Motion of Particles in Einstein's Relativistic Field Theory. VIII. Displacement Field, Fundamental Field, and Geodesics

Abstract

In several earlier papers the author developed an approximation method for finding the Lorentz-covariant equations of structure and motion of interacting particles represented by singularities in Einstein's theory of the nonsymmetric field and in Einstein's theory of the gravitational field. In this paper techniques are presented for finding in these theories the displacement field, the fundamental field, and the equations of geodesics - in terms of a field denoted by ${\ensuremath{\gamma}}_{\ensuremath{\mu}\ensuremath{\nu}}$-to any order of approximation desired. The techniques are applied, and the displacement field, fundamental field, and the equations of geodesics are found, in terms of ${\ensuremath{\gamma}}_{\ensuremath{\mu}\ensuremath{\nu}}$, to those orders of approximation needed in future work - the fourth order when dealing with charged particles (and investigating interactions over atomic and molecular distances) and the eighth order when dealing with neutral particles (and investigating higher-order gravitational effects). Certain general properties of the above-mentioned fields and equations are also discussed.