## Die Nordströmsche Gravitationstheorie vom Standpunkt des absoluten Differentialkalküls [Nordström's Theory of Gravitation from the Point of View of the Absolute Differential Calculus]

FIRST EDITION IN RARE ORIGINAL WRAPPERS of a critical paper in the development of general relativity; of “considerable interest in the history of general relativity because it contains Einstein’s first treatment of a gravitation theory in which general covariance is strictly obeyed ... and particularly notable for its new derivation of the field equation.” (Pais, p.236).

Although Einstein and Grossmann had made significant progress with their ‘Entwurf’ theory of 1913, using the tensor calculus of Levi-Civita and Ricci, it was still a theory in which the equivalence principle in general did not hold (i.e., under particular coordinate transformations the gravitational field equations were not covariant). Einstein attempted to give various ‘physical’ arguments in order to account for this deficiency, but an important step towards obtaining general covariance was made when Einstein and Fokker, the next year, examined an alternative gravitational theory, in the framework of tensor calculus, and found that using just the condition that the velocity of light is constant, and independent of the position of the physical point, they were able to derive generally covariant field equations for this theory.

“After the Einstein-Grossmann (1913) paper, Einstein’s next significant references to the curvature tensor and general covariance occur in a paper that Einstein wrote early in 1914 together with a young Dutch physicist, Adriaan D. Fokker. This paper is a discussion of a gravitational theory proposed by Gunnar Nordström, a Finish physicist then working on the problem of finding a gravitational theory compatible with the principles of special relativity. Einstein and Fokker showed that Nordström’s scalar theory can be rewritten as a metric theory of gravitation [i.e., in the framework of tensor calculus], using only generally covariant equations, if one assumes that the metric tensor is conformally related to the Minkowski metric tensor of special relativity. They phrased the latter requirement as follows: ‘Nordström’s theory … is based on the assumption that, by proper choice of reference system, it is possible to satisfy the principle of the constancy of the velocity of light’. Thus, they not only assumed the metric tensor to be conformally Minkowskian, but also adopted conformally Cartesian coordinates.” (Stachel, *Einstein and the History of General Relativity*, p.82).

“They derived its basic equations [the gravitational field equations of Nordström’s theory] in in a very simple way, directly from the condition of the constant velocity of light and Lorentz covariance. This was an important step towards the final tensor equations of general relativity of November 1915.” (*Einstein Studies*, vol. 10, p.285).

Einstein and Fokker concluded their paper remarking that it might be possible that a similar derivation of the field equations would be possible in the Einstein-Grossmann theory without need of the previous physical assumptions.

“Thus, early in 1914, just fifty years after Maxwell’s first attempt at a gravitation field theory, Einstein was not quite there but he was closing in, as the final remark of the Einstein-Fokker paper clearly indicates.” (Pais, p.237).

IN: Annalen der Physik Vol. 44, pp. 321-328. Leipzig: Johann Ambrosius Barth, 1914. Octavo, original printed wrappers. Weil 65. Rubbing to spine with a little loss. SCARCE in the notoriously fragile original *Annalen* wrappers.

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