Gauging Newton's Law

TL;DR

This paper derives Lagrangian and Hamiltonian mechanics from Newtonian mechanics by framing them as gauge theories, highlighting the role of measurement symmetries in their development.

Contribution

It introduces a gauge theory perspective to Newtonian mechanics, connecting measurement theories with fundamental formulations of mechanics.

Findings

Lagrangian mechanics emerges from simple measurement theory

Hamilton's equations arise from conformal measurement theory

Gauge theory provides a unified framework for dynamics and measurement

Abstract

We derive both Lagrangian and Hamiltonian mechanics as gauge theories of Newtonian mechanics. Systematic development of the distinct symmetries of dynamics and measurement suggest that gauge theory may be motivated as a reconciliation of dynamics with measurement. Applying this principle to Newton's law with the simplest measurement theory leads to Lagrangian mechanics, while use of conformal measurement theory leads to Hamilton's equations.