Riemann's geometry is also the basis for general relativity, which we neither need here nor want to discuss here.
To carry out this embedding two things besides Riemann's geometry are needed: firstly Michelson's and Morley's Experiment (1881) and its interpretation by special relativity for including also indefinite metrics to define Minkowski space and secondly Kaluza's Ansatz to place the dierential operators of Maxwell's equation in Christoel symbols of a curvature tensor. The embedding is presented here strictly by use of only dierential geometry (curvature tensor) with indenite metric and Maxwell's equations, without knowledge from or use of General Relativity.
As a result electromagnetic energy shows to be a source for curvature, a hint to General Relativity, but on a very dierent path than Einstein has gone. |