Wave Relativity: Unifying Quantum Mechanics and General Relativity Without New Physics

Wave Relativity re-derives the classical and semiclassical content of physics, and the architecture of the Standard Model, from one principle: equations for physically-real potentials must be self-consistent. Three structural requirements (frame-independence, index matching, and self-sourcing) are applied to three empirically-grounded starting equations. Maxwell on a physically-real four-potential A^μ yields electromagnetism with special relativity. Newton's law on a physically-real metric potential g_μν yields general relativity through a fixed-point equation iterated to all orders. The Davisson-Germer-anchored matter wave ψ, under the same requirements together with Stern-Gerlach, neutron interferometry under 4π rotation, and Pauli exclusion, yields the Dirac equation in curved spacetime as the minimal Lorentz-covariant first-order wave equation whose square is Klein-Gordon.

The three potentials (g_μν, A^μ, ψ) then assemble as aspect-content of one Dirac-spinor substrate Ψ. The matter wave is Ψ's WKB amplitude reduction on a single-spin mode; the gauge potential and metric are separate fields sourced by Ψ-built objects through Maxwell's and Einstein's equations, with gauge-class freedom and vacuum-sector solutions retained. The apparent incompatibility of quantum mechanics and general relativity dissolves: it was the artefact of treating g_μν and ψ as independent fields requiring separate quantisation. The conventional quantum-gravity programme was quantising the wrong object.

One master equation, the Dirac equation on curved spacetime 𝒞[Ψ], governs the coupled system. Under scale limits (v/c, λ_dB/L, λ_dB/ℓ_P) it reduces to classical mechanics, special relativity, general relativity, and standard quantum mechanics. No new physics is introduced, no quantisation programme is applied to gravity, and all empirical inputs are audited.

A second arc derives the Standard Model's internal-component architecture from Ψ's structure as a Dirac-spinor substrate. The internal directions on which Lorentz-scalar self-consistency closes (overall phase, an internal ℂ³_xyz factor anchored by three-constituent baryons and constituent-anticonstituent mesons, and a conversion fiber ℂ²_W on the L-projection anchored by charged-current doublet pairings) pick out the Standard Model gauge group with no postulated factors. Spin and chirality emerge as wave-geometric structure on Ψ. The particle spectrum is classified as localised normal-mode classes of Ψ. Hypercharge ratios follow from chiral-anomaly cancellation on the matter-mode trace, and the quark/lepton split follows from singlet stability under self-sourcing. The composite chiral background, Ψ's only L-R, xyz-singlet, SU(2)_W-doublet bilinear channel, plays the role of the Higgs without a postulated scalar field; closed-form weak and strong operators and a kernel-coefficient block supply the load-bearing profile coefficients. Tree-level Standard Model phenomenology recovers as a checkpoint, with master-integral residues and gauge-cancellation, UV-finiteness, and hierarchy theorems closing at the bosonic precision frontier.

v3.0 advances on three fronts. Structural rigor: the gravitational sector of the multi-particle lift carries no independent graviton operators; operator-valued metric response runs entirely through matter stress-energy on a c-number retarded kernel. Matter-sector unitarity preserves the natural one-particle inner product on Cauchy slices in the controlled regime. The outcome-uniqueness reading separates phenomenal closure from the ontological residue with three structurally-distinct routes catalogued. Parameter reduction: the CKM hierarchy ratio |V_cb|/|V_us| ≈ 0.183 closes at leading order via a sign-controlled even profile on the ν_x = 3 Pöschl-Teller ladder; the gauge-invariant family-sector content of (σ, ν) pins to one ratio. The bosonic precision-electroweak residue is reduced to a bounded master-integral computation under gauge-cancellation, UV-finiteness, and hierarchy theorems. Forward predictions: matter-wave self-gravity gives a closed-form breathing-mode frequency ω = √(4πGρ/3) depending only on material density, with a silica-versus-gold discriminator √(ρ_Au/ρ_SiO2) ≈ 2.96 at fixed mass falsifying the matter-wave-sources-COM-gravity reading if absent; non-product Ψ-configurations require a connected scaffold (common past, mediator interaction, or post-selected joint future event), with an actually-observed Bell-violating non-product correlation absent any scaffold falsifying the one-substrate-with-one-history ontology. Holographic-anchor recovery: Bekenstein-Hawking entropy S_BH = A/(4 G_N ℏ) recovers as a count of horizon-localised Ψ-modes via the Susskind-Uglum heat-kernel identification with no graviton-loop contribution on either side; Hawking radiation runs on the same Ψ-mode content with thermal flux T_H = ℏc³/(8πGMk_B). The classical-GR Schwarzschild and FLRW singularities sit beyond the projection-validity boundary; the inference from classical projected curvature divergence to substrate-level singularity does not transfer through the boundary by default, with the substrate description available throughout.

Intended for readers with undergraduate-or-first-year-graduate familiarity with special relativity, general relativity, and wave-mechanical quantum mechanics. The book requires comfort with four-vectors, tensor indices, and wave equations; it does not require fibre-bundle language or path integrals.