The Einstein-Nordstr\"om Theory

TL;DR

The paper discusses the historical development and comparison of Einstein's and Nordstr"om's theories of gravitation, highlighting the theoretical advancements and the eventual formulation of Einstein-Nordstr"om theory with a focus on covariance and reference frames.

Contribution

It presents the derivation of Einstein-Nordstr"om theory from Nordstr"om's theory using a generally covariant formalism and the concept of preferred reference systems.

Findings

Nordstr"om's theory satisfied the equivalence principle and redshift but failed to explain Mercury's perihelion and light deflection.

Einstein's theory was not generally covariant and lacked empirical support.

The Einstein-Nordstr"om theory was derived from Nordstr"om's theory assuming preferred reference frames.

Abstract

The Finnish physicist Gunnar Nordstr\"om developed a competing theory of gravitation to Einstein's 1912-1913 gravitation theory. The equivalence principle was valid in his theory and it also satisfied red shift of the spectral lines from the sun. However, it was unable to supply the Perihelion of Mercury, such as Einstein's theory; it led to a Perihelion like the one predicted by Newton's law, and, it could not explain the deflection of light near the sun, because in Nordstr\"om's theory the velocity of light was constant. Einstein's 1913-1914 theory, the field equations of which were not generally covariant, remained without empirical support. Thus a decision in favor of one or the other theory - Einstein's or Nordstr\"om's - was impossible on empirical grounds. Einstein began to study Nordstr\"om's theory from the theoretical point of view and he developed his own Einstein-Nordstr\"om theory on the basis of his conception of the natural interval. Eventually, in a joint 1914 paper with Lorentz's student Adrian Fokker, Einstein showed that a generally covariant formalism is presented from which Nordstr\"om's theory follows if a single assumption is made that it is possible to choose preferred systems of reference in such a way that the velocity of light is constant; and this was done after Einstein had failed to develop a generally covariant formulation for his own theory.