Actio-reactio equations with finite wave speed derived from the principle of inertia (Q919189)

One derives the general actio-reactio relationship under the assumption of the finite propagation speed of any type of interaction. In the derivation of the actio-reactio equations the mathematical theory of inertia developed by the author in a previous series of papers is systematically used. The basic results of this theory are given in a theorem defining the general representation of linear and continuous causal functionals which are compatible with the principle of inertia. Assuming the potentiality of actio and reactio forces, based on the compatibility with the principle of inertia as well on the invariance wit respect to a time translation and on the actio-reactio interchanging to a time reversal, the following set of equations is derived: \[ \partial \phi /\partial t=c\Delta \psi +a_ 1\phi -a_ 2\psi;\quad \partial \psi /\partial t=-c\Delta \phi +a_ 2\phi -a_ 1\psi. \] As an application these equations are applied to perform computations concerning the formation of the solar system. Further applications are given in a recently published paper ``Actio-reactio symmetry breaking model fitted to the new tower-mine gravity experiments'' [Ing.-Arch. 60, 410-417 (1990)].