BEYL, LAWRENCE MICHAEL.

A 4N-dimensional formalism is developed and a corresponding space is found.
The necessity of coupling the particle's proper times to one parameter is
discussed. The appropriate conditions and constraints which relate this
space to the ordinary 4-space are found. The transformation properties which
are consistent with general 4-space transformations are determined. These
transformation properties are used to determine the form of the 4x4 matrices
making up the 4N-dimensional metric tensor. The form of these matrices
indicates they represent interactions between particles. The diagonal
matrices are shown to represent gravitational interaction and the off-diagonal
matrices to represent other interparticle interactions. A metric theory to
cover all interparticle interactions is then proposed. The equations of
motion for one particle in this 4N-dimensional space are found. These
equations are then related to the motion of N interacting particles in 4- space .
Finally, an approximation procedure is applied to determine the first order
equations of motion.