EINSTEIN, Albert.

I. Zur allgemeinen Relativitätstheorie. II. Einheitliche Feldtheorie von Gravitation und Elektrizität. [With:] III. Riemann-Geometrie mit Aufrechterhaltung des Begriffes des Fernparallelismus [With:] IV. Neue Möglichkeit für eine einheitliche Feldtheorie von Gravitation und Elektrizität [With:] V. Zur einheitlichen Feldtheorie. Author’s presentation offprints (“Überreicht vom Verfasser”) from Sitzungsberichte der Preussichen Akademie der Wissenschaften Phys.-Math. Klasse V, 1923; XXII, 1925; XVII, 1928; XVIII, 1928; I, 1929.

Berlin: Akademie der Wissenschaften, 1923-25-28-28-29.

First edition, extremely rare author’s presentation offprints ((“Überreicht vom Verfasser”, not to be confused with the much more common trade separates – see below), from the library of the great German physicist Arnold Sommerfeld, of Einstein’s most important early publications on unified field theory. Einstein’s work on unified field theory was inspired by James Clerk Maxwell’s success in finding a unified theory of electricity and magnetism, one of the greatest achievements of nineteenth-century physics, which showed that light was a form of electromagnetic wave, and made possible modern inventions such as radio, television and the telephone. Einstein’s contributions in this area represent about a quarter of his entire research output and half his scientific production after 1920. Although he was ultimately unsuccessful, a similar vision was realized in the decades after his death in the construction of the ‘standard model’, a unified theory of electromagnetism with the weak and strong nuclear forces (which were unknown in Einstein’s time), and efforts to incorporate gravity into the model continue to this day. ‘Zur allgemeinen Relativitätstheorie’, written on board ship during his return journey from Japan, “gives us insight into the workings of Einstein’s mind as it searched for a unified theory of gravitation and electromagnetism, a search that would dominate his thinking for the rest of his life” (Collected Papers 13, p. lxxvii). ‘Einheitliche Feldtheorie von Gravitation und Elektrizität’ was the first paper to use the term ‘Unified Field Theory’ in its title. In its opening paragraph, Einstein wrote: “After incessant search during the last two years, I now believe I have found the true solution” (Pais, Subtle is the Lord, p. 343). The half-dozen papers Einstein had already written on unified field theory were reactions to the ideas of others, such as Eddington, Kaluza and Weyl; it was in this paper that Einstein put forward the first original approach of his own. “His theory rested in major part on the following arithmetical coincidence. In one of the customary ways of describing electromagnetism 6 field quantities are used. The metrical tensor [of general relativity] has a certain symmetry. Remove that symmetry and it will automatically contain not 10 but 16 field quantities. Use 10 combinations of these for gravitation and there will be 6 left over – just the number of field quantities with which to represent electromagnetism” (Hoffmann, Einstein, p. 225). In 1928, Einstein embarked upon a new approach to a unified field theory involving what he called ‘distant parallelism.’ This was introduced in ‘Riemann-Geometrie mit Aufrechterhaltung des Begriffes des Fernparallelismus’ and ‘Neue Möglichkeit für eine einheitliche Feldtheorie von Gravitation und Elektrizität.’ By early 1929 he had solved the main problems involved in writing down field equations for his unified theory and presented his solution in ‘Zur einheitlichen Feldtheorie’. “[Einstein] did propose [in this last paper] a set of field equations, but added that ‘further investigations will have to show whether [these] will give an interpretation of the physical qualities of space’. His attempt to derive his equations from a variational principle had to be withdrawn. Nevertheless, in 1929 he had ‘hardly any doubt’ that he was on the right track” (Pais, p. 346). “Within three days, the first printing of the journal offprint [i.e., the commercial separate]—a thousand copies—sold out, and another thousand copies were soon printed. Soon thereafter, Nature’s News and Views section published a more accessible account of the work, including a quote by Einstein: ‘Now, but only now, we know that the force which moves electrons in their ellipses about the nuclei of atoms is the same force which moves our earth in its annual course about the sun, and is the same force which brings to us the rays of light and heat which make life possible upon this planet.’ With Einstein’s 50th birthday approaching, his new idea rapidly caught fire, at least in the popular press. The New York Times published almost a dozen articles that year about distant parallelism, rivaling its coverage of the 1919 eclipse results” (Halpern). “In this frenzied, unscientific atmosphere, Einstein’s new theory was hailed in the press as an outstanding scientific advance. Yet Einstein had stated in his article that it was still tentative; and soon he found he had to abandon it” (Hoffman, p. 226). Only paper III was present in the collection of presentation offprints of Einstein’s son Hans Albert (Christie’s 2006), and in Einstein’s own collection (Christie’s 2008); and no other copies of any of the offprints with “Überreicht vom Verfasser” can be identified on RBH. Similarly, although several copies of each offprint can be found in institutional collections, it is unclear how many are presentation offprints as the library records do not mention “Überreicht vom Verfasser”.

Provenance: Arnold Sommerfeld (1868-1951) (his ink stamp on the front cover of III-V and characteristic numbering in red pencil on each – 40, 45, 47, 48, 49). “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).

“Einstein’s early work on the unification program after the completion of the theory of general relativity was, by and large, a reaction to approaches advanced by others. This is the case for the first geometrization of the electromagnetic field, proposed in 1918 by Hermann Weyl; for the first exploration of a five-dimensional theory suggested by Theodor Kaluza in 1919; and for the first attempt to base a unified field theory on the concept of the affine connection, rather than on the metric field, as advanced by Arthur Eddington in 1921” (Sauer, pp. 289-90).

Weyl (1885-1955) had introduced a new geometrical object into the theory that he called a “length connection,” and he used it to establish a link between the geometrical structure, given by the length connection, and the electromagnetic field. Einstein was initially enthusiastic about Weyl’s idea, calling it “a first-class stroke of genius,” but quickly found a serious objection to it, showing that it implied that the wavelength of light emitted by a radiating atom would depend on the prehistory of that atom, contrary to observation. Nevertheless, in March 1921, Einstein elaborated on Weyl’s theory in his paper ‘Uber eine naheliegende Ergänzung des Fundamentes der allgemeinen Relativitätstheorie.’

Another idea to which Einstein responded was put forward as early as 1919 by Theodor Kaluza (1885-1954), at the time Privatdozent in mathematics at the University of Königsberg; he introduced the concept of a fifth dimension to the underlying space-time manifold of general relativity and attempted to represent the electromagnetic field in terms of the additional components of the metric tensor. Einstein showed that for the equation of motion of an electron, Kaluza’s theory predicted that the influence of the gravitational field was larger by many orders of magnitude than any reasonable physical interpretation would allow for. Nevertheless, Einstein later encouraged Kaluza to publish his idea and Einstein and Jakob Grommer (1879-1933) published a response to it in 1923 (‘Beweis der Nichtexistenz eines überall regulären zentrisch symmetrischen Feldes nach der Feld-Theorie von Kaluza’).

A third approach toward a unified field theory was advanced most notably by Eddington (1882-1944) in the early twenties and was also taken up by Einstein. The idea was to base the theory on the concept of an affine connection as the fundamental mathematical quantity, rather than on the metric tensor. The associated (Ricci) curvature of spacetime is not then, in general, a symmetric tensor, and Eddington suggested that the anti-symmetric part of the curvature could be identified with the electromagnetic field, the symmetric part being the usual metric. Eddington did not, however, provide the field equations that would determine the affine connection, a problem Einstein addressed in ‘Zur allgemeinen Relativitätstheorie’ [paper I]. Einstein identified the symmetrized part of the Ricci tensor with the ‘natural’ metric of the theory, and, like Eddington, he linked the antisymmetrized Ricci tensor to the electromagnetic field. Einstein’s criticism of Eddington’s approach focused on Eddington’s failure to provide field equations that determine all forty connection coefficients, and the derivation of such field equations became the focal point of the published paper. Lastly, Einstein explicitly introduced a scale factor λ that mediates between the scale of the ‘natural’ metric defined by the Ricci tensor and that of the physical metric.

“With Einstein’s response to Weyl, Kaluza, and Eddington in the early twenties we find him reacting to approaches that had been advanced by others … The first original approach put forward by Einstein himself was published in a paper of 1925 [paper II] in which also the term ‘unified field theory’ appeared for the first time in a title. In that paper, he explored a metric-affine approach, i.e., he took both a metric tensor field and a linear affine connection at the same time as fundamental variables. Both connection and metric were assumed to be asymmetric. Parallel transport then again defines a Ricci tensor and a Riemann curvature scalar, and Einstein defined tentative field equations in terms of a variational principle, taking the Riemann scalar as a Lagrangian just as in standard general relativity. As regards the interpretation of the mathematical objects, he tried to associate the gravitational and electromagnetic fields with the symmetric and anti-symmetric parts of the metric field. In his attempt to recover the known cases, he could show that the metric was symmetric for the purely gravitational case and the usual compatibility condition for the Levi-Civita connection can be recovered. Maxwell’s equations could be recovered, in the limit of weak gravitational fields, but only in a slightly different form that is not entirely equivalent to the original equations.

“The basic problem of this approach seems to have been that Einstein did not know how to go on from here. Dealing with both an asymmetric metric tensor and an asymmetric connection opened up a vast field of possibilities inherent in the mathematical framework, and many familiar results of the theory of Riemannian geometry no longer held. In particular, verifying the existence of non-singular, spherically symmetric charge distributions posed a formidable challenge. It was also unclear how to explicitly investigate the non-vacuum case beyond the first order approximation of weak gravitational fields. Einstein did not pursue this approach any longer in print but he did take it up once more, twenty years later, as his final approach toward a unified field theory, working on it until his death” (Sauer, pp. 293-5).

“At some point in May 1928, while convalescing at home in Berlin, Einstein had an idea for what he thought was ‘an entirely new way of realizing the general theory of relativity and that may be groundbreaking.’ Key to this new approach was the notion of a field of mutually orthogonal, normal vectors, defined on the space-time manifold. This was a so-called n-Bein-Feld, or, in more modern terminology, for n = 4, a field of tetrads. Such a theory admits the definition of a natural notion of distant parallelism by identifying vectors on this orthonormal frame field. Two vectors at distant points of the manifold are parallel, by definition, if they are represented by the same vector of the orthonormal frames at the respective points. The manifold also carries a Riemannian metric, which can be expressed in terms of the tetrad field. Since the tetrad field determines the metric field, but not the other way around, the tetrads provide more degrees of freedom, which Einstein hoped could be put to use to provide a representation of the electromagnetic field.

“At Einstein’s request, on 7 June 1928, Max Planck presented a brief note on this ‘Riemannian Geometry Retaining the Concept of Distant Parallelism’ [paper III] to the Prussian Academy for publication in its Proceedings. Since Einstein was not sure at the time whether the notion of Fernparallelismus, that is, distant parallelism or teleparallelism, and its associated geometric concepts, were known in the mathematical literature, he asked Planck to inquire among his mathematician colleagues whether any of this was known before submitting the paper for publication. Planck did not find the occasion to do as requested but nevertheless submitted the paper.

“Only a week later, Einstein realized how to put the geometry of distant parallelism to use for his project of a unified theory of both the gravitational and the electromagnetic fields. The idea was to postulate a variational principle for an invariant action integral that depended on the tetrad field as the dynamical variable.

“From this perspective, the problem presented itself as a fairly well-defined mathematical problem but posed difficulties of interpretation in terms of physical concepts. From the mathematical side, the required invariance of the variational integral created a clearly defined problem. One needed to identify all possible invariants that can be constructed from the tetrads as well as a combination of these invariants that would be suitable as a Lagrangian for the variational integral. Second, variation with respect to the tetrad field would produce differential equations that had to be associated with the known field equations of gravitation and electromagnetism in certain limiting cases. Third, solutions for the differential equations had to be found. Finally, Einstein later would become interested in finding identities that would be satisfied by the tetrads by virtue of general covariance, or that might be postulated to derive field equations. As far as the physical interpretation was concerned, the metric field would take on its old role, as in the general theory, namely corresponding to the gravitational field. But the electromagnetic field also had to be identified with quantities occurring in the geometric framework.

“As a first step, Einstein identified the relevant possible invariants to be constructed from the tetrads. He also realized that in addition to the possibility of constructing a metric-compatible Levi-Civita connection from the metric, as well as the associated notion of parallel transport, the tetrad field allowed the definition of another connection with its notion of parallelism. In contrast to the Levi-Civita connection, the teleparallel connection is asymmetric and describes a geometry that has vanishing Riemann curvature. Instead, it is characterized by the nonvanishing of a tensorial quantity constructed from the teleparallel connection that is now known as the torsion tensor. Taking the mathematical expression of torsion, a third-rank tensor, Einstein tentatively identified its contraction with the electromagnetic four-potential. And settling on what seemed to be the simplest invariant to be taken as a basis for a tentative field theory, Einstein succeeded in deriving, to first approximation in the field components, both the gravitational field equations of general relativity as well as an equivalent version of the Maxwell equations.

“Again, a brief note on this work was presented by Planck to the Academy, on 14 June 1928, and was published in July under the title ‘New Possibility for a Unified Field Theory of Gravitation and Electricity’ [paper IV]. These two notes mark the beginning of a search for a unified field theory in this teleparallel framework that would preoccupy Einstein for the next two or three years …

“The new approach to unified field theory opened the possibility of finding solutions to long-standing problems, and work along these lines continued with intense phases of calculation and collaboration, partly done when Einstein withdrew from public life and spent extended periods of time in secluded residences in Scharbeutz and Gatow or, later, in Caputh. However, in mid-December 1928, difficulties in working out the consequences of the new differential equations had piled up to such a point that Einstein reconsidered the basis of their derivation by means of Hamilton’s principle. On 13 December, he wrote to [his collaborator Chaim Herman] Müntz that he had a ‘simple, bold idea that will throw Hamilton’s principle overboard’. Instead of trying to recover the Maxwell equations in some acceptable limit, he would now ‘put the cart before the horse’ and ‘choose the field equations in such a way that I can be certain that they will lead to the Maxwell equations’. But yet again, things turned out to be more difficult, and for a few days in late December he reverted to the ‘old Hamilton method once again’. But over the New Year’s break, on another retreat in Gatow, Einstein gave up again on the variational approach and derived field equations based instead on some identities. On 27 December, he wrote to Müntz: ‘EUREKA!,’ convinced that he had found a solution that was ‘so splendid, nothing nicer could be imagined’.

“The new progress was written up in a brief paper, completed by 5 January 1929. Einstein was exhausted but happy about this new paper, ‘lying finished in front of me, compressed into seven pages under the title ‘Unified Field Theory’.’ To his son Eduard, he wrote on the same day that he was ‘very happy’ because he had ‘more or less completed my life’s work’. The paper was submitted on 10 January 1929 for publication in the Prussian Academy’s Proceedings and appeared under the somewhat less assertive title ‘On Unified Field Theory’ [paper V].

“When published, the paper made a big splash in the press and received much public attention. A press release appeared in the New York Times on 11 January, and reports followed on 12 January in the German and international press. The paper was reprinted in a record number of copies, and Einstein wrote a popular exposition, English translations of which appeared in the London Times and the New York Times, as well as in the Observatory. In Britain, Nature contacted Einstein for a copy in order to report on it, a request that Einstein diverted to Eddington. The latter informed Einstein a little later about the craze that his latest publication had stirred in London, where ‘one of our great Department Stores in London (Selfridges) has pasted up in its window your paper (six pages pasted up side-by-side) so that passers-by can read it all through. Large crowds gather round to read it!’.

“The paper is indeed a rather technical brief note, as Einstein soon pointed out, and ‘no occasion for anybody to be excited about it’ as there will be ‘only a few mathematicians who will be inclined to read it’. In a letter to Karl Kerkhof, he admitted that he himself might carry some responsibility for the excitement since he ‘may have alluded to it in speaking with one or another of my friends’. Among them was Hans Reichenbach, who reported on the new approach in a column in the Vossische Zeitung before Einstein’s printed paper was actually issued, and thereby caused a deep rift between them. In any case, it soon became clear that the brief paper would not be the last word on the theory. Already the published version carried an addendum, in which Einstein indicated a simpler way of looking at things” (Collected Papers 16, pp. lxiv-lxix).

“Einstein soon was to learn that the mathematical concept of distant parallelism was by no means new and had already been explored by mathematicians, notably by Roland Weitzenböck and Élie Cartan. While immediately acknowledging the priority of others as far as the mathematics was concerned, Einstein nevertheless held high hopes for his idea of formulating a unified field theory within this structure. For him, the critical question was to find a field equation for the components of the dynamical tetrad fields. Each field of tetrads defines a metric tensor field. But the converse is not true, since the metric tensor components can only fix ten of the sixteen components of a tetrad. The additional six degrees of freedom are just what would be needed, so he thought, to accommodate the six degrees of freedom of the Maxwell field in a unified description of gravitation and electromagnetism.

“The story of the distant parallelism approach can be told largely as a story of attempts to find and justify a uniquely determined set of field equations for the tetrad components, with the demand that solutions of those field equations be given a sensible physical interpretation. The distant parallelism approach in this respect shows a number of marked similarities with Einstein’s search for general relativistic field equations of gravitation in the years 1912-15. In 1912, it had been the introduction of the metric tensor into the theory that had started Einstein’s research, and existing mathematical theorems had to be adapted to the theory. In 1928, it was the tetrad fields that allowed the investigation of a non-Euclidean geometry of vanishing curvature and, similarly, Einstein was made aware of existing mathematical results by mathematician colleagues. In both cases, Einstein’s research quickly focussed on finding a set of field equations for the dynamical variables and, in both cases, it was difficult to satisfy all heuristic requirements. In response to these difficulties, Einstein changed back and forth between two different and complementary strategies, each starting from one particular set of heuristic postulates. In both episodes, Einstein at one point settled on a set of field equations that was justified more by physical considerations rather than by mathematical soundness. In both cases, Einstein continued to work out consequences of the field equations as well as continued to find a satisfactory mathematical justification for these equations. And finally, the demise of both theories came about by a combination of realizing more and more shortcomings of the theory and by discovering that an alternative approach promised to be more successful. However, while in 1915 the more successful theory that Einstein substituted for his earlier so-called Entwurf theory was the final version of general relativity, the successor approach to the distant parallelism episode turned out to be yet another attempt at a unified field theory” (Sauer, pp. 296-7).

These author’s presentation offprints are 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 separates by the presence of ‘Überreicht vom Verfasser’ on the front wrapper.

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.

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.

I. BRL 140; Weil 131. II. BRL 155; Weil 147. III. BRL 174; Weil 161. IV. BRL 175; Weil 162. V. BRL 183; Weil *165, cf. PMM 416. Born, ‘Arnold Johannes Wilhelm Sommerfeld 1868-1951,’ Obituary Notices of Fellows of the Royal Society 8 (1952), pp. 275-296. Halpern, ‘Albert Einstein, celebrity physicist,’ Physics Today 1, April 2019, pp. 38-45. Sauer, ‘Einstein’s unified field theory program,’ Chapter 9 in: The Cambridge Companion to Einstein, Janssen & Lehner eds., 2014.

8vo (252 x 180 mm), pp. 334-340; 341-351. Original printed wrappers (portion of ink postmark stamp on lower cover just into text of publisher’s advertisements, light vertical crease for posting).

Item #6416

Price: $28,500.00