Overview
This article derives Born–Infeld-type dynamics as the unique local effective description compatible with bounded propagation or relaxation flux in relational systems. Quadratic actions allow unbounded gradients, whereas flux saturation enforces a non-linear structure.
Starting from a weighted relational Laplacian with irreversible relaxation, the analysis shows that bounded flux selects both the Born–Infeld action and a restricted class of admissible effective geometries, including Minkowski space and the Schwarzschild exterior solution.
Core contributions
- Bounded relaxation: finite maximal flux as a minimal physical constraint.
- Born–Infeld selection: unique non-linear completion compatible with saturation.
- Emergent metric: geometry reconstructed from the principal symbol of relational operators.
- Schwarzschild geometry: universal exterior solution from flux conservation.
- Horizons: saturation-induced loss of projectability rather than physical singularities.
Conceptual scope
The article does not modify Maxwell or Einstein dynamics by postulate. It identifies the structural conditions under which non-linear electrodynamics and curved spacetime geometry arise as effective descriptions of bounded relational relaxation.
How this connects to Cosmochrony
Within Cosmochrony, bounded relaxation provides the dynamical complement to non-injective projection. Together, they explain why effective descriptions exhibit both saturation phenomena and regime-dependent breakdown of geometric projectability.
References
Jérôme Beau. Bounded Relaxation and the Dynamical Selection of Spacetime Geometry. Zenodo. DOI: 10.5281/zenodo.18407505