Wave-Mechanical Gravity: A Unified Theoretical and Experimental Programme

This volume presents three companion papers forming a unified theoretical and experimental programme for a wave-mechanical account of gravitational motion. Paper 29 develops the theoretical framework in which gravitational motion emerges from constructive-interference maximum migration of de Broglie matter waves in a density-dependent refractive-index field. The gravitational field is expressed as an effective refractive-index field n(r) derived from the Schwarzschild metric. Feynman’s path-integral formalism establishes that all non-stationary paths are eliminated by oscillatory phase cancellation, and that the surviving constructive-interference maximum shifts toward regions of higher mass density. The argument proceeds through four interconnected stages — the gravitational refractive-index field, asymmetric phase accumulation, probability-density redistribution, and physical-motion identification — completed by two theorems and one derived result. The framework recovers GR geodesics in the geometric-optics limit, requires no hidden variables, and generates five classes of experimentally discriminating predictions. Paper 77 identifies slit-material mass density as an untested variable in matter-wave interferometry. The standard single-slit formula Δy ≈ λL/a contains no density term; as a result, density has never been systematically varied as an independent parameter in a century of matter-wave experiments. This paper explains the historical absence through the structural logic of theory-determined observation and the Copenhagen prohibition on mechanism questions, establishes that electrons and fullerene C₆₀ constitute a sufficient two-point experimental programme spanning six orders of magnitude in mass, specifies a three-layer control protocol to exclude slit-width artefacts, and analyses what each possible outcome establishes for the completeness of the standard formalism. Paper 78 develops a three-dimensional experimental matrix introducing slit thickness as a third independently variable parameter alongside particle species and slit-material density. The 5×5×3 design of 75 independent measurements has a random-coincidence probability of approximately 1/1,728,000. The paper derives the quantitative scaling prediction for the thickness dimension (Δx ∝ d, ratio 1:3:6 across three thickness levels), specifies a three-layer thickness control protocol, and analyses the inferential structure of partial as well as full confirmation. The experiment begins with a single laboratory session: electron diffraction through five FIB-fabricated slits of ranked density at 50 nm thickness.