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Einstein Was No Lone Genius COMMENT BESSO: BESSO FAMILY/AIP EMILIO SEGRE VISUAL ARCHIVES VISUAL EMILIO SEGRE FAMILY/AIP BESSO BESSO: GROSSMANN, EINSTEIN: ETH-BIBLIOTHEK ZÜRICH/BILDARCHIV; ZÜRICH/BILDARCHIV; ETH-BIBLIOTHEK GROSSMANN, EINSTEIN: Marcel Grossmann (left) and Michele Besso (right), university friends of Albert Einstein (centre), both made important contributions to general relativity. Einstein was no lone genius Lesser-known and junior colleagues helped the great physicist to piece together his general theory of relativity, explain Michel Janssen and Jürgen Renn. century ago, in November 1915, Technische Hochschule; ETH) — where, would account for a discrepancy of about Albert Einstein published his between 1896 and 1900, he studied to 43˝ (seconds of arc) per century between general theory of relativity in four become a school teacher in physics and Newtonian predictions and observations Ashort papers in the proceedings of the Prus- mathematics. Einstein also met his future of the motion of Mercury’s perihelion, the sian Academy of Sciences in Berlin1. The wife at the ETH, classmate Mileva Marić. point of its orbit closest to the Sun. landmark theory is often presented as the Legend has it that Einstein often skipped Einstein started to work in earnest on this work of a lone genius. In fact, the physicist class and relied on Grossmann’s notes to new theory only after he left the patent office received a great deal of help from friends pass exams. in 1909, to take up professorships first at the and colleagues, most of whom never rose Grossmann’s father helped Einstein to University of Zurich and two years later at to prominence and have been forgotten2–5. secure a position at the patent office in the Charles University in Prague. He realized (For full reference details of all Einstein texts Berne in 1902, where Besso joined him that gravity must be incorporated into the mentioned in this piece, see Supplementary two years later. Discussions between Besso structure of space-time, such that a particle Information; go.nature.com/ufcgp9.) and Einstein earned the former the sole subject to no other force would follow the Here we tell the story of how their acknowledgment in the most famous of straightest possible trajectory through a insights were woven into the final version Einstein’s 1905 papers, the one introduc- curved space-time. of the theory. Two friends from Einstein’s ing the special theory of relativity. As well In 1912, Einstein returned to Zurich and student days — Marcel Grossmann and as publishing the papers that made 1905 was reunited with Grossmann at the ETH. Michele Besso — were particularly impor- his annus mirabilis, Einstein completed The pair joined forces to generate a fully tant. Grossmann was a gifted mathemati- his dissertation that year to earn a PhD in fledged theory. The relevant mathematics cian and organized student who helped physics from the University of Zurich. was Gauss’s theory of curved surfaces, which the more visionary and fanciful Einstein at In 1907, while still at the patent office, he Einstein probably learned from Grossmann’s crucial moments. Besso was an engineer, started to think about extending the prin- notes. As we know from recollected conver- imaginative and somewhat disorganized, ciple of relativity from uniform to arbitrary sations, Einstein told Grossmann7: “You and a caring and lifelong friend to Einstein. motion through a new theory of gravity. must help me, or else I’ll go crazy.” A cast of others contributed too. Presciently, Einstein wrote to his friend Their collaboration, recorded in Einstein met Grossmann and Besso at Conrad Habicht — whom he knew from a Einstein’s ‘Zurich notebook’, resulted in a the Swiss Federal Polytechnical School in reading group in Berne mockingly called the joint paper published in June 1913, known Zurich6 — later renamed the Swiss Federal Olympia Academy by its three members — as the Entwurf (‘outline’) paper. The Institute of Technology (Eidgenössische saying that he hoped that this new theory main advance between this 1913 Entwurf 298 | NATURE | VOL 527 | 19 NOVEMBER 2015 | CORRECTED ONLINE 17 NOVEMBER 2015 © 2015 Macmillan Publishers Limited. All rights reserved COMMENT theory and the general relativity theory in their formulation of the Entwurf theory. theory using the same kind of mathematics of November 1915 are the field equa- During his Vienna lecture, Einstein called that he and Grossmann had used to for- tions, which determine how matter curves for Kottler to stand up and be recognized for mulate the Entwurf theory. Einstein and space-time. The final field equations are this work8. Fokker showed that in both theories the ‘generally covariant’: they retain their form Einstein also worked with Besso that gravitational field can be incorporated into no matter what system of coordinates is summer to investigate whether the Entwurf the structure of a curved space-time. This chosen to express them. The covariance of theory could account for the missing 43˝ per work also gave Einstein a clearer picture of the Entwurf field equations, by contrast, century for Mercury’s perihelion. Unfortu- the structure of the Entwurf theory, which was severely limited. nately, they found that it could only explain helped him and Grossmann in a second 18˝. Nordström’s theory, Besso checked later, joint paper on the theory. By the time it TWO THEORIES gave 7˝ in the wrong direction. These calcu- was published in May 1914, Einstein had In May 1913, as he and Grossmann put the lations are preserved in the ‘Einstein–Besso left for Berlin. finishing touches to their Entwurf paper, manuscript’ of 1913. Einstein was asked to lecture at the annual Besso contributed significantly to the THE BREAKTHROUGH meeting of the Society of German Natural calculations and raised interesting ques- Turmoil erupted soon after the move. Scientists and Physicians to be held that Sep- tions. He wondered, for instance, whether Einstein’s marriage fell apart and Mileva tember in Vienna, an invitation that reflects the Entwurf field equations have an unam- moved back to Zurich with their two the high esteem in which the 34-year-old biguous solution that uniquely determines young sons. Albert renewed the affair was held by his peers. the gravitational field of the Sun. Historical he had started and broken off two years In July 1913, Max Planck and Walther analysis of extant manuscripts suggests that before with his cousin Elsa Löwenthal (née Nernst, two leading physicists from Berlin, this query gave Einstein the idea for an argu- Einstein). The First World War began. Ber- came to Zurich to offer Einstein a well-paid ment that reconciled him with the restricted lin’s scientific elite showed no interest in and teaching-free position at the Prussian covariance of the Entwurf equations. This the Entwurf theory, although renowned Academy of Sciences in Berlin, which he ‘hole argument’ seemed to show that gen- colleagues elsewhere did, such as Lorentz swiftly accepted and took up in March 1914. erally covariant field equations cannot and Paul Ehrenfest in Leiden, the Nether- Gravity was not a pressing problem for Planck uniquely determine the gravitational field lands. Einstein soldiered on. and Nernst; they were mainly interested in and are therefore inadmissible9. By the end of 1914, his confidence had what Einstein could do for quantum physics. Einstein and Besso also checked whether grown enough to write a long exposition Several new theories had been proposed the Entwurf equations hold in a rotating of the theory. But in the summer of 1915, in which gravity, like electromagnetism, was coordinate system. In that case the inertial after a series of his lectures in Göttingen had represented by a field in the flat space-time forces of rotation, such as the centrifugal piqued the interest of the great mathemati- of special relativity. A particularly promising force we experience on a merry-go-round, cian David Hilbert, Einstein started to have one came from the young Finnish physicist can be interpreted as gravitational forces. serious doubts. He discovered to his dismay Gunnar Nordström. In his Vienna lecture, The theory seemed to pass this test. In that the Entwurf theory does not make Einstein compared his own Entwurf theory August 1913, however, Besso warned him rotational motion relative. Besso was right. to Nordström’s theory. Einstein worked on that it did not. Einstein did not heed the Einstein wrote to Freundlich for help: his both theories between May and late August warning, which would come back to haunt “mind was in a deep rut”, so he hoped that 1913, when he submitted the text of his lec- him. the young astronomer as “a fellow human ture for publication in the proceedings of the In his lecture in Vienna in September being with unspoiled brain matter” could tell 1913 Vienna meeting. 1913, Einstein concluded his comparison of him what he was doing wrong. Freundlich In the summer of 1913, Nordström visited the two theories with a call for experiment could not help him. Einstein in Zurich. Einstein convinced him to decide. The Entwurf theory predicts The problem, Einstein soon realized, lay that the source of the gravitational field in that gravity bends with the Entwurf field equations. Worried both their theories should be constructed light, whereas Nor- “Worried that that Hilbert might beat him to the punch, out of the ‘energy–momentum tensor’: in dström’s does not. It Hilbert might Einstein rushed new equations into print in pre-relativistic theories, the density and the would take another beat him to early November 1915, modifying them the flow of energy and momentum were repre- five years to find out. the punch, following week and again two weeks later in sented by separate quantities; in relativity Erwin Finlay Freun- Einstein subsequent papers submitted to the Prussian theory, they are combined into one quantity dlich, a junior astron- rushed new Academy.
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