3 8 D O C . 1 7 G R A V I T A T I O N A N D E L E C T R I C I T Y 17. “Unified Field Theory of Gravitation and Electricity” [Einstein 1925t] Received 9 July 1925 Published 4 September 1925 In: Preußische Akademie der Wissenschaften (Berlin). Physikalisch-mathematische Klasse. Sitzungsberichte (1925): 414–419. Theoretical physicists working in the field of the general theory of relativity may by now be convinced of the essential unity of the gravitational field and the elec- tromagnetic field. However, it appears to me that a convincing account of this con- nection has not been found as of now. My own contribution, which appeared in these proceedings (Sitzungsberichte XVII, p. 137, 1923)[1] and which was based entirely on Eddington’s fundamental ideas, does not offer the true solution to this problem either. After a relentless search during the past two years, I now believe to have found the true solution. I present it in the following. The method employed can be characterized as follows. I first sought the simplest formal expression of the gravitational field equations in the absence of an electro- magnetic field, then the most natural generalization of this law. It became apparent that this generalization contains Maxwell’s theory to first approximation. In the fol- lowing, I first provide the scheme of the general theory (§1) and then show in which sense the pure gravitational field equations (§2) and Maxwell’s theory (§3) are contained in this theory. §1. The General Theory Assume there is an affine connection in the four-dimensional continuum, i.e. a field that defines the infinitesimal transport of a vector according to the rela- tion . (1) It is is not presupposed that the are symmetric in the indices α and β.[2] We can then define the (Riemannian) tensors in terms of the Γ in their standard form: and [p. 414] Γαβ α dAμ Γαβ μ Aαdxβ –= Γαβ α νβ , α α ∂Γμν ∂xβ ----------- -– Γσν α Γμβ σ α ∂Γμβ ∂xν ----------- - Γμν σ Γσβα + + =
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