Abstract

This paper demonstrates mathematically that, in the geodesic equation of Einstein's General theory of Relativity, the fourth component ( j = 4 ), the time equation, is an invalid equation of motion. The spatial components of the geodesic equation ( j = 1,2,3 ) are shown to be equivalent to Hamilton's principle in space-time. Thus, mass particles in motion in gravity do not follow geodesics in space-time, but rather they follow Hamiltonian extremals. As the geodesic equation is not a four-vector equation, but is a 3-vector equation, the principle of general covariance is disproven, showing that the general theory of relativity is improperly formulated and requires correction. This also indicates that the corrected version of the theory must allow a separation between space and time.