Gravity in Free Fall: Einstein vs Pattern Field Theory
Overview
In Einstein’s general relativity, an observer in free fall follows a geodesic and therefore feels no weight; the floor disappears and the “force of gravity” is not locally experienced. Pattern Field Theory (PFT) preserves this observational fact but reframes it: gravity is not a separate force, but a curvature–coherence state of the π-particle substrate on the Allen Orbital Lattice (AOL). Free fall is simply unforced transport of a coherence packet along the local curvature flow of the substrate.
Translation: GR → PFT
- Spacetime geodesic (GR) → Coherence geodesic (PFT): minimal-action transport on the AOL substrate.
- Gravitational field → Curvature field \( \kappa \) of the π-substrate.
- Weightlessness in free fall → No net substrate drive: with contact removed, there is no opposing curvature imposed by a boundary, so no felt weight.
Core Equations (PFT)
Universal Field Equation (UFE): \( E = Q_H\,\chi\,\kappa^2 \), where \(Q_H\) is the substrate conversion constant, \( \chi \in [0,1] \) is coherence density, and \( \kappa \) is local curvature magnitude.
Prime-Indexed Curvature Equation (PICE): \( r = k\,s_n \) selects admissible ring states \(s_n\) (critical-line indices), constraining allowed standing/propagating modes across phenomena—light and gravity included.
Free Fall, Precisely
A supported object feels weight because the support imposes an opposing curvature at the boundary. Removing the support removes that boundary constraint: the object’s coherence follows the ambient curvature and no reaction is generated—hence weightlessness. The background curvature \( \kappa \) still governs trajectories; what vanishes is the contact-induced drive.
Consistency with Light
The same π-substrate that carries electromagnetic duplex modes also carries gravitational curvature modes. Our λ–φ duplex figures (derived from the Riemann-equilibrium AOL) that validate coherent light behavior apply to curvature spectra as well. In PFT, EM and gravity are different projections of the same substrate dynamics.
Predictions & Checks
- Micro-free-fall interferometry: Phase evolution tracks \( \kappa \)-predicted geodesics; controlled boundary curvature (gradient index media) induces shifts scaling with \( \Delta(\chi\kappa^2) \).
- Analog cavities: PICE selects narrowband resonances for curvature-wave analogs in optical/acoustic metamaterials.
- Support removal: Transition from support → free fall shows a sharp drop in the local substrate drive term while background \( \kappa \) remains, matching inertial trajectories.
Related
Provenance. The curvature-duplex geometry used here arises from the Riemann-equilibrium AOL and was cross-checked against coherent light behavior; the same lattice constraints guide gravitational curvature modes in PFT.