In his 1921 article, Kaluza established all the elements of the classical five-dimensional theory: the metric, the field equations, the equations of motion, the stress–energy tensor, and the cylinder condition. With no free parameters, it merely extends general relativity to five dimensions. One starts by hypothesizing a form of the five-dimensional metric g ~ ~ a b , where Latin indices span five dimensions. Let one also introduce the four-dimensional spacetime metric g μ μ ν ν , where Greek indices span the usual four dimensions of space and time; a 4-vector A μ μ identified with the electromagnetic vector potential; and a scalar field ϕ ϕ . Then decompose the 5D metric so that the 4D metric is framed by the electromagnetic vector potential, with the scalar field at the fifth diagonal. This can be visualized as