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

Questioning Newton's second law: What is the structure of equations of motion?