  Relativistic, scalar particles are considered, contained in a box with
periodic boundary conditions. Although interactions are not expected to be a
fundamental problem, we concentrate on free particles. By considering them to
be harmonic oscillators, it is found that their dynamical variables can be
replaced by a completely ontological set, which means that, here, quantum
mechanics does not deviate from a purely geometric, ontological particle
system. The effects of the mass terms are included. Locality holds for the
quantum theory, and seems to be fully obeyed also by the classical treatment,
although further discussion will be needed. Quantised interactions are briefly
speculated on, but mostly postponed to later. We do discuss extensively the
distinction between the quantum treatment and the classical one, even though
they produce exactly the same equations mathematically. We briefly explain how
this result can be squared with the usual quantum no-go theorems. It is
suggested to apply this theory for real time quantum model simulations.
