General covariance

Summary

General covariance is the property of a physical theory that its equations keep their form under arbitrary smooth changes of coordinates. Equivalently, they keep their form under diffeomorphisms of spacetime. It is achieved by writing all laws as equations between tensor fields on a manifold, without fixed background structures such as a preferred coordinate system. It was one of Einstein's guiding principles for general relativity, and in that theory it implies that coordinates have no physical meaning by themselves.