EINSTEIN, Albert (1879-1955). Autograph manuscript signed ("A. Einstein" on last page), constituting Einstein's lecture "The Origin of the General Theory of Relativity" ("Einiges über die Entstehung der allgemeinen Relativitätstheorie"), delivered as the first George A. Gibson Lecture at the University of Glasgow, 20 June 1933. A working draft with extensive deletions and interlinear additions. No place, undated, but ca. June 1933.
4to (8 7/8 x 6 7/8 in). 8 pages, ink on rectos only, paper watermarked Basildon Bond" with crest, paginated (1)-8 by Einstein, his penciled note at end "Vortrag in Glasgow, Juni 1933." Tiny rust mark at top of page 1 from paperclip, otherwise in very fine condition. In German with full English translation (copy supplied on request).
"ORIGINS OF THE GENERAL THEORY OF RELATIVITY": EINSTEIN'S ACCOUNT OF THE DIFFICULT PATH FROM THE SPECIAL THEORY OF RELATIVITY (1905) TO THE GENERAL THEORY OF RELATIVITY (1916): HIS MOMENTOUS DISCOVERIES IN THE CRITICAL YEARS 1905-1916
A highly important, very revealing account by Einstein of his arduous efforts--beginning with his formulation of the Special Theory of Relativity (1905)--to generalize the General Theory of Relativity, postulating a new, post-Newtonian theory of gravitation and, as a further consequence, establishing the equivalence of mass and energy (E = mc^{2}). These momentous discoveries constitute perhaps the most far-reaching, fundamental scientific advances of the Twentieth Century. Dr. Robert Schulmann, former editor of the Einstein Papers, noted that the significance of this lecture "lies in its description of Einstein's journey from the Special Theory of Relativity of 1905 to the General Theory, published in 1916. In its importance as a review, it can only be compared to the Kyoto lecture held by Einstein in 1922, for which there are only the Japanese short-hand notes and a translation back into German." Further emphasizing this manuscript's importance, Schulmann points out that the Einstein Edition itself draws on this account "for a canonical reconstruction of the path to General Relativity." The Gibson lecture was delivered in Glasgow the same year Einstein left Germany in the wake of the Nazi seizure of power; later that year he took up residence in the United States. Clearly intended for an audience familiar with modern physics, Einstein acknowledges the essential work of his predecessors (Euclid, Galileo, Newton, Maxwell), his contemporaries (H.A. Lorentz, Ernst Mach, Minkowski, Rieman, Poincaré) and his collaborators (Marcel Grossman, Michele Besso). At the end of his account, Einstein recalls his sense of elation when the theory was confirmed: "Once the validity of this mode of thought has been recognized, the final results appear almost simple; any intelligent undergraduate can understand them." But, he adds, "the years of searching in the dark, for a truth that one feels, but cannot express; the intense desire and the alternations of confidence and misgiving, until one breaks through to clarity and understanding, are only known to him who has himself experienced them."
Einstein opens his lecture with a modest expression of gratitude for the chance "to say something about the history of my own scientific work..."; and adds "it would be a mistake from a sense of false modesty to pass by an opportunity to put the story on record."
His account commences in the annus mirabilis of 1905, which saw publication of five of Einstein's most revolutionary papers: "After the special theory of relativity had shown the equivalence for formulating the laws of nature of all so-called inertial systems (1905), the question whether a more general equivalence of co-ordinate systems existed was an obvious one. In other words, if one can only attach a relative meaning to the concept of velocity, should one nevertheless maintain the concept of acceleration as an absolute one? From the purely kinematic point of view the relativity of any and every sort of motion was indubitable; from the physical point of view, however, the inertial system seemed to have a special importance..." He refers to work by Ernst Mach (1838-1916), especially "Mach's idea that inertia might not represent a resistance to acceleration as such, so much as a resistance to acceleration relative to the mass of all the other bodies in the world. This idea fascinated me; but it did not provide a basis for a new theory." At that point, "I made the first step towards the solution of this problem," by trying "to include the law of gravity in the framework of the special theory of relativity. Like most physicists..I sought a 'field law', since... the introduction of action at a distance was no longer feasible in any plausible form once the idea of simultaneity was abolished."
"The simplest way was...to keep the Laplace scalar potential of gravity and to extend the Poisson equation by adding, in such a way as to comply with the special theory of relativity, a term differentiated with respect to the time. The law of motion of the particle in a gravitational field...also had to...conform to the special theory of relativity. The way to do this was not unambiguously evident, since clearly the inertial mass of a body might depend upon the gravitational potential. Indeed, this was to be expected on account of the inertia of energy."
But these investigations "caused me grave misgivings. For, according to classical mechanics, the vertical acceleration of a body in a vertical field of gravitation was independent of the horizontal component of the velocity. It follows...that the vertical acceleration of a mechanical system (or of its centre of gravity) in such a field should be independent of its internal kinetic energy. According to this theory I was investigating... the vertical acceleration was not independent of the horizontal velocity, and...not independent of the internal energy of the system."
These experiments also conflicted with "the old, well-known empirical rule that all bodies in a gravitational field are subject to the same acceleration. This principle, which can also be stated as the law of the equivalence of inertial and gravitational mass, impressed me as being of fundamental importance." Given his contradictory results, Einstein "wondered how this law could exist, and I believed it held the key to the real understanding of inertia and gravitation. I never seriously doubted its exact validity..."
Abandoning that futile attempt, Einstein sought a new path, applying the principle of equivalence to "the problem of gravitation within the framework of the special theory of relativity...The principle of the equivalence of inertial and gravitational mass could now be formulated in a very simple and intelligible manner...[showing] that in a homogenous gravitational field all motions take place just as they would in the absence of such a field in a uniformly accelerated system. If this principle (the equivalence principle) was true...it indicated that the principle of relativity must be extended to include non-uniform motions of the co-ordinate systems [General Relativity]...to obtain an unforced, natural theory of the gravitational field. From 1908 until 1911, I concerned myself with considerations of this nature." It was abundantly clear to Einstein, "that a reasonable theory of gravitation could only be obtained by an extension of the principle of relativity."
It was imperative, he recognized, to "find and to elaborate a theory expressed in equations which did not change their form for non-linear transformations of the co-ordinates. Whether this condition was to be fulfilled for all continuous transformations of the co-ordinates or only for special ones I could not say at the outset. I saw...that the simple physical interpretation of the co-ordinates would vanish if, as required by the equivalence principle, non-linear transformations were to be permitted...." The recognition of this fact worried me...for I could not see...what the co-ordinates were to represent in these circumstances. The solution of this dilemma only came in 1912..."
Finally, Einstein recounts the breakthrough efforts that required "a new formulation of the inertial principle which would become identical with Galileo's formulation in the absence of a 'real' gravitational field. That is to say, if there existed an inertial system and if we used it as our co-ordinate system. Galileo's formulation states: -- A material particle on which no forces are acting is represented in four-dimensional space-time by a straight line...whose length has a stationery value. This concept presupposes the concept of the length of a line element...of a metric structure. In the special theory of relativity, as [Hermann] Minkowski [1864-1909] had shown, the metric was quasi-Euclidian..."
"If one introduces other co-ordinates by non-linear transformations, 'ds2' remains a homogeneous function but the co-efficients 'guv' of this form are no longer constant, but are functions of the co-ordinates. Mathematically...the physical four-dimensional continuum has a Riemann metric. Time-like lines, whose lengths, measured by this metric, have stationary values, represent the laws of motion of a material point on which, apart from gravity, no forces are acting. The coefficients 'guv' of this metric describe the gravitational field...We have thus found a natural formulation of the equivalence principle; that it was permissible to extend it to all gravitational fields was a plausible hypothesis."
He explains "the solution of the above dilemma: -- A real physical significance attaches only to the Riemann metric, not to the co-ordinates or their differences. With this idea, a workable basis for the general theory of relativity had been found. Two problems, however, remained -- (1) How can we translate a field law...in the terminology of the special theory of relativity into a Riemann metric? (2) What are the differential expressions which enter into the law governing the Riemann metric 'guv' (the law of the gravitational field)?"
He describes the great break-though: "I worked at these problems from 1912 to 1914 with my friend Grossman. We found that the mathematical method for solving the first question was ready waiting for us in the absolute differential calculus of Ricci and Levi Civita. As to the second problem, its solution obviously required that we should be able to form differential invariants of the second order of the 'guv'. We soon recognized that methods for doing this had long ago been worked out by Reimann (curvature tensor). Already two years before the publication of the general theory of relativity, we had considered the correct field equations of gravitation, but we failed to recognize that they were physically applicable. I believed, on the contrary, that one could show...that a law of gravitation that was invariant for all possible transformations...would not be compatible with the principle of casuality."
"These were errors of thinking which caused me two years of hard work before at last, in 1915, I...returned penitently to the Reimann curvature, which enabled me to find the relation to the empirical facts of astronomy. Once the validity of this mode of thought has been recognized, the final results appear almost simple...But the years of searching in the dark for a truth that one feels but cannot express; the intense desire and the alternations of confidence and misgiving, until one breaks through to clarity and understanding, are only known to him who has himself experienced them."
Translation published Glasgow University, Publication Number 30, 1933.