A contribution to modern ideas on the quantum theory

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 =gmn dxm dxn , (1) the notation being that generally adopted. The world-lines or natural tracks of free particles in this space are geodesics. From (1) we havegmn 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 thatdxm /dsis the natural extension of the velocity,dxm /dt.