The Evolution Field: An Emergent Geometric Framework for Spacetime, Lorentz Kinematics, Gravitational Evolution, and Finite-Capacity Gravity

Abstract

This paper presents the current development of the Evolution Field framework, a speculative theoretical model in which spacetime is not taken as a fundamental continuum but as a macroscopic description emerging from an underlying Evolution structure. The microscopic substrate is represented schematically as a locally invariant lattice of elementary nodes or cells.The lattice is assumed to possess a characteristic invariant separation, while macroscopic spatial continuity emerges through coarse graining.The framework introduces a normalized local Evolution variable E(x), interpreted as the local state or rate of physical becoming, with a proposed physical range Emin ≤ E ≤ 1.Operational time is associated with the local rate of physical evolution rather than being treated as an independent fundamental substance. A logarithmic Evolution potential,ΦE = c2ln E, reproduces the Newtonian potential in the weak-field limit.A second component concerns relativistic kinematics. When an underlying invariant geodesic is tilted relative to an observer’s spatial projection, the projected separation decreases while the underlying geodesic length remains invariant. With the proposedkinematic identification sin θ = v/c, this gives the Lorentz-contraction factor p1 − v2/c2.The same geometric factor gives the standard proper-time relation. This is presented as a proposed geometric interpretation of Lorentz kinematics; a complete derivation of the Lorentz transformation is left as an open problem.For gravity, a minimal emergent metric is considered, ds2 = −E2c2dt2 + E−2dr2 + r2dΩ2in the spherical unsaturated exterior. The corresponding vacuum curvature equations leadto dr(1−E2)/dr = 0, whose asymptotically flat solution is E2 = 1 − 2GM/(rc2). Thus theSchwarzschild exterior can be represented as an Evolution-field configuration. The finite-capacity postulate, however, forbids extrapolation to E = 0 as a physical microscopic state.A more general two-function metric is consequently required for a regular interior. Theresulting analysis shows that a finite-density regular core requires a mass function behavingas m(r) ∝ r3 near the center.The paper explicitly distinguishes established results of general relativity from proposed postulates, geometric ans¨atze, and intermediate results of the Evolution Field model. A complete covariant action, nonlinear saturation law, matter coupling, full Lorentz-transformation derivation, and quantitative observational discriminants remain to be developed.