Albert Einstein Hand-Annotated Presentation Offprint of "The Formal Basis of the General Theory of Relativity"

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May 10, 2023

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• Lot Description
  Author’s presentation offprint of "Die formale Grundlage der allgemeinen Relativitätstheorie [The Formal Basis of the General Theory of Relativity]" from Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, XLI, 19 November 1914. Berlin: Königlichen Akademie der Wissenschaften. 1914. Gr.-8vo. S. 1030-85. Bound in the original printed wrappers, 7 x 10, inscribed in Einstein's hand, "Mit aller Hochachtung [With all respect]," over the imprinted text, "Überreicht vom Verfasser [Submitted by the Author]." On page 1069, Einstein adds a lengthy formula in his hand, and on page 1072 he writes: "Hier ist benutzt, dass auch das System K 2 dem invarianten [oder: unvariiertem] Felde angepasst ist [Here it is used that the system K 2 is also adapted to the invariant [or: unvarying] field].". In fine condition, with a light central vertical fold, and soiling and handling wear to the covers. Accompanied by a letter of authentication from Viennese Antiquarian Book Dealer Ingo Nebehay, 1982.
  
  
  
  First edition of this extremely rare offprint, a remarkable association copy. The present paper was the crucial step between Einstein’s Entwurf theory of 1913 and the final form of general relativity which Einstein completed in November 1915: it develops the mathematical techniques necessary for the final formulation, namely the ‘absolute differential calculus’ of Tullio Levi-Civita, as well as the expression of the field equations in terms of a variational principle, which later proved to be of great importance. This author’s presentation offprint, with “Überreicht vom Verfasser” printed on upper wrapper, must not to be confused with the much more common trade offprint which lacks this printed statement (see below). We have located only one copy of this author’s presentation offprint at auction, in the collection belonging to Einstein’s son Hans Albert sold at Christie’s in 2006 (there was no copy in Einstein’s own collection of his offprints sold by Christie’s in 2008).
  
  
  
  “In summer 1914, Einstein felt that the new theory should be presented in a comprehensive review. He also felt that a mathematical derivation of the field equations that would determine them uniquely was still missing. Both tasks are addressed in a long paper, presented in October 1914 to the Prussian Academy for publication in its Sitzungsberichte. It is entitled ‘The formal foundation of the general theory of relativity’; here, for the first time, Einstein gave the new theory of relativity the epithet ‘general’ in lieu of the more cautious 'generalized' that he had used for the Entwurf” (Landmark Writings in Western Mathematics 1640-1940). “In the year that he was called to Berlin, on October 29, 1914, Einstein was able to present his work “Die formale Grundlage der allgemeinen Relativitätstheorie”‰Û_The “formal foundation” of the general theory of relativity was the tensor calculus. Without the tensor calculus, the general theory of relativity could not have been formulated‰Û_By October 1914, Einstein was finally able to present his results in mathematical form, and indeed in a manner that became the basis of his general theory of relativity of 1916. He introduced general covariants, contravariants, and also—what was new—mixed tensors, in order to represent the individual arithmetic operations, above all, the various types of multiplication. Thus the mathematical calculus necessary for the general theory of relativity was at the ready in 1914” (Reich). “The principal novelty [in the present paper] lies in the mathematical formulation of the theory. Drawing on earlier work with [Marcel] Grossman, Einstein formulated his gravitational field equations using a variation principle” (Calaprice, 47).
  
  
  
  The first important stage in the development of Einstein’s theory of gravitation was accomplished, with his friend and classmate the mathematician Marcel Grossmann, in their 1913 work Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation. “In this book, Einstein and Grossman investigated curved space and curved time as they relate to a theory of gravity. They presented virtually all the elements of the general theory of relativity with the exception of one striking omission: gravitational field equations that were not generally covariant. Einstein soon reconciled himself to this lack of general covariance through the ‘hole argument,’ which sought to establish that generally covariant gravitational field equations would be physically uninteresting” (Calaprice 40). Einstein’s ‘hole argument’, he believed, implied that general covariance was incompatible with the requirement that the distribution of mass-energy should determine the gravitational field uniquely. He believed, therefore, that the field equations should only be valid in certain coordinate systems, which he called ‘adapted’, and that only coordinate transformations from one adapted system to another adapted system should be allowed - he called these ‘justified coordinate transformations’.
  
  
  
  “Einstein’s move to Berlin in April 1914 marked the end of his collaboration with Grossmann. Fortunately, by this time Einstein no longer seems to have needed Grossmann’s mathematical guidance. By October 1914, he had completed a lengthy summary article [offered here] on his new theory, whose form and detailed nature suggest that Einstein felt his theory had reached its final form. The article contained a review of the methods of tensor calculus used in the theory and, flexing his newfound mathematical muscles, Einstein could even promise to give new and simpler derivations of the basic laws of the ‘absolute differential calculus’. Of great importance was the fact that Einstein had taken the new mathematical techniques of his last paper with Grossmann, generalized them and found in them a quite new derivation of the field equations” (Norton, p. 293).
  
  
  
  This new derivation made use, for the first time in Einstein’s work on the theory of gravity, of an action principle (or variational principle). Einstein worked initially with an action that was an arbitrary function of the metric tensor and its first derivatives, and then showed that with a particular choice of the action he could recover the Entwurf field equations. He further believed that he had found a simple general covariance condition which forced the action to take the Entwurf form. “Einstein had good reason to be pleased with this result. For it seemed to show that his theory was not just a theory of gravitation, but a generalized theory of relativity, in so far as it was concerned with establishing the widest covariance possible in its equations. His original derivation of the field equations [in Entwurf] had been based squarely on considerations in gravitation theory‰Û_The new derivation, however, focused on covariance considerations. He had found a simple way of formulating field equations that would have exactly the maximum covariance allowed by the ‘hole argument’, and they led him almost directly to his original Entwurf field equations. As a result he could promise to “recover the equations of the gravitational field in a purely-covariant-theoretical way” and claim to “have arrived at quite definite field equations in a purely formal way, i.e., without directly drawing on our physical knowledge of gravitation”‰Û_
  
  
  
  “Einstein appears to have remained satisfied with the theory he developed in 1914 through the first half of 1915. In March, April and early May he defended the theory wholeheartedly in an intense correspondence with Levi-Cività, who challenged Einstein’s derivation of the covariance properties of his gravitation tensor. But it seems that by mid-July he was less certain‰Û_By mid-October Einstein’s points of dissatisfaction with his theory had grown in number and intensity. They soon culminated in some of the most agitated and strenuous works of his life, in which generally covariant field equations were discovered‰Û_Einstein’s work [in the present paper] had brought him both temporally and conceptually closer than ever before to a generally covariant theory‰Û_It is hard to imagine that Einstein was unprepared for the ease with which his formalism of 1914 could be applied to his final generally covariant theory” (Norton, pp. 296-303).
  
  
  
  After publishing the generally covariant theory in November 1915, Einstein gave a further treatment of the variational formulation (Hamiltonsches Prinzip und allgemeine Relativitätstheorie, Sitzungsberichte (1916), pp. 1111-1116). By this time, the great German mathematician David Hilbert had published his own account of general relativity in terms of a variational principle [Die Grundlagen der Physik (Erste Mitteilung), Nachrichten der Königliche Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse, November 1915, 395-407]. This led to some controversy over who had been the first to publish the final version of general relativity (although Hilbert himself never claimed priority). “Hilbert, through his important paper of November 1915, is generally thought of as introducing the comprehensive use of these action principles to the theory. My analysis shows that although Einstein might have drawn some of his work of 1916 in this area from Hilbert’s, his basic mathematical apparatus and even the notation itself had its ancestry in his own work earlier in 1914 and 1915” (Norton, p. 303).
  
  
  
  This author’s presentation offprint is of extreme rarity, and must be distinguished from other so-called ‘offprints’ of papers from the Berlin Sitzungsberichte, many of which are commonly available on the market. The celebrated bookseller Ernst Weil (1919-1981), in the introduction to his Einstein bibliography, wrote: “I have often been asked about the number of those offprints. It seems to be certain that there were few before 1914. They were given only to the author, and mostly ‘Überreicht vom Verfasser’ (Presented by the Author) is printed on the wrapper. Later on, I have no doubt, many more offprints were made, and also sold as such, especially by the Berlin Academy.” If the term ‘offprint’ means, as we believe it should, a separate printing of a journal article given (only) to the author for distribution to colleagues, then ‘offprints’ were not commercially available. Although there is certainly some truth in Weil’s remark, in our view it requires clarification and explanation.
  
  
  
  Until about 1916, most of Einstein’s papers were published in Annalen der Physik; from 1916 until he left Germany for the United States in 1933, most were published in the Berlin Sitzungsberichte. The Sitzungsberichte differed from other journals in which Einstein published in that it made separate printings of its papers commercially available. These separate printings have ‘Sonderabdruck’ printed on the front wrapper, the usual German term for offprint, but they are not offprints according to our definition. They were available to anyone; indeed a price list of these ‘trade offprints’ is printed on the rear wrapper. True author’s presentation offprints can be distinguished from these trade offprints by the presence of ‘Überreicht vom Verfasser’ on the front wrapper.
  
  
  
  In the period 1916 to 1919 or 1920, the Sitzungsberichte trade offprints are themselves rare: for example, ABPC/RBH list only three ‘offprints’ of Einstein’s famous 1917 Sitzungsberichte paper ‘Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie’ (the auction records do not distinguish between trade and author’s presentation offprints). After 1919 or 1920, however, the trade offprints became much more common, although the author’s presentation offprints are still very rare. The reason for this change is that it was only in 1919 that Einstein became famous among the general public.
  
  
  
  It might seem obvious that Einstein’s fame dates from 1905, his ‘annus mirabilis’, in which he published his epoch-making papers on special relativity and the light quantum. However, these works did not make him immediately well known even in the physics community - many physicists did not understand or accept his work, and it was two or three years before his genius was fully accepted even by his colleagues. He secured his first academic position, at the University of Bern, in 1908. Among the general public, Einstein became well known only in late 1919, following the success of Eddington’s expedition to observe the bending of light by the Sun, which confirmed Einstein’s general theory of relativity. This was front-page news, and made Einstein universally famous. (See Chapter 16, ‘The suddenly famous Doctor Einstein’, in Pais, Subtle is the Lord, for an account of these events). Before 1919 the trade offprints of Einstein’s papers would probably only have been purchased by professional physicists; after 1919 everyone wanted a memento of the famous Dr. Einstein, whether or not they understood anything of theoretical physics, and the trade offprints of his papers were printed and sold in far greater numbers than before to meet the demand. It is telling that when these post-1919 trade offprints appear on the market, they are often in mint condition - they were never read simply because their owners were unable to understand them.
  
  
  
  Boni 65; Weil 68. Calaprice, The Einstein Almanac; Norton, ‘How Einstein Found His Field Equations: 1912-1915’, Historical Studies in the Physical Sciences 14 (1984), pp. 253-316; Norton, ‘Einstein and Nordström: some lesser-known thought experiments in gravitation,’ pp. 3-30 in The Attraction of Gravitation: New Studies in the History of General Relativity, edited by John Earman, Michel Janssen, John D. Norton, 1993; Reich, Einstein’s “Formal Foundations of the General Theory of Relativity” (1914) (http://mathineurope.eu/images/information_pic/hist_phil_pic/calendar_pic/2014einstein/Einstein_English.pdf). For the history of tensor calculus, including Einstein’s application of it to general relativity, see Reich, Die Entwicklung des Tensorkalküls, Birkhäuser 2012.
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