Angular Momentum, Mass-Center and the Inverse Square Law in Special Relativity

Abstract

It is assumed that the interaction of two particles takes place by means of streams of elementary impulses traveling with the velocity of light $c$, an impulse of energy $W$ having a momentum $\frac{W}{c}$. The momentum-energy 4-vector of a complete system and a skew-symmetric angular momentum tensor are defined in such a way that they are constants for the system, and the mass-center of the system is defined in such a way that it travels with uniform velocity relative to a Galilean frame. The formulae are similar to those of Newtonian mechanics. The two-body problem is discussed, and it is shown that for particles with constant proper masses and relative velocity small compared with $c$, the inverse square law is a consequence of the mechanical laws of conservation. The whole theory is relativistically invariant.