Matter Inferred from Geometry

It is shown that the existence of matter and some of its fundamental properties are deducible from the assumption that spacetime can be described by Riemannian geometry. Considered is a system determined by an invariant action, incorporating a metric tensor, a vector field, and paths through the fields. No matter is assumed á priori. The existence of matter in the form particles arises from the equations of motion. The particles are found to possess active gravitational masses curving spacetime, as well as inertial masses. 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 and electromagnetic fields around each particle. The particles exhibit field structures qualitatively similar to those of observed elementary particles.