Geometry and Forces in Relativistic and Pre-Relativistic Theories

It has been shown elsewhere that in the case of relativistic theories, there exists a local differential-topological criterion which distinguishes sharply between geometry and forces. This criterion is also epistemologically effective. In this paper, we explain why this local criterion fails in the pre-relativistic context. The principal reason for the difference is that the causal structure is determined by a quadratic function of 3-velocity in the relativistic case and by a linear function of 3-velocity in the pre-relativistic case.