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

TL;DR

This paper investigates the possibility of extending Newton's second law by incorporating higher order derivatives in equations of motion, leading to new interaction structures and physical phenomena like zitterbewegung, supported by a gauge principle and experimental considerations.

Contribution

It introduces a generalized framework for equations of motion with higher derivatives, derived from a gauge principle, and explores their physical implications and experimental relevance.

Findings

Higher order derivatives induce zitterbewegung.

The main motion is robust against modifications.

A gauge field with properties of a space metric emerges.

Abstract

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.