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.

Earlier editions (v2.0, v3.0) progressively tightened the structural rigor of the multi-particle lift, reduced the bosonic precision-electroweak residue to a bounded master-integral computation, and recovered the Bekenstein-Hawking entropy and Hawking flux as substrate-mode-count identities through the Susskind-Uglum heat-kernel reading; forward-prediction content (matter-wave self-gravity breathing-mode ω = √(4πGρ/3); non-product configurations requiring a connected scaffold) and the projection-validity-boundary treatment of the Schwarzschild and FLRW singularities were set in place. v4.0 carries the v3.0 forward fronts unchanged and lands three new commitments.

v4.0 dark-matter integration. The realised sterile slot N_L + ν_R commits in Ch. 26 §26.6 with the resulting 4×3 rank-three neutral mass matrix forcing one exactly massless active eigenstate and m_ββ = 0 as a strict-EFT prediction under B-L preservation. Ch. 29 §29.7 reads the heavy mostly-sterile eigenstate as the Conditional CDM Proposition at the spin-resolved PIDM closure curve m_s ∼ 10¹² GeV through gravitational production. App. A §A.6 catalogues five conditional residues for the dark-matter scenario. The two companion papers (Tan 2026a on the rank-three Dirac extension forcing the massless-active-mass conclusion, Tan 2026b on the dark-matter phenomenology of the heavy mostly-sterile state) carry the paper-level treatments referenced by the body.

v4.0 Yang-Mills mass gap on substrate ontology. Ch. 18 §§18.7-18.8 reframes the Clay Quantum Yang-Mills existence and mass-gap problem on the substrate: pure Yang-Mills is the projection of the WR substrate onto the gauge-only sector, and substrate-level positivity together with the spectral structure of the matter-mode trace deliver a structural mass-gap statement on the projected gauge theory. The companion paper (Tan 2026c) carries the paper-level treatment.

v4.0 Lovelock-anchored closed form of g_μν = 𝒞_μν[Ψ]. Ch. 20 §20.8 displays the closed form of the metric response functional through Lovelock's theorem: under four-dimensional locality, diffeomorphism invariance, and second-order field-equation structure, the gravitational response of Ψ is forced to Einstein-Hilbert plus a cosmological term, with no remaining freedom in the projection.

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.