God In The Equation Read online

  Einstein braced for an explosive reaction to the publication of this theory but was promptly disappointed. What happened the day after Jesus delivered his Sermon on the Mount? Not much, probably. So it was with Einstein: calm followed his storm. “His publication was followed by an icy silence,” his sister Maja recalled. Slowly, however, scientific recognition caught up with him. The prominent German physicist Max Planck took an interest in the paper and helped publicize its ideas. In 1908, Einstein finally left the patent office behind and moved to the University of Bern, where, with some string pulling by his allies, he began expanding the “area of applicability” of his special theory. He received some assistance in this regard from Hermann Minkowski, a Russian Jew living in Switzerland. A far more skilled mathematician than Einstein, Minkowski reconfigured the terms of the relativity equations to combine the three dimensions of space with time so that events could be described as occurring in a four-dimensional space-time, yet another novel scientific unity.

  Interweaving time and space in this way set the foundation for the concept of curved space, which became a central part of Einstein's ideas about the cause of gravity and the structure of the universe. It also helped establish the notion that space and time cannot exist without each other and so marked yet another leap in the potential scope of scientific inquiry. Minkowski's version of space-time was a big step toward general relativity, but it was not enough in itself. The Minkowski equations described a flat geometry, like the Euclidian geometry that students learn in high school. Einstein needed a curved geometry to describe gravity, and this was his ultimate goal. Minkowski's thoughtful elaborations of relativity were cut short before he was able to help in this development. He died from pneumonia in 1909.

  Six months later, Einstein formally joined the world of academia by accepting a position at the University of Zurich. He moved again, to Karl-Ferdinand University, the German university in Prague, just two years afterward. During his time there, he returned to his thoughts on the nature of gravity, this time considering its effect on light. Light is so intangible that we don't normally think of it as having weight, but Einstein believed otherwise. Starlight passing very close to the edge of the sun would be bent by the powerful gravity, displacing the star's apparent position in the sky away from the sun. Einstein realized this effect should be small but measurable. He had discussed this possibility before but examined it in greater detail, for a very practical reason: “I now see that one of the most important consequences of my former treatment is capable of being tested experimentally.” In other words, he saw a chance to prove his still-controversial theory of relativity. “It would be a most desirable thing if astronomers would take up the question here raised,” he concluded in the journal Annalen der Physik in 1911.

  By 1912, Einstein had returned to Zurich, this time to take a position with the old Polytechnic. As his ideas about gravity and space continued to percolate, Einstein called on the mathematical talents of Marcel Grossmann, a friend since his student days. This beginning of general relativity brought Einstein another dose of agony. “Compared to this problem the original relativity theory is child's play,” he wrote in a letter to Arnold Sommerfeld, the German physicist. He and Grossmann struggled for nine months and finally published a paper in 1913 that outlined a new theory of gravitation, but Einstein was not satisfied with the result and hesitantly titled the paper a “draft.” The derived equations did not have the unique simplicity he craved, and they did not fit his thinking about the incorruptibility of causality. He was groping toward a theory of the most basic aspects of reality, and he had to make sure the result felt exactly right.

  Always fond of thought problems, Einstein crafted a particularly fine one to illustrate the goal of his general theory of relativity. A man finds himself in a windowless room. He does not know where he is, but he notices that he feels his normal body weight bearing down on his feet. Is he in a room sitting on the surface of the Earth, or is he in outer space, atop a rocket that is accelerating the room, giving rise to a downward push that simulates gravity? According to Einstein, there is no way for the man to know, even if he is equipped with the most sophisticated scientific tools. Continuing with his Machist approach, he took what looked like an unfortunate subjectivity and found in it another scientific absolute. The reason the man cannot tell the difference between acceleration and gravity is that there is no difference; gravity and acceleration are perfectly equivalent. Making such an assertion is one thing. Deriving a mathematically rigorous theory that explains why the two are equivalent is, as Einstein painfully discovered, another thing entirely. It took him two more years to come up with a fully satisfactory answer.

  Meanwhile, Einstein held out for observational confirmation that he was on the right track. If the sun's gravity really could bend starlight, the only time the effect might be visible is during a solar eclipse, when the moon blots out the sun's blinding brilliance so that stars lying right beside the sun's disk would be visible. Erwin Findlay-Freundlich, an assistant at the Berlin University Observatory, heard about Einstein's prediction and planned to gather the desired data during a solar eclipse taking place in Russia in August of 1914. Einstein scrounged for funding to support the trip and, after writing to George Ellery Hale of Mount Wilson Observatory, it looked as though he had succeeded in setting up an astronomical expedition. If the result was positive, Einstein wrote to Mach in 1913, “your inspired investigations into the foundations of mechanics. . . will receive splendid confirmation.” Instead the guns of August touched off World War I and made the experiment politically impossible. In retrospect, however, the delay was a godsend for Einstein. His early calculation of how starlight would bend around the edge of the sun gave a number that was only half as large as the correct value he derived three years later. If the 1914 eclipse expedition had succeeded, it would have appeared to discredit relativity.

  By the time war struck, Einstein had returned to Germany. He had accepted a post at the University of Berlin in 1913, in a deal that was sweetened with membership in the prestigious Prussian Academy of Sciences and the promise that he would not have to expend his energies lecturing. His newly elevated circumstances, along with his conviction that he had resolved the earlier mathematical problems with his theory, contributed to a growing sense of self-confidence that bordered on intellectual arrogance. Day by day he grew less concerned about the importance of observational confirmation. He had never been much of an experimentalist, but his devotion to Mach's ideas had led him to praise the primacy of observation. Increasingly, however, Einstein seemed dazzled by the scope and logical economy of his theories. At times he sounded convinced that he was on the path to decoding the fundamental nature of God, so small details of empirical confirmation no longer mattered much. “Now I am completely satisfied and I no longer doubt the correctness of the whole system, whether the observation of the eclipse succeeds or not. The sense of the thing is too evident,” he wrote to Michele Besso. He had taken the leap of faith toward sci/religion.

  Even as Einstein was retreating from observation toward intuition, he was getting a harsh empirical lesson on realpolitik. Soon after the outbreak of the Great War, ninety-three prominent German intellectuals—including Planck, Einstein's early champion and one of the founders of quantum theory—endorsed the “Manifesto to the Civilized World.” In wounded terms, this document justified Germany's aggression as a necessary act of self-defense. In response, Einstein lent his name to the “Manifesto to Europeans,” a denunciation of the war and a call for European unity. The experience confirmed Einstein's deep antipathy toward what he saw as the aggressive and closed-minded nature of the German spirit and intensified his drive to find in physics the rational and unifying rules so grossly missing in the world of human affairs.

  War paralyzed Europe for four years, while Einstein was deeply engaged in his own battle, his struggle for enlightenment regarding the nature of gravity. Newton himself had been disappointed by the descriptive nature of his theory o
f universal gravitation: “The Cause of Gravity is what I do not pretend to know,” he wrote sullenly. For Einstein too it was not enough to know how that apple falls from the tree. He wanted science to penetrate more of the why of the universe. He became convinced that gravity results not from Newton's instantaneous, spooky force reaching through space, but through the interaction between matter and space itself. Notwithstanding his boasts to Besso, Einstein had great difficulty tying up the loose ends of his general theory of relativity. “Compared with this problem, the original relativity is child's play,” he wrote to Sommerfeld in the autumn of 1915.

  Einstein presented the results of his labor in a pair of lectures to the Prussian Academy that November. A full account appeared in the spring of 1916 as “The Foundation of the General Theory of Relativity” in Annalen der Physik. Newton's gravity had vanished, replaced by a field, springing from all matter, that bends space and any light or other radiation that happens to pass through it. A carpenter looks down a board to see if it has been planed cleanly. A child points at his ball to locate it. They take for granted that light travels in perfectly straight lines, and for our usual purposes it does. But Einstein's relentless logic led him to conclude that those lines are not perfectly straight. The geometry of space is never truly flat, according to general relativity, and the shortest path between two objects is never exactly a straight line. In the presence of very dense masses or over very long distances, the curvature of space becomes so significant that space bends, twists, even circles in on itself.

  Or so Einstein claimed. In 1916, general relativity was a grand idea with no unique observational support. It drew its strength purely from Einstein's conviction that the rules and concepts of special relativity must apply to accelerating bodies, such as the hypothetical man in the sealed room, and that this expanded theory provided a more satisfying explanation of gravity than Newton's bewildered shrug. The obvious test, still, was to look for the curvature of light during a solar eclipse. Using his revised mathematics, Einstein now calculated that starlight passing by the edge of the sun would be deflected by less than two seconds of arc, an angle about one-thousandth as wide as the full moon. Finding such an effect would require extremely careful measurements of stellar positions. Once World War I was over the political obstacles were removed, but the test would have to wait for an eclipse that occurred in a part of the world where astronomers could make good observations and at a time when the sun was in a usefully starry location in the sky.

  Fortunately nature offered another test, the weirdly migrating orbit of Mercury. Much as earlier discrepancies in planetary motions had led Kepler to abandon perfect circles, Mercury's unexplained motions hinted at a flaw in Newton's description of the force that generates the orbital ellipses. No matter how scientists tallied up all the gravitational influences in the solar system, they could not fully explain that spirograph-like orbit of Mercury. Some of the greatest minds had tried and failed to find the fix that would patch up Newton's theory of gravity. A half century earlier, the French astronomer Urbain Leverrier had proposed that Mercury's precession was caused by the gravitational pull of an undiscovered planet, Vulcan, orbiting between Mercury and the sun. Leverrier had spectacularly predicted the existence of the planet Neptune based on the similarly errant motion of Uranus. This time around, however, dogged searches for the hypothetical Vulcan proved futile. In 1895, Simon Newcomb, one of America's leading astronomers, had even proposed tinkering with Newton's gravitational equations just a little in order to make the problem go away.

  Einstein was well aware that nobody had found a satisfactory explanation for the precession of Mercury's orbit. The reason they all failed, he believed, was that they were all using Newton's theory of gravity, which worked well most of the time but failed under extreme conditions. Of all the planets, Mercury orbits closest to the sun's great mass and travels the most rapidly in its orbit. It therefore is the most strongly affected by the way the effects of general relativity warp the fabric of space and alter the flow of time. Preliminary versions of general relativity did a little better than Newtonian gravity at predicting the orbit of Mercury but still did not yield the exactly correct motion. Einstein scrapped these early drafts as mathematically flawed. But the final 1915 version of relativity not only satisfied Einstein aesthetically, it also got the orbit of Mercury exactly right, as he proudly informed the Prussian Academy of Sciences. Only then did he confess—and only in private—that he had kept throwing out his equations and devising new versions until they fit the data. As with his remarks about the solar eclipse experiment, Einstein's description of his efforts to model the motion of Mercury correctly show him growing increasingly wrapped up in his scientific theology. “I was only concerned with putting the answer into a lucid form. There was no sense in getting excited about what was self-evident,” he told journalist Alexander Moszkowski.

  More and more, Einstein relocated his search for truth to the realm of pure thought. Nevertheless, he well understood the importance of observational support for his radical new theory. Perhaps he knew that his explanation of Mercury's orbit, no matter how tidy, would not carry the level of authority he needed. Other scientists claimed to have cracked this problem before. To convince the skeptics who did not see general relativity as “self-evident,” Einstein sought better proof. A scientific prophet's claim becomes credible only when his predictions come true, and with general relativity Einstein was audaciously claiming mastery over all of space and time. He needed that eclipse test, much as the Israelites needed to see Moses' miracles or the supporters of the Copernican view of the solar system needed Galileo's telescopic evidence to show that the Earth circles the sun. But war made an eclipse expedition impossible. “Only the intrigues of miserable people prevent the execution of this last, new, important test of the theory,” an exasperated Einstein wrote in another letter to Sommerfeld in 1915.

  Einstein got his wish, although it took four more years and a roundabout set of circumstances. He had sent out a number of copies of his “General Theory” paper. One of these went to Willem de Sitter, an astronomer at the University of Leiden who would later play an important role in honing Einstein's cosmological notions. De Sitter in turn forwarded the paper to the eminent British astronomer Arthur Stanley Eddington, who immediately grasped the import of the work and, with the zeal of a convert, set out to prove it correct. Nature was on Einstein and Eddington's side. Astronomers noted that a total solar eclipse in 1919 would take place while the sun was nestled in the head of the constellation Taurus, a patch of sky inhabited by a cluster of stars called the Hyades. The region around the eclipsed sun would be packed with relatively bright stars—exactly the setting needed to make a workable search for the bending of starlight by gravity. At Eddington's urging, Sir Frank Dyson, Britain's astronomer royal, began preparing for an expedition to view the eclipse from the coast of West Africa. The observations took place as scheduled on May 29.

  After much delicate analysis, Eddington announced his results to a joint meeting of the Royal Society and the Royal Astronomical Society on November 6. The observation decisively confirmed Einstein's predicted bending of light. “The setting. . . resembled a Congregation of Rites,” wrote physicist Abraham Pais, Einstein's colleague and biographer. The society's main hall overflowed with eminences ranging from the philosopher Alfred North Whitehead to J. J. Thomson, the man who discovered the electron. A portrait of Newton looked down upon the attendees. Cecilia Payne-Gaposchkin, a British astronomer and physicist who was still a student at the time, later recalled the impact of the event: “The result was a complete transformation of my world picture. . . My world had been so shaken that I experienced something very like a nervous breakdown.” The news media smelled the excitement. REVOLUTION IN SCIENCE, screamed a headline in next day's Times of London. “On November 7, 1919, the Einstein legend began,” Pais said. Two days later, the story broke in The New York Times. The old religions were in trouble, even if they didn't know it. With Einstein'
s sudden celebrity, the authority of science was about to extend to times and places it had never gone before.

  In truth, Eddington had not approached the observation with anything close to objectivity. He opened his heart honestly years afterward when he admitted, “We don't need an eclipse of the sun to ascertain whether a man is talking coherently or incoherently.” Einstein's mystical faith in relativity was catching. Eddington believed in Einstein and discarded some of the eclipse photographs that he deemed “flawed” because they did not show the expected displacement of the stars. Nevertheless, Eddington's stamp of approval carried tremendous prestige, and the results were bolstered by a similar finding from another British team that had observed the 1919 eclipse from northwestern Brazil. Thus spake Einstein: His pronounced his theory confirmed even before Eddington announced his final results. Especially telling are his comments to a student at the University of Berlin, who asked him what he would have done if the observations had not supported general relativity. “In that case I'd have to feel sorry for God. The theory is correct anyway,” Einstein allegedly retorted. One imagines him pausing and unfolding his famously enigmatic smile, leaving the student wondering if Einstein was mocking God or merely mocking himself.

  Einstein had grown increasingly assertive in elevating his instincts into a personal religious faith. He continued in the tradition of Newton, carrying out a divine project by revealing God's handiwork. But Einstein rushed down the path that Newton had only tentatively blazed, dictating what God should want or how God should have made the universe. Not surprisingly, Einstein didn't wait for the eclipse expedition or any other test before embarking on an even grander adventure. After publishing the completed version of his general theory of relativity, Einstein reset his sights and barreled ahead. He had just demolished Newton's theory of gravity. Now Einstein was out to demolish Newton's entire cosmology.