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
Unified field Unified field In music, unified field is the 'unity of musical space' created by the free use of melodic material as harmonic material and vice versa. The technique is most associated with the twelve-tone technique, created by its 'total thematicism' where a tone-row (melody) generates all (harmonic) material. It was also used by Alexander Scriabin, though from a diametrically opposed direction, created by his use of extremely slow harmonic rhythm which eventually led to his use of unordered pitch-class sets, usually hexachords (of six pitches) as harmony from which melody may also be created. (Samson 1977) It may also be