Centre-of-mass for the finite speed of light

Abstract

In 1632, Galilei was aware of relativity of velocity and that this implies relativity of spaces- of-locations. During centuries the relativity of spaces-of-locations was ignored. Professor Harald Keres considered the space-of-locations as a congruence of world-lines, and there is no universal absolute three dimensional space-of-locations. In applications, velocities relative to centre-of-mass are important. But the concept of centre-of-mass is impossible within relativity theory postulating that each pair of reference systems is related by the Lorentz isometry group transformation. We show that centre-of-mass of many- body interacting (bound) system for the case of finite light-speed is a well defined concept within the group-free approach using algebra epimorphisms as splits. We consider the Keres space-of-locations as the Grassmann factor-algebra of differential forms where a material body with a positive mass is interpreted as idempotent algebra epimorphism of the Grassmann algebra of spacetime onto the Grassmann factor-algebra of corresponding space-of-locations of that material body. A material body as a reference system is a group- free split, and this allows us to express all motions, velocities, accelerations and rotations, as relative with respect to the choice of variable reference system.