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Two autograph letters signed ('Einstein' and 'A. Einstein') to Ludwig Hopf, [Prague, after 20 February 1912] and Zurich, 16 August 1912
Details
Albert Einstein (1879-1955)
Two autograph letters signed ('Einstein' and 'A. Einstein') to Ludwig Hopf, [Prague, after 20 February 1912] and Zurich, 16 August 1912
In German. Four pages, 171 x 112mm, and two pages, 175 x 111mm, on bifolia; in separate custom cloth boxes. Provenance: Part of the complete series of letters by Einstein to Hopf offered at Sotheby's New York, 26 June 1998, lot 419 (unsold).
‘I have found the most general equations’. The 1912 breakthrough to general relativity: the earliest surviving evidence for both Einstein’s initial formulation of a new theory of gravity in February 1912, the birth of his general theory of relativity, and his discovery of Riemannian geometry in August of the same year, which provided the mathematical formalism enabling its completion.
I work like a horse, even though the cart does not always move very far from the spot. But a few things have gone well… I have now derived the theory of gravitation for the static field in a completely rigorous manner. The thing is stunningly beautiful and amazingly simple (letter of February 1912)
The work on gravitation is going splendidly. Unless I am completely wrong, I have found the most general equations (letter of 16 August 1912)
No earlier references to these respective breakthroughs are recorded in the Collected Papers: the February letter is approximately a month before Einstein submitted his first published paper on the new theory, ‘On the theory of the static gravitational field’ (Weil 48: submitted on 23 March 1912), while Einstein’s biographer Abraham Pais dates ‘the great transition to Riemannian geometry’ to the week before his August letter to Hopf (Subtle is the Lord, 1982, 212).
The February letter to Hopf is rich in scientific content even beyond its discussion of general relativity, and is notable for showing how closely Einstein’s life is involved with the quantum revolution at this date: the gravitation announcement aside, every other topic he mentions in the letter is, in one way or another, directly linked to radiation and quanta. He gives pride of place, even before his new theory of gravity, to the news that ‘I derived the laws of photochemical equivalents by way of thermodynamics, without quanta’; he notes that he will engage in ‘a heavy verbal duel’ with Max Abraham over his ‘completely wrong’ alternative theory of gravitation (a dispute referred to again in his August letter) and refers to Walther Nernst’s proof of the third law of thermodynamics (which Einstein also considers ‘totally wrong’). On top of this, he is ‘wrestling with dispersion in the infrared’; and discusses Edgar Meyer's work on gamma-ray absorption. The letter concludes with a report of the first Solvay Conference, the scientific forum that jump-started the quantum revolution: ‘To be sure nothing came out of Brussels, but it was a very pretty spectacle. No one could bring up anything against the theory of fluctuations’ (which Einstein in 1909 applied to black-body radiation and found that it revealed the radiation to have a dual wave-particle nature). But, he goes on. ‘I still understand the thing just as badly as I did then. True enough, the quanta do what they are supposed to do, but they do not exist, like the luminiferous ether at rest’. The shorter letter of 16 August congratulates Hopf on his marriage and refers to the progress of his dispute with Max Abraham, whose competing theory of gravity he describes as ‘a stately steed, but one that is lacking three legs’; and he mocks Abraham for misattributing Einstein’s discovery of mass-energy equivalence to a 19th-century forebear, Robert Meyer.
Einstein published his revolutionary new theory of gravity, ‘On the theory of the static gravitational field’ (Weil 48), on 23 May 1912. The first major step toward the formalisation of general relativity, Einstein’s theory was radically at variance not only with Newton’s mechanical paradigm of gravity, but even with his own special theory of relativity. For the first time, Einstein formally introduced the equivalence principle of gravity – ‘the equivalence of uniformly accelerated reference frames and static homogeneous gravitational fields’ (Collected Papers, IV, 122) – and he further deviated from special relativity with the premise that the velocity of light is both variable and locally determined (something he had proved in his 1911 paper on the bending of light by gravity, ‘Influence of gravitation on the propagation of light’, Weil 43). The result is the deduction that gravitational mass and inertial mass are identical, and that the activity of matter and space are interconnected in a dynamic geometry (as John Wheeler later put it, ‘Spacetime tells matter how to move; matter tells spacetime how to curve’). Einstein tried to develop and extend his gravitational theory over the course of 1912, but lacked the thinking tools that would enable him to conceive and express the field equations of the dynamic gravitational field. This impasse was resolved only in August 1912, when his friend Marcel Grossmann introduced him to Riemannian geometry (as confirmed by Einstein in a speech ten years later: ‘This problem remained insoluble to me until 1912, when I suddenly realized that Gauss’s theory of surfaces holds the key for unlocking this mystery … However, I did not know at that time that Riemann had studied the foundations of geometry in an even more profound way … My dear friend the mathematician Grossman was there when I returned from Prague to Zurich. From him I learned for the first time about Ricci and later about Riemann’). With this mathematical formalism in hand, Einstein was able to complete the development of the theory of general relativity.
The general theory of relativity is the greatest scientific achievement of the 20th century and has been described as ‘the greatest intellectual achievement of any one person’. Einstein’s theory of the static gravitational field constitutes general relativity’s core, and the development of the theory is due to Einstein’s discovery and application of Riemannian geometry. The two letters here are extraordinary examples of the fertility of Einstein’s mind at the birth of general relativity, showing Einstein rising to the height of scientific greatness. The letters are published in Collected Papers, 4, nos 364 and 416. Ludwig Hopf (1884-1939) had worked as an assistant to Einstein during his first posting at the University of Zurich, briefly following him to Prague: they collaborated on two papers on statistical aspects of radiation published in 1910.
Two autograph letters signed ('Einstein' and 'A. Einstein') to Ludwig Hopf, [Prague, after 20 February 1912] and Zurich, 16 August 1912
In German. Four pages, 171 x 112mm, and two pages, 175 x 111mm, on bifolia; in separate custom cloth boxes. Provenance: Part of the complete series of letters by Einstein to Hopf offered at Sotheby's New York, 26 June 1998, lot 419 (unsold).
‘I have found the most general equations’. The 1912 breakthrough to general relativity: the earliest surviving evidence for both Einstein’s initial formulation of a new theory of gravity in February 1912, the birth of his general theory of relativity, and his discovery of Riemannian geometry in August of the same year, which provided the mathematical formalism enabling its completion.
I work like a horse, even though the cart does not always move very far from the spot. But a few things have gone well… I have now derived the theory of gravitation for the static field in a completely rigorous manner. The thing is stunningly beautiful and amazingly simple (letter of February 1912)
The work on gravitation is going splendidly. Unless I am completely wrong, I have found the most general equations (letter of 16 August 1912)
No earlier references to these respective breakthroughs are recorded in the Collected Papers: the February letter is approximately a month before Einstein submitted his first published paper on the new theory, ‘On the theory of the static gravitational field’ (Weil 48: submitted on 23 March 1912), while Einstein’s biographer Abraham Pais dates ‘the great transition to Riemannian geometry’ to the week before his August letter to Hopf (Subtle is the Lord, 1982, 212).
The February letter to Hopf is rich in scientific content even beyond its discussion of general relativity, and is notable for showing how closely Einstein’s life is involved with the quantum revolution at this date: the gravitation announcement aside, every other topic he mentions in the letter is, in one way or another, directly linked to radiation and quanta. He gives pride of place, even before his new theory of gravity, to the news that ‘I derived the laws of photochemical equivalents by way of thermodynamics, without quanta’; he notes that he will engage in ‘a heavy verbal duel’ with Max Abraham over his ‘completely wrong’ alternative theory of gravitation (a dispute referred to again in his August letter) and refers to Walther Nernst’s proof of the third law of thermodynamics (which Einstein also considers ‘totally wrong’). On top of this, he is ‘wrestling with dispersion in the infrared’; and discusses Edgar Meyer's work on gamma-ray absorption. The letter concludes with a report of the first Solvay Conference, the scientific forum that jump-started the quantum revolution: ‘To be sure nothing came out of Brussels, but it was a very pretty spectacle. No one could bring up anything against the theory of fluctuations’ (which Einstein in 1909 applied to black-body radiation and found that it revealed the radiation to have a dual wave-particle nature). But, he goes on. ‘I still understand the thing just as badly as I did then. True enough, the quanta do what they are supposed to do, but they do not exist, like the luminiferous ether at rest’. The shorter letter of 16 August congratulates Hopf on his marriage and refers to the progress of his dispute with Max Abraham, whose competing theory of gravity he describes as ‘a stately steed, but one that is lacking three legs’; and he mocks Abraham for misattributing Einstein’s discovery of mass-energy equivalence to a 19th-century forebear, Robert Meyer.
Einstein published his revolutionary new theory of gravity, ‘On the theory of the static gravitational field’ (Weil 48), on 23 May 1912. The first major step toward the formalisation of general relativity, Einstein’s theory was radically at variance not only with Newton’s mechanical paradigm of gravity, but even with his own special theory of relativity. For the first time, Einstein formally introduced the equivalence principle of gravity – ‘the equivalence of uniformly accelerated reference frames and static homogeneous gravitational fields’ (Collected Papers, IV, 122) – and he further deviated from special relativity with the premise that the velocity of light is both variable and locally determined (something he had proved in his 1911 paper on the bending of light by gravity, ‘Influence of gravitation on the propagation of light’, Weil 43). The result is the deduction that gravitational mass and inertial mass are identical, and that the activity of matter and space are interconnected in a dynamic geometry (as John Wheeler later put it, ‘Spacetime tells matter how to move; matter tells spacetime how to curve’). Einstein tried to develop and extend his gravitational theory over the course of 1912, but lacked the thinking tools that would enable him to conceive and express the field equations of the dynamic gravitational field. This impasse was resolved only in August 1912, when his friend Marcel Grossmann introduced him to Riemannian geometry (as confirmed by Einstein in a speech ten years later: ‘This problem remained insoluble to me until 1912, when I suddenly realized that Gauss’s theory of surfaces holds the key for unlocking this mystery … However, I did not know at that time that Riemann had studied the foundations of geometry in an even more profound way … My dear friend the mathematician Grossman was there when I returned from Prague to Zurich. From him I learned for the first time about Ricci and later about Riemann’). With this mathematical formalism in hand, Einstein was able to complete the development of the theory of general relativity.
The general theory of relativity is the greatest scientific achievement of the 20th century and has been described as ‘the greatest intellectual achievement of any one person’. Einstein’s theory of the static gravitational field constitutes general relativity’s core, and the development of the theory is due to Einstein’s discovery and application of Riemannian geometry. The two letters here are extraordinary examples of the fertility of Einstein’s mind at the birth of general relativity, showing Einstein rising to the height of scientific greatness. The letters are published in Collected Papers, 4, nos 364 and 416. Ludwig Hopf (1884-1939) had worked as an assistant to Einstein during his first posting at the University of Zurich, briefly following him to Prague: they collaborated on two papers on statistical aspects of radiation published in 1910.
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