Electromagnetic and gravitational interactions from Lagrangian mechanics

TL;DR

This paper shows that electromagnetic and gravitational interactions naturally emerge from the low kinetic energy limit of Lagrangian systems, and extends this to dynamic Einstein-Maxwell fields, suggesting a universal origin of these forces.

Contribution

It demonstrates that electromagnetic and gravitational interactions can be derived from Lagrangian mechanics and introduces a way to promote the Lagrangian to a dynamic field, linking fundamental forces to Lagrangian systems.

Findings

Electromagnetic and gravitational backgrounds are universal in low kinetic energy Lagrangian systems.

Einstein-Maxwell theory can be derived from Lagrangian mechanics assuming test particle motion.

Higher energy interactions may be relevant at the Planck scale, but are too weak to detect in current physics.

Abstract

Background fields of electromagnetic and gravitational type emerge in the low kinetic energy limit of any regular Lagrangian system and, in particular, in the corresponding limit of any spacetime theory in which the free motion of test particles is described by an unspecified regular Lagrangian. Electromagnetic and gravitational type interactions are therefore a universal feature of low kinetic energy Lagrangian systems. These background interactions can be consistently turned into dynamic Einstein-Maxwell fields by promoting the Lagrangian function to a dynamic scalar field on the tangent bundle of the configuration space. Accordingly, Einstein-Maxwell theory can be deduced from the assumption that the motion of elementary test particles in spacetime is described by Lagrangian mechanics. For higher kinetic energy-type values, identified with the square of the invariant mass of the particle, the Lagrangian induces higher rank interactions that seem however too weak to have been detected in spacetime physics, but which might prove relevant at the Planck scale.