Autograph letter signed ('A. Einstein') to Cornelius Lanczos, n.p., 23 January 1940

Albert Einstein (1879-1955)
Autograph letter signed ('A. Einstein') to Cornelius Lanczos, n.p., 23 January 1940
In German. In green ink, two pages, 280 x 216mm, including six scientific equations. Provenance: Sotheby's, 26 November 1980, lot 161.

'We are only making slow progress in our investigation and are suffering indescribably. But it is so much fun': a detailed critique of a draft paper, warning against the dangers of 'artificial ad-hoc hypotheses'. Einstein plunges directly into a response to a paper from Lanczos: 'It seems to me that the work you sent me must be based on an error. I denote as an “illusory field” [Scheinfeld] one that occurs through a mere coordinate transformation from a field of type / ds² = - dx₁² - . - . + dx₄². What you are now looking at is a field that is, to a first approximation, an illusory field ... Now however there certainly exists a strictly illusory field which, to a first approximation, is identical to the illusory field on which you base your analysis. This strictly illusory field exactly fulfills the condition R_iklm = 0, thus also R_ik = 0 / It is therefore impossible to get from an illusory field to a real field taking as a basis the equations R_ik = 0 alone if one considers the higher approximations'. At this point, Einstein takes a step back to a more conceptual approach: 'So much for the mathematical method. But now I'm wondering more generally what chances there are to explain the electrostatic interactions between two particles using the gravitational equations of empty space'. He recharacterises Lanczos's statement in terms of the effects on their polarities of the interaction between two particles, noting that the possibility Lanczos implies 'is not excluded by our investigation of the movement problem', and concluding 'In my opinion any idea of this sort can only be justified if it emerges in itself from the consideration of the particle as a singularity-free solution. The desire to operate with the simplest possible theoretical foundations is certainly justified; but it must not lead to an accumulation of the most artificial ad-hoc hypotheses'. On this basis, Einstein is not convinced that he should recommend the publication of Lanczos's paper to Annals of Mathematics. In a postscript, he adds a characteristically upbeat note: 'We are only making slow progress in our investigation and are suffering indescribably. But it is so much fun'.