Kaluza–Klein theory

The Kaluza - Klein theory was one of the first attempts to unify the fundamental interactions of gravitation and electromagnetism.

1921 Advanced Theodor Kaluza the four-dimensional space-time of general relativity ( one time dimension and three space-like dimensions) by adding a further, fourth space-like dimension to a total of five dimensions. Interestingly, the resulting equations can be separated into the Einstein field equations and the Maxwell equations. Thus Minkowski space and Maxwell's equations in vacuum in a 5 -dimensional Riemann curvature tensor can be embedded. From Einstein's general theory of relativity, in which an energy -momentum tensor represents the sources to Kaluza's equations also differ in that they are sourceless.

Later Oskar Klein extended the theory of Kaluza and argued that the fourth spatial dimension is rolled up and is therefore not observed. ( To explain an analogy: A straw looks from a distance like a one-dimensional line, on closer inspection it turns out to be a two-dimensional cylinder surface. ) This small compaction could also explain a quantization of charge.

Generally, however, was the Kaluza - Klein theory (so far ) can not be quantized, so with increasing success of quantum mechanics waned interest in the Kaluza - Klein theory. The idea to use kompaktifizierte additional dimensions to unify the fundamental forces, but was further developed later in string theory, where it is referred to as the Kaluza-Klein compactification.