EINSTEIN, Albert (1879-1955). Autograph letter signed ('Albert') to Michele Besso, n.p., n.d. [Berlin, December 1916].
Including a diagram of a point in a circular field. In German, 5 pages, on two bifolia, 210 x 133mm and 210 x 127mm. Provenance: by descent from Michele Besso.
The birth of the cosmological constant: a detailed explanation of the development of one of Einstein's most famous concepts.
'On to the matter of ? = 1/R': virtually the entire letter is devoted to explaining the process of reasoning behind the introduction of ? -- the cosmological constant -- into the equations of general relativity, providing an opportunity of following Einstein's extraordinary mind in is process of reasoning. Einstein begins: if one were to choose a set of Galilean coordinates and to develop the system commensurately, how will they behave 'if I go enormously far away, in space and in time? Is it possible to organise the calculations in such a way that the [coordinates] are really determined solely by matter, as the relativistic conception requires?'. Einstein goes on to elaborate his reasoning: 'Let's begin with the most important part. Begin with the Newtonian theory as a basis. You suggest that one might consider that a mass evenly distributed in space until infinity would produce no field. But this is not accurate': Einstein then with the aid of a diagram posits the case of a point P, supposed to have no field, at the centre of a surface which necessarily, according to Gauss's principle, must have a gravitational flux, and demonstrates the inherent contradiction, concluding characteristically 'Jehovah did not build the universe on such a mad basis'. He goes on: 'If the universe is to have a lasting existence, movement must impede fall (centrifugal forces). This is the case with the solar system. But this is only true if one allows the average density of matter at infinity to tend in a compatible way towards zero, as otherwise infinitely great differences of potential emerge. // Such a conception is already unsatisfactory according to Newton ... It is even more unsatisfactory according to the theory of relativity, as relativity does not comply with inertia ... I do not think I seriously believe that the universe is in a state of statistical-mechanical equilibrium, even when I myself use this argument. The stars would then all have to clump together (if the available volume was finite) ... What is certain is that infinitely great differences of potential would necessarily produce stellar speeds of very considerable size, which would no doubt long ago have become apparent. Small differences of potential associated with infinite dimensions of the universe require an emptiness of the universe at infinity ... in contradiction with relativity if sensibly understood. Only a closed universe frees one from the dilemma; this is also suggested by the fact that the curvature has everywhere the same sign, as the density of energy in accordance with experience does not become negative'. He therefore explains the newly introduced ? in his equations, noting in passing that astronomy of fixed stars implies an order of magnitude of the universe of 107 light years, whereas the distance of the furthest visible stars is estimated at 104 light years.
At the conclusion of this remarkable exposition, Einstein comes 'back to earth, which is only so ugly because we see and experience it too closely': he discusses his children, and looks forward to seeing them and Besso in Zurich the next year. He is delighted to hear that Besso and his son Vero are taking an interest in Einstein's elder son, Hans Albert; he is also pleased with reports of 'my poor little boy' (his second son, Eduard), about whose condition however he has not much hope: 'One must be able to look reality in the face, even when it is so hard'. He has no intention at all of taking Hans Albert to live with him in Berlin against his mother's wishes ('I am not a brute'): as long as he is happy in Zurich, then he is content for him to remain there.
The cosmological constant, denoting the value of the energy density of the vacuum of space, was an addition to the general theory of relativity introduced by Einstein in order to achieve a static universe -- or as he puts it here, to prevent all matter from 'clumping together'. After Hubble demonstrated that galaxies are receding from us, Einstein described this as his 'greatest blunder': more recently however it has been reintroduced to the standard model as the simplest means of accounting for 'dark energy'. Einstein's publication of the constant (in the paper 'Kosmologische Betrachtungen zur allgemeinen Relativitaetstheorie') dates from 1917 -- the year after this letter.
Published (in French and German) in Pierre Speziali (ed. and tr.). Albert Einstein. Michele Besso. Correspondance 1903-1955. Paris: Hermann, 1972. No. 29.