  Interactions are explored through the observation of the dynamics of
particles. On the classical level the basic underlying assumption in that
scheme is that Newton's second law holds. Relaxing the validity of this axiom
by, e.g., allowing for higher order time derivatives in the equations of motion
would allow for a more general structure of interactions. We derive the
structure of interactions by means of a gauge principle and discuss the physics
emerging from equations of motion of higher order. One main result is higher
order derivatives induce a zitterbewegung. As a consequence the main motion
resulting from the second order equation of motion is rather robust against
modifications. The gauge principle leads to a gauge field with the property of
a space metric. We confront this general scheme with experimental data.
