, had still not been observed
. This meant one could say that Einstein’s law (that is, the mathematical formulas) had been proved, but the theory itself (that is, the ideas from which the formulas came) could still be questioned. This gave him some wiggle room in which he was able to say “Einstein is right” without having to grapple with thorny issues such as the nature of space-time or the curvature of the universe.

  The chair of the meeting, J. J. Thomson (Nobel Prize winner for the discovery of the electron), then took over. He said that the deflection was not an isolated fact, rather it was “part of a whole continent of scientific ideas affecting the most fundamental concepts of physics.” His commentary was extraordinary:

  This is the most important result obtained in connection with the theory of gravitation since Newton’s day, and it is fitting that it should be announced at a meeting of the Society so closely connected with him. . . . If it is sustained that Einstein’s reasoning holds good—and it has survived two very severe tests in connection with the perihelion of Mercury and the present eclipse—then it is the result of one of the highest achievements in human thought.

  Thomson had been no Einstein devotee like Eddington, and he had almost certainly had the opportunity to inspect the results closely before the meeting. For him to place Einstein on the level of Newton, to call relativity one of the highest achievements in human thought, was an astonishing embrace of a theory that just a year before had been barricaded behind battleships and barbed wire. He did, however, close his statement with a complaint about the difficult mathematics Einstein had used.

  Alfred Fowler, president of the RAS, was then given the floor. Fowler was not quite as impressed as Thomson. With a slightly backhanded compliment he suggested that perhaps this should not be the final word: “The conclusion is so important that no effort should be spared in seeking confirmation in other ways.”