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
Pasadena Unified School District Pasadena Unified School District The Pasadena Unified School District is a unified school district that is responsible for the schools of Pasadena, California. , it has four high schools, five middle schools, three K–8 schools and 15 K–5 elementary schools. The number of elementary schools was reduced from 18 at the end of the 2010–11 school year. The district also serves the city of Sierra Madre and the unincorporated community of Altadena. PUSD is run by a board of education, whose members serve four-year terms. Duties of the board include budgeting, approving expenditures, establishing policy, making employment decisions, approving textbooks