General relativity endows spacetime with a causal structure described by observer-invariant light cones. This locally incorporates the theory of special relativity: the velocity of light is the same for all observers. Points inside a light cone are causally connected with its vertex, while points outside the same light cone are out-of-causal contact with its vertex. Light describes null-generators on the light cone. This simple structure suffices to capture the kinematic features of special relativity. We illustrate these ideas by looking at relativistic motion in the nearby quasar 3C273.

Lorentz transformations

Maxwell's equations describe the propagation of light in the form of electromagnetic waves. These equations are linear. The Michelson–Morley experiment[372] shows that the velocity of light is constant, independent of the state of the observer. Lorentz derived the commensurate linear transformation on the coordinates, which leaves Maxwell equations form-invariant. It will be appreciated that form invariance of Maxwell's equations implies invariance of the velocity of electromagnetic waves. This transformation was subsequently rederived by Einstein, based on the stipulation that the velocity of light is the same for any observer. It is non-Newtonian, in that it simultaneously transforms all four spacetime coordinates.