From Phase Dynamics to Lorentz Kinematics: Constitutive Transitions in a Two-Sheeted Field Geometry
Year: 2026
Type: preprint
Abstract: We consider a two-sheeted field geometry formed by two longitudinal parent fields in reciprocal interpenetration, whose contraction and expansion phases periodically synchronise and desynchronise. Their interpenetration generates a common four-sector core composed of two longitudinal and two transverse subfields, whose physical geometry depends on the relative phase of the parent fields. The purpose of this work is to distinguish two operations that arise within this construction. A Lorentz boost describes how an already formed inclined transverse subspace is represented from the reference axes of the longitudinal subspace. The formation of that transverse state itself, however, is a physical transition generated by the relative phase of the two parent fields. In the synchronised regime, the relevant longitudinal sectors have the same contraction response. Desynchronisation allows one parent field to remain in contraction while the other enters expansion, producing an asymmetric transverse configuration with opposite-oriented sectorial curvature faces, unequal areas of influence, and a physical inclination relative to the longitudinal reference frame. The sign of a curvature face and the magnitude of its dynamical thrust are distinct quantities: the active convex face is assigned positive orientation in the fixed geometrical convention even though its associated expansion-side thrust is smaller than the contraction-side thrust. The central structural conclusion is that the change from a same-sign longitudinal response to an opposite-sign transverse response is a physical consequence of the phase transition and cannot itself be generated by a Lorentz transformation. The corresponding signed sectorial response forms belong to different inertia classes under Sylvester’s law, so no nonsingular congruence transformation can map one into the other. The phase dynamics therefore determines the physical constitution and orientation of the transverse subspace first; the Lorentz transformation enters subsequently as the kinematic relation required to express that already formed state in the retained longitudinal frame. This separation provides a route for investigating whether Lorentz kinematics can emerge as the effective symmetry of a deeper phase-dependent field geometry, and whether the same expansion mechanism responsible for the transverse asymmetry can also contribute, through an extrinsic-to-intrinsic curvature map, to a positive-curvature spacetime branch.
Author: De Miguel Bueno, Alfonso
Language: enc
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204893148