1 1 0 D O C . 9 2 E L E C T R O N A N D G E N E R A L R E L A T I V I T Y 92. “The Electron and the General Theory of Relativity” [Einstein 1925w] Dated before 21 October 1925[1] Received 21 October 1925[1] Published Nov–Dec 1925 In: Physica 5 (1925): 330–334. The following remark is of such a simple nature that I do not think I am saying anything new. But since the theorem to be proven was new to me personally, I do believe that its exposition will be welcome to some. The theorem states: If it is true that the electromagnetic field is to be represented by an antisymmetric tensor ( ) of rank 2, then there cannot be general covariant equations that 1) contain the negative electron as a solution.[2] 2) contain no solution that would correspond to a positive electron of equal mass. Proof. I assume the existence of a solution that corresponds to a negative elec- tron at rest, and possessing electric charge ε and mechanical mass μ. Assume fur- ther that the solution is characterized by the electromagnetic tensor ( ) and the metric tensor ( ). If I perform the space-time transformation that is characterized by the equations:[3] , (1) then we obtain a mathematically new solution that is linked to the original one by the relations: (2) If we interpret as components of the magnetic field strength, and as components of the electric field strength, then the , etc., vanish. But the components of the electric field strength change their sign when the trans- [p. 330] fμν [p. 331] fμν gμν x′1 x1 x x1 = = = x′2 y1 y x2 = = = x′3 z1 z x3 = = = x′4 t1 t x4 = = = g′11 g11 = …… g′44 g44 = g′33 g33 = f ′23 f23 = f ′31 f31 = f ′12 f12 = f ′14 f14 –= f ′24 f24 –= f ′34 f34 –= f23, f31, f12 f14, f24, f34 f23