Princeton, 14 May 1954

A long and detailed mathematical exposition about general relativity.

Einstein responds to a question from Besso: 'We start from a system of coordinates in which there is a homogenous gravitational field. Here free bodies fall in a uniform way. We determine the gravitational field, which we presuppose to be small, by the acceleration of the freefall'. The fall is determined by the equation of the geodesic line, which Einstein sets out, and then transforms on the basis of its proximity to the Euclidean case, in order to provide the third equation of movement. The next stage is the supposition that the gravitational field is static, which enables a further transformation of the movement equation, thus providing the mathematical form for the gravitational field: 'This gravitational field will undergo only a negligible influence from the suspended mass-point and from the tension of the string. Once the string is cut, the point will move according to the above movement equation'. Given that the system can be chosen so that falling bodies undergo no acceleration, the gravitational field becomes purely Euclidian.

This is the point at which Besso had halted, apparently because he wished to choose his system of coordinates in a way that ensured that his mass-point remained at rest after the string was cut: in order to do this, Besso simply needed to use the initial set of gravitational equations until the string was cut, and thereafter the Euclidian equations – Einstein concedes that this mixed choice of coordinates is confusing, although logically it is justified. He concludes with a reflection on his own work on unified field theory: 'If only everything were so transparent! But in the generalised field theory the thing is so fiendish that I am not even clear myself whether I should believe in its truth. Many more people will break their heads against it when I have deservedly bitten the dust [wenn ich an das wohlverdiente Gras gebissen habe]'.