A contribution to modern ideas on the quantum theory

Source abstract

Abstract The relativity theory of gravitation indicates that space-time is a four dimensional continuum in which the line element is measured by the equation (ds)2 = gmndxmdxn, (1) the notation being that generally adopted. The world-lines or natural tracks of free particles in this space are geodesics. From (1) we have gmn dxm/ds . dxn/ds = 1, (2) the quantity on the left being an expression corresponding to the kinetic energy of ordinary dynamics for a particle of unit mass. This correspondence is readily appreciated if it be noted that dxm/ds is the natural extension of the velocity, dxm/dt.