Über den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes [On the influence of gravity on the propagation of light]. Offprint from: Annalen der Physik, Vierte Folge, Band 35.

Leipzig: Johann Ambrosius Barth, 1911.

First edition, rare author’s presentation offprint (with ‘Überreicht vom Verfasser’ (Presented by the Author) stamped on front wrapper), and the copy of Einstein’s son Hans Albert, 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.

Provenance: Hans Albert Einstein (1904-73) (ownership stamp on front wrapper). The second child and first son of Albert Einstein and Mileva Marić, Hans Albert moved to the US in 1938, and spent most of his career at the University of California, Berkeley, where he was a professor of hydraulic engineering.

“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 metres.

“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).

Princeton document 23; Parkinson p. 471; Weil 43* (Boni 39). The Collected Papers of Albert Einstein vol. 3, The Swiss Years: Writings, 1909–1911 (Princeton: Princeton University Press, 1994). 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, stamped ‘A. Einstein. Überreicht vom Verfasser’ above printed title. A fine copy.

Item #5081

Price: $40,000.00

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