Gravity as the Constructive Interference of Matter Waves:Mass Density, Refractive Index, and the Origin of Gravitation

YOUNG HO GOH

YOUNG HO GOH

This paper proposes that gravity arises from the constructive interference of de Broglie matter waves in a density-dependent refractive medium. The argument proceeds in five steps: (1) greater mass implies greater density; (2) by Snell's law, greater density implies a higher refractive index; (3) a higher refractive index implies a shorter wavelength; (4) when matter waves propagate outward from an object in all directions, the wavelength is shorter on the side facing the larger mass; (5) constructive interference is stronger and more densely packed where the wavelength is shorter, so the object is preferentially redistributed toward the side of greater mass. This shows gravity to be a wave-mechanical phenomenon: matter is not pulled toward mass by some force; it is redistributed toward mass through the constructive interference of its own matter wave. Newton and Einstein described the trajectory and the geometric structure of gravitational motion; this paper proposes the physical mechanism by which that motion occurs. This paper makes three propositions explicit, with carefully distinguished epistemic status: (A) the mass distribution determines the effective refractive medium through which matter waves propagate — an experimentally established fact, confirmed independently by the COW experiment (1975) and by semiconductor heterojunction experiments confirming Snell's law for matter waves at density boundaries; (B) the displacement of the constructed-interference maximum is the physical mechanism of actual gravitational motion — the paper's sole new physical identification, going beyond Born's rule as standardly stated; it is consistent with but not compelled by the COW data, and constitutes the primary target of experimental falsification (Section 6.6d); (C) the COW fringe shift is a direct measurement of the gravitational mechanism — a logical corollary that follows necessarily from (A) and (B), not an independent assumption. Section 6.6d translates these propositions into five differentiating experimental predictions, ordered by experimental accessibility, including an immediately executable reanalysis of existing COW data and a novel slit-material density experiment that provides a clean differential test between the present framework and standard wave optics.

YOUNG HO GOH

YOUNG HO GOH

This collection comprises four papers that together establish a complete mechanistic account of gravitational motion at the quantum level. The central claim is that gravity — the phenomenon Newton described mathematically in 1687 and Einstein reframed geometrically in 1915 — is the constructive interference of de Broglie matter waves in an asymmetric medium created by the presence of mass. Neither Newton nor Einstein provided a physical mechanism for why matter moves toward other matter. This collection proposes and establishes that mechanism through three independent derivations and their mathematical unification. The three companion papers (Papers 29, 30, 52) derive the same conclusion — gravity is matter-wave constructive interference — through three completely independent physical routes, each starting from a different physical principle and confirmed by different experimental evidence: Paper Starting point Physical principle Experimental basisP29 Mass creates a density gradient → refractive index gradient Snell’s law of refraction Optical refraction universality (400 years, zero exceptions); neutron reflectometryP30 Falling particle gains kinetic energy → shorter de Broglie wavelength Energy conservation + de Broglie relation COW experiment (1975): direct measurement of gravitational wavelength shiftP52 Time flows more slowly near mass → matter-wave phase accumulates asymmetrically Feynman path integral + gravitational time dilation GPS time dilation; Pound-Rebka; QED precision (12 significant figures) Each of these papers is self-contained and independently verifiable. No result from the other papers is required to follow any single paper’s argument. The synthesis paper (Paper 41) proves two results that the three companion papers individually leave open. First, it proves that the three routes are mathematically identical — not merely analogous — because all three key variables (refractive index n, time dilation ratio dt/dτ, and wavelength compression ratio λ₀/λ) are different expressions of the same Schwarzschild metric coefficient g₀₀:n(r) = dt/dτ = λ₀/λ(r) = 1/√(1 − 2GM/rc²) ...(I)This identity is exact and proved from first principles. Second, Paper 41 derives Newton’s inverse-square law F = GMm/r² from this identity in four lines of algebra, and analyses the structural reasons why: the c² cancellation is a self-consistency theorem (not a numerical coincidence), the exponent 2 is the algebraic derivative of the exponent 1 in the 1/r refractive index (itself a consequence of Gauss’s law in three spatial dimensions), and Newton’s empirical (inductive) law agrees with the theoretical (deductive) derivation because both have the same mathematical source. The epistemological significance of the triple convergence is analysed using the concepts of consilience (Whewell, 1840) and robustness (Wimsatt, 1981): the conclusion ‘gravity = matter-wave constructive interference’ is supported by three independent physical principles from three different centuries, confirmed by three independent experimental traditions, and protected by the logical structure that to overturn it one must simultaneously defeat Snell’s law, energy conservation, and the Feynman path integral — which is to say, it cannot be overturned. No new physics is introduced in any of the four papers. All physical principles used — Snell’s law, de Broglie matter waves, energy conservation, gravitational time dilation, Feynman path integrals, Born’s rule — are independently established and experimentally confirmed. The contribution of this collection is the identification that these principles, connected in specific causal chains, produce the phenomenon we have called gravity for 338 years.

Leo Stodolsky

Jürgen Audretsch, Cláus Lämmerzahl, Friedrich W. Hehl