Kaluza-Klein Theory

Christine Marie Egnatuk

Kaluza-Klein Theory attempts to unify electromagnetism and General Relativity by adding an extra dimension. The fifth dimension is considered to be compact, uncoupled and rolled into a circle at every point in space. Expanding Einstein's field equations to 4+1 dimensions results in Einstein's equations for gravity along with Maxwell's equations of electromagnetism. The split in the Ricci Scalar of 4+1 dimensions between the classical General Relativity in a vacuum and the Maxwell field equations is known as the "Kaluza-Klein miracle". The momentum in the fifth dimension is the electric charge of the particle. Since the fifth dimension is compact, charge must be quantized.