EINSTEIN, AlbertBiblio.com
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1916ref. 6408Berlin: Königlichen Akademie der Wissenschaften 1916. First edition. 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. . THE GRAVITATIONAL EQUATIONS FROM A VARIATIONAL PRINCIPLE. 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. 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. "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 . "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 . "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 . "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 . "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. 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. "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. "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. 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 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. 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 . 8vo 252 x 180 mm pp. 1111-1116. Original orange printed wrappers light vertical crease for posting. Königlichen Akademie der Wissenschaften unknown
1911ref. 6407Leipzig: Johann Ambrosius Barth 1911. First edition. First edition an extremely rare author's presentation offprint with 'Überreicht vom Verfasser' - Presented by the Author from the library of the eminent German physicist Arnold Sommerfeld of Einstein's "first paper completely devoted to general relativity" Brandt Harvest of a Century. In this groundbreaking work Einstein applied the equivalence principle - the idea that acceleration and gravitation are physically indistinguishable - to predict two profound effects of gravity on light: the gravitational redshift and the bending of light by massive bodies. These predictions would later be spectacularly confirmed notably in the 1919 solar eclipse observations cementing Einstein's reputation worldwide. . GRAVITATIONAL RED-SHIFT AND THE BENDING OF LIGHT . First edition extremely rare author's presentation offprint with 'Überreicht vom Verfasser' Presented by the Author stamped on front wrapper from the library of the great German physicist Arnold Sommerfeld of Einstein's "first paper completely devoted to general relativity" Brandt p. 105. This epochal paper applies the equivalence principle that acceleration and gravitation are equivalent in their physical effects to demonstrate two effects of gravity on light: the gravitational bending of light and the gravitational redshift. "In 1911 Einstein proceeded to revise and improve his earlier presentation in 1907 making the principle of equivalence the central feature of his treatment. Einstein now included an elegant proof based on a cyclic process reminiscent of thermodynamics that the gravitational mass of a body as well as its inertial mass is increased by the amount E/c2 when the body absorbs energy E c being the speed of light" Collected Papers p. xxix. Einstein applies this result to show first that if light of frequency ν travels a distance d against a gravitational field which would exert an acceleration g on a gravitating body its frequency is reduced by Δν = νgd/c2 - this is the gravitational redshift. And second Einstein deduced the deflection of a light ray moving in the gravitational field of a spherical body - he finds that the light suffers a deflection toward the source given by 2Gm/dc2 where d is the distance of closest approach to the body of mass m and G is the gravitational constant. "The paper ends with a plea to the astronomers: 'It is urgently desirable that astronomers concern themselves with the question brought up here even if the foregoing considerations might seem insufficiently founded or even adventurous'" Pais p. 200. The bending of light was famously observed by Eddington and his team during a solar eclipse in 1919; the gravitational redshift was more difficult to measure but Einstein's prediction was confirmed by Pound & Rebka at Harvard in 1960 using a laboratory experiment not astronomical observations. "Thus in 1911 we discern the first glimpses of the new Einstein program: to derive the equivalence principle from a new theory of gravitation. This cannot be achieved within the framework of what he called the ordinary relativity theory the special theory. Therefore one must look for a new theory not only of gravitation but also of relativity. Another point made in this paper likewise bears on that new program. 'Of course one cannot replace an arbitrary gravitational field by a state of motion without gravitational field as little as one can transform to rest by means of a relativity transformation all points of an arbitrarily moving medium.' This statement would continue to be true in the ultimate general theory of relativity" Pais pp. 195-196. OCLC lists three copies: King's College London; Württembergische Landesbibliothek; Swiss National Library. RBH list only two other copies both sold by Christie's: the Plotnick copy in 2002 and that in Einstein's own collection of his offprints in 2008. Provenance: Arnold Sommerfeld 1868-1951 his characteristic numbering in red pencil '20' 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. "In 1907 still working at the patent office in Bern Einstein began to study the laws of physics in reference frames with an accelerated relative motion. When he completed this work in 1915 he called it the General Theory of Relativity. At various occasions Einstein recalled his starting point in this project. It struck him that a man falling from the top of a roof he said did not feel his own weight. In the reference frame of the building it is the weight or gravitational force which make the man fall but in a reference frame moving with the man there is another force exactly counteracting the weight so that there is no net force. In that frame the man stays at rest. Einstein realized that acceleration and gravitation are equivalent to each other. That was later called the equivalence principle. If he would be able to extend his theory of relativity to accelerated reference frames he would be able to do for the theory of gravitation what he had done for electrodynamics with special relativity. He gave a first glimpse at his new topic in a review article on special relativity written in 1907 'Über das Relativitätprinzip und die aus demselben gezogenen Folgerungen' Jahrbuch der Radioaktivität und Elektronik Bd. 4 pp. 411-62" Brandt p. 105. "A few months before the Solvay Congress Einstein had returned to the questions concerning gravitation and accelerated frames of reference that he first raised in his 1907 review article on relativity. These subjects had gone unmentioned in his papers for four years and hardly ever appear in his correspondence during that time. But in June 1911 Einstein completed a short paper 'On the Influence of Gravitation on the Propagation of Light.' This was only a month after his letter to Besso announcing that he was abandoning his efforts to create a new theory of radiation. It looks as though his renunciation of that quest set him free to focus his attention once more on gravitation" Collected Papers p. xxix. "It is characteristic for Einstein that in the same paper he proposed a way to verify his predictions experimentally . From his formula for the gravitational redshift he computed that the frequency of a spectral line emitted by an atom on the surface of the sun would be reduced by two parts in a million when that light reached the earth. Thus a line spectrum originating from the sun is shifted to lower frequencies and therefore to longer wavelengths compared to a spectrum emitted in the laboratory. This redshift is difficult to measure because the surface of the sun is a nasty environment with high pressure storms and magnetic fields all influencing spectral lines. But with modern techniques it has been well established even in the laboratory with radiation climbing against the earth's gravitation for only a few meters. "Einstein also computed the bending of light by gravitation. If the light of a star passes near the surface of the sun and is then observed by an astronomer on the earth the star appears to be in a slightly different position because the light was attracted by the sun and thus the ray was bent on its way from star to the earth. Einstein found a bending angle of 0.83 seconds of an arc. This number was too small by a factor of two but nobody knew because the effect had not been measured. However Einstein himself realized that his theory had to be refined. For a homogeneous gravitational field a field that is constant everywhere he could replace gravitation by a single transformation to an accelerated coordinate system. For a more complicated field like that of the sun or that of all stars the transformation would have to be different for every point in space. That seemed a formidable problem" Brandt p. 106. The correct calculation of light bending was made only in 1915 when Einstein had the final version of general relativity. "His 1911 paper was specifically prompted by his new realization that it should be possible to observe the gravitational bending of light . One had to observe a star whose light would travel close by the sun on its way to the observer. This could be done during a total eclipse of the sun . "Einstein took the initiative in consulting experimental colleagues about the possibilities for checking these results. In August 1911 he began corresponding with W.H. Julius of Utrecht about the gravitational redshift among other matters. At about the same time he raised with Erwin Freundlich at Berlin the question of observing the deflecting of starlight by the gravitational field of the sun a subject on which he corresponded with George Ellery Hale at the Mount Wilson Observatory two years later. There would however be no reliable results on either of these subjects for years to come. But whether or not there were experimental results to help in guiding his work generalizing relativity and creating a new theory of gravitation became the problem that absorbed his attention for the next few years. 'I am just now lecturing on the foundations of that poor dead mechanics which is so beautiful' he wrote to Zangger a month after the Solvay Congress. 'What will its successor look like With that question I torment myself ceaselessly'" Collected Papers pp. xxix-xxx. "English interest in the bending of light developed soon after copies of Einstein's general relativity papers were sent from Holland by de Sitter to Arthur Stanley Eddington at Cambridge . a subsequent report by Eddington . stressed the importance of the deflection of light. In March 1917 the Astronomer Royal Sir Frank Watson Dyson drew attention to the excellence of the star configuration on May 29 1919 another eclipse date for measuring the alleged deflection . Two expeditions were mounted one to Sobral in Brazil led by Andrew Crommelin from the Greenwich Observatory and one to Principe Island off the coast of Spanish Guinea led by Eddington. Before departing Eddington wrote 'The present eclipse expeditions may for the first time demonstrate the weight of light i.e. the Newton value; or they may confirm Einstein's weird theory of non-Euclidean space which predicted twice the Newton value; or they may lead to a result of yet more far-reaching consequences - no deflection' . The expeditions returned. Data analysis began. According to a preliminary report by Eddington to the meeting of the British Association held in Bournemouth on September 9-13 the bending of light lay between 0.87 and double that value. Word reached Lorentz. Lorentz cabled Einstein . Then came November 6 1919 the day on which Einstein was canonized . the setting a joint meeting of the Royal Society and the Royal Astronomical Society resembled a Congregation of Rites. Dyson acted as postulator ably assisted by Crommelin and Eddington as advocate-procurators. Dyson speaking first concluded his remarks with the statement 'After a careful study of the plates I am prepared to say that they confirm Einstein's prediction. A very definite result has been obtained that light is deflected in accordance with Einstein's law of gravitation'" Pais pp. 304-305. The gravitational bending of light has recently found a new application - the search for extra-solar planets. ". the 'most curious effect' of the bending of starlight by the gravity of intervening foreground stars - now commonly referred to as 'gravitational microlensing' - has become one of the successfully applied techniques to detect planets orbiting stars other than the Sun while being quite unlike any other . Gravitational microlensing favours a range of orbital separations that covers planets whose orbital periods are too long to allow detection by other indirect techniques but which are still too close to their host star to be detected by means of their emitted or reflected light. Rather than being limited to the Solar neighbourhood a unique opportunity is provided for inferring a census of planets orbiting stars belonging to two distinct populations within the Milky Way with a sensitivity not only reaching down to Earth mass but even below with ground-based observations. The capabilities of gravitational microlensing extend even to obtaining evidence of a planet orbiting a star in another galaxy" Dominik. BRL 39; Parkinson p. 471; Weil 43. The Collected Papers of Albert Einstein vol. 3 The Swiss Years: Writings 1909-1911 Princeton: Princeton University Press 1994. Born 'Arnold Johannes Wilhelm Sommerfeld 1868-1951' Obituary Notices of Fellows of the Royal Society 8 1952 pp. 275-296. Brandt The Harvest of a Century Oxford: Oxford University Press 2009. Dominik 'Studying planet populations with Einstein's blip' Philosophical Transactions of the Royal Society A: Mathematical Physical and Engineering Sciences vol. 368 no. 1924 2010. Pais Subtle is the Lord Oxford: Clarendon Press 1982. 8vo 222 x 144 mm pp. 1 blank 898-908. Original printed orange wrappers light vertical crease for posting. Johann Ambrosius Barth unknown
1906ref. 6413Leipzig: Johann Ambrosius Barth 1906. First edition. First edition a very rare author's presentation offprint with 'Überreicht vom Verfasser' from the library of the eminent German physicist Arnold Sommerfeld of this important sequel to Einstein's revolutionary 1905 paper introducing the light-quantum hypothesis - the foundation of quantum theory. In this follow- up work Einstein further develops the implications of his light-quantum hypothesis arguing that Max Planck's black-body radiation law implicitly relies on the same assumption: that light itself consists of discrete quanta of energy. . EINSTEIN ON HIS LIGHT-QUANTUM HYPOTHESIS . First edition very rare author's presentation offprint "Überreicht vom Verfasser" from the library of the great German physicist Arnold Sommerfeld of this brilliant follow-up to Einstein's landmark 1905 paper on the photoelectric effect for which he was awarded the 1921 Nobel Prize in physics. "Thomas Kuhn has argued that it is not to Planck in 1900 but to Einstein in 1905 that we owe the origins of quantum theory" Cassidy. In the 1905 paper 'On a heuristic point of view concerning the production and transformation of light' Einstein had explained the photoelectric effect-the emission of electrons from a metal when irradiated by light-by making the revolutionary proposal that light rather than consisting of continuous waves was instead made up of discrete particles of energy "light quanta" which transferred their entire payload of energy to an electron on impact. In the 1905 paper Einstein made use of Planck's formula for blackbody radiation which had introduced the concept of energy quantization. "In a companion paper published in 1906 offered here Einstein exposed appeal to the quantum as fundamentally counter to the ethos of classical physics: 'the theoretical bases on which Planck's radiation theory rests are different from those of Maxwell's theory'. Planck had not initially intended to quantify light-radiation itself but Einstein demonstrated that his own 'light-quantum hypothesis' was implicit in Planck's earlier work" Honner p. 31. "At first Einstein believed that the light-quantum hypothesis was merely 'heuristic': light behaved only as if it consisted of discontinuous quanta . In his 1906 paper Einstein used his statistical mechanics to demonstrate that when light interacts with matter Planck's entire formula can arise only from the existence of light quanta-not from waves" Cassidy. As Einstein stated when he published the 1905 paper "Planck's theory of radiation seemed to me in a certain respect the antithesis of my own. New considerations which are presented in section 1 of this paper demonstrated to me however that the theoretical bases on which Planck's radiation theory rests are different from those of Maxwell's theory and of electron theory. The difference furthermore is precisely that Planck's theory implicitly makes use of the light-quantum hypothesis" p. 199 of the present paper translation from Kuhn p. 182. Later in the paper p. 203 Einstein is forced to make the following assumption: "Although Maxwell's theory is not applicable to elementary resonators the average energy of such a resonator in a radiation field is the same as that which one would compute from Maxwell's theory". "That statement marks the emergence of the basic paradox of the old quantum theory. The theory has recourse to both Maxwell's equations and those of classical mechanics but its further formulation is incompatible with one or both of those classical theories. Other physicists were to exploit the resulting inconsistency as an argument against any form of quantum discontinuity and Einstein himself was deeply disturbed by it . But neither he nor anyone else was successful in finding a classical resolution of the quantum paradox. When two decades later Bohr and others found a way to resolve it Einstein was unable to accept their fundamentally non-classical interpretation" Kuhn pp. 184-185. RBH lists 4 other copies: in the offprint collections of Einstein himself Christie's June 17 2008 lot 100 Richard Green Christie's June 17 2008 lot 101 Hans Albert Einstein Christie's June 14 2006 lot 264 and Harvey Plotnick Christie's October 4 2002 lot 105. This copy was presented by Einstein to one of the leading physicists of the time surely hoping to make himself known in the scientific world when he was still a technical expert in the Swiss Patent Office. Provenance: Arnold Sommerfeld 1868-1951 his signature and characteristic numbering in red pencil '8' 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. "Einstein started to study black-body radiation well before 1905. Mach's Wärmelehre which Einstein read in 1897 or shortly thereafter contains two chapters on thermal radiation culminating in a discussion of Kirchhoff's work. Kirchhoff showed that the energy emission spectrum of a perfectly black body defined as one absorbing all incident radiation at a given temperature is a universal function of the temperature and wavelength. He inferred that equilibrium thermal radiation in a cavity with walls maintained at a certain temperature behaves like radiation emitted by a black body at the same temperature. "H. F. Weber Einstein's physics professor at the ETH attempted to determine the universal black-body radiation function. He made measurements of the energy spectrum and proposed an empirical formula for the distribution function . anticipating Wien's formulation of the displacement law for black-body radiation. Weber described his work in a course at the ETH given during the winter semester of 1898-1899 for which Einstein registered. "By March 1899 Einstein had started to think seriously about the problem of radiation. In the spring of 1901 he was closely following Planck's work on black-body radiation. Originally Planck had hoped to explain irreversibility by studying electromagnetic radiation but came to recognize that this could not be done without introducing statistical elements into the argument. In a series of papers published between 1897 and 1900 Planck utilized Maxwell's electrodynamics to develop a theory of thermal radiation in interaction with one or more identical charged harmonic oscillators within a cavity. He was only able to account for the irreversible approach to thermal equilibrium by employing methods analogous to those Boltzmann used in kinetic theory. Planck introduced the notion of 'natural' that is maximally disordered radiation which he defined in analogy with Boltzmann's definition of molecular chaos . "Planck calculated the average energy of an oscillator by making assumptions about the entropy of the oscillators that enabled him to derive Wien's law for the blackbody spectrum which originally seemed well supported by the experimental evidence. But by the turn of the century new observations showed systematic deviations from Wien's law for large values of temperature. "Planck in 1900 presented a new energy density distribution formula that agreed closely with observations over the entire spectrum . this expression now known as Planck's law or Planck's formula involves a new constant h later called Planck's constant. To derive this formula Planck calculated the entropy of the oscillators using what Einstein later called 'the Boltzmann principle': S = k log W where S is the entropy of a macroscopic state of the system the probability of which is W and k is 'Boltzmann's constant'. Following Boltzmann Planck took W proportional to the number of 'complexions' or possible microconfigurations of the system corresponding to its state. He calculated this number by dividing the total energy of the state into a finite number of elements of equal magnitude and counting the number of possible ways of distributing these energy elements among the individual oscillators. If the size of the energy elements is set equal to hv where v is the frequency of the oscillators an expression for the entropy of an oscillator results that leads to Planck's formula . "In the 1905 paper Einstein showed that the expression for the volume dependence of the entropy of radiation at a given frequency is similar in form to that of the entropy of an ideal gas. He concluded that 'monochromatic radiation of low density behaves thermodynamically as though it consisted of quanta of energy which are independent of one another' . Einstein opened the paper by pointing out the 'fundamental formal distinction' between current theories of matter in which the energy of a body is represented as a sum over a finite number of degrees of freedom and Maxwell's theory in which the energy is a continuous spatial function having an infinite number of degrees of freedom. He suggested that the inability of Maxwell's theory to give an adequate account of radiation might be remedied by a theory in which radiant energy is distributed discontinuously in space. Einstein formulated 'the light quantum hypothesis' that the energy of a light ray emitted from a point is not continuously distributed over an ever increasing space but consists of a finite number of energy quanta which are localized at points in space which move without dividing and which can only be produced and absorbed as complete units . Einstein asserted that Planck's derivation implicitly assumes quantization of the energies of charged oscillators" Papers pp. 134-142. "In 1905 Einstein could not make sense of Planck's derivation of Planck's law. In fact he seems to have deliberately avoided any reference to Planck's law in his reasoning . The following year Einstein ceased to avoid Planck's law as he discovered a new way to justify Planck's formal steps toward this law. If a resonator of frequency ν can only emit or absorb full light quanta Einstein reasoned then its energy can only be an integral multiple of hν and Planck's characterization of the complexions for a set of resonators receives a dynamical justification. The only remaining difficulty is that Planck's derivation of the relation between the average energy of a resonator and the spectral density of radiation becomes void. Einstein expressed the need of a new derivation based on some quantized dynamics for the interaction between matter and radiation. Ten years elapsed however before he filled the gap" Janssen & Lehner p. 126. In the final section of this paper Einstein gives a new application of his 'heuristic principle' to the explanation of the 'Volta effect' - that when two different metals are placed in contact a potential difference between them is observed. BRL 12; Weil 12. Shields "Writings of Albert Einstein" in Albert Einstein: Philosopher-Scientist 1948 pp. 689-758 no. 13; also included in Shields' "Chronological list of principal works" on p. 757. The Cambridge Companion to Einstein Janssen & Lehner eds. 2014. The Collected Papers of Albert Einstein Vol. 2: The Swiss Years: Writings 1900-1909. Born 'Arnold Johannes Wilhelm Sommerfeld 1868-1951' Obituary Notices of Fellows of the Royal Society 8 1952 pp. 275-296. Cassidy "Einstein on the Photoelectric Effect." Einstein: Image and Impact. American Institute of Physics n.d. Honner The Description of Nature 1988. Kuhn Black-Body Theory and the Quantum Discontinuity 1894-1912 1978. Pais Subtle is the Lord 1982. 8vo 222 x 144 mm pp. 199-206. Original printed wrappers small chip from upper edge of front wrapper. Johann Ambrosius Barth unknown
1915ref. 6406Berlin: Königlichen Akademie der Wissenschaften 1915. First edition. First editions very rare offprint issue of the first two papers published in November 1915 that document Einstein's final formulation of the general theory of relativity - the culmination of nearly a decade of theoretical work. These papers represent a turning point not only in Einstein's career but in the history of modern physics. Delivered to the Prussian Academy on 4 and 11 November 1915 they contain the essential framework and mathematical formalism of the completed theory preceding the famous final paper of 25 November by just days. Collectively the November papers form the core of Einstein's definitive breakthrough. "In the half century and more of Einstein's work in science one discovery stands above all as his greatest achievement. It is his general theory of relativity" Norton. . EINSTEIN'S COMPLETION OF THE GENERAL THEORY OF RELATIVITY . 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 the first two of the papers published in November 1915 that document Einstein's final version of the general theory of relativity. "In the half century and more of Einstein's work in science one discovery stands above all as his greatest achievement. It is his general theory of relativity" Norton. "There was difficulty reconciling the Newtonian theory of gravitation with its instantaneous propagation of forces with the requirements of special relativity; and Einstein working on this difficulty was led to a generalization of relativity - which was probably the greatest scientific discovery that was ever made" Dirac quoted in Chandrasekhar p. 3. Einstein's special theory of relativity 1905 showed that the laws of physics are the same in all inertial i.e. non-accelerating frames of reference. It was then natural to ask whether it was possible to extend this principle of relativity to the more general case of frames of reference in arbitrary states of motion. This problem became linked to a theory of gravitation with Einstein's 'equivalence principle' of 1907 according to which the effects of gravity are locally equivalent to those of accelerated motion. Einstein's first steps towards a geometrical theory of gravitation were taken in August 1912 when his friend Marcel Grossmann provided the necessary mathematical tools. "Some time between August 10 and August 16 it became clear to Einstein that Riemannian geometry is the correct mathematical tool for what we now call general relativity theory. The impact of this abrupt realization was to change his outlook on physics and physical theory for the rest of his life" Pais p. 210. The resulting 'Entwurf' theory 1913 had much in common with the final theory of 1915 but based on a fallacious argument Einstein abandoned the requirement that the theory should be 'generally-covariant' i.e. that arbitrary frames of reference should be allowed. "After three years of fruitless peregrinations the revelation came to Einstein that he had been constantly on the wrong track although in 1913 he had been so near to the right solution" Lanczos p. 211. On November 4 1915 he presented to a plenary session of the Prussian Academy a new version of general relativity 'Zur allgemeinen Relativitätstheorie' "based on the postulate of covariance with respect to transformations with determinant 1" and stated that he had "completely lost confidence" in the 'Entwurf' equations. On November 18 he published his calculation of the precession of the perihelion of Mercury based on the new theory: its agreement with observation confirmed that the theory was correct the Entwurf theory predicted half the observed value of the precession. Provenance: Arnold Sommerfeld 1868-1951 his characteristic numbering in red pencil '30' 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. "In June 1905 while still a patent examiner in Bern Einstein submitted his famous work on the electrodynamics of moving bodies to the Annalen der Physik. This work contained his special theory of relativity in which he asserted the equivalence of all inertial frames of reference as a fundamental postulate of physics. The question which then naturally arose was whether it was possible to extend this principle of relativity to the more general case of frames of reference in arbitrary states of motion. But he could find no workable basis for such an extension until he tried to incorporate gravitation into his new special theory of relativity for a review article in 1907 'Uber das Relativitätsprinzip und die ausdemselben gezogenen Folgerungen' Jahrbuch der Radioaktivitat und Elektronik 4 1907 411-62. The difficulties of this task led him to a new principle later to be called the 'principle of equivalence.' "On the basis of the fact that all bodies fall alike in a gravitational field Einstein postulated the complete physical equivalence of a homogeneous gravitational field and a uniform acceleration of the frame of reference. This extended the principle of relativity to the case of uniform acceleration. It also foreshadowed the problem whose complete solution would lead him to his general theory of relativity: the construction of a relativistically acceptable theory of gravitation based on the principle of equivalence" Norton p. 258. One application of the equivalence principle proved crucial to the subsequent development of his ideas on general relativity. Einstein considered an observer standing on a rotating disc - a non-inertial accelerating reference frame. According to special relativity measuring rods aligned with the circumference of the disc will contract due to their motion whereas measuring rods positioned along the radius of the disc will not. Hence the ratio of the circumference of the disc to its diameter will be less than π. "The spatial geometry for the rotating observer is therefore non-euclidean. Invoking the equivalence principle Einstein concluded that this will be true for an observer in a gravitational field as well. This then is what first suggested to Einstein that gravity should be represented by curved space-time. "To describe curved space-time Einstein turned to Gauss's theory of curved surfaces a subject he vaguely remembered from his student days at the ETH in Zürich. He had learned it from the notes of his classmate Marcel Grossmann. Upon his return to his alma mater as a full professor of physics in 1912 Einstein learned from Grossmann now a colleague in the mathematics department of the ETH about the extension of Gauss's theory to spaces of higher dimension by Riemann and others. Riemann's theory provided Einstein with the mathematical object with which he could unify the effects of gravity and acceleration: the metric field" Janssen p. 65. The first product of this collaboration was the Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation published before the end of June 1913 which contained many of the essential features of the final general theory of relativity; most importantly it introduced the 'metric' of space-time. In Minkowski's formulation of special relativity 1908 the most important quantity is the 'world function' of two events which determines the metric and causal structure of space-time. If these events have coordinates x y z t and x' y' z' t' in some inertial reference frame the world function is: c2t' - t2 - x' - x2 - y' - y2 - z' - z2 where c is the speed of light. Its crucial property is that it depends only on the two events and not on the choice of inertial reference frame - in other words it is unchanged 'invariant' when x y z t and x' y' z' t' are both subjected to any Lorentz transformation. Einstein and Grossmann began with the world function in differential form: ds2 = c2dt2 - dx2 - dy2 - dz2 If we now subject x y z t to an arbitrary coordinate transformation not necessarily a Lorentz transformation this takes the general form ds2 = g11dx12 g12dx1dx2 . ; the collection of quantities gμν which in general depend on the coordinates x1 x2 x3 x4 is called the metric. Based on analogy with Newton's theory Einstein expected that the gravitational equations should be of the form Gμν = Tμν where Gμν is a purely geometric quantity constructed solely from the metric gμν and its derivatives up to the second order and the 'stress-energy tensor' Tμν contains the information about the matter that is producing the gravitational field including energy density momentum fluxes and stresses. The question was: what exactly should Gμνbe Einstein and Grossmann found that generally covariant equations did not seem to be compatible with energy-momentum conservation or reduce to the equations of Newtonian gravitational theory for weak static fields both essential requirements of the correct theory. Einstein therefore decided to settle in the 'Entwurf' for equations with very limited covariance - instead of arbitrary changes in coordinates only linear ones were allowed. The restricted covariance of the 'Entwurf' field equations continued to bother him until in late August 1913 he convinced himself that such restrictions are unavoidable by means of the infamous "hole argument" first published as an addendum to the reprint of the 'Entwurf' article in Zeitschrift für Physik in January 1914. This ingenious argument showed correctly that if the gravitational equations were generally covariant the metric gμν would not be uniquely determined by the matter distribution i.e. by Tμν. He concluded incorrectly that this implied that general covariance must be ruled out the hole argument does not work if only linear coordinate transformations are allowed. The appropriate analogy is with electromagnetism: the metric is analogous to the scalar and vector potentials of electromagnetism and it was well known certainly to Einstein that these potentials are not uniquely determined by the charges and currents producing the electromagnetic field. That the 'Entwurf' theory was incorrect was made clear by Einstein's attempt in collaboration with Michele Besso another former classmate to explain the motion of the perihelion of Mercury. In 1859 Urbain Jean Joseph Le Verrier had observed the 'precession' of Mercury's orbit: this orbit is an ellipse but the ellipse is not fixed in space but slowly rotates. From early on in his search for a new relativistic theory of gravitation Einstein had been interested in the problem of Mercury's perihelion. In a letter to his friend Conrad Habicht in 1907 Einstein had already expressed his hope that such a theory would explain the anomalous advance of Mercury's perihelion. Besso visited Einstein in Zürich in June 1913 and the two men calculated the precession expected on the basis of the 'Entwurf' theory. Disappointingly it was only about half the observed anomaly. Einstein left Zürich in March 1914 to take up a professorship in Berlin which was to be his home until December 1932. He made no further progress on the gravitational equations until the summer of 1915 although a detailed exposition of the 'Entwurf' theory was published in October 1914 in which Einstein maintained the need for restricted covariance and even claimed that this determined the gravitational Lagrangian uniquely. "Einstein still believed in the 'old' theory as late as July 1915 between July and October he found objections to that theory and his final version was conceived and worked out between late October and November 25 . What made Einstein change his mind between July and October Letters to Sommerfeld and Lorentz show that he had found at least three objections against the old theory: 1 its restricted covariance did not include uniform rotations 2 the precession of the perihelion of Mercury came out too small by a factor of about 2 and 3 his proof of October 1914 of the uniqueness of the gravitational Lagrangian was incorrect. Einstein got rid of all these shortcomings in a series of four brief articles offered here . "On November 4 Einstein presented to the plenary session of the Prussian Academy a new version of general relativity 'based on the postulate of covariance with respect to transformations with determinant 1'. He began this paper by stating that he had 'completely lost confidence' in the equations proposed in October 1914. At that time he had given a proof of the uniqueness of the gravitational Lagrangian. He had realized meanwhile that this proof 'rested on misconception' and so he continued 'I was led back to a more general covariance of the field equations a requirement which I had abandoned only with a heavy heart in the course of my collaboration with my friend Grossmann three years earlier' . "Einstein and Grossmann had concluded that the gravitational equations could be invariant under linear transformations only and Einstein's justification for this restriction was based on the belief that the gravitational equations ought to determine the gμν uniquely a point he continued to stress in October 1914. In his new paper he finally liberated himself from this three-year-old prejudice. That is the main advance on November 4. His answers were still not entirely right. There was still one flaw a much smaller one which he eliminated three weeks later. But the road lay open. He was lyrical. 'No one who has really grasped it can escape the magic of this new theory.' "The remaining flaw was of course Einstein's unnecessary restriction to unimodular transformations. The reasons which led him to introduce this constraint were not deep I believe. He simply noted that this restricted class of transformations permits simplifications of the tensor calculus . The new equations are a vast improvement over the Einstein-Grossmann equations and cure one of the ailments he had diagnosed only recently: unimodular transformations do include rotations with arbitrarily varying angular velocities. In addition he proved that the new equations can be derived from a variational principle and that the conservation laws are satisfied" Pais pp. 250-252. On November 11 he submitted a 'Nachtrag' to his paper of a week earlier. "Einstein proposes a scheme that is even tighter than the one of a week earlier. Not only shall the theory be invariant with respect to unimodular transformations . but more strongly it shall satisfy the condition that the determinant of the matrix gμν is equal to minus one . During the next two weeks Einstein believed that this new condition had brought him closer to general covariance . One week later he remarked that 'no objections of principle' can be raised against it" ibid. pp. 252-253. Norton p. 309 points out that Einstein had in fact made a significant advance in this paper: namely he had finally found generally covariant field equations that reduced to the Newtonian equations in the weak field limit" ibid. p. 253. On November 18 still retaining the restrictions of his paper of a week earlier Einstein presented in 'Erklarung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie'"two of his greatest discoveries. Each of these changed his life. The first result was that his theory explains . quantitatively . the secular rotation of the orbit of Mercury discovered by Le Verrier . without the need of any special hypothesis. This discovery was I believe by far the strongest emotional experience in Einstein's scientific life perhaps in all his life. Nature had spoken to him. He had to be right. 'For a few days I was beside myself with joyous excitement'. Later he told Fokker that his discovery had given him palpitations of the heart. What he told de Haas is even more profoundly significant: when he saw that his calculations agreed with the unexplained astronomical observations he had the feeling that something actually snapped in him . "Einstein's discovery resolved a difficulty that was known for more than sixty years. Urbain Jean Joseph Le Verrier had been the first to find evidence for an anomaly in the orbit of Mercury and also the first to attempt to explain this effect . In 1859 he found that the perihelion of Mercury advances by thirty-eight seconds per century due to 'some as yet unknown action on which no light has been thrown . a grave difficulty worthy of attention by astronomers'" ibid. pp. 253-254. A more accurate measurement of 43 seconds was made by Simon Newcomb in 1882 and this was precisely the value predicted by the new theory. The prediction of the bending of light in a gravitational field was treated only briefly in 'Erklarung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie' probably because no accurate measurement of it had been made so this prediction could not be confirmed at the time. Einstein had realised in 1907 based on the equivalence principle that some bending of light should occur but he believed that the effect was too small to be observed. In 1911 he realized that the effect could be detected for starlight grazing the sun during a total eclipse and found that the amount of bending in that case is 0''.87 - this value could in fact have been computed by Newton from his law of gravitation and his corpuscular theory of light. In 3 Einstein discovered that general relativity implies a bending of light by the sun equal to 1".74 twice the Newtonian value. This factor of 2 set the stage for a confrontation between Newton and Einstein. "It was not until May 1919 that two British expeditions obtained the first useful photographs and not until November 1919 that their results were formally announced . In March 1917 the Astronomer Royal Sir Frank Watson Dyson drew attention to the excellence of the star configuration on May 29 1919 an eclipse date for measuring the alleged deflection . Two expeditions were mounted one to Sobral in Brazil led by Andrew Crommelin from the Greenwich Observatory and one to Principe Island off the coast of Spanish Guinea led by Eddington. Before departing Eddington wrote 'The present eclipse expeditions may for the first time demonstrate the weight of light i.e. the Newton value; or they may confirm Einstein's weird theory of non-Euclidean space; or they may lead to a result of yet more far-reaching consequences - no deflection' . The expeditions returned. Data analysis began. According to a preliminary report by Eddington to the meeting of the British Association held in Bournemouth on September 9-13 the bending of light lay between 0''.87 and double that value. Word reached Lorentz. Lorentz cabled Einstein . Then came November 6 1919 the day on which Einstein was canonized" Pais 304-305. At a joint meeting of the Royal Society and the Royal Astronomical Society on that date Dyson concluded his remarks with the statement "'After a careful study of the plates I am prepared to say that they confirm Einstein's prediction. A very definite result has been obtained that light is deflected in accordance with Einstein's law of gravitation'" ibid. p. 305. Three remarks may be made on the speed with which after eight years of struggle Einstein completed these final papers on his theory. The first is that Einstein had come very close to the correct gravitational equations in the second half of 1912 - they are recorded in his 'Zurich notebook' - but he discarded them because of his arguments against general covariance as we have seen. Once he no longer believed in these arguments he could return to the work carried out in the Zurich notebook and complete it. The second is that the detailed calculations in 3 relating to Mercury's perihelion were in fact very similar to those he had carried out with Besso in 1913 and so required relatively little extra effort. The final point is that Einstein was in competition with the great Göttingen mathematician David Hilbert. 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 as in the present offprint. In the period 1916 to 1919 or 1920 the Sitzungsberichte trade offprints are themselves rare: for example 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 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. 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. In our view Einstein's author's presentation offprints are rare from any journal and any period though of course some are rarer than others. Before 1919 or 1920 the Sitzungsberichte trade offprints are also rare although not are rare as the author's presentation offprints; after 1919 or 1920 the trade offprints are much more common. BRL 74; Weil 75; Born 'Arnold Johannes Wilhelm Sommerfeld 1868-1951' Obituary Notices of Fellows of the Royal Society 8 1952 pp. 275-296. Chandrasekhra 'The general theory of relativity: Why "It is probably the most beautiful of all existing theories" Journal of Astrophysics 5 1984 pp. 3-11; Eisenstaedt The Curious History of Relativity 2006; Janssen 'Of pots and holes: Einstein's bumpy road to general relativity' Annalen der Physik 14 Supplement 2005 pp. 58-85; Lanczos Einstein Decade: 1905-1915 1974; Norton 'How Einstein found his field equations: 1912-1915' Historical Studies in the Physical Sciences 14 1984 pp. 253-316; Pais Subtle is the Lord 1982. Large 8vo 252 x 180mm pp. 778-786; 799-801. Original printed wrappers light vertical crease from posting. Königlichen Akademie der Wissenschaften unknown
1925ref. 6417Berlin: Königlich Akademie der Wissenschaften 1925. First edition. First edition very rare author's presentation offprint from the library of the great German physicist Arnold Sommerfeld with his signature and annotations of Einstein's third paper on his quantum theory of the ideal gas of 1924-1925 Einstein's "last major innovative contribution to physics" Pais Subtle is the Lord. "The arguments advanced in this third paper do not make use of the new Bose-Einstein statistics. Instead Einstein invokes arguments involving dimensional analysis and adiabatic compression" Papers Vol. 14. . BOSE-EINSTEIN STATISTICS - WITHOUT THE STATISTICS. First edition very rare author's presentation offprint not to be confused with the more common trade separate - see below from the library of the great German physicist Arnold Sommerfeld with his signature and annotations of Einstein's third paper on his quantum theory of the ideal gas of 1924-1925 Einstein's "last major innovative contribution to physics" Pais Subtle is the Lord p. 343. In 1924 Einstein received a copy of the Indian physicist S. N. Bose's paper 'Planck's law and the hypothesis of light quanta.' Einstein immediately recognized its importance and had it published shortly followed by a paper of his own applying Bose's ideas to ideal gases rather than radiation molecules rather than light quanta. These two papers laid the foundations of 'Bose-Einstein statistics.' Einstein published a second paper in which he showed that the new statistics led to the prediction of a new state of matter the 'Bose-Einstein condensate' the creation of which in the laboratory was the topic of the 2001 Nobel Prize in Physics. At the time however many of Einstein's colleagues in particular his close friend Paul Ehrenfest were sceptical of the new statistics. Einstein therefore attempted in the present paper to justify his quantum theory of the ideal gas by more traditional methods rather than the novel statistics he had used in his two previous papers. "It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein's confusion with his initial success in extending Bose's results and in realizing the consequences of what later came to be called Bose-Einstein statistics . Its arguments are based on Einstein's belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as well as of dimensional analysis. These techniques were well known to Einstein from earlier work on Wien's displacement law Planck's radiation theory and the specific heat of solids" Pérez & Sauer. "In a letter to Ehrenfest he writes that on his next visit in Leyden 'I shall then convince you completely of the gas-degeneracy-equation. I found another safe though not entirely complete approach to it free of the incriminating statistics'. The arguments advanced in this third paper indeed do not make use of the new statistics. Instead Einstein invokes arguments involving dimensional analysis and adiabatic compression" Papers p. lxx. The only other copy of this offprint listed on RBH is that in Einstein's own collection Christie's 2008. Provenance: Arnold Sommerfeld 1868-1951 his signature and characteristic numbering in red pencil '44' on front cover and three annotations in the text. The annotations consist of corrections to formulas 5 on p. 20 11 and 12 on p. 21 16a on p. 23 and 19 on p. 24 to the equation on the last line of p. 22 and to two mathematical symbolson lines 2 and 3 of p. 25. "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. The motivation for the publication of this paper is given by Einstein in the opening paragraph translation from Papers Vol. 14 English Translation Supplement: 'Stimulated by a derivation of Planck's radiation formula originating from Bose which consistently supports itself on the light-quantum hypothesis I recently postulated a quantum theory for ideal gas. This theory seems legitimate when one starts out from the conviction that a light quantum disregarding its polarization property differs from a monatomic molecule essentially only in that the quantum's mass at rest is vanishingly small. But because the presupposition of this analogy is certainly not accepted by all researchers and furthermore because the statistical method used by Mr. Bose and me is certainly not beyond doubt but rather just seems justified a posteriori by its success in the case of radiation I looked for other considerations on the quantum theory of ideal gas that are as free of arbitrary hypotheses as possible. These considerations shall be communicated in the following. They provide an effective support for the theory postulated earlier even though the results attained do not yield a full substitute for that theory. Here it is a matter of establishing considerations in the field of gas theory by a method and with results largely analogous to those in the field of radiation theory leading to Wien's displacement law.' "Einstein followed an approach in this paper that was not based only on statistical considerations and that was closer to thermodynamics. He tried to find general conditions that any theory of the ideal gas would have to satisfy mainly by establishing and exploiting analogies with radiation where the displacement law at least provided some hints as to what the radiation law should look like" Pérez & Sauer. The problem Einstein wished to solve was to find the distribution function Ï = ÏL κT V m where L is the kinetic energy κ the Boltzmann constant T the temperature V the volume and m the mass of the molecules. The distribution law will be of the form dn = ÏL κT V mVdp1dp2dp3 / h3 where dn is the number of molecules whose Cartesian components of the momenta are in the range p1 p2 p3 to p1 dp1 p2 dp2 p3 dp3 h is Planck's constant. Einstein did not assume that collisions between molecules are governed by the laws of mechanics. He asserted that if that were the case one would arrive at the classical Maxwell's distribution law. He neglected interactions among molecules this being essentially the definition of an ideal gas. Einstein first used dimensional analysis to place a restriction on the possible forms of the distribution function. He had used similar arguments in his 1909 paper 'Zum gegenwärtigen Stand des Strahlungsproblems' Physikalische Zeitschrift 10 185-193 to deduce Wien's displacement law and in his 1911 paper on the quantum theory of solids 'Elementare Betrachtungen über die thermische Molekularbewegung in festen Körpern' Annalen der Physik 35 679-694. Since Ï is dimensionless a pure number it had to be a function only of dimensionless combinations of L κT V m and h. There are two independent such combinations which means that Ï is reduced to a function of two variables rather than five: A = L/κT and B = mV/N2/3κT/h2. To reduce Ï to a function of a single variable Einstein needed further restrictions. "Einstein proposed two of those: The entropy of an ideal gas does not change in an 'infinitely slow adiabatic' sic compression. The required velocity distribution is valid for an ideal gas also in an external field of conservative forces. Einstein argued that these two properties should be valid disregarding collisions. But the neglect of intermolecular collisions made their assumption unprovable even if they would be 'very natural.' In support of both he announced they would lead not only to the same result but also to a result according to which Maxwell's distribution law is valid in the region where quantum effects can be neglected" Pérez & Sauer. Einstein deduced from these assumptions that Ï = ΨA χB where Ψ and χ are universal functions of dimensionless variables. Einstein then looked at the case in which the constant h disappears from the expression for dn i.e. at the classical limit. He found that Ï = Be-A i.e. the Maxwell-Boltzmann law. In contrast Einstein's statistical theory had produced the expression Ï = B/eA - 1. "Summarizing Einstein pointed out that two aims have been achieved: 'First we found a general condition equation which has to be satisfied by any theory of the ideal gas. Second it follows from the above that the equation of state which I derived will not be changed by either adiabatic compression or by the existence of conservative force fields'" Pérez & Sauer. Why was this paper little noticed by Einstein's colleagues "The practically immediate appearance of the revolutionary contributions of 1925 to quantum theory eclipsed any possible interest of Einstein's paper. The arguments it contains only concern the ideal gas from a thermodynamic perspective. But what is more important it includes hypotheses that were in open contradiction with the course quantum researches had taken. Many physicists had rejected already the laws of mechanics and Einstein assumed their validity for describing the motions of the gas molecules. "The papers of the twenties that refer to Einstein's theory usually mention all three instalments. This indicates that in spite of the almost complete lack of comments on it its existence was known. We are inclined to think that it simply was not of any interest to Einstein's colleagues. Einstein justified the considerations of the non-statistical paper with the deep dissatisfaction over the statistical route by which he had arrived at the new distribution function. However the problem was not whether his colleagues saw Bose's statistics favourably but that in the following months the physicists' ideas around the quantum issues changed substantially. Bose's statistics in spite of implying a way of counting that was incompatible with classical statistics led to an already accepted result. This was much more than could be said of other attempts of explaining for example the Zeeman effect or multielectronic spectra . "In retrospect Einstein's initial suspicion about Bose's statistics will turn into one of the first symptoms of his later distancing himself from quantum mechanics. For this reason we find no justification for the neglect of Einstein's paper by historians of physics. Perhaps we are dealing here with Einstein's last attempt to contribute positively to the construction of the quantum theory for which he had done so much. In addition this paper closed the circle he initiated in 1905 with the hypothesis of energy quanta. First the analogy was going one way now finally it was also going the other way. The statistical dependence among light quanta which had limited the analogy with an ideal gas now was found also among molecules. Hence for the first time the analogy was complete . "The last 'positive contribution' of Einstein to statistical physics includes a paper in which he offered arguments independent of the 'incriminated statistics' because what nowadays is called Bose-Einstein's statistics was not more according to its creator than a calculatory artifice absolutely devoid of any physical meaning. It was simply a consequence of using the wrong mechanics or of not considering some kind of interaction. As Einstein explained to Halpern it 'cannot be considered as giving a true theoretical basis to Planck's law'" Pérez & Sauer. This author's presentation offprint is very rare 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 as in the present offprint. In the period 1916 to 1919 or 1920 the Sitzungsberichte trade offprints are themselves rare: for example 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 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. Weil 145. Shields "Writings of Albert Einstein" in Albert Einstein: Philosopher-Scientist 1948 pp. 689-758 no. 195. Born 'Arnold Johannes Wilhelm Sommerfeld 1868-1951' Obituary Notices of Fellows of the Royal Society 8 1952 pp. 275-296. The Collected Papers of Albert Einstein digital Vol. 14: The Berlin Years: Writings & Correspondence April 1923-May 1925. Pais Subtle is the Lord 1982. Pérez & Sauer 'Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics' Archive for History of Exact Sciences 64 2010 pp. 561-612. 8vo 255 x 183 mm pp. 18-25. Original orange printed wrappers. Königlich Akademie der Wissenschaften unknown
1907ref. 6410Leipzig: S. Hirzel 1907. First edition. First edition an extremely rare offprint from the library of the renowned German physicist Arnold Sommerfeld of one of the most important transitional papers in Einstein's scientific career. In this landmark work Einstein first articulated the equivalence principle - the insight that uniform acceleration and gravitation are physically indistinguishable - a profound realization he later described as "the happiest thought of my life." This concept became the foundation of general relativity marking a pivotal departure from special relativity and setting Einstein on the path toward a relativistic theory of gravitation. . THE EQUIVALENCE PRINCIPLE 'THE HAPPIEST THOUGHT OF MY LIFE' . First edition extremely rare author's presentation offprint with 'Überreicht vom Verfasser' Presented by the Author stamped on front wrapper from the library of the great German physicist Arnold Sommerfeld of this crucially important transitional paper in which Einstein introduced the equivalence principle that uniform acceleration and gravitation are equivalent in their physical effects which launched him on his path to general relativity. "Einstein's efforts to incorporate gravitation into the theory of relativity led him in 1907 to formulate a new formal principle later named the principle of equivalence. He stressed that when gravitational effects are taken into account it is impossible to maintain the privileged role that inertial frames of reference still have in the original relativity theory. He concluded that if gravitation is to be included it is necessary to extend the relativity principle. The search for a group of transformations wider than the Lorentz group under which the laws of physics remain invariant when gravitation is included lasted from 1907 until the end of 1915 leading finally to what Einstein considered his greatest achievement the general theory of relativity" Collected Papers 2 p. xxix. "On p. 443 are probably the first explicit statements both of the equivalence of inertial and gravitational mass and of the equation for mass in terms of energy E = mc2 now regarded as the theoretical basis for the release of atomic energy" Weil. In 1905 "Einstein said that all energy of whatever sort has mass. It took even him two years more to come to the stupendous realization that the reverse must also hold: that all mass of whatever sort must have energy. . With mass and energy thus wholly equivalent Einstein was able in 1907 in a long and mainly expository paper published in the Jahrbuch der Radioactivität the offered paper to write his famous equation E = mc2 . In presenting his equation in 1907 Einstein spoke of it as the most important consequence of his theory of relativity" Hoffmann Albert Einstein p. 81. "Of greatest importance is the last part of the paper which generalizes the principle of relativity from uniformly moving systems to uniformly 'accelerated' systems. . He introduces the principle of equivalence which claims that the problem of a uniform and stationary gravitational field on the one hand and the system moving with a constant acceleration without any gravitation on the other hand are physically indistinguishable situations. This principle put him in a position to find out what effect gravitation has on an arbitrary physical phenomenon because all he had to do was to observe that phenomenon from an accelerated reference system. He thus obtains the speeding up of clocks in a field of increased gravitational potential which must lead to a universal red shift of the spectral lines coming from the Sun and likewise to a bending of light rays near to the limb of the Sun. Furthermore this hypothesis at once makes it clear why inertial mass and gravitational mass must be under all circumstances strictly proportional to one another. . Hence the principle of the energy value of inertial mass must be extended to the gravitational mass" Lanczos The Einstein Decade p. 153. Later Einstein wrote that when he was working on this paper "There occurred to me the happiest thought of my life in the following form. The gravitational field has only a relative existence in a way similar to the electric field generated by magnetoelectric induction. Because for an observer falling freely from the roof of a house there exists - at least in his immediate surroundings - no gravitational field" Einstein's emphasis Pais Subtle is the Lord p. 178. Although Einstein submitted the paper on 4 December 1907; it was published in the January 22 issue of the Jahrbuch. This is one of Einstein's rarest major papers in offprint form. RBH lists three copies: Plotnick Christie's 2002; Einstein's own collection of his offprints Christie's 2008; and Richard Green Christie's 2008. OCLC lists 6 copies worldwide Morgan; Princeton; Stanford; Trinity College Cambridge; Queen's University Kingston ON; Thomas Fisher. This copy was presented by Einstein to one of the leading physicists of the time surely hoping to make himself known in the scientific world when he was still a technical expert in the Swiss Patent Office. Provenance: Arnold Sommerfeld 1868-1951 his signature and characteristic numbering in red pencil '11' 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. "His first important paper on relativity theory after 1905 is the 1907 review. This article was written at the request of Johannes Stark the editor of the Jahrbuch. On September 25 1907 Einstein had accepted this invitation. On November 1 Einstein further wrote to Stark: 'I am now ready with the first part of the work for your Jahrbuch. I am working zealously on the second part in my unfortunately scarce spare time.' Since this second part contains the remarks on gravitation it seems probable that Einstein's 'happiest thought' came to him sometime in November 1907. We certainly know where he was when he had this idea. In his Kyoto lecture he told the story: 'I was sitting in a chair in the patent office at Bern when all of a sudden a thought occurred to me. 'If a person falls freely he will not feel his own weight!' I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation' . "Three main issues are raised in Section V of the Jahrbuch article. The Equivalence Principle. 'Is it conceivable that the principle of relativity also holds for systems which are accelerated relative to each other' That is Einstein's starting question. Then he gives the standard argument. A reference frame Σ1 is accelerated in the x direction with a constant acceleration γ. A second frame Σ2 is at rest in a homogeneous gravitational field which imparts an acceleration -γ in the x direction to all objects. 'In the present state of experience we have no reason to assume that . Σ1 and Σ2 are distinct in any respect and in what follows we shall therefore assume the complete physical equivalence of a gravitational field and the corresponding acceleration of the reference frame. This assumption extends the principle of relativity to the case of uniformly accelerated motion of the reference frame . he began by applying his new postulate to the Maxwell equations always for uniform acceleration. He did not raise the question of the further extension to nonuniform acceleration until 1912 the year he first referred to his hypothesis as the 'equivalence principle.' The Gravitational Red Shift. Many textbooks on relativity ascribe to Einstein the method of calculating the red shift by means of the Doppler effect of light falling from the top to the bottom of an upwardly accelerating elevator. That is indeed the derivation he gave in 1911. However he was already aware of the red shift in 1907. The derivation he gave at that time is less general more tortured and yet oddly more sophisticated. It deserves particular mention because it contains the germ of two ideas that were to become cornerstones of his final theory: the existence of local Lorenz frames and the constancy of the velocity of light for infinitesimally small paths . Maxwell's Equations; Bending of Light; Gravitational Energy = mc2. Indomitably Einstein goes on. He tackles the Maxwell equations next. He concludes that Maxwell's equations have the same form in a uniformly accelerated reference frame as in a non-accelerated frame but with a modified velocity of light. 'It follows that the light rays . are bent by the gravitational field.' Second he examines the energy conservation law in the accelerated frame and finds 'a very notable result . In a gravitational field one must associate with every energy E an additional position-dependent energy which equals the position-dependent energy of a 'ponderable' mass of magnitude E/mc2. The law E = mc2 therefore holds not only for inertial but also for gravitational mass' . "This review does not have the perfection of the 1905 paper on special relativity. The approximations are clumsy and mask the generality of the conclusions. Einstein was the first to say so in 1911. The conclusion about the bending of light is qualitatively correct quantitatively wrong - though in 1907 not yet logically wrong. Einstein was the first to realize this in 1915. Despite all this I admire this article at least as much as the perfect relativity paper on 1905 not as much for its details as for its courage" Pais pp. 179-182. "In 1920 Einstein recalled how he first arrived at the ideas behind the equivalence principle: 'While I was occupied in 1907 with a comprehensive survey of the special theory for the 'Yearbook for Radioactivity and Electronics' I also had to attempt to modify Newton's theory of gravitation in such a way that its laws fitted into the theory. Attempts along these lines showed the feasibility of this enterprise but did not satisfy me because they had to be based on physical hypotheses that were not well-founded. Then there came to me the most fortunate thought of my life in the following form: 'Like the electric field generated by electromagnetic induction . the gravitational field only has a relative existence. Because for an observer freely falling from the roof of a house during his fall there exists-at least in his immediate neighborhood-no gravitation field. Indeed if the observer lets go of any objects relative to him they remain in a state of rest or uniform motion independently of their particular chemical or physical composition note by AE: air resistance is naturally ignored in this argument. The observer is thus justified in interpreting his state as being at rest. 'Through these considerations the unusually extraordinary experimental law that all bodies fall with equal acceleration in the same gravitational field immediately obtains a deep physical significance. For if there were just one single thing that fell differently from the others in the gravitational field then with its help the observer could recognize that he was falling in a gravitational field. If such a thing does not exist-which experiment has shown with great precision-then there is no objective basis for the observer to regard himself as falling in a gravitational field. Rather he has the right to regard his state as one of rest and with respect to a gravitational field his neighborhood as field free. The experimental fact of the material-independence of the acceleration due to gravity is thus a powerful argument for the extension of the relativity postulate to coordinate systems in non-uniform relative motion with respect to each other . The generalization of the relativity principle thus indicates a speculative path towards the investigation of the properties of the gravitational field.' "Einstein alludes here to his initial attempts to set up a special-relativistic theory of gravitation but gives no details. In 1933 he gave the fullest account of how he 'arrived at the equivalence principle by a detour Umweg' through such attempts. After mentioning his doubts after 1905 about the privileged dynamical role of inertial systems and his early fascination by Mach's idea that the acceleration of a body is not absolute but relative to the rest of the bodies in the universe he turns to the events of 1907: 'I first came a step closer to the solution of the problem when I attempted to treat the law of gravitation within the framework of special relativity. Like most authors at the time I attempted to establish a field law for gravitation since the introduction of an unmediated action at a distance was no longer possible at least in any sort of natural way on account of the abolition of the concept of absolute simultaneity. 'The simplest thing naturally was to preserve the Laplacian scalar gravitational potential and to supplement Poisson's equation in the obvious way by a term involving time derivatives so that the special theory of relativity was satisfactorily taken into account. The equation of motion of a particle also had to be modified to accord with the special theory. The way to do so was less uniquely prescribed since the inertial mass of a body might well depend on its gravitational potential. This was even to be expected on the basis of the law of the inertia of energy. 'However such investigations led to a result that made me highly suspicious. For according to classical mechanics the vertical acceleration of a body in a vertical gravitational field is independent of the horizontal component of its velocity. This is connected with the fact that the vertical acceleration of a mechanical system or rather of its center of mass in such a gravitational field turns out to be independent of its internal kinetic energy. According to the theory I was pursuing however such an independence of the gravitational acceleration from the horizontal velocity or from the internal energy of a system did not occur. 'This did not accord with an old fact of experience that all bodies experience the same acceleration in a gravitational field. This law which can also be formulated as the law of equality of inertial and gravitational mass now appeared to me in its deep significance. I was most highly amazed by it and guessed that in it must lie the key to the deeper under- standing of inertia and gravitation.' "Turning from later reminiscences let us see how Einstein presented his approach to gravitation in 1907: 'Up to now we have only applied the principle of relativity i.e. the presupposition that the laws of nature are independent of the state of motion of the reference system to acceleration-free reference systems. Is it conceivable that the principle of relativity also holds for systems that are accelerated relative to each other 'This is not the place for an exhaustive treatment of this question. Since however it is bound to occur to anyone who has followed the previous applications of the relativity principle I shall not avoid taking a position on the question here. Consider two systems in motion Σ1 and Σ2. Let Σ1 be accelerated in the direction of its X -axis and let γ be the magnitude constant in time of this acceleration. Let Σ2 be at rest but in a homogeneous gravitational field that imparts an acceleration -γ in the direction of the X -axis to all objects. As far as we know the laws of physics with respect to Σ1do not differ from those with respect to Σ2; this is due to the circumstance that all bodies in a gravitational field are equally accelerated. So we have no basis in the current state of our experience for the assumption that the systems Σ1and Σ2differ from each other in any respect; and therefore in what follows shall assume the complete physical equivalence of a gravitational field and the corresponding acceleration of a reference system. 'This assumption extends the principle of relativity to the case of uniformly-accelerated translational motion of the reference system. The heuristic value of this assumption lies in the circumstance that it allows the replacement of a homogeneous gravitational field by a uniformly accelerated reference system which to a certain extent is amenable to theoretical treatment.' "Some further comments on this equivalence in his next paper on gravitation in 1911 are illuminating. He notes that in both systems objects subject to no other forces fall with constant acceleration: 'For the accelerated system K′ corresponding to the 1907 Σ1 this follows directly from the Galileian principle of inertia; for the system K at rest in a homogeneous gravitational field corresponding to the 1907 Σ2 however it follows from the experimental fact that in such a field all bodies are equally strongly uniformly accelerated. This experience of the equal falling of all bodies in a gravitational field is the most universal with which the observation of nature has provided us; in spite of that this law has not found any place in the foundations of our physical picture of the world . From this standpoint one can as little speak of the absolute acceleration of a reference system as one can of the absolute velocity of a system according to the usual special theory of relativity. Naturally one cannot replace an arbitrary gravitational field by a state of motion of the system without a gravitational field; just as little as one can trans- form all points of an arbitrarily moving medium to rest by a relativity transformation. From this standpoint the equal falling of all bodies in a gravitational field is obvious. 'As long as we confine ourselves to purely mechanical processes within the realm of validity of Newtonian mechanics we are certain of the equivalence of the systems K and K′. Our point of view will only have a deeper significance however if the systems K and K′ are equivalent with respect to all physical processes i.e. if the laws of nature with respect to K agree completely with those with respect to K′. By assuming this we obtain a principle that if it really is correct possesses a great heuristic significance. For by means of theoretical consideration of processes that take place relative to a uniformly accelerated reference system we obtain conclusions about the course of processes in a homogeneous gravitational field.' "With hindsight one can see that Einstein's attempt to find the best way to implement mathematically the physical insights about gravitation incorporated in the equivalence principle was hampered significantly by the absence of the appropriate mathematical concepts. His insight as he put is a few years later that gravitation and inertia are "essentially the same" wesensgleich cries out for implementation by their incorporation into a single inertio-gravitational field represented mathematically by a non-flat affine connection on a four-dimensional manifold. But the concept of such a connection was only developed after and largely in response to the formulation of the general theory. So Einstein had to make do with what was available: Riemannian geometry and the tensor calculus as developed by the turn of the century i.e. based on the concept of the metric tensor without a geometrical interpretation of the covariant derivative" Stachel pp. 83-86. BRL 20; Stanitz 94; Weil 21. Born 'Arnold Johannes Wilhelm Sommerfeld 1868-1951' Obituary Notices of Fellows of the Royal Society 8 1952 pp. 275-296. Stachel 'The first two acts' pp. 81-112 in: Gravitation in the Twilight of Classical Physics. The Promise of Mathematics Renn & Schemmel eds. 2007. 8vo 231 x 157 mm pp. 411-462. Original printed wrappers upper cover a bit soiled lower part of spine worn light vertical crease for posting faint ink stain to page 418 spine strip with wear and tear. S. Hirzel unknown
1905ref. 6412Leipzig: Johann Ambrosius Barth 1905. First edition. First edition rare author's presentation offprint 'Überreicht vom Verfasser' from the library of Arnold Sommerfeld - carrying his ink signature the red-pencil accession number '4' of his Einstein-offprint collection and his autograph pencil calculations on two pages - of the paper on light quanta and the photoelectric effect for which Einstein was awarded the 1921 Nobel Prize and the only one of his four annus mirabilis papers that he called sehr revolutionär. From Wien's radiation law he shows that the entropy of high-frequency radiation has the thermodynamic form of an ideal gas of independent quanta of energy hv and applies it to Stokes's rule photoionisation and the photoelectric effect. Sommerfeld's pencil decodes Einstein's β as h/k on p. 136 using the refined constants of Planck's 1906 Vorlesungen and on p. 146 computes Rβ/E the predicted slope h/e of the photoelectric line that Millikan would measure 1912-1916. Sommerfeld with Debye in 1913 argued the equation could be recovered without the light quantum; Compton's 1923 scattering results won him over. . Einstein's Nobel Prize Paper. First edition rare author's presentation offprint 'Überreicht vom Verfasser' from the library of Arnold Sommerfeld - carrying his ink signature the red-pencil accession number '4' of his Einstein-offprint collection beneath Einstein's printed name and his autograph pencil calculations in the margins of two crucial pages - of the paper on light quanta and the photoelectric effect for which Einstein was awarded the 1921 Nobel Prize in Physics. Of the four epochal papers Einstein produced during his annus mirabilis this is the only one he himself described as revolutionary and the one that most squarely broke with the nineteenth-century physics in which he had been trained. It is also the paper on which Thomas Kuhn built his argument that the origin of quantum theory belongs not to Planck in 1900 but to Einstein in 1905. Provenance: Arnold Sommerfeld 1868-1951 with his ink signature the red-pencil accession number '4' of his Einstein-offprint collection beneath Einstein's printed name on the front wrapper and his pencil calculations in the margins of pp. 136 and 146 with a pencilled mark on p. 145. Appointed to the chair of theoretical physics at Munich in 1906 the year after the present paper appeared he held it for more than three decades. Trained at Königsberg under Hurwitz and Lindemann he came to theoretical physics through mathematics and remained one of its greatest teachers. His Munich institute became the most important training ground in the discipline: Heisenberg Pauli Debye Bethe Ewald Landé Laporte and Morse were among his doctoral students and the institute's seminar room served as the workshop in which the old quantum theory took shape. Sommerfeld's own contributions to that theory - the quantisation of elliptical orbits the fine-structure formula the introduction of the fine-structure constant the systematics of selection rules and later the free-electron theory of metals - place him among the founders of modern atomic physics. His textbook Atombau und Spektrallinien first published in 1919 and repeatedly revised was for a generation the standard exposition of the subject. When the ageing professor was due to retire in 1936 in favour of Heisenberg the National Socialist authorities blocked the succession on the grounds that Sommerfeld and his nominee were insufficiently aligned with party science; the chair remained vacant until 1939 and passed in the end to a political appointment. Sommerfeld returned to his institute after the war and continued working until his death in a road accident in Munich in 1951. Max Born in his Royal Society obituary described him as combining classical clarity with the pioneering instinct. The red-pencil '4' on the front wrapper is one entry in a systematic accession numbering that runs in red chinagraph across Sommerfeld's collection of Einstein offprints. Thirteen numbered copies have so far been documented and their numbers are strictly chronological in the papers' publication dates: 4 on the present 1905 paper; 20 on the 1911 paper on gravitation and the propagation of light; 30 on the November 1915 'Zur allgemeinen Relativitätstheorie' with its Nachtrag; 33 and 34 on two duplicate copies of the 1916 'Hamiltonsches Prinzip' taking consecutive numbers; 36 on the 1917 'Kosmologische Betrachtungen'; and 40 44 45 46 47 48 and 49 on papers of 1923-1929 ending with the unified-field-theory series - the sequence resolved to the month even within a single year 44 on a January 1925 paper 45 on a July 1925 paper. The scheme is thus a running ledger of the collection in order of publication and the '4' identifies the present offprint as the fourth Einstein item in it implying just three earlier papers - necessarily drawn from Einstein's handful of Annalen papers of 1901-1904 - ahead of it. One of the documented copies also bears the pre-1918 stamp of Sommerfeld's Munich institute where his papers and library are recorded as having remained for decades after his death in 1951 consistent with the collection surviving intact long into the twentieth century. No published account of the Sommerfeld offprint collection exists; the reconstruction of the scheme rests on the documented copies themselves of which the present one is the earliest. Completed in Bern on 17 March 1905 and dispatched to Annalen der Physik the following day the paper was the first of Einstein's great 1905 contributions - the others being the doctoral dissertation on molecular dimensions the paper on Brownian motion and the two papers founding the special theory of relativity. Einstein was at the time a twenty-six-year-old technical expert third class at the Swiss Patent Office in Bern without academic affiliation without institutional laboratory with his doctorate not yet conferred and with a circle of scientific correspondents that ran to little more than his old Olympia Academy companions Conrad Habicht and Maurice Solovine. The regular correspondence with Planck Laue Stark Sommerfeld Wien and Lorentz that would bring him into the German-speaking academic world lay still in the future; his first surviving letter to Sommerfeld is dated 5 January 1908. The printed presentation formula on the wrapper marks the present copy as one of the small stock of author's offprints Einstein had in hand by the spring of 1905; how and when it reached Sommerfeld is not documented. Their acquaintance in fact opens over relativity rather than light quanta - the 1908 letter discusses the velocity of signals and the two men first met in person at the Salzburg Naturforscherversammlung of September 1909 - but the pencil annotations described below place the close study of this copy in precisely those years as Sommerfeld newly installed in the Munich chair of theoretical physics was turning himself and his school toward the quantum theory of radiation. Writing to Habicht in May 1905 Einstein sketched the four papers that were about to appear and reserved a particular adjective for this one alone. The first he explained concerned radiation and the energetic properties of light and was sehr revolutionär. The second determined the true sizes of atoms from the viscosity of dilute solutions. The third derived the irregular motion of small bodies suspended in a liquid from the molecular-kinetic theory of heat. The fourth still in draft would treat the electrodynamics of moving bodies and would alter as Einstein promised the theory of space and time. In that taxonomy only the light-quantum paper is singled out as revolutionary and Einstein's self-assessment has proved durable. Relativity consummated a line of nineteenth-century thought extending from Maxwell through Lorentz and Poincaré; the light-quantum hypothesis set itself against that entire line. The paper opens from a formal asymmetry that physicists had tolerated without remark. The state of a gas or any ponderable body is described by the positions and velocities of a finite if very large number of atoms and electrons so that the energy of such a body is a sum over a discrete basis. The state of an electromagnetic field by contrast is given by continuous functions in space so that in Maxwell's theory the energy of radiation is an integral over an infinite number of degrees of freedom. Einstein proposes that this asymmetry is not merely formal but physical - that radiation energy like matter may in certain circumstances behave as if it were concentrated into a finite number of localised packets. The wave theory he grants is magnificent where it applies but its predictions refer to time-averaged field values so that nothing in the experimental record rules out a granular structure on short timescales or at low densities of the radiation. The positive case for light quanta rests on a thermodynamic analogy that Einstein develops with remarkable economy. Using Wien's radiation law valid in the high-frequency tail of the black-body spectrum he writes down the entropy of monochromatic radiation of fixed frequency as a function of its volume. The resulting expression has exactly the form of the entropy of an ideal gas whose particle number equals the radiation energy divided by hv. In the Wien region in other words radiation behaves thermodynamically as a collection of independent energy quanta of magnitude hv. This simple audacious conclusion - that the entropy-volume relation of radiation is that of a gas of particles - is the paper's load-bearing result and it arrives without any appeal to detailed mechanical models of emission or absorption. From this thermodynamic footing Einstein advances to three predictions. Stokes's rule stating that fluorescent light has a lower frequency than the exciting light follows directly on the hypothesis that one absorbed quantum of energy hv can re-emit at most one quantum of no greater energy: the emitted frequency cannot exceed the absorbed frequency because the emitted quantum cannot exceed hv in energy. Photoionisation of gases by ultraviolet light follows from the condition that the ionisation energy of a molecule cannot be greater than the energy of the absorbed quantum. And the photoelectric effect in which metallic surfaces release electrons under illumination is reformulated into what became known as Einstein's photoelectric equation: the maximum kinetic energy of the ejected electron equals hv minus the work function of the metal. The linearity of electron energy in frequency and the independence of the slope from the material are predictions derived from the quantum hypothesis. It is on precisely these last two sections of the paper that the Sommerfeld copy speaks most directly. At the foot of p. 136 beside Einstein's statement of Planck's formula with the constants α = 6.10 × 10−56 and β = 4.866 × 10−11 Sommerfeld has written in pencil β = h/κ = 6.548 × 10−27 / 1.346 × 10−16 grad·sec. Einstein throughout his paper uses Planck's 1901 constants α and β without explicitly connecting them back to Planck's action quantum h and to what would later be called Boltzmann's constant k. Sommerfeld's pencil step reconstructs the bridge - Einstein's β is nothing other than the ratio h/k and 'grad·sec' is that ratio's correct unit - and the numbers he inserts identify the very book he was working from. The pair h = 6.548 × 10−27 erg·sec and k = 1.346 × 10−16 erg/grad appears in exactly this form as equation 252 of Planck's Vorlesungen über die Theorie der Wärmestrahlung Leipzig 1906 p. 162 - Planck's own refinement of the rounder values of his 1901 paper - and so far as can be established nowhere else: Planck's second edition of 1913 revised the figure to 6.415 and the later determinations of Millikan 1916 and Birge 1919 differ again. Planck's 1906 text even cites Einstein's paper by page in the passage immediately preceding that equation. The annotation thus records a reader checking Einstein's constants against Planck's newest determination with the textbook open beside the offprint at some point between 1906 and about 1912 - the very years in which Sommerfeld entered the quantum theory of radiation. On p. 146 the second pencil annotation sits beside Einstein's derivation of the photoelectric equation ΠE = Rβv − P′ where E = 9.6 × 103 is the charge of a gram-equivalent of a monovalent ion and Π is the stopping potential required to arrest the photoelectrons. Sommerfeld has written out Rβ/E = 8.31 × 107 · 4.866 × 10−11 / 9.6 × 103 - that is the slope dΠ/dv of the stopping potential against frequency. Because Rβ = Rh/k = Nh and the Faraday E = Ne this ratio reduces algebraically to h/e. What Sommerfeld is pencilling in the margin is therefore the predicted slope of Einstein's photoelectric line - the very constant that Robert Andrews Millikan would spend the years 1912-1916 measuring and whose accurate determination by the straight-line fit of electron energy against frequency delivered in 1916 both the most stringent early confirmation of Einstein's equation and a precise new value of Planck's h. On p. 145 a small pencilled '2' and two double dashes in the outer margin bracket a single sentence of §8 - Einstein's caveat that it should not be excluded 'daß Elektronen die Energie von Lichtquanten nur teilweise aufnehmen' that electrons might take up the energy of light quanta only partially. That is precisely the loophole on which the semi-classical readings of the photoelectric equation would later be built Sommerfeld's own among them. That Sommerfeld should have traced those calculations on his own copy is more than incidental. In January 1910 he told Lorentz that he was 'old-fashioned enough to resist for now the light quanta in Einstein's conception' and through the 1910s he was himself among the physicists who argued that Einstein's photoelectric equation could be recovered on semi-classical non-Einsteinian grounds - that is that the equation stood while the light-quantum hypothesis from which Einstein had derived it need not be accepted. Planck Debye Lorentz and O. W. Richardson held variants of the same position; the fullest contemporaneous statement of this approach is Debye and Sommerfeld 'Theorie des lichtelektrischen Effektes vom Standpunkt des Wirkungsquantums' Annalen der Physik 346 1913 pp. 873-930. It would take the Compton experiments of 1922-1923 to change Sommerfeld's mind - at which point he declared with characteristic decisiveness that Compton's scattering results sounded the death knell of the classical wave theory of radiation a position he made public in the preface to the fourth edition of Atombau und Spektrallinien Vieweg 1924 pp. vii-viii where he wrote that he had clung to the wave theory as long as possible before being 'impelled to adopt more and more the position of the extreme light quantum theory'. The two pencil derivations on this copy then are the working-notes precursors to nearly twenty years of sustained theoretical engagement by one of the foremost teachers of modern physics with the very pages marked. The audacity of Einstein's argument was not lost on his contemporaries and neither was its precariousness. The light-quantum hypothesis demanded that a century of evidence for the wave theory - diffraction interference polarisation the entire edifice of physical optics - be folded into a picture in which radiation also travelled as discrete packets. Einstein himself acknowledged the strain and used the word heuristisch in his title to temper it. For nearly two decades after 1905 his contemporaries resisted the hypothesis even as they accepted the equation. When Planck Nernst Rubens and Warburg proposed Einstein for election to the Prussian Academy in 1913 they prefaced their glowing recommendation by asking that he not be held too severely to account for those of his speculations that had missed their mark - their example being precisely the hypothesis of light quanta. Millikan reporting the decisive experimental confirmation of Einstein's photoelectric equation in 1916 went out of his way to describe the underlying quantum hypothesis as untenable and reached instead for classical interpretations. Only with Compton's scattering experiments in 1923 did the physics community at large concede that light itself and not merely its interaction with matter demanded the quantum. The prehistory of the paper runs back to Einstein's undergraduate years. Mach's Wärmelehre which he read in Aarau or shortly thereafter devoted two chapters to thermal radiation and closed with an account of Kirchhoff's universal black-body law. H. F. Weber's physics course at the ETH in the winter of 1898-1899 for which Einstein registered presented measurements of the energy spectrum of thermal radiation and an empirical distribution function that anticipated Wien's displacement law. By March 1899 Einstein had begun thinking seriously about radiation and by the spring of 1901 he was reading Planck with care and scepticism. Planck had derived the black-body formula of 1900 by dividing the energy of a collection of charged oscillators into discrete elements of size hv and counting the ways these elements could be distributed - a procedure that as Einstein would later show is only consistent if one admits that the oscillators themselves can hold only energies that are integer multiples of hv. Planck himself had been unwilling to draw that conclusion. Einstein in 1905 draws it without apology and goes further: if oscillators can hold only quantised energies then the radiation field with which they are in equilibrium must also at least in some regimes be granular. Einstein prepared himself for this step with a long study of the foundations of statistical physics conducted between 1902 and 1904. That work yielded three tools that became indispensable to his quantum argument. The first was the canonical ensemble which gave him a general framework for calculating mean values in thermal equilibrium. The second was a careful reinterpretation of the Boltzmann principle S = k log W in which the probability W is counted over the accessible microstates of the system. The third was a method for computing mean-square fluctuations of state variables at equilibrium. Applied to radiation in thermal equilibrium the fluctuation method reproduced Wien's displacement law and more tellingly suggested that radiation behaved as if its phase space had a finite dimension - an intimation of the quantum granularity the 1905 paper would go on to assert. Two features make the 1905 quantum paper unique even within Einstein's own subsequent work on the subject. It does not rely on Planck's radiation law; it uses only the Wien limit. And it does not rely on the apparatus of the canonical ensemble that Einstein had developed; the argument proceeds through a thermodynamic analogy between radiation entropy and gas entropy. This austerity is part of its power: by leaning on nothing but thermodynamics and the Wien law Einstein removes every interpretive crutch that might soften the conclusion. The radiation is behaving as a gas of particles because the thermodynamic form of its entropy says so. Einstein submitted the paper to Annalen der Physik on 18 March 1905. It appeared in the first issue of Band 17 distributed on 9 June 1905. By April 1905 however - and therefore weeks before the journal issue was bound up and circulated - Einstein had already received his allotment of offprints: his letter to Habicht announcing the four forthcoming papers indicates that he had separates in hand. On the priority of issue then the offprint precedes the journal printing and the printed presentation statement 'Überreicht vom Verfasser' on the wrapper of copies such as the present one marks them as part of the small stock that passed through Einstein's own hands. That circle was small. Weil in the standard bibliography of Einstein's writings notes that the number of offprints produced of papers before 1914 appears to have been very modest that they were given to the author only and that the wrappers usually carry the printed presentation formula. Later trade-attributed testimony from Hans Albert Einstein's copy of the Brownian-motion offprint puts the typical print run for Einstein's early offprints at twenty-five to thirty copies. Of the light-quantum paper in particular offprints in any condition are now encountered only very occasionally in commerce and copies preserved in their original wrappers are rarer still. References: Norman 689 - Weil Einstein Bibliography 6 - Boni Russ & Laurence Bibliographical Checklist 7 - Pais Subtle Is the Lord pp. 364-368 - Planck Vorlesungen über die Theorie der Wärmestrahlung Leipzig: Barth 1906 p. 162 the source of the annotated constants - Eckert Arnold Sommerfeld: Science Life and Turbulent Times Springer 2013 - Born 'Sommerfeld 1868-1951' Obituary Notices of Fellows of the Royal Society 8 1952 pp. 275-296 - Cassidy 'Einstein on the Photoelectric Effect' in Einstein: Image and Impact American Institute of Physics - Stachel et al. eds The Collected Papers of Albert Einstein vol. 2 pp. 134-142 and vol. 5 doc. 72 Einstein to Sommerfeld 5 January 1908 - Eckert & Märker eds Arnold Sommerfeld: Wissenschaftlicher Briefwechsel Band 1: 1892-1918 GNT-Verlag 2000 - Stuewer 'Einstein's Revolutionary Light-Quantum Hypothesis' Acta Physica Polonica B 37 2006 pp. 543-558 - Printing and the Mind of Man 391 Planck's precursor quantum papers. Offprint from Annalen der Physik 4. Folge 17. Band 1905. 8vo 222 × 144 mm pp. 1 132-148. Original printed wrappers with 'A. Einstein. Überreicht vom Verfasser' printed in bold type on the front cover upper outer corner of rear wrapper with loss well clear of the printed area; small chips to the lower outer corner of the front wrapper and to the foot of the spine; faint vertical creases to the front wrapper. . Johann Ambrosius Barth unknown
1931ref. 021909New York: Covici Friede 1931. First Edition. hardcover. Some pencil markings in text title page and endpapers darkened not really affecting Einstein's inscription; covers a little soiled. Good to Very Good and quite scarce. With a long biographical note and an appreciation by George Bernard Shaw. Subjects include Disarmament Pacifism the Jewish Homeland and more. This copy INSCRIBED and SIGNED by the author with his scarcer full signature on the front endpaper: "To little Pauline/Albert Einstein/1933." An uncommon title to find signed by the man of the century. With a letter of authenticity from James Spence if you need that kind of security blanket. Covici Friede hardcover
ref. 10361210-6Taylor & Francis Group. Used - Very Good. Former library copy. Pages intact with possible writing/highlighting. Binding strong with minor wear. Dust jackets/supplements may not be included. Includes library markings. Stock photo provided. Product includes identifying sticker. Better World Books: Buy Books. Do Good. Taylor & Francis Group unknown
ref. A9780691246161Paperback / softback. New. paperback
ref. A9780393097337Hardback. New. An illustrated history of musical thought in the nineteenth century and its relationship to the Romantic movement. hardcover
1919ref. 6166Berlin: Verlag der Akademie der Wissenschaften In Kommission bei Walter de Gruyter Reichsdruckerei 1919. First edition. First edition extremely rare author's presentation offprint 'Überreicht vom Verfasser' and the copy of Einstein's son Hans Albert of "Einstein's first attempt at a unified field theory" Pais Subtle is the Lord. Once Einstein completed work on the general theory of relativity at the end of 1915 "his attention shifted to the search for a unified theory of the electromagnetic and gravitational fields out of which he hoped to be able to explain the structure of matter. Quantum effects were to be derived from such a theory rather than postulated ad hoc. This remained his approach for the rest of his life" Cao Conceptual foundations of quantum field theory. . EINSTEIN'S FIRST ATTEMPT AT A UNIFIED FIELD THEORY" PAIS HANS ALBERT EINSTEIN'S COPY OF THE PRESENTATION OFFPRINT. First edition extremely rare author's presentation offprint 'Überreicht vom Verfasser' and the copy of Einstein's son Hans Albert of "Einstein's first attempt at a unified field theory" Pais Subtle is the Lord p. 287. Once Einstein completed work on the general theory of relativity at the end of 1915 "his attention shifted to the search for a unified theory of the electromagnetic and gravitational fields out of which he hoped to be able to explain the structure of matter. Quantum effects were to be derived from such a theory rather than postulated ad hoc. This remained his approach for the rest of his life" Cao Conceptual foundations of quantum field theory pp. 166-167. "As so often the case in relativity the story of quantum gravity begins with Einstein himself. Soon after the final formulation of general relativity he pointed out the need for a quantum modification of the theory. In his first paper on gravitational radiation the 1916 paper 'Näherungsweise Integration der Feldgleichungen der Gravitation' 'Approximate Integration of the Field Equations of Gravitation' Einstein argued that quantum effects must modify the general theory of relativity. Two years later he reiterated this conclusion the 1918 paper 'Über Gravitationswellen' 'On Gravitational Waves': 'As already emphasized in my previous paper the final result of this argument which demands a gravitational energy loss by a body due to its thermal agitation must arouse doubts about the universal validity of the theory. It appears that a fully developed quantum theory must also bring about a modification of the theory of gravitation.' Einstein writing in the 1919 paper offered here soon began to speculate whether gravitation plays a role in the atomistic structure of matter: 'There are reasons for thinking that the elementary formations which go to make up the atom are held together by gravitational forces. The above reflections show the possibility of a theoretical construction of matter out of the gravitational field and the electromagnetic field alone' In order to construct such a model of an 'elementary particle' Einstein shows that it is necessary to modify the original gravitational field equations .The major interest of this paper is that his attention now shifted from possible quantum modifications of general relativity to the search for a unified theory of the electromagnetic and gravitational fields on the basis of which he hoped to explain the structure of matter. Quantum effects are to be derived from such a theory rather than postulated ad hoc. Einstein remained committed to this approach for the rest of his life: the search for a 'natural' mathematical extension of the general theory in the hope that such a theory would somehow explain the quantization of matter and energy" Iyer and Bhawal Black Holes Gravitational Radiation and the Universe pp. 525-526. 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 inventios such as radio television and the telephone. Einstein continued his attempts to devise a unified theory of gravitation and electromagnetism for the rest of his life; his 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. RBH lists three copies. OCLC lists only one copy none in US. Provenance: Hans Albert Einstein 1904-73 ink stamp and pencil notes on front wrapper. Hans Albert Einstein was a Swiss-American engineer and educator the second child and first son of physicists Albert Einstein and Mileva Marić. He was a long-time professor of hydraulic engineering at the University of California Berkeley. "As early as 1909 in his fundamental paper 'Zum gegenwärtigen Stand des Strahlungsproblems' 'On the current status of the radiation problem' which resulted from a discussion with Walter Ritz Einstein remarks 'dass des elektrische Elementarquantum e ein Fremdling ist in der Maxwell-Lorentzschen Elektrodynamik' 'that the electrical elementary quantum e is alien to Maxwell-Lorentz electrodynamics'. Einstein expressed the hope that 'die gleiche Modifikation der Theorie welche das Elementarquantum e als Konsequenz enthält auch die Quantenstruktur der Strahlung als Konsequenz enthalten wird' 'the same modification of the theory which contains the elementary quantum e as a consequence will also contain the quantum structure of radiation as a consequence'. Pauli 1949 in his review about 'Einstein's Contribution to Quantum theory' pointed out that though quantum theory later on deduced the quantum structure of radiation it has not solved Einstein's first problem and the elementary charge 'auch in der Quantenmechanik ein Fremdling geblieben ist' 'has also remained alien to quantum mechanics'. He emphasized that just this fact had been one of the strongest arguments to Einstein against the finality of the steps leading to quantum mechanics. "So during his Berlin years Einstein made it his task to find a synthesis of his general theory of relativity GRT and the then nascent quantum physics. In this connection he attributed logical primacy to the relevant relativistic field theory because it had reached a high degree of maturity in the GRT. After all Einstein's general-relativistic gravitation theory is the first theory on the fundamentals of physics working with genuinely non-linear equations and Einstein observed that such a nonlinearity is necessary for understanding the existence of the 'discrete field-quanta.' A linear theory allowing arbitrary superposition of fields would without further restrictions in the form of boundary and uniqueness conditions never lead to a discrete spectrum of solutions. But recourse to such restrictions means that the fields are held together by the operation of entities outside the scope of the theory . "In Einstein's view the problem of incorporating the elementary particles into field physics involved the question of finding field-theoretical models of electrons and protons which were the only known particles at that time. Einstein searched for solutions or general-relativistic field equations for the combined gravitational and electromagnetic fields representing mass and charge distributions with central symmetry and he hoped there would emerge self-consistent solutions only for discrete values of the mass and charge parameters i.e. for a 'particle spectrum.' "This 'Einstein particle problem' pursued ideas that had been developed already in the framework of the special theory of relativity and the Maxwell-Lorentz electrodynamics for instance in the nonlinear theory of the electromagnetic field by G. Mie and D. Hilbert. As an essential progress by the general-relativistic treatment Einstein regarded the genuine nonlinearity of the field equations which Mie and Hilbert had to introduce ad hoc and full consideration of the particle dynamics in the sense of the general-relativistic problem of motion. The generalizations of the Maxwell equations considered by Mie and Hilbert contain a too small number of components for the integrability conditions to determine the particle dynamics whereas the Einstein problem of motion in the GRT furnishers just this dynamics as a consequence of the integrability conditions for the field equations of gravitation. It is the GRT that with its metric field for the first time embraces inertia and gravity that is just those properties which are characteristic of all particles. "Einstein in fact succeeded in driving self-consistent gravitational and electromagnetic fields which can be interpreted as particle models of that kind. But his success depended on a weakening of his own equations of gravitation which physically amounts to the introduction of an additional hypothetical cosmical field of the 'Poincaré pressure.' By this weakening it becomes possible to set up self-consistent particle models with spherical symmetry for arbitrary centrosymmetric mass and charge distributions. In 1919 Einstein presented his result to the academy in his paper 'Spielen Gravitationsfelder im Aufbau der materiellen Elementarteilchen eine wesentliche Rolle' His answer to the question says that in his particle models the electrical field energy contributes ¾ and the gravitational energy ¼ of the total energy. "Einstein's first discourses on the particle problem in the GRT were closely related to the 1917/18 papers in which he laid the foundations of relativistic cosmology. In his Academy report 'Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie' 'Cosmological considerations on the general theory of relativity' 1917 Einstein had by introducing the term λgμν with the 'cosmological constant' λ extended his equations of gravitation to his cosmological equations of gravitation Rμν - ½ gμνR λgμν = - κ Tμν . He could show that these equations permit as a particular solution with λ > 0 and constant positive mass density a statical model of the universe representing a closed spheric or elliptic three devotional Riemannian space . "In his paper of 1919 about the role of gravitation in the structure of elementary particles Einstein also interpreted the cosmological constant λ as the universal 'Poincaré' pressure' which according to a hypothesis of H. Poincaré is to guarantee the stability of Lorentz's electrons against their own repulsion forces. Einstein's ideas concerning this matter partly resulted from a controversial discussion with E. Schrödinger 1918 about the gravitational energy in the GRT and the structure of the energy tensor" Treder pp. 149-151. Indeed Schrödinger had pointed out another way of treating the cosmological constant: moving it from the left-hand side of equation where it represents a contribution to space-time curvature to the right-hand side where it represents a contribution to the energy-matter distribution. Then it would correspond physically to a kind of cosmic pressure. Schrödinger believed this might be the pressure postulated by Poincaré to maintain the stability of charged particles: an electric charge on the surface of a sphere creates a force pushing outwards so without any opposing force the charged sphere would explode outwards. Einstein never liked the cosmological constant. In the present paper he acknowledged that his introduction of the cosmological constant was "gravely detrimental to the formal beauty of the theory" Cambridge Companion to Einstein p. 257. Boni-Russ-L. 111; Schilpp 123; Weil 106. Treder 'Antimatter and the particle problem in Einstein's cosmology and field theory of elementary particles A historical essay on Einstein's work at the Akademie der Wissenschaften zu Berlin' Astronomische Nachrichten 296 1975 pp. 149-161. Large 8vo 254 x 182 mm pp. 349-356. Original printed wrappers. A very fine copy. Verlag der Akademie der Wissenschaften, In Kommission bei Walter de Gruyter [Reichsdruckerei] unknown
1916ref. 6164Braunschweig: Druck und Verlag von Friedr. Vieweg and Son 1916. First edition. First edition complete journal issue in original printed wrappers inscribed by Einstein to fellow Nobel Laureate Walther Bothe. "This work represents a major step forward in quantum theory" Calaprice p. 297. It introduced the concept of stimulated emission of radiation the theoretical basis for the laser; it also contained a new derivation of Planck's radiation law which provided as a by-product a justification of the frequency rule forming the basis of Bohr's theory of atomic spectra. . DISCOVERY OF STIMULATED EMISSION OF RADIATION THE PRINCIPLE OF THE LASER INSCRIBED BY EINSTEIN TO A FELLOW NOBEL LAUREATE. First edition complete journal issue in original printed wrappers inscribed by Einstein to fellow Nobel Laureate Walther Bothe. "This work represents a major step forward in quantum theory" Calaprice p. 297. It introduced the concept of stimulated emission of radiation the theoretical basis for the laser; it also contained a new derivation of Planck's radiation law which provided as a by-product a justification of the frequency rule forming the basis of Bohr's theory of atomic spectra. "According to Albert Einstein when more atoms occupy a higher energy state than a lower one under normal temperature equilibrium it is possible to force atoms to return to an unexcited state by stimulating them with the same energy as would be emitted naturally" Britannica. This is 'stimulated emission.' "To claim that Einstein almost invented the laser would be an exaggeration but the laser's underlying mechanism stimulated emission of radiation was a creation of his radiation theory" Kleppner pp. 32-33. "During the summer of 1916 less than a year after he had completed the general theory of relativity Einstein made a new major contribution to the quantum theory. The two papers he wrote then deal with the quantum theory of radiation by arguments that do not depend on the classical electromagnetic theory as had all earlier treatments of Planck's radiation law . When Einstein returned to the radiation problem in 1916 the quantum theory had undergone a major change. Niels Bohr's papers had opened a new and fertile domain for the application of quantum concepts - the explanation of atomic structure and atomic spectra. In addition Bohr's work and its generalizations by Arnold Sommerfeld and others constituted a fresh approach to the foundations of the quantum theory of matter" DSB. In this paper "Einstein considers a system of atoms in equilibrium with an external radiation field. An atom can change its internal energy state by absorbing or emitting radiation. Einstein introduces three basic assumptions about these exchanges of energy between matter and field. First the probability of absorption of radiation is proportional to the radiation density. Second there are two kinds of emission processes: one - spontaneous - following a law like that of radioactive decay; the other - stimulated - induced by the radiation field and with probability proportional to the radiation density. Third at equilibrium the atoms are distributed among their internal states according to the Boltzmann distribution law. From these assumptions Planck's law follows in a simple way. Einstein was very pleased with his derivation which he characterized in a letter to Besso: 'An amazingly simple derivation of Planck's formula I should like to say the derivation.' As a bonus from his derivation Einstein found that the energy difference between two internal energy states of the atom had to be equal to hv with v the frequency of the radiation absorbed or emitted in transitions between these two states thus confirming one of the postulates of Niels Bohr's theory of spectra" Papers 6 xxiii-xxiv. "Einstein meant the second part of this study a proof of the oriented character of the emission process to be his most essential contribution to quantum radiation theory this second paper was published later in 1916 as 'Zür Quantentheorie der Strahlung'. Instead Bohr gave more importance to the new deduction of the blackbody law; for this deduction reinforced the basic assumptions of his atomic theory and completed them with a statistical description of radiation processes" Darrigol p. 120. Provenance: Inscribed by Einstein on front wrapper "für. Dr Bothe" i.e. Walther Bothe 1891-1957. "In 1929 in collaboration with W. Kolhörster Bothe introduced a new method for the study of cosmic and ultraviolet rays by passing them through suitably arranged Geiger counters and by this method demonstrated the presence of penetrating charged particles in the rays and defined the paths of individual rays. For his discovery of the 'method of coincidence' and the discoveries subsequently made by it which laid the foundations of nuclear spectroscopy Bothe was awarded jointly with Max Born the Nobel Prize in Physics 1954" . While Einstein commended Planck's epoch-making derivation of his radiation law in 1900 which ushered in the quantum era he had also noted its limitations. Einstein also saw inconsistencies in Planck's derivation of his law. For Einstein this inconsistency was no reason to reject Planck's quantum theory but it was a reason to study the foundations of traditional radiation theory and if needed revise them. "As Einstein had noted in 1906 Planck's derivation of the Rayleigh-Jeans law uν = 8πν2/c3 kT between average resonator energy uν and radiation spectrum ν only applied to classical resonators T is the temperature k is Boltzmann's constant. A new quantum-theoretical picture of the interaction between matter and radiation was needed. Einstein found it in the summer of 1916 after the completion of his general theory of gravitation left him more time for quantum meditation. "The new picture presumably emerged from a combination of three elements: Einstein's derivation of the law of photochemical equivalence his analogy between quantum states and chemical species and Niels Bohr's theory of atomic spectra. According to Bohr atoms and molecules can only exist in a series of quantum states S0 S1 . . . Sn . . . with well-defined energies E0 E1 . . . En . . . Their interaction with radiation occurs through quantum jumps with characteristic values of the frequency of the emitted or absorbed radiation. Regarding the quantum states as chemical species and remembering his photochemical reasoning Einstein knew that he could derive Wien's law by balancing the absorption process Sn hν → Sn1 with the emission process Sn1 → Sn hν and by making the probability of the first reaction proportional to the density of radiation at frequency ν. Something in this reasoning needed to be altered in order to get Planck's law instead of Wien's. "At this point Einstein appealed to an analogy between classical and quantum theory. According to classical theory an oscillating dipole spontaneously emits radiation whether or not radiation is initially present in its surroundings. When external radiation encounters this dipole it may either be absorbed if the phase of the incoming wave agrees with that of the oscillator or it may be amplified in the contrary case. In the quantum theory of radiation Einstein similarly admitted the existence of three kinds of processes: spontaneous emission Ausstrahlung absorption negative Einstrahlung and stimulated emission positive Einstrahlung. The modern terminology is Bohr's. For the probability per time unit of the respective sorts of quantum jump Einstein assumed the forms Anm ÏνBnm ÏνBmn where n is the upper quantum state m the lower one and Ïν is the density of radiation at the frequency ν. "Einstein did not say much on the nature of the probabilities he thus introduced. He only commented that his theory had the weakness to leave to chance the instant and direction of the spontaneous emission of light. He also noted the similarity between spontaneous emission and radioactive decay. Undoubtedly he would have preferred a theory in which the emission and absorption probabilities were deduced from an underlying deterministic theory. He nonetheless expressed his 'full trust in the present way of reasoning'. The probabilistic description of the interaction was a natural counterpart of the discrete character of quantum states: if a quantum system evolves mostly through quantum jumps then the probability of a quantum jump obviously is the main quantity of physical interest. Instead of speculating on the precise timing and fine structure of the jumps Einstein proceeded to show what could be done by means of the new probability coefficients. "At thermal equilibrium Einstein reasoned statistical mechanics requires the number of atoms in a quantum state n to be proportional to exp−En /kT. The kinetic equilibrium between the atoms and surrounding radiation further requires that the number of quantum jumps from m to n should be equal to the number of reverse jumps: ÏνBnm exp−Em /kT = ÏνBnm Anm exp−En /kT. In the high temperature limit for which Ïν → ∞ this condition gives Bnm = Bmn. Therefore the equilibrium value uν of the density Ïν is given by uνexpEn − Em/kT - 1 = Anm / Bnm. According to a thermodynamic theorem by Wien uν/ν3 must be a function of ν/T only. Hence En − Em must be proportional to ν. Einstein thus derived Bohr's strange frequency rule ΔE = hν with complete generality and without recourse to any of the empirical laws of spectra. He then required the expression of uν to agree with the Rayleigh-Jeans law in the low-frequency limit. The outcome was Planck's law as well as the relation Anm / Bnm = 8πhν3/c3 between Einstein's two probability coefficients . "Einstein's new theory of radiation is now remembered for the introduction of stimulated emission which famously permitted the conception of masers and lasers. For Einstein and for his contemporaries the importance of these memoirs lay elsewhere. First Einstein filled an important gap in the derivation of Planck's law by means of a simple statistical description of radiation processes. Second he corroborated two basic assumptions of Bohr's atomic theory: the existence of stationary states and the frequency rule. In this regard it should be emphasized that before Einstein's and Sommerfeld's contributions of 1916 Bohr believed that his frequency rule only applied to strictly periodic systems. For instance he regarded the Zeeman effect as a violation of this rule. Einstein's new considerations established its complete generality" Darrigol in Cambridge Companion to Einstein pp. 134-136. "The implication of Einstein's theory of stimulated emission was that if one arranges for a large number of atoms to be in identical excited states a stray photon of the right energy can stimulate one atom to emit another photon which stimulates another. and all the atoms release their excess energy in a sudden cascade. What's more the photon released by stimulated emission will be in phase - coherent - with the one that stimulated it and so all the light produced in the cascade will be coherent. "In 1955 American physicist Charles Townes of Columbia University in New York an expert in molecular spectroscopy and his co-workers showed how stimulated emission could be used to make a device for generating or amplifying microwaves which they called a maser microwave amplified stimulated emission of radiation. Three years later Townes and Arthur Schawlow explained how to extend the idea to visible and infrared frequencies to make an 'optical maser' - in effect the laser. "They proposed using ordinary incoherent light to pump atoms into an excited state setting up the 'population inversion' in which the atoms are primed to return to their ground state by emitting photons. And their design used an optical cavity - basically two mirrors between which photons would bounce - to trap the emitted photons while they stimulated more emission. The device they explained would generate 'extremely monochromatic single-wavelength and coherent light'. Theodore Maiman of the Hughes Research Laboratories in Malibu California described such a device using a ruby crystal already used for masers as the lasing medium in 1960" 'A century ago Einstein sparked the notion of the laser' Physics World History Blog 31 August 2017. Weil 85. Calaprice An Einstein Encyclopedia 2015. Darrigol From c-numbers to q-numbers 1992. Kleppner 'Rereading Einstein on radiation' Physics Today 58 2005 pp. 30-33. Pais Subtle is the Lord 1982. 8vo 228 x 154 mm pp. 315-332. Original printed wrappers. A fine copy. Druck und Verlag von Friedr. Vieweg and Son unknown
1931ref. 60051931. First edition. An important group of photographs documenting Einstein's visit to Caltech. The main purpose of the visit was to discuss Edwin Hubble's observations made in 1929 with the 100-inch telescope at the Mount Wilson Observatory which showed that light from distant nebulae galaxies was red-shifted indicating that the universe was expanding. Einstein had believed that the universe is static and had introduced his 'cosmological constant' into his equations of general relativity to allow for a static solution. When Einstein met Hubble at the Mount Wilson Observatory in January and February 1931 he was visibly moved with Hubble's discovery and reportedly said with tears in his eyes that "It was the most beautiful and satisfying interpretation of astronomical science." In light of the new evidence Einstein published a paper two months later renouncing the concept of a cosmological constant whose invention Einstein denounced as "the greatest blunder of my life." . 'the greatest blunder of my life'. An important group of photographs documenting Einstein's second visit to America and his first to the California Institute of Technology which began at the end of December 1930. The main purpose of the visit was to discuss Edwin Hubble's observations made in 1929 with the 100-inch telescope at the Mount Wilson Observatory then the largest telescope in the world which showed that light from distant nebulae galaxies was red-shifted indicating that the universe was expanding. Einstein had believed that the universe is static and had introduced his 'cosmological constant' into his equations of general relativity to allow for a static solution. When Einstein met Hubble at the Mount Wilson Observatory in January and February 1931 he was visibly moved with Hubble's discovery and reportedly said with tears in his eyes that "It was the most beautiful and satisfying interpretation of astronomical science." In light of the new evidence Einstein published a paper two months later renouncing the concept of a cosmological constant whose invention Einstein denounced as "the greatest blunder of my life." Einstein was accompanied on his visit by Walther Mayer 1887-1948 who had been appointed as his mathematical assistant in 1929. Mayer and Einstein worked together on several approaches towards a unified field theory. "On the way over Einstein and his mathematical calculator Walther Mayer holed up working on revisions to his unified field theory in an upper-deck suite with a sailor guarding the door" Isaacson p. 368. Two of the photographs are of Einstein at Mount Wilson one with Mayer and the observatory's director Walter Adams 1876-1956 who had confirmed Einstein's prediction of the gravitational red-shift although his observations were later shown to be faulty; the other with Mayer and solar physicist Charles St. John 1857-1935 who had assisted Hubble with his red-shift observations. Another photograph shows Einstein between fellow Nobel Laureates Albert Michelson 1852-1931 and Robert Millikan 1868-1953 Caltech's "chairman of the executive council" effectively its president. Together with Edward Morley Michelson had in 1887 carried out the famous Michelson-Morley experiment which failed to detect evidence of the existence of the luminiferous ether; this provided crucial evidence for the early acceptance of special relativity. On this trip Einstein "paid tribute to the aging Michelson carefully praising his famous experiments that detected no ether drift without explicitly saying that they were a basis for his special theory of relativity" Isaacson p. 372. "In the early 1930s Einstein came to California specifically to consult with scientists at the California Institute of Technology. Few members of the general public understood the nature of his visits but they idolized him all the same. From the moment his boat docked in San Diego on December 31 1930 the reception accorded him by Californians was one part show business one part hero worship and one part genuine affection. Groups of children dressed in blue and white middies serenaded him and thrust wreaths of flowers into his hands two bands struck up tunes and in Los Angeles a theatrical group the Yale Puppeteers opened a play called Mr. Noah in which the ark landed on Mt. Wilson instead of on Mt. Ararat . "As early as 1913 Einstein was looking for experimental verification for the correctness of his theory of general relativity and he had been in correspondence with Caltech's George Ellery Hale asking him to make an astronomical measurement. He was anxious to know if Hale could detect the influence of the sun's gravitation field upon a light ray. Hale replied that in order to try he needed a solar eclipse. The experiment was finally carried out in 1919 by two British expedition teams and again in 1922 by an American team of astronomers - and it did confirm the theory of general relativity. "There were cosmological implications in this theory and they attracted a lot of attention in the 1920s and 1930s - nowhere more than at Caltech. Millikan had been urging Einstein to visit the campus for some time and in the fall of 1930 he agreed to spend the winter quarter in Pasadena. Not only would he be able to discuss his theory and its interpretation with distinguished scientists; he would also be meeting old friends again - Richard Tolman the cosmologist; Paul Epstein the theoretical physicist; and Theodore von Karman the aerodynamicist . "The new Athenaeum at Caltech was the setting for many dinners to honor Einstein. At the first on January 15 1931 the guests included the physicist and Nobel Laureate A. A. Michelson and 200 members of the California Institute Associates. Several weeks later a second dinner was held at which all the astronomers from the Institute and the Mt. Wilson Observatory were present. Edwin Hubble was there as was Charles E. St. John who verified the third prediction of the theory of general relativity the gravitational red-shift. Colleagues came from Berkeley including Tolman's close friend and co-author G. N. Lewis who wrote to say he was coming with a friend - though not without some mildly humorous trepidation. As he put it in his letter to Tolman: 'I have just accepted an invitation from Oppenheimer to drive me down. Do you think I should take out accident insurance' "Einstein was not without a sense of humor himself. At a farewell luncheon in his honor on February 24 1931 which was sponsored by the Pasadena Chamber of Commerce he said: "I want to thank the extraordinary group of scholars in the fields of physics and astronomy who have afforded me glimpses of their work. They have conducted me not only into the world of atoms and crystals but also to the surface of the sun and into the outermost depths of space. There I saw worlds which are flying away from us with incomprehensible rapidity in spite of the fact that their inhabitants do not know us well enough to justify any such action'" Goodstein. "Millikan was a physicist who had won the Nobel Prize in 1923 for having 'verified experimentally Einstein's all-important photoelectric equation.' He likewise verified Einstein's interpretation of Brownian motion. So it was understandable that as he was building Caltech into one of the world's pre-eminent scientific institutions he worked diligently to bring Einstein there. "Despite al they had in common Millikan and Einstein were different enough in their personal outlooks that they were destined to have an awkward relationship. Millikan was so conservative scientifically that he resisted Einstein's interpretation of the photoelectric effect and his dismissal of the ether even after they were apparently verified by his own experiments. And he was even more conservative politically. A robust and athletic son of an Iowa preacher he had a penchant for patriotic militarism that was as pronounced as Einstein's aversion to it" Isaacson p. 373. "To physics posterity Viennese mathematician Walther Mayer is mostly known as 'Einstein's calculator'. He had apparently been called that at the California Institute of Technology in Pasadena which Einstein and Mayer visited together in the winter of 1930/31. It is true that in order to advance in his studies to construct a unified field theory Einstein relied on the expertise of mathematicians. With his unified field theory Einstein attempted to formally join his own theory of general relativity with Maxwell's electromagnetism. "When Einstein was looking for a new mathematics assistant in 1929 Mayer was hired on the recommendation of eminent mathematician Richard von Mises. Like Einstein von Mises at that time held a professorship in Berlin. Walther Mayer then served as private lecturer at the University of Vienna finishing the second volume of a very well received textbook series on differential geometry which he co-authored with fellow Viennese mathematician Adalbert Duschek. Subsequently Mayer and Einstein worked together on several approaches towards a unified field theory consisting of 1 the analysis of solutions to Einstein's so-called distant teleparallelism approach 2 the invention of a variant of the Kaluza-Klein theory in which not space-time but attached vector spaces are 5-dimensional and finally 3 the construction of a formalism they referred to as "semi-vectors" for interpreting Dirac-spinors in simpler classical field-theoretical terms and reformulating the Dirac equation accordingly. Their joint work was published in 7 papers over a period of roughly four years 1930-1934 . "While being humbly appreciative of the vital improvement that Einstein brought to his career Mayer was at the same time also quite unhappy about his role as Einstein's 'appendage'. Einstein however was aware of and respected this sentiment of Mayer's: When he bargained his Princeton position with Abraham Flexner a founding director of Princeton's Institute for Advanced Study he insisted on an independent professorship for Mayer as well. After some back and forth this was indeed granted at the last minute. However the question of Mayer's legitimacy as an independent professor at Princeton surfaced again after their arrival. Feeling unwelcomed and not sufficiently supported by Einstein Mayer finally ended their collaboration after just one further joint paper in 1934. He felt that his career would be advanced best if from now on he would focus entirely on his own studies in pure mathematics. In the end Mayer was able to retain his tenure at Princeton for the rest of his life but he subsequently appeared to have wished to no longer be associated with work on unified field theory. On the outside Einstein and Mayer remained in friendly contact while Einstein found new collaborators. The ones immediately succeeding Walther Mayer at Princeton were Boris Podolsky and Nathan Rosen" Lessel. The photographs are accompanied by a number of letters from Mayer to his brother Arthur in Austria discussing Einstein's work Hitler and the Nazis. Mayer was Jewish and it was only through Einstein's intervention that he was given the title of professor at the University of Vienna. Mayer immediately took a leave of absence from this position to continue his collaboration with Einstein when he had returned to Berlin. At a press conference on his arrival in New York Einstein was asked "'What do you think of Adolf Hitler' Einstein replied 'He is living on the empty stomach of Germany. As soon as economic conditions improve he will no longer be important'" Isaacson p. 369. "On the day he left New York Einstein revised slightly one of the statements he had made on his arrival. Asked again about Hitler he declared that if the Nazis were ever able to gain control he would consider leaving Germany" ibid. p. 371. In April 1933 Einstein discovered that the new German government had passed laws barring Jews from holding any official positions including teaching at universities. He left Germany in summer 1933 and took up a position at the Institute for Advanced Study in Princeton despite Millikan's efforts to lure him to Caltech. He remained at the Institute until his death in 1955. Goodstein 'Albert Einstein in California' Engineering and Science May-June 1979 pp. 17-19 - Isaacson Einstein. His Life and Universe 2007. Lessel 'Walther Mayer - more than 'Einstein's calculator'' - ;/span> . unknown
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1915ref. 5863Berlin: Königlichen Akademie der Wissenschaften 1915. First edition. First editions very rare offprint of the first two of the papers published in November 1915 that document his final version of the general theory of relativity. "In the half century and more of Einstein's work in science one discovery stands above all as his greatest achievement. It is his general theory of relativity" Norton. . EINSTEIN'S COMPLETION OF THE GENERAL THEORY OF RELATIVITY. First editions very rare offprint of the first two of the papers published in November 1915 that document Einstein's final version of the general theory of relativity. "In the half century and more of Einstein's work in science one discovery stands above all as his greatest achievement. It is his general theory of relativity" Norton. "There was difficulty reconciling the Newtonian theory of gravitation with its instantaneous propagation of forces with the requirements of special relativity; and Einstein working on this difficulty was led to a generalization of relativity - which was probably the greatest scientific discovery that was ever made" Dirac quoted in Chandrasekhar p. 3. Einstein's special theory of relativity 1905 showed that the laws of physics are the same in all inertial i.e. non-accelerating frames of reference. It was then natural to ask whether it was possible to extend this principle of relativity to the more general case of frames of reference in arbitrary states of motion. This problem became linked to a theory of gravitation with Einstein's 'equivalence principle' of 1907 according to which the effects of gravity are locally equivalent to those of accelerated motion. Einstein's first steps towards a geometrical theory of gravitation were taken in August 1912 when his friend Marcel Grossmann provided the necessary mathematical tools. "Some time between August 10 and August 16 it became clear to Einstein that Riemannian geometry is the correct mathematical tool for what we now call general relativity theory. The impact of this abrupt realization was to change his outlook on physics and physical theory for the rest of his life" Pais p. 210. The resulting 'Entwurf' theory 1913 had much in common with the final theory of 1915 but based on a fallacious argument Einstein abandoned the requirement that the theory should be 'generally-covariant' i.e. that arbitrary frames of reference should be allowed. "After three years of fruitless peregrinations the revelation came to Einstein that he had been constantly on the wrong track although in 1913 he had been so near to the right solution" Lanczos p. 211. On November 4 1915 he presented to a plenary session of the Prussian Academy a new version of general relativity 'Zur allgemeinen Relativitätstheorie' "based on the postulate of covariance with respect to transformations with determinant 1" and stated that he had "completely lost confidence" in the 'Entwurf' equations. On November 18 he published his calculation of the precession of the perihelion of Mercury based on the new theory: its agreement with observation confirmed that the theory was correct the Entwurf theory predicted half the observed value of the precession. "In June 1905 while still a patent examiner in Bern Einstein submitted his famous work on the electrodynamics of moving bodies to the Annalen der Physik. This work contained his special theory of relativity in which he asserted the equivalence of all inertial frames of reference as a fundamental postulate of physics. The question which then naturally arose was whether it was possible to extend this principle of relativity to the more general case of frames of reference in arbitrary states of motion. But he could find no workable basis for such an extension until he tried to incorporate gravitation into his new special theory of relativity for a review article in 1907 'Uber das Relativitätsprinzip und die ausdemselben gezogenen Folgerungen' Jahrbuch der Radioaktivitat und Elektronik 4 1907 411-62. The difficulties of this task led him to a new principle later to be called the 'principle of equivalence.' "On the basis of the fact that all bodies fall alike in a gravitational field Einstein postulated the complete physical equivalence of a homogeneous gravitational field and a uniform acceleration of the frame of reference. This extended the principle of relativity to the case of uniform acceleration. It also foreshadowed the problem whose complete solution would lead him to his general theory of relativity: the construction of a relativistically acceptable theory of gravitation based on the principle of equivalence" Norton p. 258. One application of the equivalence principle proved crucial to the subsequent development of his ideas on general relativity. Einstein considered an observer standing on a rotating disc - a non-inertial accelerating reference frame. According to special relativity measuring rods aligned with the circumference of the disc will contract due to their motion whereas measuring rods positioned along the radius of the disc will not. Hence the ratio of the circumference of the disc to its diameter will be less than π. "The spatial geometry for the rotating observer is therefore non-euclidean. Invoking the equivalence principle Einstein concluded that this will be true for an observer in a gravitational field as well. This then is what first suggested to Einstein that gravity should be represented by curved space-time. "To describe curved space-time Einstein turned to Gauss's theory of curved surfaces a subject he vaguely remembered from his student days at the ETH in Zürich. He had learned it from the notes of his classmate Marcel Grossmann. Upon his return to his alma mater as a full professor of physics in 1912 Einstein learned from Grossmann now a colleague in the mathematics department of the ETH about the extension of Gauss's theory to spaces of higher dimension by Riemann and others. Riemann's theory provided Einstein with the mathematical object with which he could unify the effects of gravity and acceleration: the metric field" Janssen p. 65. The first product of this collaboration was the Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation published before the end of June 1913 which contained many of the essential features of the final general theory of relativity; most importantly it introduced the 'metric' of space-time. In Minkowski's formulation of special relativity 1908 the most important quantity is the 'world function' of two events which determines the metric and causal structure of space-time. If these events have coordinates x y z t and x' y' z' t' in some inertial reference frame the world function is: c2t' - t2 - x' - x2 - y' - y2 - z' - z2 where c is the speed of light. Its crucial property is that it depends only on the two events and not on the choice of inertial reference frame - in other words it is unchanged 'invariant' when x y z t and x' y' z' t' are both subjected to any Lorentz transformation. Einstein and Grossmann began with the world function in differential form: ds2 = c2dt2 - dx2 - dy2 - dz2 If we now subject x y z t to an arbitrary coordinate transformation not necessarily a Lorentz transformation this takes the general form ds2 = g11dx12 g12dx1dx2 . ; the collection of quantities gμν which in general depend on the coordinates x1 x2 x3 x4 is called the metric. Based on analogy with Newton's theory Einstein expected that the gravitational equations should be of the form Gμν = Tμν where Gμν is a purely geometric quantity constructed solely from the metric gμν and its derivatives up to the second order and the 'stress-energy tensor' Tμν contains the information about the matter that is producing the gravitational field including energy density momentum fluxes and stresses. The question was: what exactly should Gμνbe Einstein and Grossmann found that generally covariant equations did not seem to be compatible with energy-momentum conservation or reduce to the equations of Newtonian gravitational theory for weak static fields both essential requirements of the correct theory. Einstein therefore decided to settle in the 'Entwurf' for equations with very limited covariance - instead of arbitrary changes in coordinates only linear ones were allowed. The restricted covariance of the 'Entwurf' field equations continued to bother him until in late August 1913 he convinced himself that such restrictions are unavoidable by means of the infamous "hole argument" first published as an addendum to the reprint of the 'Entwurf' article in Zeitschrift für Physik in January 1914. This ingenious argument showed correctly that if the gravitational equations were generally covariant the metric gμν would not be uniquely determined by the matter distribution i.e. by Tμν. He concluded incorrectly that this implied that general covariance must be ruled out the hole argument does not work if only linear coordinate transformations are allowed. The appropriate analogy is with electromagnetism: the metric is analogous to the scalar and vector potentials of electromagnetism and it was well known certainly to Einstein that these potentials are not uniquely determined by the charges and currents producing the electromagnetic field. That the 'Entwurf' theory was incorrect was made clear by Einstein's attempt in collaboration with Michele Besso another former classmate to explain the motion of the perihelion of Mercury. In 1859 Urbain Jean Joseph Le Verrier had observed the 'precession' of Mercury's orbit: this orbit is an ellipse but the ellipse is not fixed in space but slowly rotates. From early on in his search for a new relativistic theory of gravitation Einstein had been interested in the problem of Mercury's perihelion. In a letter to his friend Conrad Habicht in 1907 Einstein had already expressed his hope that such a theory would explain the anomalous advance of Mercury's perihelion. Besso visited Einstein in Zürich in June 1913 and the two men calculated the precession expected on the basis of the 'Entwurf' theory. Disappointingly it was only about half the observed anomaly. Einstein left Zürich in March 1914 to take up a professorship in Berlin which was to be his home until December 1932. He made no further progress on the gravitational equations until the summer of 1915 although a detailed exposition of the 'Entwurf' theory was published in October 1914 in which Einstein maintained the need for restricted covariance and even claimed that this determined the gravitational Lagrangian uniquely. "Einstein still believed in the 'old' theory as late as July 1915 between July and October he found objections to that theory and his final version was conceived and worked out between late October and November 25 . What made Einstein change his mind between July and October Letters to Sommerfeld and Lorentz show that he had found at least three objections against the old theory: 1 its restricted covariance did not include uniform rotations 2 the precession of the perihelion of Mercury came out too small by a factor of about 2 and 3 his proof of October 1914 of the uniqueness of the gravitational Lagrangian was incorrect. Einstein got rid of all these shortcomings in a series of four brief articles offered here . "On November 4 Einstein presented to the plenary session of the Prussian Academy a new version of general relativity 'based on the postulate of covariance with respect to transformations with determinant 1'. He began this paper by stating that he had 'completely lost confidence' in the equations proposed in October 1914. At that time he had given a proof of the uniqueness of the gravitational Lagrangian. He had realized meanwhile that this proof 'rested on misconception' and so he continued 'I was led back to a more general covariance of the field equations a requirement which I had abandoned only with a heavy heart in the course of my collaboration with my friend Grossmann three years earlier' . "Einstein and Grossmann had concluded that the gravitational equations could be invariant under linear transformations only and Einstein's justification for this restriction was based on the belief that the gravitational equations ought to determine the gμν uniquely a point he continued to stress in October 1914. In his new paper he finally liberated himself from this three-year-old prejudice. That is the main advance on November 4. His answers were still not entirely right. There was still one flaw a much smaller one which he eliminated three weeks later. But the road lay open. He was lyrical. 'No one who has really grasped it can escape the magic of this new theory.' "The remaining flaw was of course Einstein's unnecessary restriction to unimodular transformations. The reasons which led him to introduce this constraint were not deep I believe. He simply noted that this restricted class of transformations permits simplifications of the tensor calculus . The new equations are a vast improvement over the Einstein-Grossmann equations and cure one of the ailments he had diagnosed only recently: unimodular transformations do include rotations with arbitrarily varying angular velocities. In addition he proved that the new equations can be derived from a variational principle and that the conservation laws are satisfied" Pais pp. 250-252. On November 11 he submitted a 'Nachtrag' to his paper of a week earlier. "Einstein proposes a scheme that is even tighter than the one of a week earlier. Not only shall the theory be invariant with respect to unimodular transformations . but more strongly it shall satisfy the condition that the determinant of the matrix gμν is equal to minus one . During the next two weeks Einstein believed that this new condition had brought him closer to general covariance . One week later he remarked that 'no objections of principle' can be raised against it" ibid. pp. 252-253. Norton p. 309 points out that Einstein had in fact made a significant advance in this paper: namely he had finally found generally covariant field equations that reduced to the Newtonian equations in the weak field limit" ibid. p. 253. On November 18 still retaining the restrictions of his paper of a week earlier Einstein presented in 'Erklarung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie'"two of his greatest discoveries. Each of these changed his life. The first result was that his theory explains . quantitatively . the secular rotation of the orbit of Mercury discovered by Le Verrier . without the need of any special hypothesis. This discovery was I believe by far the strongest emotional experience in Einstein's scientific life perhaps in all his life. Nature had spoken to him. He had to be right. 'For a few days I was beside myself with joyous excitement'. Later he told Fokker that his discovery had given him palpitations of the heart. What he told de Haas is even more profoundly significant: when he saw that his calculations agreed with the unexplained astronomical observations he had the feeling that something actually snapped in him . "Einstein's discovery resolved a difficulty that was known for more than sixty years. Urbain Jean Joseph Le Verrier had been the first to find evidence for an anomaly in the orbit of Mercury and also the first to attempt to explain this effect . In 1859 he found that the perihelion of Mercury advances by thirty-eight seconds per century due to 'some as yet unknown action on which no light has been thrown . a grave difficulty worthy of attention by astronomers'" ibid. pp. 253-254. A more accurate measurement of 43 seconds was made by Simon Newcomb in 1882 and this was precisely the value predicted by the new theory. The prediction of the bending of light in a gravitational field was treated only briefly in 'Erklarung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie' probably because no accurate measurement of it had been made so this prediction could not be confirmed at the time. Einstein had realised in 1907 based on the equivalence principle that some bending of light should occur but he believed that the effect was too small to be observed. In 1911 he realized that the effect could be detected for starlight grazing the sun during a total eclipse and found that the amount of bending in that case is 0''.87 - this value could in fact have been computed by Newton from his law of gravitation and his corpuscular theory of light. In 3 Einstein discovered that general relativity implies a bending of light by the sun equal to 1".74 twice the Newtonian value. This factor of 2 set the stage for a confrontation between Newton and Einstein. "It was not until May 1919 that two British expeditions obtained the first useful photographs and not until November 1919 that their results were formally announced . In March 1917 the Astronomer Royal Sir Frank Watson Dyson drew attention to the excellence of the star configuration on May 29 1919 an eclipse date for measuring the alleged deflection . Two expeditions were mounted one to Sobral in Brazil led by Andrew Crommelin from the Greenwich Observatory and one to Principe Island off the coast of Spanish Guinea led by Eddington. Before departing Eddington wrote 'The present eclipse expeditions may for the first time demonstrate the weight of light i.e. the Newton value; or they may confirm Einstein's weird theory of non-Euclidean space; or they may lead to a result of yet more far-reaching consequences - no deflection' . The expeditions returned. Data analysis began. According to a preliminary report by Eddington to the meeting of the British Association held in Bournemouth on September 9-13 the bending of light lay between 0''.87 and double that value. Word reached Lorentz. Lorentz cabled Einstein . Then came November 6 1919 the day on which Einstein was canonized" Pais 304-305. At a joint meeting of the Royal Society and the Royal Astronomical Society on that date Dyson concluded his remarks with the statement "'After a careful study of the plates I am prepared to say that they confirm Einstein's prediction. A very definite result has been obtained that light is deflected in accordance with Einstein's law of gravitation'" ibid. p. 305. Three remarks may be made on the speed with which after eight years of struggle Einstein completed these final papers on his theory. The first is that Einstein had come very close to the correct gravitational equations in the second half of 1912 - they are recorded in his 'Zurich notebook' - but he discarded them because of his arguments against general covariance as we have seen. Once he no longer believed in these arguments he could return to the work carried out in the Zurich notebook and complete it. The second is that the detailed calculations in 3 relating to Mercury's perihelion were in fact very similar to those he had carried out with Besso in 1913 and so required relatively little extra effort. The final point is that Einstein was in competition with the great Göttingen mathematician David Hilbert. Weil 75 76 77; Chandrasekhra 'The general theory of relativity: Why "It is probably the most beautiful of all existing theories" Journal of Astrophysics 5 1984 pp. 3-11; Eisenstaedt The Curious History of Relativity 2006; Janssen 'Of pots and holes: Einstein's bumpy road to general relativity' Annalen der Physik 14 Supplement 2005 pp. 58-85; Lanczos Einstein Decade: 1905-1915 1974; Norton 'How Einstein found his field equations: 1912-1915' Historical Studies in the Physical Sciences 14 1984 pp. 253-316; Pais Subtle is the Lord 1982. Large 8vo 253 x 180 mm pp. 778-786 & 799-801. Original printed wrappers. Königlichen Akademie der Wissenschaften unknown
ref. 109875Stockholm Aldus / Bonnier 1964. 8:o. 332 4 s. Mörkblått halvmarokängband blekt guldornerad rygg med upphöjda bind och med omslaget medbundet ryggen har blekts till grönt. Ur Lars Berglöfs bibliotek med hans initialer i guld på ryggen. Fint exemplar av en bok som annars sällan överhuvudtaget är inbunden! Det tyska originalet ”Mozart - sein Character sein Werk” utkom 1945 och denna svenska översättning av Kajsa Rootzén utkom första gången 1956. unknown
2013ref. DADAX0415854717Routledge 2013-07-02. 1. paperback. New. 5.08x0.44x7.80. Buy with confidence. Excellent Customer Service & Return policy. Routledge paperback
ref. B9780195007329Paperback / softback. New. paperback
ref. B9781258115357Paperback / softback. New. paperback
ref. 1568219830.Gpaperback. Good. Access codes and supplements are not guaranteed with used items. May be an ex-library book. paperback
1931ref. SKU1139774Simon and Schuster 1931. Hardcover. Good. New York 1931; black boards with gold cover titles and spine titles; mild corner and edge wear; some discoloration at edges; orange dust jacket with black cover titles and spine titles; light chipping at jacket edges; parts of jacket edges taped over; 8vo - over 7 3/4" to 9 3/4" tall; "ex libris" sticker on front pastedown; rest of interior is clean and unmarked. 333 pages. Simon and Schuster hardcover
1945ref. 5054Lancaster PA: American Physical Society 1945. First edition. First edition extremely rare offprints of Einstein & Straus's introduction of the 'Swiss-cheese' model of the universe. "By the spring of 1945 Einstein and Straus had found a new type of possible universe using Einstein's equations . This was a step towards a more realistic universe in which the matter was not smoothly spread with the same density everywhere but gathered up into lumps like galaxies which were spread about in empty space" Barrow The Book of Universes pp. 106-107. . EINSTEIN'S 'SWISS-CHEESE' MODEL OF THE UNIVERSE - OFFPRINT ISSUE. First edition extremely rare offprints of Einstein & Straus's introduction of the 'Swiss-cheese' model of the universe. "After a decade and a half of sometimes intense work on cosmology Einstein returned to the subject only occasionally in his later years. His most significant later contribution was a discussion of the impact of cosmological expansion on the gravitational field surrounding a star i.e. the offered papers . This was an important first step in understanding the impact of global cosmological expansion on local physics" Janssen & Lehner pp. 257-8. In the 1920s and 1930s a general relativistic model of the universe was developed called the Friedmann-Lemaître-Robertson-Walker FLRW model which correctly described the expansion of the universe discovered by Edwin Hubble. But the FLRW model was 'homogeneous' - it described a universe which looks the same wherever the observer is located. The actual universe however is manifestly inhomogeneous - it contains stars galaxies and clusters of galaxies. Einstein and Straus's papers represent the first serious attempt to model an inhomogeneous universe. "By the spring of 1945 Einstein and Straus had found a new type of possible universe using Einstein's equations. It described a universe which looked largely like one of the simple expanding universes of Friedmann and Lemaître containing material like galaxies which exerted no pressure. But it had spherical regions removed from it like bubbles in a Swiss cheese. Each empty hole then had a mass placed at its centre. The mass was equal in magnitude to what had been excavated to create the hole. This was a step towards a more realistic universe in which the matter was not smoothly spread with the same density everywhere but gathered up into lumps like galaxies which were spread about in empty space" Barrow pp. 106-107. Not on OCLC; no copies in auction records. In 1916 just a few months after Einstein had formulated his general theory of relativity Karl Schwarzschild had found a solution of Einstein's equations which described the gravitational field in the vicinity of a spherical distribution of mass such as a star or to anticipate later developments a black hole. This was in fact the first exact solution of Einstein's equations to be found - Einstein had earlier calculated an approximate solution which was enough to show that his theory correctly accounted for the advance of Mercury's perihelion. However at great distances from the star Schwarzschild's solution approaches the flat Minkowski spacetime with zero curvature and not the FLRW solution that represented an expanding universe. It seemed therefore that Schwarzschild's solution could not correctly describe the gravitational field of a star in an expanding FLRW universe. If the expansion of the universe meant that Schwarzschild's solution had to be modified this could make it possible to detect and measure the expansion of the universe by making local observations rather than by observing the motion of distant galaxies as Hubble had done. The problem of describing the gravitational field of a star in an expanding FLRW universe was addressed by Einstein and Straus in the offered papers. "In the early 1930s theorists began to develop a richer account of the evolution of the universe based on expanding models. Hubble's results qualitatively agreed with the redshift effect calculated in these models but the utility of the simple dynamical models depends on whether the universe is approximately uniform. The status of this assumption was the focus of lively debate . Relativistic cosmologists regarded the idealized uniformity of the FLRW models as a simplifying assumption . The unrelenting uniformity built into the FLRW models conflicts with the clear non-uniformity of the stars star clusters and galaxies of the local universe but the models might still serve as a useful approximation if the non-uniformities are negligible at larger scales" Janssen & Lehner p. 256. "By 1944 Einstein had recruited a new assistant at Princeton. His assistants were always talented young mathematicians who could make up for Einstein's self-confessed weakness in this area. Ernst Straus 1922-1983 was something of a mathematical prodigy . He was born in Munich but after the Nazis came to power in 1933 his family fled to Palestine where he was educated at high school and at the Hebrew University in Jerusalem. Straus didn't stay to take an undergraduate degree and instead while still a teenager moved to New York's Columbia University in 1941 to begin graduate research. In 1944 he found himself recruited as Einstein's new research assistant at the Institute for Advanced Study in Princeton. The young Straus had no background in physics and his mathematical inclinations were towards number theory and 'pure' mathematical topics but he lost no time in filling the gap left by the departures of Nathan Rosen 1935-45 and Leopold Infeld 1936-38" Barrow pp. 105-6. Einstein and Straus found an exact solution of the equations of general relativity in which a spherical 'hole' is cut out of an FLRW universe and the hole is replaced by a single mass point e.g. a star surrounded by a spherical cavity. The initially homogeneous matter within the cavity can be thought of as having been "condensed into the star". Einstein and Straus found that the interior of the cavity is described by the standard Schwarzschild solution. The radius of the hole is such that at its spherical boundary the outward pull from the cosmological masses is just balanced by the inward pull from the star. The cavity boundary expands according to the Hubble expansion of the whole universe. The universe outside the cavity is described by the standard expanding homogeneous FLRW solution. The possibility of exactly matching the Schwarzschild solution near the star to the FLRW solution outside it showed that it was not in fact possible to detect the expansion of the universe by making observations close to the star. There were similar solutions with more than one hole - Einstein said that this reminded him of the holes in Swiss cheese. The static vacuum region inside the cavity is now called an 'Einstein-Straus vacuole'. The methods introduced by Einstein and Straus in these papers have been used extensively to model inhomogeneities in the universe. For example in 1968 Martin Rees and Dennis Sciama investigated the effects of large-scale inhomogeneities such as superclusters of galaxies on the cosmic microwave background the so-called 'Rees-Sciama effect'. The Swiss-cheese model has also been used in the study of inflationary models of the early universe. According to this theory the universe expanded exponentially in the first tiny fraction of a second after the big bang with some parts of space-time expanding more quickly than others. This created 'bubbles' in space-time. The Swiss-cheese "embodies a natural way to model physical problems such as describing the boundary between a galaxy and intergalactic space or the relation between bubbles at the end of an inflationary era by taking two different regions where the behaviour is smooth and joining them at a surface of discontinuity" Ellis et al. p. 426. In the last decade several authors have suggested that Swiss-cheese models might solve a long-standing problem on the rate of expansion of the universe. Distant supernovas have been observed to be dimmer than expected on the basis of standard cosmological theories indicating that the universe is expanding faster than these theories predict. This has been explained by hypothesizing the existence of 'dark energy' although exactly what dark energy might be is a mystery. But if the light from distant supernovas had to cross large vacuoles in reaching an observer on the earth these would act like concave lenses making the supernovas appear dimmer and further away than they really are. Other authors have noted that the Milky Way is near the centre of a region that has fewer galaxies than other parts of the universe and that we might be living near the centre of a particularly large vacuole perhaps more than a billion light years in diameter see for example Bonnor. Weil 216. Barrow The Book of Universes 2011. Bonnor 'A generalisation of the Einstein-Straus vacuole' Classical and Quantum Gravity 17 2000 pp. 2739-2748. Ellis Maartens & MacCallum Relativistic Cosmology 2012. Janssen & Lehner eds. The Cambridge Companion to Einstein 2014. Together two offprints 4to 267 x 200 mm pp. 120-124 & 148-149. Stapled as issued in original self-wrappers. American Physical Society unknown
1920ref. B6223Toronto; London: the Ryerson Press.; Methuen & Co. Edition. 1920. A near fine example text and illustrations clean and crisp. . Edition: First Canadian Edition. after the first London. Binding: Contemporary full red cloth title on flat spine debossed stamped title on the upper board lacks the dust jacket. Notes: Albert Einstein 1879 – 1955 was a German-born theoretical physicist who developed the theory of relativity one of the two pillars of modern physics alongside quantum mechanics. His work is also known for its influence on the philosophy of science. He is best known to the general public for his mass–energy equivalence formula which has been dubbed "the world's most famous equation". He received the 1921 Nobel Prize in Physics "for his services to theoretical physics and especially for his discovery of the law of the photoelectric effect" a pivotal step in the development of quantum theory. Size: Octavo 8vo. Illustration: Illustrated with five diagrams and numerous in text mathematical equations. A foundation work in physics and astronomy. Category: Book Canada; Book Science & Technology; the Ryerson Press.; Methuen & Co. Edition. hardcover
