D O C . 4 4 3 G E N E R A L R E L AT I V I T Y A N D M O T I O N 4 2 5 443. “General Theory of Relativity and Equations of Motion” [Einstein and Grommer 1927] Presented 6 January 1927 Published 24 February 1927 In: Preußische Akademie der Wissenschaften (Berlin). Physikalisch-mathematische Klasse. Sitzungsberichte (1927): 2–13. Introduction If one regards Newton’s theory of gravitation as a field theory, then total content of the theory can be separated into two logically independent parts: it contains, first, Poisson’s field equation (possibly extended by a temporal term) second, the law of motion of a material point. Poisson’s law yields the field for a given motion of matter Newton’s equation of motion yields the motion of matter under the in- fluence of a given field. Maxwell-Lorentz Electrodynamics is based in an analogous way on two funda- mental laws that are logically independent of each other namely, first, on the Maxwell-Lorentz field equations, which determine the field due to the motion of electrically charged matter second, on the law of motion for electrons under the influence of the Lorentz forces of the electromagnetic field. It easily becomes clear from the special case of two electrons at rest that both laws of the Maxwell-Lorentz theory really are independent of each other. The field with the electrostatic potential satisfies the field equations. Thus, these equations alone do not allow us to con- clude that both electrons cannot stay at rest (but must get into motion under the in- fluence of their interaction).[1] It follows very easily from their linearity that the Maxwell-Lorentz field equa- tions of the electromagnetic field say nothing about the motion of electrons. For to an arbitrarily moving electron E1 there belongs a field (f1) generated by it that is determined by the field equations. For a differently moving single electron E2 in arbitrary motion, the equations determine the field (f2) accordingly. If both our [p. 2] φ ε r1 ε r2 -+=2-----1----