Interpretation of Γ[jk]i in a Huygens Model

Abstract

We describe a classical field theory based on Huygens' principle which is characterized by an additional degree of freedom which, to our knowledge, has not been discussed previously. This additional degree of freedom asserts that the forward propagation cone is different from the backward cone. The purpose of this paper is to find a function which describes this degree of freedom, and next, to understand this effect in reference to other theories. We find that this additional degree of freedom can be described by means of Γ[jk]i. The object Γ[jk]i is then related to the torsion of a preferred-frame geometric theory. The additional degree of freedom is of interest since it enables one to introduce Γ[jk]i in a framework involving characteristic equations, described by gij, and bicharacteristics described by Γ(jk)i, such that the role of Γ[jk]i can be understood. Also, the theory furnishes a generalized framework for gravitational theory. Paths with noncontinuous slopes appear also in Feynman's path-integral approach. Thus, this type of discontinuity has physical interest here also, although we do not pursue this point in this paper.