The Principle of Relativity

by Albert Einstein; H. Minkowski

{ div H = 0.

The first Maxwellian system is obtained by a generalisation of the form given by Minkowski.

We introduce the contra-variant six-vector F_αβ by the equation

(62) F^μν = g^μα g^νβ F_αβ,

and also a contra-variant four-vector J^μ, which is the electrical current-density in vacuum. Then remembering (40) we can establish the system of equations, which remains invariant for any substitution with determinant 1 (according to our choice of co-ordinates).

(63) ∂F^μν/∂x_ν = J^μ

If we put

{ F²³ = H′_x F¹⁴ = -E′_x

{

(64) { F³¹ = H′_y F²⁴ = -E′_y