The Einstein-Besso Manuscript: A Glimpse Behind the Curtain of the Wizard

1 Freshman Colloquium “Introduction to the Arts and Sciences” Fall 2002 Michel Janssen The Einstein-Besso Manuscript: A Glimpse Behind the Curtain of the Wizard Michel Janssen Program in History of Science and Technology In my segment of the course, I want to show you slides of some pages of a set of research notes produced by Albert Einstein (1879–1955) and his closest friend and confidant Michele Besso (1873–1955). These notes, known collectively as the Einstein-Bess
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   1Freshman Colloquium “Introduction to the Arts and Sciences”Fall 2002Michel Janssen  The Einstein-Besso Manuscript: A Glimpse Behind the Curtain of the Wizard  Michel JanssenProgram in History of Science and Technology   In my segment of the course, I want to show you slides of some pages of a set of research notes produced by Albert Einstein (1879–1955) and his closest friend and confidant Michele Besso(1873–1955). These notes, known collectively as the Einstein-Besso manuscript, are from the period 1913–1914, when Einstein was still developing his general theory of relativity. Einstein first published the theory in the form in which physicists still use it today in the last of a series of  four papers in the Proceedings of the Berlin Academy of Science in November 1915. Manuscript material such as the Einstein-Besso manuscript offers historians and philosophers of science aunique glimpse behind the scenes of Einstein at work. Before I tell you more about the manuscript, let me tell you a little bit about myself and myinterest in Einstein and the Einstein-Besso manuscript. My training is in theoretical physics and in history and philosophy of science. Before I came to the University of Minnesota in the fall of 2000, I worked for several years for the Einstein Papers Project, then located at Boston Univer-sity (the project has since moved to Caltech in Pasadena, California). The goal of the EinsteinPapers Project is to publish the definitive edition of Einstein’s collected papers. This not onlyincludes his published papers and books on physics and a range of other subjects (such as Zion-ism, pacifism, philosophy, obituaries, etc.) but also his correspondence, his lecture notes, hisresearch notebooks, the occasional newspaper article or interview, etc. To date, eight of a pro- jected twenty-nine volumes have appeared, covering Einstein’s early years 1879–1902 (Vol. 1),his writings for the period 1902–1921 (Vols. 2, 3, 4, 6, 7), and his correspondence for the period 1902–1918 (Vols. 5, 8). I worked on material dealing with general relativity for Vols. 4, 7, and 8.The Einstein-Besso manuscript was published in Vol. 4. As a historian and philosopher of science, I am interested in how Einstein came up with sucha spectacular and strikingly novel theory as general relativity, which explains gravity in terms of the curvature of space-time. The analysis of documents such as the Einstein-Besso manuscript hashelped me understand to some extent“how Einstein did it.” And this is precisely what I want todiscuss in my segment of the course. Rather than talk about Einstein’s MO in the abstract (whichwould be pure speculation) or look at what Einstein himself said about it reflecting on his work  years later (which turns out to be highly misleading), I want examine the specific case of generalrelativity in the making. There is no better document to do so without extensive prior knowledge of the mathematics needed to formulate the theory than the Einstein-Besso manuscript. We canadmire Einstein’s magic from afar. But this manuscript actually allows us to take a peek behind the curtain of the wizard …   2  A Brief Characterization of the Einstein-Besso Manuscript and Its Importance  There are only two manuscripts still extant with research notes documenting Einstein’s worktoward the general theory of relativity. These two manuscripts are the so-called Zurich Notebookof late 1912/early 1913 and the Einstein-Besso manuscript, the bulk of which stems from June1913. Of these two manuscripts, only the latter is in private hands. The Zurich Notebook is part of the Einstein Archives at Hebrew University in Jerusalem. The published portion of the Einstein-Besso manuscript consists of about 52 loose pages, half of them in Einstein’s hand, the other half in Besso’s. There is no continuous numbering, whichmakes it hard to establish the exact order of the pages. The manuscript was brought to the atten-tion of the editors of the Einstein Papers Project in 1988. Robert Schulmann, then the director of the project, was approached by Pierre Speziali, who told him that he had been given a manuscriptby Vero Besso (1898–1971), the son of Michele, with whom he had become friendly in the courseof editing the Einstein-Besso correspondence (Speziali 1972). Speziali made a copy of this manu-script available to the Einstein Papers Project, hoping that authentication of the manuscript by theEinstein editors would increase its value of this manuscript. Speziali wanted to sell the manuscriptat auction to provide for his two daughters after his death. (I never got to meet Speziali, but he toldRobert Schulmann that he liked my annotation of “his” manuscript. He died before Vol. 4 of theEinstein edition finally went to press.) The manuscript was eventually sold at auction by Christie’sin 1996, fetching $360,000. The essay that you are about to read is adapted from the essay I wrotefor the auction catalog. The current owner, a collector of scientific manuscripts in Chicago, hascontacted Christie’s to resell the manuscript at auction this fall along with some other Einsteinmaterial in his possession. In the summer of 1998, Robert Schulmann obtained an additional four-teen pages of the manuscript and there might well be more. This material is still in the possessionof Besso’s heirs. Negotations are underway with the Besso family to secure the necessary permis-sions to publish some of this additional material in a new book on Einstein’s path to general rela-tivity (Renn et al. forthcoming) . Here I will focus on the 52 pages that have appeared as Doc. 14of Vol. 4 of the Einstein edition. The aim of most of the calculations in the Einstein-Besso manuscript is to see whether anearly version of the general theory of relativity, which Einstein had published in June 1913, canaccount for a tiny discrepancy between the observed motion of Mercury and the motion predictedon the basis of Newton’s theory of gravity. This discrepancy is known as the anomalous advanceof Mercury’s perihelion. Exactly what that means will be explained below. The results of the cal-culations by Einstein and Besso were disappointing. The theory, as it stood, could only accountfor part of the discrepancy between observation and Newtonian theory. However, Einstein andBesso’s efforts would not be in vain. The techniques developed in the manuscript for doing thesecalculations could be taken over virtually unchanged in November 1915 to compute the motion of Mercury predicted by the general theory of relativity in its final form. Einstein found that the finaltheory can account for the full effect left unexplained by Newtonian theory. As he later told a col-league, he was so excited about this result that it gave him heart palpitations (Pais 1982, p. 253).The explanation of the anomalous advance of Mercury’s perihelion would become one of thethree classical tests of general relativity. Einstein found and published it in a time span of no morethan a week. With the discovery of the Einstein-Besso manuscript, this impressive feat becomesmore understandable: Einstein had done essentially the same calculation together with Besso twoyears earlier. The study of these earlier calculations has contributed to a fuller understanding of the 1915 perihelion paper.   3  The Einstein-Besso manuscript is not only the key document for understanding the celebratedapplication of the general theory of relativity to the problem of Mercury’s perihelion, but is also of great significance for the historical reconstruction of the genesis of the theory. In letters writtenshortly after his papers of November 1915, Einstein listed three reasons for abandoning the earlierversion of his theory. The fact that the perihelion motion did not come out right was one of them.Another problem he mentioned was that the earlier theory was incompatible with the relativity of rotation. The Einstein-Besso manuscript contains an ingenious calculation, the whole purpose of which was to check whether the theory is compatible with this notion. Einstein was able to con-vince himself that the theory passed this test. However, he made some trivial errors in this calcula-tion. More than two years later, in September 1915, he redid the calculation, this time withoutmaking any errors, and discovered, to his dismay, that the theory failed. In all likelihood, this dis-covery triggered the unraveling of the theory and led Einstein to return to ideas considered andrejected in the Zurich Notebook of some three years earlier. Using the same ideas, he was able tocomplete, in a little over a month, the general theory of relativity as we know it today.  Einstein and Besso: the Eagle and the Sparrow  Einstein’s historic 1905 paper “On the Electrodynamics of Mov-ing Bodies,” in which the theory now known as special relativitywas announced, was unusual for a scientific paper in that it car-ried none of the usual references to the literature of theoreticalphysics. The only individual credited with any contribution to the1905 paper was Michele Angelo Besso, whom Einstein thankedfor “many useful suggestions.” Besso, whom Einstein once char-acterized as a perpetual student, had studied mechanical engineer-ing at the Zurich Polytechnic during the years Einstein wasenrolled in the physics section. The two met at a musical eveningin Zurich and remained lifelong friends. In 1904, on the recom-mendation of Einstein, Besso took a position at the Swiss PatentOffice. Whenever they could, the two friends engaged in long discussions of physics and mathe-matics. Besso played a very important role as a “sounding board” for Einstein, and when Einsteinmoved to Zurich and later Berlin, the two men visited and kept up a lively correspondence. When, shortly after taking up his position in Berlinin 1914, Einstein sent his wife Mileva and his sons Hans-Albert and Eduard back to Zurich, Besso and his wifetook on the role of intermediary between the feudingpartners as their marriage was dissolving. They evencared for the couple’s two sons during Mileva’s illness. In 1913, when Einstein and Besso collaborated onthe calculations in the manuscript under discussion here,Besso was living in Gorizia, near Trieste. The manu-script shows that in this case Besso functioned as consid-erably more than just a sounding board. Although he leftthe hardest parts to Einstein, he did take responsibilityfor some important parts of the calculations. In lateryears, Besso described his scientific collaboration withEinstein with a charming simile: Einstein was an eagle, and he, Besso, a sparrow. Under theeagle’s wing, the sparrow had been able to fly higher than on its own. Michele Besso and his wifeAnna Besso-WintelerAlbert Einstein and Mileva Einstein-Maric(Wedding portrait, 1903)   4  From Special Relativity to General Relativity  Einstein started on the path that would lead him to the general theory of relativity in late 1907. Hewas writing a review article about his 1905 special theory of relativity. The last section of this arti-cle was devoted to gravity. In it, Einstein argued that a satisfactory theory of gravity cannot beachieved within the framework of special relativity and that a generalization of that theory isneeded. This was an extraordinary step to take at the time. Other researchers, such as the greatmathematicians Henri Poincaré and Hermann Minkowski, felt that a perfectly adequate theory of gravitation could be constructed simply by modifying Newton’s theory of gravitation somewhatto meet the demands of special relativity.As Einstein was pondering the problem of gravitation, a thought occurred to him which helater described as “the happiest thought of my life” (Einstein 1920, [p. 21]). It had been knownsince Galileo that all bodies fall alike in a given gravitational field. This is the point of the famous,though most likely apocryphal, story of Galileo dropping bodies of different mass from the lean-ing tower of Pisa and watching them hit the ground simultaneously. Galileo’s insight was incorpo-rated but not explained in Newton’s theory of gravity. It just happens to be the case that two verydifferent quantities in Newton’s theory have the same numerical value: the gravitational mass, ameasure of a body’s susceptibility to gravity, and the inertial mass, a measure of a body’s resis-tance to acceleration. Einstein found it unsatisfactory that the equality of inertial and gravitational mass was just acoincidence in Newton’s theory. He felt that there had to be some deeper reason for it. He pro-posed to explain it by assuming that acceleration and gravity are essentially just one and the samething. If that is true, it is not surprising that inertial mass, having to do with resistance to accelera-tion, and gravitational mass, having to do with susceptibility to gravity, are equal to one another.This idea is the core of what Einstein later dubbed the equivalence principle. Initially, Einsteinformulated the equivalence principle as follows: the situation of an observer uniformly accelerat-ing in the absence of a gravitational field is fully equivalent to the situation of an observer at restin a homogeneous gravitational field. In particular, both observers will find that all free particleshave the same acceleration with respect to them. Formulated in this way, one can readily understand why Einstein felt that the equivalenceprinciple could be used to extend the principle of relativity of his special theory of relativity of 1905, which only holds for uniform motion (i.e., motion with constant velocity), to arbitrarymotion (i.e., accelerated motion, motion with changing velocity). An accelerated observer, Ein-stein reasoned, can always claim to be at rest in some gravitational field equivalent to his or heracceleration. In this manner, Einstein thought he could eliminate once and for all Newton’s con-cept of absolute acceleration and formulate a theory in which all motion is relative: a general the-ory of relativity.Unfortunately, the relation between acceleration and gravity turned out not to be quite as sim-ple as Einstein initially thought. It took him till early 1918—more than two years after he hadpublished the theory in the form in which it is still used today—to give a more accurate formula-tion of the relation between gravity and acceleration. He changed the definition of the equivalenceprinciple accordingly, although he continued to use the old definition in popular expositions of histheory. The connection between gravity and acceleration or inertia is not that the two are alwaysinterchangeable. Rather it is that the effects we ascribe to gravity and the effects we ascribe togravity are both produced by one and the same structure, a structure we now call the inertio-grav-itational field, and which is represented in Einstein’s theory by curved space-time. Observers in
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