Classical unified field theories since antisymmetry seemed essential for electromagnetism, the symmetry requirement was relaxed for one or both fields. Einstein's proposed unified-field equations (fundamental laws of physics) were generally derived from a variational principle expressed in terms of the Riemann curvature tensor for the presumed space-time manifold. In field theories of this kind, particles appear as limited regions in space-time in which the field strength or the energy density are particularly high. Einstein and coworker Leopold Infeld managed to demonstrate that, in Einstein's final theory of the unified field, true singularities of the field did have trajectories resembling point particles. However, singularities are
Fundamental interaction distance". Conversely, during the 1820s, when explaining magnetism, Michael Faraday inferred a "field" filling space and transmitting that force. Faraday conjectured that ultimately, all forces unified into one. In 1873, James Clerk Maxwell unified electricity and magnetism as effects of an electromagnetic field whose third consequence was light, travelling at constant speed in a vacuum. The electromagnetic field theory contradicted predictions of Newton's theory of motion, unless physical states of the luminiferous aether—presumed to fill all space whether within matter or in a vacuum and to manifest the electromagnetic field—aligned all phenomena and thereby held valid the Newtonian principle relativity