Matter Inferred from Geometry

It is shown that the existence of matter and its fundamental properties are deducible from the assumption that spacetime can be described by Riemannian geometry. Considered is a system whose behavior is determined by an invariant action incorporating a metric tensor, a vector field, and paths through the fields. No matter is assumed à priori. The existence of matter in the form of point particles arises from the equations of motion of the system. The particles are found to possess both a gravitational mass, i.e. a parameter acting as a source of spacetime curvature, and an inertial mass. Both types of mass associated with a given particle are shown to be proportional to the same geometric entity, namely the magnitude of a tangent vector along the particle's world line. Consequently, the equality of gravitational and inertial mass is an output of the model. A modified Nordström/Reissner metric describes the gravitational field of each particle. The point particles exhibit characteristics qualitatively similar to properties of observed particles.