Einstein

1916 · 6408 — Berlin: Königlichen Akademie der Wissenschaften 1916. First edition. <p>First editions extremely rare author's presentation offprint not to be confused with the much more common trade separate - see below from the library of the great German physicist Arnold Sommerfeld of Einstein's derivation of the field equations of gravitation from a variational principle. This was the first time Einstein had derived the field equations of gravitation in arbitrary coordinates - in his celebrated 1915 papers he derived the equations in generally-covariant form but only in special 'unimodular' coordinates.</p>. THE GRAVITATIONAL EQUATIONS FROM A VARIATIONAL PRINCIPLE. <p>First editions extremely rare author's presentation offprint not to be confused with the much more common trade separate - see below from the library of the great German physicist Arnold Sommerfeld of Einstein's derivation of the field equations of gravitation from a variational principle. This was the first time Einstein had derived the field equations of gravitation in arbitrary coordinates - in his celebrated 1915 papers he derived the equations in generally-covariant form but only in special 'unimodular' coordinates. In the early 19th century William Rowan Hamilton 1805-65 showed that Newton's equations of motion for a classical mechanical system were equivalent to the statement that the 'action' of the system now called the Lagrangian has a stationary value generally a minimum. A first variational approach to the gravitational field equations of general relativity was unsuccessfully sketched by Einstein and Marcel Grossmann in 1913-1914 and subsequently by Einstein himself in 1914 the so-called Entwurf Theory. But Einstein's 1914 theory was invalidated by a misconception related to the physically unjustified requirement of restricting the covariance of the gravitational field equations and by some mathematical errors in a crucial proof in the theory. Between March and May 1915 the Italian mathematician Tullio Levi-Civita 1873-1941 in his private correspondence with Einstein singled out the mathematical flaws of the Entwurf theory setting Einstein back on the path of general covariance which eventually brought him in November 1915 to the correct formulation of the gravitational field equations. Also in November 1915 the great German mathematician David Hilbert 1862-1943 published an article in which he correctly showed that Einstein's gravitational field equations could be obtained from a variational principle at least in the presence of an electromagnetic field. Five days later independently of Hilbert Einstein obtained in the present paper the same results thus obtaining the definitive variational formulation of the field equations. Einstein considered his approach to be more general than Hilbert's as Hilbert had made some hypotheses about matter which Einstein dispensed with Einstein also refused to accept the electromagnetic origin of matter which Hilbert had assumed. In the course of this paper Einstein also proved a special case of Emmy Noether's second theorem on the relation between symmetry and conservation laws which she published in full generality two years later. The only author's presentation offprint listed on RBH is that is the collection of Einstein's son Hans Albert Christie's 2006; it was not in Einstein's own collection of his offprints Christie's 2008.</p> <br /> <p>Provenance: Arnold Sommerfeld 1868-1951 his characteristic numbering in red pencil '33' on front cover. "The son of a physician Sommerfeld was educated at the University of Königsberg. After teaching briefly at the universities of Göttingen Clausthal and Aachen he was appointed professor of physics at the University of Münich in 1906. Sommerfeld should have retired in 1936 in favour of his pupil Werner Heisenberg. Opposition from the Nazi party to Heisenberg's appointment prolonged Sommerfeld's tenure and it was not in fact until late 1939 that he finally retired to be succeeded not by Heisenberg but by Wilhelm Müller a Nazi aerodynamicist without a single publication in physics to his credit. Although Sommerfeld and Heisenberg were not Jewish they were regarded by the Nazis as Jewish sympathizers. Sommerfeld however survived the war and returned to his Münich chair in 1945 continuing to work at physics until he died in a car accident in 1951" Oxford Reference. "Arnold Sommerfeld was one of the most distinguished representatives of the transition period between classical and modern theoretical physics. The work of his youth was still firmly anchored in the conceptions of the nineteenth century; but when in the first decennium of the century the flood of new discoveries experimental and theoretical broke the dams of tradition he became a leader of the new movement and in combining the two ways of thinking he exerted a powerful influence on the younger generation. This combination of a classical mind to whom clarity of conception and mathematical rigour are essential with the adventurous spirit of a pioneer are the roots of his scientific success while his exceptional gift of communicating his ideas by spoken and written word made him a great teacher" Max Born p. 275. </p> <br /> <p>"Einstein's first paper on a metric theory of gravity co-authored with his mathematician friend Marcel Grossmann was published as a separatum in early 1913 and was reprinted the following year in Zeitschrift für Mathematik und Physik. Most of the formalism of general relativity as we know it today was already in place in this Einstein-Grossmann theory. Still missing were the generally-covariant Einstein field equations .</p> <br /> <p>"In the fall of 1915 Einstein came to the painful realization that the 'Entwurf' field equations are untenable. Casting about for new field equations he fortuitously found his way back to equations of broad covariance that he had reluctantly abandoned three years earlier . on November 4 1915 presented the rediscovered old equations to the Berlin Academy. He returned a week later with an important modification and two weeks after that with a further modification .</p> <br /> <p>"When it was all over Einstein commented with typical self-deprecation: 'unfortunately I have immortalized my final errors in the academy-papers;' and 'it's convenient with that fellow Einstein every year he retracts what he wrote the year before.' What excused Einstein's rushing into print was that he knew that the formidable Göttingen mathematician David Hilbert was hot on his trail. Nevertheless these hastily written communications to the Berlin Academy proved hard to follow even for Einstein's staunchest supporters such as the Leyden theorists H. A. Lorentz and Paul Ehrenfest . Ehrenfest's queries undoubtedly helped Einstein organize the material of November 1915 for an authoritative exposition of the new theory .</p> <br /> <p>"In March 1916 Einstein sent his new review article 'Die Grundlage der Relativitätstheorie' to Wilhelm Wien editor of the Annalen . In this paper the field equations and energy-momentum conservation are not developed in generally-covariant form but only in special coordinates. Einstein had found the Einstein field equation in terms of these coordinates in November 1915. This part of the review paper is basically a sanitized version of the argument that had led Einstein to these equations in the first place .</p> <br /> <p>"As he was writing his review article he was already considering redoing the discussion of the field equations and energy-momentum conservation in arbitrary coordinates. In November 1916 he published such a generally-covariant account in the Berlin Sitzungsberichte the offered paper. This paper is undoubtedly much more satisfactory mathematically than the corresponding part of the review article but it does not offer any insight into how Einstein actually found his theory.</p> <br /> <p>Reading the offered paper without having read the November 1915 papers and the 1916 review article one easily comes away with the impression that Einstein hit upon the Einstein field equations simply by picking the mathematically most obvious candidate for the gravitational part of the Lagrangian for the metric field namely the Riemann curvature scalar. This is essentially how Einstein himself came to remember his discovery of general relativity. He routinely trotted out this version of events to justify the purely mathematical speculation he resorted to in his work on unified field theory.</p> <br /> <p>"In this paper he derived the generally-covariant field equations from an action principle with the Riemann curvature scalar as the Lagrangian . The present paper fills two important gaps in the review article. First Einstein derived the generally-covariant version of the Bianchi identities which in conjunction with the field equations imply energy-momentum conservation . Second Einstein showed that the identities guaranteeing energy-momentum conservation are a direct consequence of the covariance of the action functional. Einstein had thus in a mathematically impeccable way found a special case of one of Noether's theorems published two years later.</p> <br /> <p>"From a purely mathematical point of view the discussion of the field equations and energy-momentum conservation in the present paper is far more elegant than in the review article. This more elegant treatment however obscures the way in which Einstein found the Einstein field equations. It makes it look as if it was a matter ofpicking the most obvious candidate for the Lagrangian the Riemann curvature scalar at which point everything else fell into place. Ironically this is exactly what Einstein in his later years came to believe himself in part no doubt because it made his successful search for the field equations of general relativity look so similar to his fruitless search for a unified field theory. The clumsier discussion in unimodular coordinates in the review article however may serve as a reminder that-whatever he believed said or wrote about it later on-Einstein only discovered the mathematical high road to the Einstein field equations after he had already found these equations at the end of a poorly paved road through physics. Serving as road signs were Newton's gravitational theory Maxwell's electrodynamics and such key results of special relativity as the law of energy-momentum conservation. Considerations of mathematical elegance played only a subsidiary role" Janssen.</p> <br /> <p>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.</p> <br /> <p>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 separates by the presence of 'Überreicht vom Verfasser' on the front wrapper.</p> <br /> <p>In the period 1916 to 1919 or 1920 the Sitzungsberichte trade separates are themselves rare. After 1919 or 1920 however the trade separates become 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.</p> <br /> <p>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. Einstein did not secure an academic position until 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 separates 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 separates 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 separates appear on the market they are often in mint condition - they were never read simply because their owners were unable to understand them.</p> <br /> <p>BRL 90; Weil 88. Born 'Arnold Johannes Wilhelm Sommerfeld 1868-1951' Obituary Notices of Fellows of the Royal Society 8 1952 pp. 275-296. Janssen 'Einstein's First Systematic Exposition of General Relativity' 2004 .</p> <br/> <br/> 8vo 252 x 180 mm pp. 1111-1116. Original orange printed wrappers light vertical crease for posting. Königlichen Akademie der Wissenschaften unknown