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Autograph manuscript calculations and prose drafts on the perihelion of Mercury and the 'Entwurf' theory of general relativity, [June 1913 - 1916]
細節
Michele Besso (1873-1955)
Autograph manuscript calculations and prose drafts on the perihelion of Mercury and the 'Entwurf' theory of general relativity, [June 1913 - 1916]
In German. Seven fragments, comprising approximately 16 pages, various sizes (between 178 x 112mm and 274 x 212mm), on paper from differing sources, one on graph paper, another on paper reused from an envelope, another on paper reused from a typed letter.
Calculations and drafts produced during Besso's collaboration with Albert Einstein on the Einstein-Besso manuscript. The manuscripts include three draft calculations on the perihelion of Mercury which directly belong to the Einstein-Besso manuscript, four drafts for Besso's expansion of the Einstein-Besso manuscript, in which Besso drew upon his work with Einstein to envisage an ambitious paper in which he would compare Einstein's theory of gravity with those of Gunnar Nordström, Max Abraham and Gustav Mie, and two drafts of later notes on general relativity, one in 1916 in connection with a paper on the foundations of relativity in its final form which he was asked to present at a colloquium at the University of Zurich.
In June 1913 Einstein published his 'Entwurf' (or 'Outline') theory of general relativity, in a joint paper with Marcel Grossmann entitled 'Outline of a generalised theory of relativity and of a theory of gravitation'. Although the theory turned out to be untenable in itself (its chief flaw being that its gravitational equations are not covariant), it was to be a crucial breakthrough, establishing the basic approach used by Einstein in his final theory of general relativity in November 1915. In the month of the 'Entwurf' paper's publication, Einstein took advantage of a visit by his friend Michele Besso to his home in Zurich to test whether the theory could account for a known anomaly in Newtonian theory concerning the precession of the perihelion of the planet Mercury: the result is 53 pages of dense mathematical collaboration, and the only substantial working scientific manuscript to survive from this early stage of Einstein's career. Although their efforts were unsuccessful, Einstein was able to reuse the mathematical approach of the Einstein-Besso manuscript in November 1915 to demonstrate that his final theory of relativity did indeed account for the perihelion of Mercury. The fragments in the present lot are a record of Michele Besso's contribution to this historic collaboration. A number of these drafts are discussed in Michele Janssen, ‘What Did Einstein Know and When Did He Know It? A Besso Memo Dated August 1913’ (Jürgen Renn, ed., The Genesis of General Relativity. 2007, 2, 785-837).
Calculations and drafts belonging to the Einstein-Besso manuscript itself, datable to June 1913 (the first two) and 1914⁄1915 (the third):
1 and 2. Calculation involving the area law, part of a calculation in the Einstein-Besso manuscript (p.8) of the orbit of a planet in the field of the sun, with a second leaf of similar calculations, probably a continuation. One page, 178 x 112mm, on a larger sheet roughly folded in four, and one page, approx. 135 x 190mm, roughly torn from a larger sheet (the verso preserving the end of a typed letter signed 'G. Gieré').
3. The verso comprises 'a page of calculations related to p. 53 of the published portion of the Einstein-Besso manuscript, which summarizes Besso’s analysis of the perihelion motion predicted by the Nordström theory' (Janssen, op. cit., p. 794 and n.29); on the recto is a paragraph on the problem of rotation and other questions, beginning with an equation quoted from Einstein's 23 September 1913 lecture in Vienna which 'expresses the vanishing of the divergence of the sum of a mixed tensor density describing the energy-momentum density of matter and a similar quantity for the gravitational field' (translated in Janssen, op. cit., p.798). Two pages, 270 x 214mm
Drafts for Besso's expansion of his contributions on pp.45-53 of the Einstein-Besso manuscript, datable to 1914⁄1915:
4. Heavily-corrected draft (on pp.2-3) of the introduction to Besso's intended paper on the perihelion problem ('perspectives emerge for a supplement to Newton's law of gravitation and laws of motion of the planets, which are to be explored in the present work'), concluding (p.4) with an outline for a table listing 'the theories under consideration and the observable elements to which they are to be applied' (Janssen, op. cit., p.795: 'The overly ambitious character of Besso’s paper becomes even clearer if we look at a table on another one of the new pages. The table has rows for scalar theories, four-vector theories, and six-vector theories ... Nordström, Laue (with a question mark) and Mie are listed under scalar theories and get one row each. The final row, labeled “tensor theory,” is for the Entwurf theory'); p.1 comprises a draft of four numbered points in relation to the perihelion problem, presumably questions Besso hoped to answer in his paper; p.3 also includes extensive calculations, likely on the same subject. Four pages, 274 x 212mm, on graph paper
5. A further draft introduction for Besso's paper, including eight numbered equations (the last two incomplete) for the iterative approximation procedure used in the Einstein-Besso manuscript to calculate the field of the sun. 1 ½ pages, 211 x 135mm
6 and 7. Numbered list of 16 questions Besso hoped to answer in his paper (see Janssen op. cit. p. 795: 'How much of the work for Besso’s magnum opus remained to be done, is further illustrated by two pages with a numbered list of sixteen problem areas that Besso was still planning to address. One of the entries in this list is related to the problem of rotation: / 15. Final result about centrifugal forces without Coriolis forces? Would that not have astronomical consequences as well?'); the verso of no.6 lists deviations for Mercury, Venus, Earth and Mars, with a few calculations. 1 ½ pages, 237 x 146, on paper reused from an envelope, and one page, 215 x 135mm
Later drafts on relativity:
8. Section headings for a planned article giving an ambitious overview of all of physics, with, on verso, a series of calculations. Two pages, 212 x 136mm
9. Heavily corrected outline for a paper on special and general relativity, based mainly on Einstein's 1916 review article, comprising three numbered points on special relativity and fourteen on general relativity. Two pages, 212 x 269mm
Autograph manuscript calculations and prose drafts on the perihelion of Mercury and the 'Entwurf' theory of general relativity, [June 1913 - 1916]
In German. Seven fragments, comprising approximately 16 pages, various sizes (between 178 x 112mm and 274 x 212mm), on paper from differing sources, one on graph paper, another on paper reused from an envelope, another on paper reused from a typed letter.
Calculations and drafts produced during Besso's collaboration with Albert Einstein on the Einstein-Besso manuscript. The manuscripts include three draft calculations on the perihelion of Mercury which directly belong to the Einstein-Besso manuscript, four drafts for Besso's expansion of the Einstein-Besso manuscript, in which Besso drew upon his work with Einstein to envisage an ambitious paper in which he would compare Einstein's theory of gravity with those of Gunnar Nordström, Max Abraham and Gustav Mie, and two drafts of later notes on general relativity, one in 1916 in connection with a paper on the foundations of relativity in its final form which he was asked to present at a colloquium at the University of Zurich.
In June 1913 Einstein published his 'Entwurf' (or 'Outline') theory of general relativity, in a joint paper with Marcel Grossmann entitled 'Outline of a generalised theory of relativity and of a theory of gravitation'. Although the theory turned out to be untenable in itself (its chief flaw being that its gravitational equations are not covariant), it was to be a crucial breakthrough, establishing the basic approach used by Einstein in his final theory of general relativity in November 1915. In the month of the 'Entwurf' paper's publication, Einstein took advantage of a visit by his friend Michele Besso to his home in Zurich to test whether the theory could account for a known anomaly in Newtonian theory concerning the precession of the perihelion of the planet Mercury: the result is 53 pages of dense mathematical collaboration, and the only substantial working scientific manuscript to survive from this early stage of Einstein's career. Although their efforts were unsuccessful, Einstein was able to reuse the mathematical approach of the Einstein-Besso manuscript in November 1915 to demonstrate that his final theory of relativity did indeed account for the perihelion of Mercury. The fragments in the present lot are a record of Michele Besso's contribution to this historic collaboration. A number of these drafts are discussed in Michele Janssen, ‘What Did Einstein Know and When Did He Know It? A Besso Memo Dated August 1913’ (Jürgen Renn, ed., The Genesis of General Relativity. 2007, 2, 785-837).
Calculations and drafts belonging to the Einstein-Besso manuscript itself, datable to June 1913 (the first two) and 1914⁄1915 (the third):
1 and 2. Calculation involving the area law, part of a calculation in the Einstein-Besso manuscript (p.8) of the orbit of a planet in the field of the sun, with a second leaf of similar calculations, probably a continuation. One page, 178 x 112mm, on a larger sheet roughly folded in four, and one page, approx. 135 x 190mm, roughly torn from a larger sheet (the verso preserving the end of a typed letter signed 'G. Gieré').
3. The verso comprises 'a page of calculations related to p. 53 of the published portion of the Einstein-Besso manuscript, which summarizes Besso’s analysis of the perihelion motion predicted by the Nordström theory' (Janssen, op. cit., p. 794 and n.29); on the recto is a paragraph on the problem of rotation and other questions, beginning with an equation quoted from Einstein's 23 September 1913 lecture in Vienna which 'expresses the vanishing of the divergence of the sum of a mixed tensor density describing the energy-momentum density of matter and a similar quantity for the gravitational field' (translated in Janssen, op. cit., p.798). Two pages, 270 x 214mm
Drafts for Besso's expansion of his contributions on pp.45-53 of the Einstein-Besso manuscript, datable to 1914⁄1915:
4. Heavily-corrected draft (on pp.2-3) of the introduction to Besso's intended paper on the perihelion problem ('perspectives emerge for a supplement to Newton's law of gravitation and laws of motion of the planets, which are to be explored in the present work'), concluding (p.4) with an outline for a table listing 'the theories under consideration and the observable elements to which they are to be applied' (Janssen, op. cit., p.795: 'The overly ambitious character of Besso’s paper becomes even clearer if we look at a table on another one of the new pages. The table has rows for scalar theories, four-vector theories, and six-vector theories ... Nordström, Laue (with a question mark) and Mie are listed under scalar theories and get one row each. The final row, labeled “tensor theory,” is for the Entwurf theory'); p.1 comprises a draft of four numbered points in relation to the perihelion problem, presumably questions Besso hoped to answer in his paper; p.3 also includes extensive calculations, likely on the same subject. Four pages, 274 x 212mm, on graph paper
5. A further draft introduction for Besso's paper, including eight numbered equations (the last two incomplete) for the iterative approximation procedure used in the Einstein-Besso manuscript to calculate the field of the sun. 1 ½ pages, 211 x 135mm
6 and 7. Numbered list of 16 questions Besso hoped to answer in his paper (see Janssen op. cit. p. 795: 'How much of the work for Besso’s magnum opus remained to be done, is further illustrated by two pages with a numbered list of sixteen problem areas that Besso was still planning to address. One of the entries in this list is related to the problem of rotation: / 15. Final result about centrifugal forces without Coriolis forces? Would that not have astronomical consequences as well?'); the verso of no.6 lists deviations for Mercury, Venus, Earth and Mars, with a few calculations. 1 ½ pages, 237 x 146, on paper reused from an envelope, and one page, 215 x 135mm
Later drafts on relativity:
8. Section headings for a planned article giving an ambitious overview of all of physics, with, on verso, a series of calculations. Two pages, 212 x 136mm
9. Heavily corrected outline for a paper on special and general relativity, based mainly on Einstein's 1916 review article, comprising three numbered points on special relativity and fourteen on general relativity. Two pages, 212 x 269mm
榮譽呈獻
Eugenio Donadoni
Senior Specialist, Medieval & Renaissance Manuscripts